0.00/0.10 % 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 0.11/0.31 % Computer : n010.cluster.edu 0.11/0.31 % Model : x86_64 x86_64 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.31 % Memory : 8042.1875MB 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.31 % CPULimit : 960 0.11/0.31 % WCLimit : 120 0.11/0.31 % DateTime : Thu Jul 2 08:48:42 EDT 2020 0.11/0.32 % CPUTime : 0.77/0.97 % Running in FOF/CNF-non-UEQ mode 3.90/4.11 # No SInE strategy applied 3.90/4.11 # Auto-Mode selected heuristic C07_19_nc_SAT001_MinMin_rr 3.90/4.11 # and selection function SelectMaxLComplexAvoidPosPred. 3.90/4.11 # 3.90/4.11 # Presaturation interreduction done 3.90/4.11 # Number of axioms: 7333 Number of unprocessed: 5931 3.90/4.11 # Tableaux proof search. 3.90/4.11 # 5931 beginning clauses after preprocessing and clausification 3.90/4.11 # Creating start rules for all conjectures. 3.90/4.11 # 1513 unit axioms, 1 start rules, and 4418 other extension candidates. 3.90/4.11 ## Beginning tableaux proof search with 1 start rule applications. 4.02/4.26 # Beginning deep saturation check 4.02/4.26 # Saturate returned empty clause 0x514f2c0. 4.02/4.26 # Success 4.02/4.26 # SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p 4.02/4.26 # SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 4.02/4.26 # Begin clausification derivation 4.02/4.26 fof(fact_diff__bin__simps_I2_J, axiom, ![X107]:c_Int_Osucc(X107)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X107),c_Int_OMin), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I2_J)). 4.02/4.26 fof(fact_succ__Min, axiom, c_Int_OPls=c_Int_Osucc(c_Int_OMin), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_succ__Min)). 4.02/4.26 fof(fact_succ__def, axiom, ![X107]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Int_Osucc(X107), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_succ__def)). 4.02/4.26 fof(fact_succ__pred, axiom, ![X13]:c_Int_Osucc(c_Int_Opred(X13))=X13, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_succ__pred)). 4.02/4.26 fof(fact_add__Min__right, axiom, ![X107]:c_Int_Opred(X107)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),c_Int_OMin), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Min__right)). 4.02/4.26 fof(fact_Pls__def, axiom, c_Int_OPls=c_Groups_Ozero__class_Ozero(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pls__def)). 4.02/4.26 fof(fact_add__Min, axiom, ![X107]:c_Int_Opred(X107)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X107), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Min)). 4.02/4.26 fof(fact_rel__simps_I42_J, axiom, ![X47]:c_Int_OMin!=c_Int_OBit0(X47), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I42_J)). 4.02/4.26 fof(fact_pred__Bit1, axiom, ![X107]:c_Int_OBit0(X107)=c_Int_Opred(c_Int_OBit1(X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__Bit1)). 4.02/4.26 fof(fact_Bit1__def, axiom, ![X107]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X107)),X107)=c_Int_OBit1(X107), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Bit1__def)). 4.02/4.26 fof(fact_diff__bin__simps_I4_J, axiom, ![X47]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X47))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I4_J)). 4.02/4.26 fof(fact_Bit0__def, axiom, ![X107]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),X107)=c_Int_OBit0(X107), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Bit0__def)). 4.02/4.26 fof(fact_add__Pls__right, axiom, ![X107]:X107=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),c_Int_OPls), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Pls__right)). 4.02/4.26 fof(fact_upt__0, axiom, ![X46]:c_List_Oupt(X46,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)). 4.02/4.26 fof(fact_sorted__list__of__set__range, axiom, ![X20, X21]:c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X21),X20))=c_List_Oupt(X21,X20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set__range)). 4.02/4.26 fof(fact_vimage__Collect__eq, axiom, ![X56, X22, X7, X4]:hAPP(c_Set_Ovimage(X4,X7,X22),hAPP(c_Set_OCollect(X7),X56))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(X7,tc_HOL_Obool,X4),X56),X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Collect__eq)). 4.02/4.26 fof(fact_Collect__def, axiom, ![X56, X4]:hAPP(c_Set_OCollect(X4),X56)=X56, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__def)). 4.02/4.26 fof(fact_Collect__mem__eq, axiom, ![X3, X4]:X3=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__mem__eq)). 4.02/4.26 fof(fact_Collect__split, axiom, ![X112, X56, X7, X4]:hAPP(c_Set_OCollect(tc_prod(X4,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),X56))),X112)))=hAPP(hAPP(c_Product__Type_OSigma(X4,X7),hAPP(c_Set_OCollect(X4),X56)),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_Set_OCollect(X7),X112))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__split)). 4.02/4.26 fof(fact_power2__eq__1__iff, axiom, ![X26, X4]:(class_Rings_Oring__1__no__zero__divisors(X4)=>(c_Groups_Oone__class_Oone(X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))<=>(hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))=X26|c_Groups_Oone__class_Oone(X4)=X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__eq__1__iff)). 4.02/4.26 fof(fact_zero__less__power2, axiom, ![X26, X4]:(class_Rings_Olinordered__idom(X4)=>(X26!=c_Groups_Ozero__class_Ozero(X4)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),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_zero__less__power2)). 4.02/4.26 fof(fact_less__2__cases, axiom, ![X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X5|X5=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__2__cases)). 4.02/4.26 fof(fact_power2__less__0, axiom, ![X11, X4]:(class_Rings_Olinordered__idom(X4)=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__less__0)). 4.02/4.26 fof(fact_nat__number__of, axiom, ![X53]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X53)=hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of)). 4.02/4.26 fof(fact_number__of__is__id, axiom, ![X107]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X107)=X107, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__is__id)). 4.02/4.26 fof(fact_pred__def, axiom, ![X107]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X107),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Int_Opred(X107), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__def)). 4.02/4.26 fof(fact_Collect__neg__eq, axiom, ![X56, X4]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),X56))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OCollect(X4),X56)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__neg__eq)). 4.02/4.26 fof(fact_removeAll__filter__not, axiom, ![X32, X4, X9, X56]:(~(hBOOL(hAPP(X56,X9)))=>hAPP(c_List_Ofilter(X4,X56),X32)=hAPP(c_List_OremoveAll(X4,X9),hAPP(c_List_Ofilter(X4,X56),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_removeAll__filter__not)). 4.02/4.26 fof(fact_removeAll__filter__not__eq, axiom, ![X9, X4]:c_List_Ofilter(X4,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(c_fequal,X9)))=c_List_OremoveAll(X4,X9), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_removeAll__filter__not__eq)). 4.02/4.26 fof(fact_Collect__conj__eq, axiom, ![X112, X56, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OCollect(X4),X56)),hAPP(c_Set_OCollect(X4),X112))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),X56)),X112)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__conj__eq)). 4.02/4.26 fof(fact_rel__simps_I21_J, axiom, ![X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X28)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I21_J)). 4.02/4.26 fof(fact_rel__simps_I4_J, axiom, ![X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X28))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I4_J)). 4.02/4.26 fof(fact_eq__int__code_I3_J, axiom, ![X57]:(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X57))<=>hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I3_J)). 4.02/4.26 fof(fact_rel__simps_I27_J, axiom, ![X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X28)),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I27_J)). 4.02/4.26 fof(fact_rel__simps_I10_J, axiom, ![X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X28)),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I10_J)). 4.02/4.26 fof(fact_rel__simps_I25_J, axiom, ![X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X28))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I25_J)). 4.02/4.26 fof(fact_rel__simps_I8_J, axiom, ![X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X28))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I8_J)). 4.02/4.26 fof(fact_rel__simps_I28_J, axiom, ![X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X28)),c_Int_OMin))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I28_J)). 4.02/4.26 fof(fact_rel__simps_I11_J, axiom, ![X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X28)),c_Int_OMin))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I11_J)). 4.02/4.26 fof(fact_rel__simps_I44_J, axiom, ![X28]:(c_Int_OBit0(X28)=c_Int_OPls<=>X28=c_Int_OPls), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I44_J)). 4.02/4.26 fof(fact_eq__int__code_I9_J, axiom, ![X58]:(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X58),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X58)),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I9_J)). 4.02/4.26 fof(fact_neg__number__of__Bit0, axiom, ![X23]:(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X23))))<=>hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__number__of__Bit0)). 4.02/4.26 fof(fact_rel__simps_I49_J, axiom, ![X47, X107]:c_Int_OBit0(X107)!=c_Int_OBit1(X47), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I49_J)). 4.02/4.26 fof(fact_eq__int__code_I7_J, axiom, ![X289]:~(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X289)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I7_J)). 4.02/4.26 fof(fact_eq__int__code_I11_J, axiom, ![X153]:~(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X153)),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I11_J)). 4.02/4.26 fof(fact_eq__int__code_I4_J, axiom, ![X289]:~(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X289)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I4_J)). 4.02/4.26 fof(fact_eq__int__code_I10_J, axiom, ![X153]:~(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X153)),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I10_J)). 4.02/4.26 fof(fact_rel__simps_I46_J, axiom, ![X107]:c_Int_OPls!=c_Int_OBit1(X107), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I46_J)). 4.02/4.26 fof(fact_length__transpose, axiom, ![X32, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),c_List_Otranspose(X4,X32))=c_List_Ofoldr(tc_List_Olist(X4),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X4)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),X32,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__transpose)). 4.02/4.26 fof(fact_foldr__foldl, axiom, ![X26, X32, X22, X4, X7]:c_List_Ofoldr(X7,X4,X22,X32,X26)=hAPP(c_List_Ofoldl(X4,X7,hAPP(c_COMBC(X7,X4,X4),X22),X26),hAPP(c_List_Orev(X7),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldr__foldl)). 4.02/4.26 fof(fact_add__Suc, axiom, ![X5, X2]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X5)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Suc)). 4.02/4.26 fof(fact_add__Suc__shift, axiom, ![X5, X2]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X5)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Suc__shift)). 4.02/4.26 fof(fact_transpose__aux__filter__head, axiom, ![X134, X4]:hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),X4),c_List_Ohd(X4)),hAPP(c_List_Ofilter(tc_List_Olist(X4),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X4)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(X4),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X4)))),X134))=c_List_Oconcat(X4,hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_Olist__case(tc_List_Olist(X4),X4,c_List_Olist_ONil(X4),hAPP(hAPP(c_COMBB(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),X4),c_COMBK(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_COMBC(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)),c_List_Olist_ONil(X4))))),X134)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__aux__filter__head)). 4.02/4.26 fof(fact_concat__conv__foldl, axiom, ![X134, X4]:hAPP(c_List_Ofoldl(tc_List_Olist(X4),tc_List_Olist(X4),c_List_Oappend(X4),c_List_Olist_ONil(X4)),X134)=c_List_Oconcat(X4,X134), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__conv__foldl)). 4.02/4.26 fof(fact_singleton__conv, axiom, ![X26, X4]:hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_singleton__conv)). 4.02/4.26 fof(fact_singleton__conv2, axiom, ![X26, X4]:hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X4),hAPP(c_fequal,X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_singleton__conv2)). 4.02/4.26 fof(fact_transpose__aux__filter__tail, axiom, ![X134, X4]:hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Otl(X4)),hAPP(c_List_Ofilter(tc_List_Olist(X4),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X4)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(X4),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X4)))),X134))=c_List_Oconcat(tc_List_Olist(X4),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X4)),X4,c_List_Olist_ONil(tc_List_Olist(X4)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4))),X4),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4)),tc_List_Olist(tc_List_Olist(X4))),c_List_Olist_OCons(tc_List_Olist(X4))),c_List_Olist_ONil(tc_List_Olist(X4)))))),X134)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__aux__filter__tail)). 4.02/4.26 fof(fact_diff__bin__simps_I9_J, axiom, ![X47, X107]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X107),X47))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X107)),c_Int_OBit0(X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I9_J)). 4.02/4.26 fof(fact_zadd__commute, axiom, ![X53, X29]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X29),X53)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),X29), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__commute)). 4.02/4.26 fof(fact_diff__bin__simps_I5_J, axiom, ![X47]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X47))=c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I5_J)). 4.02/4.26 fof(fact_zadd__assoc, axiom, ![X259, X216, X217]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X217),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X216),X259))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X217),X216)),X259), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__assoc)). 4.02/4.26 fof(fact_Diff__Int__distrib2, axiom, ![X8, X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)),X8)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X8)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X6),X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Int__distrib2)). 4.02/4.26 fof(fact_Int__Diff, axiom, ![X8, X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X6),X8))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)),X8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Diff)). 4.02/4.26 fof(fact_divmod__int__pdivmod, axiom, ![X60, X28]:((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(X28,X60)<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X28)&(((X60!=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,X60))),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)),X60)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X28))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X28,X60)),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),X60))))),c_Divides_Opdivmod(X28,X60))))=c_Divides_Odivmod__int(X28,X60))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X60=>hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X28)=c_Divides_Odivmod__int(X28,X60)))<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__pdivmod)). 4.02/4.26 fof(fact_apsnd__def, axiom, ![X22, X4, X49, X7]:c_Product__Type_Oapsnd(X7,X49,X4,X22)=c_Product__Type_Omap__pair(X4,X4,X7,X49,c_Fun_Oid(X4),X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apsnd__def)). 4.02/4.26 fof(fact_divmod__int__code, axiom, ![X60, X28]:((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(X28,X60)<=X28=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(((X60=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>c_Divides_Odivmod__int(X28,X60)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X28))&(X60!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>c_Divides_Odivmod__int(X28,X60)=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,X60))),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,X28)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X60))),c_Divides_Opdivmod(X28,X60)),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),X60))))),c_Divides_Opdivmod(X28,X60))))))<=X28!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__code)). 4.02/4.26 fof(fact_of__int__num, axiom, ![X28, X4]:(((((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(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X28)))=hAPP(c_Int_Oring__1__class_Oof__int(X4),X28))&(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X4,X4)),tc_fun(tc_Int_Oint,X4)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,X4),X4),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X4,X4)),tc_fun(tc_Int_Oint,X4)),tc_Int_Oint),c_COMBB(tc_fun(X4,X4),X4,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X4,tc_fun(tc_fun(X4,X4),X4),tc_Int_Oint),c_HOL_OLet(X4,X4)),c_Int_Oring__1__class_Oof__int(X4)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X4,X4),tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,X4)),tc_fun(tc_fun(X4,X4),tc_fun(X4,X4)),tc_Int_Oint),c_COMBS(X4,X4,X4)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X4,X4),tc_fun(X4,tc_fun(X4,X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,X4)),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_fun(X4,X4))),tc_Int_Oint),c_COMBB(X4,tc_fun(X4,X4),X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),tc_Int_Oint),c_If(X4)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X4,X4,X4),c_Groups_Oplus__class_Oplus(X4)),c_COMBI(X4))))),hAPP(hAPP(c_COMBC(X4,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X4),c_Groups_Oplus__class_Oplus(X4)),hAPP(hAPP(c_COMBS(X4,X4,X4),c_Groups_Oplus__class_Oplus(X4)),c_COMBI(X4)))),c_Groups_Oone__class_Oone(X4))))),c_Divides_Odivmod__int(X28,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=hAPP(c_Int_Oring__1__class_Oof__int(X4),X28)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))<=X28!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(hAPP(c_Int_Oring__1__class_Oof__int(X4),X28)=c_Groups_Ozero__class_Ozero(X4)<=X28=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__num)). 4.02/4.26 fof(fact_power2__diff, axiom, ![X43, X13, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X13),X43)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X43),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X13)),X43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__diff)). 4.02/4.26 fof(fact_numeral__2__eq__2, axiom, 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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_numeral__2__eq__2)). 4.02/4.26 fof(fact_power2__sum, axiom, ![X43, X13, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X13),X43)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X43),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X13)),X43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__sum)). 4.02/4.26 fof(fact_neg__zmod__mult__2, axiom, ![X12, X11]:(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),X12),c_Groups_Oone__class_Oone(tc_Int_Oint)),X11))),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)))),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__zmod__mult__2)). 4.02/4.26 fof(fact_pos__zmod__mult__2, axiom, ![X12, X11]:(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)))),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X11))=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,X12,X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__zmod__mult__2)). 4.02/4.26 fof(fact_int__of__code, axiom, ![X107]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(c_Code__Numeral_Oint__of,X107)<=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X107)&(X107!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=>((c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X107,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=>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),X107),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))=hAPP(c_Code__Numeral_Oint__of,X107))&(hAPP(c_Code__Numeral_Oint__of,X107)=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),X107),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))<=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X107,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__of__code)). 4.02/4.26 fof(fact_zmod__number__of__Bit1, axiom, ![X1, X53]:((~(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),X53))))=>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),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X53)))),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(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X53))))&(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),X53)))=>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),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X53)))),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(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X53))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__number__of__Bit1)). 4.02/4.26 fof(fact_neg__zdiv__mult__2, axiom, ![X12, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X11))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12),c_Groups_Oone__class_Oone(tc_Int_Oint))),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__zdiv__mult__2)). 4.02/4.26 fof(fact_pos__zdiv__mult__2, axiom, ![X12, X11]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X11)=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)))),X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X11))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__zdiv__mult__2)). 4.02/4.26 fof(fact_sum__power2__le__zero__iff, axiom, ![X17, X9, X4]:(class_Rings_Olinordered__idom(X4)=>((X17=c_Groups_Ozero__class_Ozero(X4)&X9=c_Groups_Ozero__class_Ozero(X4))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X9),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X17),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__power2__le__zero__iff)). 4.02/4.26 fof(fact_sum__power2__gt__zero__iff, axiom, ![X17, X9, X4]:(((X9!=c_Groups_Ozero__class_Ozero(X4)|X17!=c_Groups_Ozero__class_Ozero(X4))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X9),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X17),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__power2__gt__zero__iff)). 4.02/4.26 fof(fact_sum__power2__ge__zero, axiom, ![X43, X13, X4]:(class_Rings_Olinordered__idom(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X43),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__power2__ge__zero)). 4.02/4.26 fof(fact_sum__power2__eq__zero__iff, axiom, ![X17, X9, X4]:(class_Rings_Olinordered__idom(X4)=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X9),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X17),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_Groups_Ozero__class_Ozero(X4)<=>(X17=c_Groups_Ozero__class_Ozero(X4)&X9=c_Groups_Ozero__class_Ozero(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__power2__eq__zero__iff)). 4.02/4.26 fof(fact_transpose__rectangle, axiom, ![X20, X4, X32]:((hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X4)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X4)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X4),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X4)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X4)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X4),hAPP(hAPP(c_COMBB(tc_List_Olist(X4),tc_fun(tc_Nat_Onat,X4),tc_Nat_Onat),c_List_Onth(X4)),hAPP(c_List_Onth(tc_List_Olist(X4)),X32))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),X32)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20))=c_List_Otranspose(X4,X32)<=![X42]:(X20=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X4)),X32),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(X4))),X32)))))<=(c_List_Olist_ONil(tc_List_Olist(X4))=X32=>X20=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__rectangle)). 4.02/4.26 fof(fact_atLeastLessThan0, axiom, ![X21]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X21),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan0)). 4.02/4.26 fof(fact_vimage__def, axiom, ![X6, X22, X7, X4]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),X4),c_member(X7)),X22)),X6))=hAPP(c_Set_Ovimage(X4,X7,X22),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__def)). 4.02/4.26 fof(fact_lists__eq__set, axiom, ![X3, X4]:c_List_Olists(X4,X3)=hAPP(c_Set_OCollect(tc_List_Olist(X4)),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X4)),c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool))),c_List_Oset(X4))),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__eq__set)). 4.02/4.26 fof(fact_power__odd__eq, axiom, ![X5, X11, X4]:(class_Groups_Omonoid__mult(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),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)))),X5)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__odd__eq)). 4.02/4.26 fof(fact_negDivAlg_Opinduct, axiom, ![X56, X70, X119]:((![X27, X78]:((hBOOL(hAPP(hAPP(X56,X27),X78))<=(hBOOL(hAPP(hAPP(X56,X27),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)))),X78)))<=~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X78),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),X27),X78)))))))<=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),X27),X78))))=>hBOOL(hAPP(hAPP(X56,X119),X70)))<=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),X119),X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg_Opinduct)). 4.02/4.26 fof(fact_power__minus__even, axiom, ![X5, X11, X4]:(class_Rings_Oring__1(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)),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)))),X5))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),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)))),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__minus__even)). 4.02/4.26 fof(fact_Sup__Inf, axiom, ![X3, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>c_Complete__Lattice_OSup__class_OSup(X4,X3)=c_Complete__Lattice_OInf__class_OInf(X4,hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OAll(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fimplies),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3)))),hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X4))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__Inf)). 4.02/4.26 fof(fact_Collect__ball__eq, axiom, ![X56, X3, X7, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X7),c_Set_OCollect(X4)),hAPP(c_COMBC(X4,X7,tc_HOL_Obool),X56)))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OAll(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fimplies),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X3)))),X56))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__ball__eq)). 4.02/4.26 fof(fact_Inf__Sup, axiom, ![X3, X4]:(c_Complete__Lattice_OSup__class_OSup(X4,hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OAll(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fimplies),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3)))),c_Orderings_Oord__class_Oless__eq(X4)))))=c_Complete__Lattice_OInf__class_OInf(X4,X3)<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__Sup)). 4.02/4.26 fof(fact_Suc__eq__number__of, axiom, ![X64, X20]:(hAPP(c_Nat_OSuc,X20)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)<=>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(X64))),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)),X20)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__eq__number__of)). 4.02/4.26 fof(fact_Collect__imp__eq, axiom, ![X112, X56, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OCollect(X4),X56))),hAPP(c_Set_OCollect(X4),X112))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fimplies),X56)),X112)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__imp__eq)). 4.02/4.26 fof(fact_Compl__Diff__eq, axiom, ![X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X3)),X6)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__Diff__eq)). 4.02/4.26 fof(fact_posDivAlg_Opinduct, axiom, ![X56, X70, X119]:((hBOOL(hAPP(hAPP(X56,X119),X70))<=![X27, X78]:(((~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X27),X78))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X78),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))=>hBOOL(hAPP(hAPP(X56,X27),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)))),X78))))=>hBOOL(hAPP(hAPP(X56,X27),X78)))<=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),X27),X78)))))<=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),X119),X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_posDivAlg_Opinduct)). 4.02/4.26 fof(fact_Nitpick_Oprod__def, axiom, ![X6, X3, X7, X4]:hAPP(c_Set_OCollect(tc_prod(X4,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7)),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)),X3)))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X6))))=c_Nitpick_Oprod(X4,X7,X3,X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oprod__def)). 4.02/4.26 fof(fact_power__even__eq, axiom, ![X5, X11, X4]:(class_Groups_Omonoid__mult(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),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)))),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__even__eq)). 4.02/4.26 fof(fact_less__Suc__number__of, axiom, ![X64, X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)))<=>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(X64))),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),X20)),c_Int_Onat)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Suc__number__of)). 4.02/4.26 fof(fact_le__Suc__number__of, axiom, ![X64, X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)))<=>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(X64))),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),X20)),c_Int_Onat)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__Suc__number__of)). 4.02/4.26 fof(fact_abs__power2, axiom, ![X11, X4]:(hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__power2)). 4.02/4.26 fof(fact_power2__abs, axiom, ![X11, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__abs)). 4.02/4.26 fof(fact_power2__minus, axiom, ![X11, X4]:(class_Rings_Oring__1(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__minus)). 4.02/4.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J, axiom, ![X5, X13, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),X5)))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),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)))),X5)))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J)). 4.02/4.26 fof(fact_mod2__gr__0, axiom, ![X21]:(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,X21,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,X21,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)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod2__gr__0)). 4.02/4.26 fof(fact_refl__on__def_H, axiom, ![X18, X3, X4]:(c_Relation_Orefl__on(X4,X3,X18)<=>(![X19]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X19),X18))=>hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3))),X19)))&![X19]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X19)),X18))<=hBOOL(hAPP(hAPP(c_member(X4),X19),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__def_H)). 4.02/4.26 fof(fact_dropWhile__neq__rev, axiom, ![X9, X32, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X32))=>(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))=>hAPP(hAPP(c_List_Olist_OCons(X4),X9),hAPP(c_List_Orev(X4),c_List_OtakeWhile(X4,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X9)),X32)))=c_List_OdropWhile(X4,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X9)),hAPP(c_List_Orev(X4),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__neq__rev)). 4.02/4.26 fof(fact_dropWhile__eq__drop, axiom, ![X32, X56, X4]:c_List_OdropWhile(X4,X56,X32)=hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X56,X32))),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__eq__drop)). 4.02/4.26 fof(fact_of__nat__double, axiom, ![X13, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onat,X13))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onat,X13)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X13))))<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__double)). 4.02/4.26 fof(fact_not__sum__power2__lt__zero, axiom, ![X43, X13, X4]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X43),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__sum__power2__lt__zero)). 4.02/4.26 fof(fact_negDivAlg_Osimps, axiom, ![X12, X11]:((c_Divides_OnegDivAlg(X11,X12)=hAPP(c_Divides_Oadjust(X12),c_Divides_OnegDivAlg(X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X12)))<=~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),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),X11),X12))))))&(hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11),X12))=c_Divides_OnegDivAlg(X11,X12)<=(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11),X12)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg_Osimps)). 4.02/4.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, axiom, ![X5, X13, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),X5))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),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)))),X5))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J)). 4.02/4.26 fof(fact_negDivAlg__eqn, axiom, ![X11, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11),X12))))=>hAPP(c_Divides_Oadjust(X12),c_Divides_OnegDivAlg(X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X12)))=c_Divides_OnegDivAlg(X11,X12))&(hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11),X12))=c_Divides_OnegDivAlg(X11,X12)<=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),X11),X12)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg__eqn)). 4.02/4.26 fof(fact_less__number__of__Suc, axiom, ![X20, X64]:(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(X64))),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)),X20))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)),hAPP(c_Nat_OSuc,X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__number__of__Suc)). 4.02/4.26 fof(fact_le__number__of__Suc, axiom, ![X20, X64]:(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(X64))),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)),X20))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)),hAPP(c_Nat_OSuc,X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__number__of__Suc)). 4.02/4.26 fof(fact_posDivAlg_Osimps, axiom, ![X12, X11]:((c_Divides_OposDivAlg(X11,X12)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11)<=(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),X12))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))&(~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),X12))))=>c_Divides_OposDivAlg(X11,X12)=hAPP(c_Divides_Oadjust(X12),c_Divides_OposDivAlg(X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X12))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_posDivAlg_Osimps)). 4.02/4.26 fof(fact_odd__power__less__zero, axiom, ![X5, X11, X4]:(class_Rings_Olinordered__idom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),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)))),X5)))),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_odd__power__less__zero)). 4.02/4.26 fof(fact_posDivAlg__eqn, axiom, ![X11, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))=>((c_Divides_OposDivAlg(X11,X12)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),X12)))&(c_Divides_OposDivAlg(X11,X12)=hAPP(c_Divides_Oadjust(X12),c_Divides_OposDivAlg(X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X12)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),X12)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_posDivAlg__eqn)). 4.02/4.26 fof(fact_power__minus1__odd, axiom, ![X5, X4]:(class_Rings_Oring__1(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X5)))=hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__minus1__odd)). 4.02/4.26 fof(fact_Suc__n__div__2__gt__zero, axiom, ![X5]:(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),X5),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)),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__n__div__2__gt__zero)). 4.02/4.26 fof(fact_zminus__zadd__distrib, axiom, ![X53, X29]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X53))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X29),X53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zminus__zadd__distrib)). 4.02/4.26 fof(fact_diff__int__def, axiom, ![X53, X29]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X29),X53)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X29),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__int__def)). 4.02/4.26 fof(fact_power__m1__odd, axiom, ![X5, X4]:(hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X5)))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__m1__odd)). 4.02/4.26 fof(fact_inj__vimage__singleton, axiom, ![X26, X22, X7, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X7,X22),hAPP(hAPP(c_Set_Oinsert(X7),X26),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X4),c_HOL_OThe(X4,hAPP(hAPP(c_COMBC(X4,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,tc_HOL_Obool),X4),c_fequal),X22)),X26))),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))<=c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__vimage__singleton)). 4.02/4.26 fof(fact_enum__the__def, axiom, ![X56, X4]:c_Enum_Oenum__the(X4,X56)=c_HOL_OThe(X4,X56), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__the__def)). 4.02/4.26 fof(fact_half__gt__zero__iff, axiom, ![X18, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X18))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X18),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))<=(class_Int_Onumber__ring(X4)&class_Fields_Olinordered__field__inverse__zero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_half__gt__zero__iff)). 4.02/4.26 fof(fact_power__minus1__even, axiom, ![X5, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X5))=c_Groups_Oone__class_Oone(X4)<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__minus1__even)). 4.02/4.26 fof(fact_takeWhile__neq__rev, axiom, ![X9, X32, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))=>c_List_OtakeWhile(X4,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X9)),hAPP(c_List_Orev(X4),X32))=hAPP(c_List_Orev(X4),hAPP(c_List_Otl(X4),c_List_OdropWhile(X4,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X9)),X32))))<=hBOOL(hAPP(c_List_Odistinct(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__neq__rev)). 4.02/4.26 fof(fact_drop__tl, axiom, ![X45, X5, X4]:hAPP(c_List_Otl(X4),hAPP(hAPP(c_List_Odrop(X4),X5),X45))=hAPP(hAPP(c_List_Odrop(X4),X5),hAPP(c_List_Otl(X4),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__tl)). 4.02/4.26 fof(fact_drop__Suc, axiom, ![X45, X5, X4]:hAPP(hAPP(c_List_Odrop(X4),X5),hAPP(c_List_Otl(X4),X45))=hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_OSuc,X5)),X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Suc)). 4.02/4.26 fof(fact_zero__le__even__power_H, axiom, ![X5, X11, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),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)))),X5))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__even__power_H)). 4.02/4.26 fof(fact_zdiv__number__of__Bit1, axiom, ![X1, X53]:((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),X53)))=>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),X53))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X53))))&(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),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X53))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X53)))<=~(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),X53)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__number__of__Bit1)). 4.02/4.26 fof(fact_power__number__of__odd, axiom, ![X16, X23, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23)))=>hAPP(hAPP(c_HOL_OLet(X4,X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X16),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X23))),hAPP(hAPP(c_COMBS(X4,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X4),c_Groups_Otimes__class_Otimes(X4)),hAPP(c_Groups_Otimes__class_Otimes(X4),X16))),c_COMBI(X4)))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X16),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X23))))&(~(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),X23))))=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),X16),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X23)))=c_Groups_Oone__class_Oone(X4)))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__number__of__odd)). 4.02/4.26 fof(fact_power__m1__even, axiom, ![X5, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X5))=c_Groups_Oone__class_Oone(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__m1__even)). 4.02/4.26 fof(fact_div__2__gt__zero, axiom, ![X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5))=>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),X5),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)). 4.02/4.26 fof(fact_zpower__number__of__odd, axiom, ![X16, X23]:((c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X16),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X23)))<=~(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),X23)))))&(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),X23)))=>hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X16),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X23))),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),X16))),c_COMBI(tc_Int_Oint)))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X16),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zpower__number__of__odd)). 4.02/4.26 fof(fact_zero__le__power2, axiom, ![X11, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__power2)). 4.02/4.26 fof(fact_mult__2, axiom, ![X29, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X29),X29)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__2)). 4.02/4.26 fof(fact_length__take, axiom, ![X45, X5, X4]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),X5)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Otake(X4),X5),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__take)). 4.02/4.26 fof(fact_mult__2__right, axiom, ![X29, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X29),X29)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X29),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__2__right)). 4.02/4.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, axiom, ![X13, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X13),X13)<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J)). 4.02/4.26 fof(fact_power2__eq__square, axiom, ![X11, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X11)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))<=class_Groups_Omonoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power2__eq__square)). 4.02/4.26 fof(fact_power3__eq__cube, axiom, ![X11, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X11)),X11)<=class_Groups_Omonoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power3__eq__cube)). 4.02/4.26 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)). 4.02/4.26 fof(fact_trancl__trans, axiom, ![X24, X18, X25, X26, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X25),X24)),c_Transitive__Closure_Otrancl(X4,X18)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X24)),c_Transitive__Closure_Otrancl(X4,X18))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),c_Transitive__Closure_Otrancl(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__trans)). 4.02/4.26 fof(fact_trancl__unfold__right, axiom, ![X18, X4]:c_Transitive__Closure_Otrancl(X4,X18)=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),c_Transitive__Closure_Ortrancl(X4,X18)),X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__unfold__right)). 4.02/4.26 fof(fact_one__add__one__is__two, axiom, ![X4]:(hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Oone__class_Oone(X4))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__add__one__is__two)). 4.02/4.26 fof(fact_power__number__of__even, axiom, ![X23, X16, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_HOL_OLet(X4,X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X16),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X23))),hAPP(hAPP(c_COMBS(X4,X4,X4),c_Groups_Otimes__class_Otimes(X4)),c_COMBI(X4)))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X16),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__number__of__even)). 4.02/4.26 fof(fact_divmod__nat__def, axiom, ![X20, X21]:c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X21,X20))=c_Divides_Odivmod__nat(X21,X20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__def)). 4.02/4.26 fof(fact_zero__eq__power2, axiom, ![X26, X4]:(class_Rings_Oring__1__no__zero__divisors(X4)=>(c_Groups_Ozero__class_Ozero(X4)=X26<=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),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_zero__eq__power2)). 4.02/4.26 fof(fact_rtrancl__trancl__trancl, axiom, ![X16, X18, X17, X9, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X16)),c_Transitive__Closure_Otrancl(X4,X18)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X17),X16)),c_Transitive__Closure_Otrancl(X4,X18))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),c_Transitive__Closure_Ortrancl(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__trancl__trancl)). 4.02/4.26 fof(fact_trancl__rtrancl__trancl, axiom, ![X24, X18, X25, X26, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X24)),c_Transitive__Closure_Otrancl(X4,X18)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X25),X24)),c_Transitive__Closure_Ortrancl(X4,X18))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),c_Transitive__Closure_Otrancl(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__rtrancl__trancl)). 4.02/4.26 fof(fact_zero__power2, axiom, ![X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Ozero__class_Ozero(X4)<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__power2)). 4.02/4.26 fof(fact_one__power2, axiom, ![X4]:(class_Rings_Osemiring__1(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),c_Groups_Oone__class_Oone(X4)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oone__class_Oone(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__power2)). 4.02/4.26 fof(fact_map__removeAll__inj__on, axiom, ![X32, X9, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,hAPP(hAPP(c_Set_Oinsert(X4),X9),hAPP(c_List_Oset(X4),X32)))=>hAPP(hAPP(c_List_Omap(X4,X7),X22),hAPP(c_List_OremoveAll(X4,X9),X32))=hAPP(c_List_OremoveAll(X7,hAPP(X22,X9)),hAPP(hAPP(c_List_Omap(X4,X7),X22),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__removeAll__inj__on)). 4.02/4.26 fof(fact_trancl__into__trancl2, axiom, ![X24, X18, X25, X26, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),X18))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X25),X24)),c_Transitive__Closure_Otrancl(X4,X18)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X24)),c_Transitive__Closure_Otrancl(X4,X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__into__trancl2)). 4.02/4.26 fof(fact_Transitive__Closure_Otrancl__into__trancl, axiom, ![X24, X18, X25, X26, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),c_Transitive__Closure_Otrancl(X4,X18)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X25),X24)),X18))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X24)),c_Transitive__Closure_Otrancl(X4,X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Transitive__Closure_Otrancl__into__trancl)). 4.02/4.26 fof(fact_map__removeAll__inj, axiom, ![X32, X9, X22, X7, X4]:(hAPP(c_List_OremoveAll(X7,hAPP(X22,X9)),hAPP(hAPP(c_List_Omap(X4,X7),X22),X32))=hAPP(hAPP(c_List_Omap(X4,X7),X22),hAPP(c_List_OremoveAll(X4,X9),X32))<=c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__removeAll__inj)). 4.02/4.26 fof(fact_Nitpick_Oof__frac__def, axiom, ![X14, X4, X7]:((class_Rings_Oring__1(X7)&class_Rings_Oinverse(X7))=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),hAPP(c_Int_Oring__1__class_Oof__int(X7),hAPP(c_Nitpick_Onum(X4),X14))),hAPP(c_Int_Oring__1__class_Oof__int(X7),hAPP(c_Nitpick_Odenom(X4),X14)))=c_Nitpick_Oof__frac(X4,X7,X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oof__frac__def)). 4.02/4.26 fof(fact_Nitpick_Onum__def, axiom, ![X4]:hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X4,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X4))=c_Nitpick_Onum(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Onum__def)). 4.02/4.26 fof(fact_Nitpick_Odenom__def, axiom, ![X4]:hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X4,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X4))=c_Nitpick_Odenom(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Odenom__def)). 4.02/4.26 fof(fact_nat__number__of__Bit1, axiom, ![X23]:((hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X23)),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(X23))<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23)))))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23)))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of__Bit1)). 4.02/4.26 fof(fact_trancl__subset__Sigma, axiom, ![X3, X18, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X4,X18)),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X3))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__subset__Sigma)). 4.02/4.26 fof(fact_odd__0__le__power__imp__0__le, axiom, ![X5, X11, X4]:(class_Rings_Olinordered__idom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),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)))),X5)))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_odd__0__le__power__imp__0__le)). 4.02/4.26 fof(fact_flat__lub__def, axiom, ![X25, X3, X4]:((c_HOL_OThe(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X25),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=c_Partial__Function_Oflat__lub(X4,X25,X3)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X25),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))&(X25=c_Partial__Function_Oflat__lub(X4,X25,X3)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X25),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_flat__lub__def)). 4.02/4.26 fof(fact_rtrancl__into__trancl1, axiom, ![X24, X18, X25, X26, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),c_Transitive__Closure_Ortrancl(X4,X18)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X24)),c_Transitive__Closure_Otrancl(X4,X18)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X25),X24)),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__into__trancl1)). 4.02/4.26 fof(fact_r__r__into__trancl, axiom, ![X24, X39, X25, X26, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X25),X24)),X39))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X24)),c_Transitive__Closure_Otrancl(X4,X39))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_r__r__into__trancl)). 4.02/4.26 fof(fact_dropWhile__nth, axiom, ![X32, X56, X4, X38]:(hAPP(hAPP(c_List_Onth(X4),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X38),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X56,X32))))=hAPP(hAPP(c_List_Onth(X4),c_List_OdropWhile(X4,X56,X32)),X38)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X38),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OdropWhile(X4,X56,X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__nth)). 4.02/4.26 fof(fact_removeAll_Osimps_I2_J, axiom, ![X45, X4, X43, X13]:((X43=X13=>hAPP(c_List_OremoveAll(X4,X13),hAPP(hAPP(c_List_Olist_OCons(X4),X43),X45))=hAPP(c_List_OremoveAll(X4,X13),X45))&(hAPP(c_List_OremoveAll(X4,X13),hAPP(hAPP(c_List_Olist_OCons(X4),X43),X45))=hAPP(hAPP(c_List_Olist_OCons(X4),X43),hAPP(c_List_OremoveAll(X4,X13),X45))<=X43!=X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_removeAll_Osimps_I2_J)). 4.02/4.26 fof(fact_trancl__Int__subset, axiom, ![X40, X18, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),X40))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X4,X18)),X40)),X18)),X40))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X4,X18)),X40)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__Int__subset)). 4.02/4.26 fof(fact_eq__int__code_I13_J, axiom, ![X57, X58]:(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X58),X57))<=>hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X58)),c_Int_OBit0(X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I13_J)). 4.02/4.26 fof(fact_rel__simps_I14_J, axiom, ![X60, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),X60))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X28)),c_Int_OBit0(X60)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I14_J)). 4.02/4.26 fof(fact_rel__simps_I31_J, axiom, ![X60, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X28)),c_Int_OBit0(X60)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28),X60))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I31_J)). 4.02/4.26 fof(fact_number__of__Bit0, axiom, ![X53, X4]:(hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(X53))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X53))),hAPP(c_Int_Onumber__class_Onumber__of(X4),X53))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__Bit0)). 4.02/4.26 fof(fact_Collect__disj__eq, axiom, ![X112, X56, X4]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fdisj),X56)),X112))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OCollect(X4),X56)),hAPP(c_Set_OCollect(X4),X112)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__disj__eq)). 4.02/4.26 fof(fact_double__number__of__Bit0, axiom, ![X53, X4]:(hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(X53))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Oone__class_Oone(X4))),hAPP(c_Int_Onumber__class_Onumber__of(X4),X53))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__number__of__Bit0)). 4.02/4.26 fof(fact_tranclD, axiom, ![X39, X17, X9, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),c_Transitive__Closure_Otrancl(X4,X39)))=>?[X36]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X36),X17)),c_Transitive__Closure_Ortrancl(X4,X39)))&hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X36)),X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tranclD)). 4.02/4.26 fof(fact_tranclD2, axiom, ![X39, X17, X9, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),c_Transitive__Closure_Otrancl(X4,X39)))=>?[X36]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X36),X17)),X39))&hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X36)),c_Transitive__Closure_Ortrancl(X4,X39))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tranclD2)). 4.02/4.26 fof(fact_trancl__mono, axiom, ![X40, X18, X51, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),X40))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X51),c_Transitive__Closure_Otrancl(X4,X40))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X51),c_Transitive__Closure_Otrancl(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__mono)). 4.02/4.26 fof(fact_nat__minus__add__max, axiom, ![X2, X5]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X5),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),X2)),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__minus__add__max)). 4.02/4.26 fof(fact_nat__add__commute, axiom, ![X5, X2]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__commute)). 4.02/4.26 fof(fact_rel__simps_I15_J, axiom, ![X60, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X28)),c_Int_OBit1(X60)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28),X60))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I15_J)). 4.02/4.26 fof(fact_less__eq__int__code_I14_J, axiom, ![X57, X58]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X58),X57))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X58)),c_Int_OBit1(X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__int__code_I14_J)). 4.02/4.26 fof(fact_rel__simps_I16_J, axiom, ![X60, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X28)),c_Int_OBit0(X60)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),X60))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I16_J)). 4.02/4.26 fof(fact_less__eq__int__code_I15_J, axiom, ![X57, X58]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X58)),c_Int_OBit0(X57)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X58),X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__int__code_I15_J)). 4.02/4.26 fof(fact_diff__special_I2_J, axiom, ![X1, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X1)),c_Groups_Oone__class_Oone(X4))=hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__special_I2_J)). 4.02/4.26 fof(fact_diff__special_I1_J, axiom, ![X53, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),c_Groups_Oone__class_Oone(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X53))=hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X53)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__special_I1_J)). 4.02/4.26 fof(fact_rtranclD, axiom, ![X39, X25, X26, X4]:((X26=X25|(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),c_Transitive__Closure_Otrancl(X4,X39)))&X25!=X26))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),c_Transitive__Closure_Ortrancl(X4,X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtranclD)). 4.02/4.26 fof(fact_Suc__diff__eq__diff__pred, axiom, ![X2, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X5))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__diff__eq__diff__pred)). 4.02/4.26 fof(fact_negDivAlg__minus1, axiom, ![X12]:c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X12)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12),c_Groups_Oone__class_Oone(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg__minus1)). 4.02/4.26 fof(fact_fst__eqD, axiom, ![X11, X43, X13, X7, X4]:(hAPP(c_Product__Type_Ofst(X4,X7),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X13),X43))=X11=>X11=X13), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__eqD)). 4.02/4.26 fof(fact_trancl__power, axiom, ![X39, X51, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X51),c_Transitive__Closure_Otrancl(X4,X39)))<=>?[X104]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X104))&hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X51),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X104),X39))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__power)). 4.02/4.26 fof(fact_acyclicI, axiom, ![X18, X4]:(c_Wellfounded_Oacyclic(X4,X18)<=![X19]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X19)),c_Transitive__Closure_Otrancl(X4,X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclicI)). 4.02/4.26 fof(fact_acyclic__def, axiom, ![X18, X4]:(![X19]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X19)),c_Transitive__Closure_Otrancl(X4,X18))))<=>c_Wellfounded_Oacyclic(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclic__def)). 4.02/4.26 fof(fact_snd__eqD, axiom, ![X11, X43, X13, X4, X7]:(X11=X43<=X11=hAPP(c_Product__Type_Osnd(X7,X4),hAPP(hAPP(c_Product__Type_OPair(X7,X4),X13),X43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__eqD)). 4.02/4.26 fof(fact_Nitpick_Oless__frac__def, axiom, ![X18, X180, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X4),c_Nitpick_Oplus__frac(X4,X180,c_Nitpick_Ouminus__frac(X4,X18)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>c_Nitpick_Oless__frac(X4,X180,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oless__frac__def)). 4.02/4.26 fof(fact_Nitpick_Oless__eq__frac__def, axiom, ![X18, X180, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X4),c_Nitpick_Oplus__frac(X4,X180,c_Nitpick_Ouminus__frac(X4,X18)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>c_Nitpick_Oless__eq__frac(X4,X180,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oless__eq__frac__def)). 4.02/4.26 fof(fact_add__special_I2_J, axiom, ![X53, X4]:(class_Int_Onumber__ring(X4)=>hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X53))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X53))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__special_I2_J)). 4.02/4.26 fof(fact_add__special_I3_J, axiom, ![X1, X4]:(hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OBit1(c_Int_OPls)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X1)),c_Groups_Oone__class_Oone(X4))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__special_I3_J)). 4.02/4.26 fof(fact_psubset__insert__iff, axiom, ![X6, X9, X3, X4]:(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X6))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))&(~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))))<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),X6))))&(hBOOL(hAPP(hAPP(c_member(X4),X9),X6))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X3),X6))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubset__insert__iff)). 4.02/4.26 fof(fact_psubset__eq, axiom, ![X6, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X3),X6))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))&X6!=X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubset__eq)). 4.02/4.26 fof(fact_eq__int__code_I16_J, axiom, ![X57, X58]:(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X58)),c_Int_OBit1(X57)))<=>hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X58),X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I16_J)). 4.02/4.26 fof(fact_less__int__code_I16_J, axiom, ![X57, X58]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X58)),c_Int_OBit1(X57)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X58),X57))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__int__code_I16_J)). 4.02/4.26 fof(fact_less__eq__int__code_I16_J, axiom, ![X57, X58]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X58),X57))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X58)),c_Int_OBit1(X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__int__code_I16_J)). 4.02/4.26 fof(fact_list__ex1__simps_I2_J, axiom, ![X32, X9, X56, X4]:(c_List_Olist__ex1(X4,X56,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32))<=>((~(hBOOL(hAPP(X56,X9)))=>c_List_Olist__ex1(X4,X56,X32))&(hBOOL(hAPP(X56,X9))=>c_List_Olist__all(X4,hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),X56))),hAPP(c_fequal,X9)),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex1__simps_I2_J)). 4.02/4.26 fof(fact_filter__filter, axiom, ![X32, X112, X56, X4]:hAPP(c_List_Ofilter(X4,hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),X112)),X56)),X32)=hAPP(c_List_Ofilter(X4,X56),hAPP(c_List_Ofilter(X4,X112),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__filter)). 4.02/4.26 fof(fact_Collect__conv__if2, axiom, ![X4, X26, X56]:((hBOOL(hAPP(X56,X26))=>hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(c_fequal,X26))),X56))=hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))&(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(c_fequal,X26))),X56))<=~(hBOOL(hAPP(X56,X26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__conv__if2)). 4.02/4.26 fof(fact_eq__special_I2_J, axiom, ![X17, X4]:((c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X17))))<=>c_Groups_Oone__class_Oone(X4)=hAPP(c_Int_Onumber__class_Onumber__of(X4),X17))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__special_I2_J)). 4.02/4.26 fof(fact_eq__special_I4_J, axiom, ![X9, X4]:(class_Int_Onumber__ring(X4)=>(hAPP(c_Int_Onumber__class_Onumber__of(X4),X9)=c_Groups_Oone__class_Oone(X4)<=>c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__special_I4_J)). 4.02/4.26 fof(fact_number__of__Bit1, axiom, ![X53, X4]:(class_Int_Onumber__ring(X4)=>hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit1(X53))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X53))),hAPP(c_Int_Onumber__class_Onumber__of(X4),X53))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__Bit1)). 4.02/4.26 fof(fact_setsum__set__upt__conv__listsum__nat, axiom, ![X20, X21, X22, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X4),X22),c_List_Oupt(X21,X20)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X21,X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__set__upt__conv__listsum__nat)). 4.02/4.26 fof(fact_set__upt, axiom, ![X38, X37]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X37),X38)=hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X37,X38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__upt)). 4.02/4.26 fof(fact_upt__Suc__append, axiom, ![X135, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),X135))=>c_List_Oupt(X46,hAPP(c_Nat_OSuc,X135))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X46,X135)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X135),c_List_Olist_ONil(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__Suc__append)). 4.02/4.26 fof(fact_iszero__number__of__Bit0, axiom, ![X23, X4]:((c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),X23))<=>c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit0(X23))))<=(class_Int_Oring__char__0(X4)&class_Int_Onumber__ring(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_iszero__number__of__Bit0)). 4.02/4.26 fof(fact_less__special_I2_J, axiom, ![X17, X4]:((class_Int_Onumber__ring(X4)&class_Rings_Olinordered__idom(X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X17)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__special_I2_J)). 4.02/4.26 fof(fact_le__special_I2_J, axiom, ![X17, X4]:((class_Rings_Olinordered__idom(X4)&class_Int_Onumber__ring(X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Oone__class_Oone(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X17)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__special_I2_J)). 4.02/4.26 fof(fact_less__special_I4_J, axiom, ![X9, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9),c_Int_OBit1(c_Int_OPls)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X9)),c_Groups_Oone__class_Oone(X4))))<=(class_Int_Onumber__ring(X4)&class_Rings_Olinordered__idom(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__special_I4_J)). 4.02/4.26 fof(fact_le__special_I4_J, axiom, ![X9, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X9)),c_Groups_Oone__class_Oone(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9),c_Int_OBit1(c_Int_OPls))))<=(class_Int_Onumber__ring(X4)&class_Rings_Olinordered__idom(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__special_I4_J)). 4.02/4.26 fof(fact_Suc__nat__number__of__add, axiom, ![X5, X1]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))=>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)),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5))&(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)),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X1))),X5)<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__nat__number__of__add)). 4.02/4.26 fof(fact_upt__eq__Cons__conv, axiom, ![X32, X9, X38, X37]:(hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X9),X32)=c_List_Oupt(X37,X38)<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37),X38))&X32=c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X38))&X37=X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__eq__Cons__conv)). 4.02/4.26 fof(fact_trancl__into__rtrancl, axiom, ![X18, X25, X26, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),c_Transitive__Closure_Ortrancl(X4,X18)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),c_Transitive__Closure_Otrancl(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__into__rtrancl)). 4.02/4.26 fof(fact_dom__map__of__conv__image__fst, axiom, ![X145, X7, X4]:hAPP(c_Set_Oimage(tc_prod(X4,X7),X4,c_Product__Type_Ofst(X4,X7)),hAPP(c_List_Oset(tc_prod(X4,X7)),X145))=c_Map_Odom(X4,X7,hAPP(c_Map_Omap__of(X4,X7),X145)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__map__of__conv__image__fst)). 4.02/4.26 fof(fact_fst__eq__Domain, axiom, ![X39, X7, X4]:hAPP(c_Set_Oimage(tc_prod(X4,X7),X4,c_Product__Type_Ofst(X4,X7)),X39)=hAPP(c_Relation_ODomain(X4,X7),X39), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__eq__Domain)). 4.02/4.26 fof(fact_irrefl__tranclI, axiom, ![X9, X18, X4]:(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X4,X4),X18)),c_Transitive__Closure_Ortrancl(X4,X18))=>~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X9)),c_Transitive__Closure_Otrancl(X4,X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_irrefl__tranclI)). 4.02/4.26 fof(fact_rel__simps_I48_J, axiom, ![X60, X28]:(X60=X28<=>c_Int_OBit0(X28)=c_Int_OBit0(X60)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I48_J)). 4.02/4.26 fof(fact_Suc__diff__number__of, axiom, ![X2, X1]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),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)))=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))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__diff__number__of)). 4.02/4.27 fof(fact_divide__numeral__1, axiom, ![X11, X4]:((class_Int_Onumber__ring(X4)&class_Fields_Ofield(X4))=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit1(c_Int_OPls)))=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__numeral__1)). 4.02/4.27 fof(fact_r__into__trancl_H, axiom, ![X18, X51, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X51),X18))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X51),c_Transitive__Closure_Otrancl(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_r__into__trancl_H)). 4.02/4.27 fof(fact_nat__of__aux__code, axiom, ![X5, X46]:((X46=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=>c_Code__Numeral_Onat__of__aux(X46,X5)=X5)&(c_Code__Numeral_Onat__of__aux(X46,X5)=c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X46),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X5))<=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__of__aux__code)). 4.02/4.27 fof(fact_nat__of__aux__def, axiom, ![X5, X46]:c_Code__Numeral_Onat__of__aux(X46,X5)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X46)),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__of__aux__def)). 4.02/4.27 fof(fact_mult__numeral__1, axiom, ![X11, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit1(c_Int_OPls))),X11)=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__numeral__1)). 4.02/4.27 fof(fact_mult__numeral__1__right, axiom, ![X11, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit1(c_Int_OPls)))=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__numeral__1__right)). 4.02/4.27 fof(fact_removeAll__id, axiom, ![X32, X9, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32))))=>X32=hAPP(c_List_OremoveAll(X4,X9),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_removeAll__id)). 4.02/4.27 fof(fact_distinct__remove1__removeAll, axiom, ![X13, X45, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X45))=>hAPP(c_List_OremoveAll(X4,X13),X45)=c_List_Oremove1(X4,X13,X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__remove1__removeAll)). 4.02/4.27 fof(fact_nat__number__of__diff__1, axiom, ![X1]:((~(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)))&(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)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of__diff__1)). 4.02/4.27 fof(fact_finite__trancl, axiom, ![X18, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X4)),X18))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X4)),c_Transitive__Closure_Otrancl(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__trancl)). 4.02/4.27 fof(fact_eq__int__code_I12_J, axiom, ![X58]:(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X58)),c_Int_OMin))<=>hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X58),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I12_J)). 4.02/4.27 fof(fact_rel__simps_I13_J, axiom, ![X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X28)),c_Int_OMin))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I13_J)). 4.02/4.27 fof(fact_rel__simps_I12_J, axiom, ![X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X28)),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I12_J)). 4.02/4.27 fof(fact_rel__simps_I30_J, axiom, ![X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28),c_Int_OMin))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X28)),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I30_J)). 4.02/4.27 fof(fact_rel__simps_I29_J, axiom, ![X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X28)),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I29_J)). 4.02/4.27 fof(fact_neg__number__of__Bit1, axiom, ![X23]:(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X23)))<=>hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__number__of__Bit1)). 4.02/4.27 fof(fact_wf__converse__trancl, axiom, ![X18, X4]:(c_Wellfounded_Owf(X4,hAPP(c_Relation_Oconverse(X4,X4),c_Transitive__Closure_Otrancl(X4,X18)))<=c_Wellfounded_Owf(X4,hAPP(c_Relation_Oconverse(X4,X4),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__converse__trancl)). 4.02/4.27 fof(fact_eq__int__code_I8_J, axiom, ![X57]:(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X57))<=>hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I8_J)). 4.02/4.27 fof(fact_rel__simps_I9_J, axiom, ![X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X28)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I9_J)). 4.02/4.27 fof(fact_rel__simps_I5_J, axiom, ![X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X28)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I5_J)). 4.02/4.27 fof(fact_rel__simps_I26_J, axiom, ![X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X28)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I26_J)). 4.02/4.27 fof(fact_rel__simps_I22_J, axiom, ![X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X28)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I22_J)). 4.02/4.27 fof(fact_add__Pls, axiom, ![X107]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X107)=X107, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Pls)). 4.02/4.27 fof(fact_nat__1__add__number__of, axiom, ![X1]:((~(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),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_Int_Osucc(X1)))&(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),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))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__1__add__number__of)). 4.02/4.27 fof(fact_numeral__1__eq__1, axiom, ![X4]:(hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit1(c_Int_OPls))=c_Groups_Oone__class_Oone(X4)<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_numeral__1__eq__1)). 4.02/4.27 fof(fact_rel__simps_I51_J, axiom, ![X60, X28]:(X28=X60<=>c_Int_OBit1(X60)=c_Int_OBit1(X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I51_J)). 4.02/4.27 fof(fact_number__of__succ, axiom, ![X107, X4]:(class_Int_Onumber__ring(X4)=>hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_Osucc(X107))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X107))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__succ)). 4.02/4.27 fof(fact_wf__trancl, axiom, ![X18, X4]:(c_Wellfounded_Owf(X4,c_Transitive__Closure_Otrancl(X4,X18))<=c_Wellfounded_Owf(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__trancl)). 4.02/4.27 fof(fact_upt__Suc, axiom, ![X135, X46]:((c_List_Oupt(X46,hAPP(c_Nat_OSuc,X135))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X46,X135)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X135),c_List_Olist_ONil(tc_Nat_Onat)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),X135)))&(c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X46,hAPP(c_Nat_OSuc,X135))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),X135))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__Suc)). 4.02/4.27 fof(fact_Suc__nat__number__of, axiom, ![X1]:((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))=c_Groups_Oone__class_Oone(tc_Nat_Onat))&(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))<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__nat__number__of)). 4.02/4.27 fof(fact_neg__number__of__pred__iff__0, axiom, ![X64]:(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X64))))<=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__number__of__pred__iff__0)). 4.02/4.27 fof(fact_iszero__number__of__Bit1, axiom, ![X53, X4]:(~(c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit1(X53))))<=(class_Int_Onumber__ring(X4)&class_Int_Oring__char__0(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_iszero__number__of__Bit1)). 4.02/4.27 fof(fact_not__iszero__Numeral1, axiom, ![X4]:(~(c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OBit1(c_Int_OPls))))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__iszero__Numeral1)). 4.02/4.27 fof(fact_rel__simps_I47_J, axiom, ![X28]:(X28=c_Int_OMin<=>c_Int_OMin=c_Int_OBit1(X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I47_J)). 4.02/4.27 fof(fact_code__numeral_Oinject, axiom, ![X305, X197]:(c_Code__Numeral_OSuc__code__numeral(X305)=c_Code__Numeral_OSuc__code__numeral(X197)<=>X305=X197), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Oinject)). 4.02/4.27 fof(fact_Suc__code__numeral__def, axiom, ![X107]:c_Code__Numeral_OSuc__code__numeral(X107)=hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X107))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__code__numeral__def)). 4.02/4.27 fof(fact_eq__int__code_I14_J, axiom, ![X289, X153]:~(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X153)),c_Int_OBit1(X289)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I14_J)). 4.02/4.27 fof(fact_eq__int__code_I15_J, axiom, ![X289, X153]:~(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X153)),c_Int_OBit0(X289)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I15_J)). 4.02/4.27 fof(fact_code__numeral_Osimps_I2_J, axiom, ![X215]:c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=c_Code__Numeral_OSuc__code__numeral(X215), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osimps_I2_J)). 4.02/4.27 fof(fact_trancl__insert, axiom, ![X18, X9, X17, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X4,X18)),hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4))),hAPP(hAPP(c_COMBC(X4,X4,tc_prod(X4,X4)),c_Product__Type_OPair(X4,X4)),X17))),c_Transitive__Closure_Ortrancl(X4,X18))))),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4))),hAPP(c_Product__Type_OPair(X4,X4),X9))),c_Transitive__Closure_Ortrancl(X4,X18))))))=c_Transitive__Closure_Otrancl(X4,hAPP(hAPP(c_Set_Oinsert(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X17),X9)),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__insert)). 4.02/4.27 fof(fact_sublist__shift__lemma, axiom, ![X37, X32, X3, X4]:hAPP(hAPP(c_List_Omap(tc_prod(X4,tc_Nat_Onat),X4),c_Product__Type_Ofst(X4,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X4,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X4,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X4,tc_Nat_Onat))),X3)),hAPP(hAPP(c_List_Ozip(X4,tc_Nat_Onat),X32),c_List_Oupt(X37,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))))))=hAPP(hAPP(c_List_Omap(tc_prod(X4,tc_Nat_Onat),X4),c_Product__Type_Ofst(X4,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X4,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X4,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X4,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(X4,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X4,tc_Nat_Onat))),X37))),X3)),hAPP(hAPP(c_List_Ozip(X4,tc_Nat_Onat),X32),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__shift__lemma)). 4.02/4.27 fof(fact_arith__series__int, axiom, ![X20, X102, X26]: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),X26)),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))),X102))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26),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),X20),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X102)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_arith__series__int)). 4.02/4.27 fof(fact_zmod__number__of__Bit0, axiom, ![X53, 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)))),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),X53)))=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(X53))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__number__of__Bit0)). 4.02/4.27 fof(fact_transpose__max__length, axiom, ![X32, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),hAPP(c_List_Ofilter(tc_List_Olist(X4),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X4)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(X4),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X4)))),X32))=c_List_Ofoldr(tc_List_Olist(X4),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X4)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),c_List_Otranspose(X4,X32),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__max__length)). 4.02/4.27 fof(fact_add__Bit1__Bit1, axiom, ![X47, X107]:c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),c_Int_Osucc(X47)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X107)),c_Int_OBit1(X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Bit1__Bit1)). 4.02/4.27 fof(fact_nat__mult__2, axiom, ![X29]: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)))),X29)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X29), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__2)). 4.02/4.27 fof(fact_nat__mult__2__right, axiom, ![X29]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X29)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X29),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__2__right)). 4.02/4.27 fof(fact_maps__simps_I1_J, axiom, ![X32, X9, X22, X4, X7]:hAPP(hAPP(c_List_Oappend(X4),hAPP(X22,X9)),c_List_Omaps(X7,X4,X22,X32))=c_List_Omaps(X7,X4,X22,hAPP(hAPP(c_List_Olist_OCons(X7),X9),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_maps__simps_I1_J)). 4.02/4.27 fof(fact_concat__map__maps, axiom, ![X32, X22, X7, X4]:c_List_Oconcat(X4,hAPP(hAPP(c_List_Omap(X7,tc_List_Olist(X4)),X22),X32))=c_List_Omaps(X7,X4,X22,X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__map__maps)). 4.02/4.27 fof(fact_foldl__conv__concat, axiom, ![X134, X32, X4]:hAPP(hAPP(c_List_Oappend(X4),X32),c_List_Oconcat(X4,X134))=hAPP(c_List_Ofoldl(tc_List_Olist(X4),tc_List_Olist(X4),c_List_Oappend(X4),X32),X134), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__conv__concat)). 4.02/4.27 fof(fact_zpower__number__of__even, axiom, ![X23, X16]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X16),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X23)))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X16),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X23))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zpower__number__of__even)). 4.02/4.27 fof(fact_add__Bit0__Bit1, axiom, ![X47, X107]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X107)),c_Int_OBit1(X47))=c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Bit0__Bit1)). 4.02/4.27 fof(fact_add__Bit1__Bit0, axiom, ![X47, X107]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X107)),c_Int_OBit0(X47))=c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Bit1__Bit0)). 4.02/4.27 fof(fact_mult__Bit1, axiom, ![X47, X107]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X107)),X47)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X107),X47))),X47), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Bit1)). 4.02/4.27 fof(fact_nat__number__of__Bit0, axiom, ![X23]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X23))=hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X23)),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))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of__Bit0)). 4.02/4.27 fof(fact_mult__Bit0, axiom, ![X47, X107]:c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X107),X47))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X107)),X47), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Bit0)). 4.02/4.27 fof(fact_succ__Bit1, axiom, ![X107]:c_Int_Osucc(c_Int_OBit1(X107))=c_Int_OBit0(c_Int_Osucc(X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_succ__Bit1)). 4.02/4.27 fof(fact_com_Osize_I12_J, axiom, ![X231, X232]:hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X232,X231))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X232)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X231))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I12_J)). 4.02/4.27 fof(fact_nat__add__assoc, axiom, ![X107, X5, X2]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X107))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X5)),X107), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__assoc)). 4.02/4.27 fof(fact_Suc__eq__plus1, axiom, ![X5]:hAPP(c_Nat_OSuc,X5)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),c_Groups_Oone__class_Oone(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__eq__plus1)). 4.02/4.27 fof(fact_com_Osize_I4_J, axiom, ![X231, X232]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X232)),c_Com_Ocom_Ocom__size(X231))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X232,X231)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I4_J)). 4.02/4.27 fof(fact_adjust__def, axiom, ![X25]:c_Divides_Oadjust(X25)=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)),X25))))),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)),X25))))),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))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_adjust__def)). 4.02/4.27 fof(fact_adjust__eq, axiom, ![X18, X180, X25]:hAPP(c_Divides_Oadjust(X25),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X180),X18))=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),X18),X25)),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)))),X180)),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)))),X180)),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_adjust__eq)). 4.02/4.27 fof(fact_Nitpick_Oplus__frac__def, axiom, ![X18, X180, X4]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X4),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X4),X180),hAPP(c_Nitpick_Odenom(X4),X18))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X4),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X4),tc_Int_Oint),c_Nitpick_Ofrac(X4)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X4),X180))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X4),X180))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X4),X18))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X4),X18)))))),c_COMBI(tc_Int_Oint)))=c_Nitpick_Oplus__frac(X4,X180,X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oplus__frac__def)). 4.02/4.27 fof(fact_transpose_Osimps_I3_J, axiom, ![X134, X32, X9, X4]:hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X9),c_List_Oconcat(X4,hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_Olist__case(tc_List_Olist(X4),X4,c_List_Olist_ONil(X4),hAPP(hAPP(c_COMBB(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),X4),c_COMBK(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_COMBC(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)),c_List_Olist_ONil(X4))))),X134)))),c_List_Otranspose(X4,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X4)),X32),c_List_Oconcat(tc_List_Olist(X4),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X4)),X4,c_List_Olist_ONil(tc_List_Olist(X4)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4))),X4),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4)),tc_List_Olist(tc_List_Olist(X4))),c_List_Olist_OCons(tc_List_Olist(X4))),c_List_Olist_ONil(tc_List_Olist(X4)))))),X134)))))=c_List_Otranspose(X4,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)),X134)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose_Osimps_I3_J)). 4.02/4.27 fof(fact_transpose__aux__max, axiom, ![X134, X7, X32, X4]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))),c_List_Ofoldr(tc_List_Olist(X7),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X7)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X7))),X134,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)),c_List_Ofoldr(tc_List_Olist(X7),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X7)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X7)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X7)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X7),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X7)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_List_Olist(X7),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X7)))),X134),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__aux__max)). 4.02/4.27 fof(fact_nat__rec__add__eq__if, axiom, ![X20, X64, X22, X26, X4]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X64))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X4,X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),tc_Int_Oint),c_If(X4)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X4,X26,X22),X20))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X4,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X4,X4),tc_Int_Oint),X22),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)),X20))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Int_Oint),c_Nat_Onat_Onat__rec(X4,X26,X22)),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)),X20)))))=hAPP(c_Nat_Onat_Onat__rec(X4,X26,X22),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)),X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__rec__add__eq__if)). 4.02/4.27 fof(fact_nat__case__add__eq__if, axiom, ![X20, X64, X22, X26, X4]:c_Nat_Onat_Onat__case(X4,X26,X22,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)),X20))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X64))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X4,X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),tc_Int_Oint),c_If(X4)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X4,X26,X22,X20))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Int_Oint),X22),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)),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__case__add__eq__if)). 4.02/4.27 fof(fact_Inter__eq, axiom, ![X3, X4]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X3)=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OAll(tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),X4),hAPP(c_COMBS(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X4,tc_HOL_Obool))),X3)))),c_member(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__eq)). 4.02/4.27 fof(fact_Id__def, axiom, ![X4]:hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X4,X4)),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBC(tc_prod(X4,X4),tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_HOL_Obool)),tc_prod(X4,X4)),c_COMBB(tc_prod(X4,X4),tc_HOL_Obool,X4)),c_fequal)),hAPP(hAPP(c_COMBS(X4,X4,tc_prod(X4,X4)),c_Product__Type_OPair(X4,X4)),c_COMBI(X4)))))=c_Relation_OId(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__def)). 4.02/4.27 fof(fact_rtrancl__empty, axiom, ![X4]:c_Relation_OId(X4)=c_Transitive__Closure_Ortrancl(X4,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__empty)). 4.02/4.27 fof(fact_max__Suc__number__of, axiom, ![X20, X64]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)),hAPP(c_Nat_OSuc,X20))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X64))),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,X20))),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)),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__Suc__number__of)). 4.02/4.27 fof(fact_nat__rec__number__of, axiom, ![X64, X22, X26, X4]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X64))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X4,X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),tc_Int_Oint),c_If(X4)),c_Nat__Numeral_Oneg)),X26)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X4,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X4,X4),tc_Int_Oint),X22),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Int_Oint),c_Nat_Onat_Onat__rec(X4,X26,X22)),c_Int_Onat))))=hAPP(c_Nat_Onat_Onat__rec(X4,X26,X22),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__rec__number__of)). 4.02/4.27 fof(fact_min__Suc__number__of, axiom, ![X20, X64]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X64))),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)),X20))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)),hAPP(c_Nat_OSuc,X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__Suc__number__of)). 4.02/4.27 fof(fact_Nitpick_Otimes__frac__def, axiom, ![X101, X14, X4]:c_Nitpick_Otimes__frac(X4,X14,X101)=hAPP(hAPP(c_Nitpick_Ofrac(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X4),X14)),hAPP(c_Nitpick_Onum(X4),X101))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X4),X14)),hAPP(c_Nitpick_Odenom(X4),X101))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Otimes__frac__def)). 4.02/4.27 fof(fact_div2__Suc__Suc, axiom, ![X2]:hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),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,X2))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div2__Suc__Suc)). 4.02/4.27 fof(fact_mod2__Suc__Suc, axiom, ![X2]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X2)),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,X2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod2__Suc__Suc)). 4.02/4.27 fof(fact_max__number__of__Suc, axiom, ![X64, X20]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X64))),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,X20))),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),X20)),c_Int_Onat))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__number__of__Suc)). 4.02/4.27 fof(fact_min__number__of__Suc, axiom, ![X64, X20]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X64))),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),X20)),c_Int_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__number__of__Suc)). 4.02/4.27 fof(fact_int__ge__less__than__def, axiom, ![X102]:c_Int_Oint__ge__less__than(X102)=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),X102)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__ge__less__than__def)). 4.02/4.27 fof(fact_SetCompr__Sigma__eq, axiom, ![X112, X56, X7, X4]:hAPP(c_Set_OCollect(tc_prod(X4,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X4,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),X56))),X112)))=hAPP(hAPP(c_Product__Type_OSigma(X4,X7),hAPP(c_Set_OCollect(X4),X56)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),c_Set_OCollect(X7)),X112)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SetCompr__Sigma__eq)). 4.02/4.27 fof(fact_sublist__def, axiom, ![X3, X32, X4]:c_List_Osublist(X4,X32,X3)=hAPP(hAPP(c_List_Omap(tc_prod(X4,tc_Nat_Onat),X4),c_Product__Type_Ofst(X4,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X4,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X4,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X4,tc_Nat_Onat))),X3)),hAPP(hAPP(c_List_Ozip(X4,tc_Nat_Onat),X32),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__def)). 4.02/4.27 fof(fact_The__split__eq, axiom, ![X17, X9, X7, X4]:c_HOL_OThe(tc_prod(X4,X7),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(c_fequal,X9)))),hAPP(c_fequal,X17))))=hAPP(hAPP(c_Product__Type_OPair(X4,X7),X9),X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_The__split__eq)). 4.02/4.27 fof(fact_nat__case__number__of, axiom, ![X64, X22, X26, X4]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X64))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X4,X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),tc_Int_Oint),c_If(X4)),c_Nat__Numeral_Oneg)),X26)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Int_Oint),X22),c_Int_Onat)))=c_Nat_Onat_Onat__case(X4,X26,X22,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__case__number__of)). 4.02/4.27 fof(fact_add__Bit0__Bit0, axiom, ![X47, X107]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X107)),c_Int_OBit0(X47))=c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Bit0__Bit0)). 4.02/4.27 fof(fact_the__inv__into__def, axiom, ![X9, X22, X3, X7, X4]:hAPP(c_Fun_Othe__inv__into(X4,X7,X3,X22),X9)=c_HOL_OThe(X4,hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3))),hAPP(hAPP(c_COMBC(X4,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,tc_HOL_Obool),X4),c_fequal),X22)),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__into__def)). 4.02/4.27 fof(fact_diff__bin__simps_I7_J, axiom, ![X47, X107]:c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X107),X47))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X107)),c_Int_OBit0(X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I7_J)). 4.02/4.27 fof(fact_dom__def, axiom, ![X21, X7, X4]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(hAPP(c_COMBC(X4,tc_Option_Ooption(X7),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X7),tc_fun(tc_Option_Ooption(X7),tc_HOL_Obool),X4),c_fequal),X21)),c_Option_Ooption_ONone(X7))))=c_Map_Odom(X4,X7,X21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__def)). 4.02/4.27 fof(fact_diff__bin__simps_I8_J, axiom, ![X47, X107]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X107)),X47))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X107)),c_Int_OBit1(X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I8_J)). 4.02/4.27 fof(fact_add__self__div__2, axiom, ![X2]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=X2, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__self__div__2)). 4.02/4.27 fof(fact_zdiv__number__of__Bit0, axiom, ![X53, X1]: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),X53))=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(X53))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__number__of__Bit0)). 4.02/4.27 fof(fact_trancl__reflcl, axiom, ![X18, X4]:c_Transitive__Closure_Otrancl(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),c_Relation_OId(X4)))=c_Transitive__Closure_Ortrancl(X4,X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__reflcl)). 4.02/4.27 fof(fact_rtrancl__reflcl, axiom, ![X39, X4]:c_Transitive__Closure_Ortrancl(X4,X39)=c_Transitive__Closure_Ortrancl(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X39),c_Relation_OId(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__reflcl)). 4.02/4.27 fof(fact_add__2__eq__Suc_H, axiom, ![X5]:hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__2__eq__Suc_H)). 4.02/4.27 fof(fact_New__DSequence_Opos__not__seq__def, axiom, ![X37, X143]:hAPP(c_New__DSequence_Opos__not__seq(X143),X37)=c_Lazy__Sequence_Ohb__not__seq(hAPP(X143,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)))),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__not__seq__def)). 4.02/4.27 fof(fact_Nitpick_Ouminus__frac__def, axiom, ![X14, X4]:c_Nitpick_OAbs__Frac(X4,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(X4),X14))),hAPP(c_Nitpick_Odenom(X4),X14)))=c_Nitpick_Ouminus__frac(X4,X14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Ouminus__frac__def)). 4.02/4.27 fof(fact_diff__bin__simps_I10_J, axiom, ![X47, X107]:c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X107),X47))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X107)),c_Int_OBit1(X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I10_J)). 4.02/4.27 fof(fact_trancl__subset__Field2, axiom, ![X18, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X4,X18)),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),hAPP(c_Relation_OField(X4),X18)),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_Relation_OField(X4),X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__subset__Field2)). 4.02/4.27 fof(fact_diff__bin__simps_I3_J, axiom, ![X47]:c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X47))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I3_J)). 4.02/4.27 fof(fact_Nitpick_Oint__lcm__def, axiom, ![X43, X13]:c_Nitpick_Oint__lcm(X13,X43)=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),X13)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oint__lcm__def)). 4.02/4.27 fof(fact_Nitpick_Onat__lcm__def, axiom, ![X43, X13]:c_Nitpick_Onat__lcm(X13,X43)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13),X43)),c_Nitpick_Onat__gcd(X13,X43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Onat__lcm__def)). 4.02/4.27 fof(fact_nat__abs__mult__distrib, axiom, ![X29, X53]:hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),X29)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X53))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__abs__mult__distrib)). 4.02/4.27 fof(fact_minus__Bit1, axiom, ![X107]:c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X107)))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__Bit1)). 4.02/4.27 fof(fact_diff__bin__simps_I6_J, axiom, ![X47]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X47))=c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I6_J)). 4.02/4.27 fof(fact_rev__concat, axiom, ![X32, X4]:hAPP(c_List_Orev(X4),c_List_Oconcat(X4,X32))=c_List_Oconcat(X4,hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Orev(X4)),hAPP(c_List_Orev(tc_List_Olist(X4)),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__concat)). 4.02/4.27 fof(fact_minus__Bit0, axiom, ![X107]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X107))=c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__Bit0)). 4.02/4.27 fof(fact_trancl__unfold, axiom, ![X18, X4]:c_Transitive__Closure_Otrancl(X4,X18)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),c_Transitive__Closure_Otrancl(X4,X18)),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__unfold)). 4.02/4.27 fof(fact_Diff__Int2, axiom, ![X6, X8, X3, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X8)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X6),X8))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X8)),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Int2)). 4.02/4.27 fof(fact_rtrancl__unfold, axiom, ![X18, X4]:c_Transitive__Closure_Ortrancl(X4,X18)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Relation_OId(X4)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),c_Transitive__Closure_Ortrancl(X4,X18)),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__unfold)). 4.02/4.27 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J, axiom, ![X56]: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)))),X56))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J)). 4.02/4.27 fof(fact_transfer__nat__int__list__functions_I1_J, axiom, ![X2, X47]:hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X47),X2)=c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(X47)),c_List_Oembed__list(X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__list__functions_I1_J)). 4.02/4.27 fof(fact_return__list__def, axiom, ![X60]:c_List_Oreturn__list(X60)=hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X60), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_return__list__def)). 4.02/4.27 fof(fact_embed__list__def, axiom, ![X60]:c_List_Oembed__list(X60)=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X60), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_embed__list__def)). 4.02/4.27 fof(fact_foldl__foldr, axiom, ![X32, X26, X22, X7, X4]:c_List_Ofoldr(X7,X4,hAPP(c_COMBC(X4,X7,X4),X22),hAPP(c_List_Orev(X7),X32),X26)=hAPP(c_List_Ofoldl(X4,X7,X22,X26),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__foldr)). 4.02/4.27 fof(fact_map__Suc__upt, axiom, ![X20, X21]:hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X21,X20))=c_List_Oupt(hAPP(c_Nat_OSuc,X21),hAPP(c_Nat_OSuc,X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__Suc__upt)). 4.02/4.27 fof(fact_image__Suc__atLeastLessThan, axiom, ![X38, X37]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X37)),hAPP(c_Nat_OSuc,X38))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X37),X38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Suc__atLeastLessThan)). 4.02/4.27 fof(fact_atLeastLessThanSuc__atLeastAtMost, axiom, ![X115, X60]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X60),hAPP(c_Nat_OSuc,X115))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X60,X115), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThanSuc__atLeastAtMost)). 4.02/4.27 fof(fact_trancl__range, axiom, ![X18, X4]:hAPP(c_Relation_ORange(X4,X4),c_Transitive__Closure_Otrancl(X4,X18))=hAPP(c_Relation_ORange(X4,X4),X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__range)). 4.02/4.27 fof(fact_trancl__domain, axiom, ![X18, X4]:hAPP(c_Relation_ODomain(X4,X4),c_Transitive__Closure_Otrancl(X4,X18))=hAPP(c_Relation_ODomain(X4,X4),X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__domain)). 4.02/4.27 fof(fact_the__eq__trivial, axiom, ![X26, X4]:c_HOL_OThe(X4,hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X26))=X26, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__eq__trivial)). 4.02/4.27 fof(fact_code__numeral_Osize_I4_J, axiom, ![X276]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X276)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X276)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osize_I4_J)). 4.02/4.27 fof(fact_card__greaterThanAtMost__int, axiom, ![X115, X60]:hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X115),X60))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X60,X115)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__greaterThanAtMost__int)). 4.02/4.27 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int, axiom, ![X115, X60]:c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X60,X115)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),c_Groups_Oone__class_Oone(tc_Int_Oint)),X115), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastPlusOneAtMost__greaterThanAtMost__int)). 4.02/4.27 fof(fact_card__atLeastAtMost__int, axiom, ![X115, X60]:hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X60,X115))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X115),X60)),c_Groups_Oone__class_Oone(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__atLeastAtMost__int)). 4.02/4.27 fof(fact_trancl__rtrancl__absorb, axiom, ![X39, X4]:c_Transitive__Closure_Ortrancl(X4,X39)=c_Transitive__Closure_Ortrancl(X4,c_Transitive__Closure_Otrancl(X4,X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__rtrancl__absorb)). 4.02/4.27 fof(fact_rel__simps_I2_J, axiom, ~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I2_J)). 4.02/4.27 fof(fact_rotate__is__Nil__conv, axiom, ![X32, X20, X4]:(c_List_Olist_ONil(X4)=hAPP(c_List_Orotate(X4,X20),X32)<=>X32=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__is__Nil__conv)). 4.02/4.27 fof(fact_rotate__def, axiom, ![X20, X4]:c_List_Orotate(X4,X20)=hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X4),tc_List_Olist(X4)),X20),c_List_Orotate1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__def)). 4.02/4.27 fof(fact_atLeastAtMost__upt, axiom, ![X21, X20]:hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X20,hAPP(c_Nat_OSuc,X21)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X20,X21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastAtMost__upt)). 4.02/4.27 fof(fact_empty__def, axiom, ![X4]:hAPP(c_Set_OCollect(X4),hAPP(c_COMBK(tc_HOL_Obool,X4),c_fFalse))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__def)). 4.02/4.27 fof(fact_atLeastLessThan__singleton, axiom, ![X21]:hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X21),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X21),hAPP(c_Nat_OSuc,X21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__singleton)). 4.02/4.27 fof(fact_code__numeral_Osize_I2_J, axiom, ![X276]:c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X276))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X276)),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)). 4.02/4.27 fof(fact_code__numeral_Osimps_I5_J, axiom, ![X197, X129, X130, X4]:c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X4,X130,X129,c_Code__Numeral_OSuc__code__numeral(X197))=hAPP(X129,X197), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osimps_I5_J)). 4.02/4.27 fof(fact_Suc__code__numeral__minus__one, axiom, ![X5]:X5=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X5)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__code__numeral__minus__one)). 4.02/4.27 fof(fact_card__greaterThanAtMost, axiom, ![X115, X60]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X115),X60)=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X60,X115)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__greaterThanAtMost)). 4.02/4.27 fof(fact_atLeastSucAtMost__greaterThanAtMost, axiom, ![X115, X60]:c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X60,X115)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X60),X115), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastSucAtMost__greaterThanAtMost)). 4.02/4.27 fof(fact_zadd__zminus__inverse2, axiom, ![X29]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29)),X29), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__zminus__inverse2)). 4.02/4.27 fof(fact_UNIV__def, axiom, ![X4]:hAPP(c_Set_OCollect(X4),hAPP(c_COMBK(tc_HOL_Obool,X4),c_fTrue))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__def)). 4.02/4.27 fof(fact_setsum__mult__setsum__if__inj, axiom, ![X6, X3, X76, X22, X7, X4, X49]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X49),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X49),X22),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X49),X76),X6))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X49,X49),c_Fun_Oid(X49)),hAPP(c_Set_OCollect(X49),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X49),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X7,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool),X49),hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X7))),hAPP(hAPP(c_COMBC(X49,tc_fun(X4,tc_fun(X7,tc_HOL_Obool)),tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),tc_fun(tc_fun(X4,tc_fun(X7,tc_HOL_Obool)),tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),X49),c_COMBS(X4,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X4,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool))),X49),hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X7,tc_HOL_Obool)),tc_fun(X4,tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X49),hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj))),hAPP(hAPP(c_COMBC(X49,tc_fun(X4,tc_fun(X7,X49)),tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,X49),tc_fun(X7,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_fun(X7,X49)),tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),X49),c_COMBB(tc_fun(X7,X49),tc_fun(X7,tc_HOL_Obool),X4)),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_HOL_Obool),tc_fun(tc_fun(X7,X49),tc_fun(X7,tc_HOL_Obool)),X49),c_COMBB(X49,tc_HOL_Obool,X7)),c_fequal))),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,X49),tc_fun(X7,X49)),hAPP(hAPP(c_COMBB(tc_fun(X49,X49),tc_fun(tc_fun(X7,X49),tc_fun(X7,X49)),X4),c_COMBB(X49,X49,X7)),hAPP(hAPP(c_COMBB(X49,tc_fun(X49,X49),X4),c_Groups_Otimes__class_Otimes(X49)),X22))),X76)))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7)),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)),X3)))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X6)))))))<=c_Fun_Oinj__on(tc_prod(X4,X7),X49,hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,X49),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,X49),tc_fun(X7,X49)),hAPP(hAPP(c_COMBB(tc_fun(X49,X49),tc_fun(tc_fun(X7,X49),tc_fun(X7,X49)),X4),c_COMBB(X49,X49,X7)),hAPP(hAPP(c_COMBB(X49,tc_fun(X49,X49),X4),c_Groups_Otimes__class_Otimes(X49)),X22))),X76)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),X6))))<=class_Rings_Osemiring__0(X49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__mult__setsum__if__inj)). 4.02/4.27 fof(fact_min__max_Osup__Inf2__distrib, axiom, ![X6, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X6=>c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),tc_fun(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X4),c_COMBS(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_fun(X4,X4)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_fun(X4,X4)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X4),c_COMBB(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool),X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal))),c_Orderings_Oord__class_Omax(X4)))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X6)))))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X3)),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))<=X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__Inf2__distrib)). 4.02/4.27 fof(fact_min__max_Oinf__Sup2__distrib, axiom, ![X6, X3, X4]:(class_Orderings_Olinorder(X4)=>(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>(c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),tc_fun(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X4),c_COMBS(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_fun(X4,X4)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_fun(X4,X4)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X4),c_COMBB(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool),X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal))),c_Orderings_Oord__class_Omin(X4)))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X6)))))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X3)),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X6))<=X6!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__Sup2__distrib)). 4.02/4.27 fof(fact_sup__Inf2__distrib, axiom, ![X6, X3, X4]:(((((hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),c_Big__Operators_Olattice__class_OInf__fin(X4,X3)),c_Big__Operators_Olattice__class_OInf__fin(X4,X6))=c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),tc_fun(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X4),c_COMBS(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_fun(X4,X4)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_fun(X4,X4)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X4),c_COMBB(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool),X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X4)))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X6)))))))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X6)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Lattices_Odistrib__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__Inf2__distrib)). 4.02/4.27 fof(fact_inf__Sup2__distrib, axiom, ![X6, X3, X4]:(((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3=>((X6!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),tc_fun(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X4),c_COMBS(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_fun(X4,X4)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_fun(X4,X4)),tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X4),c_COMBB(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool),X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X4)))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X6)))))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),c_Big__Operators_Olattice__class_OSup__fin(X4,X3)),c_Big__Operators_Olattice__class_OSup__fin(X4,X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Lattices_Odistrib__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__Sup2__distrib)). 4.02/4.27 fof(fact_setsum__setsum__restrict, axiom, ![X39, X22, X105, X7, X86, X4, X49]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X105))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X49),hAPP(hAPP(c_COMBS(X7,tc_fun(X4,tc_HOL_Obool),X49),hAPP(hAPP(c_COMBB(tc_fun(X4,X49),tc_fun(tc_fun(X4,tc_HOL_Obool),X49),X7),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X49)),hAPP(c_COMBC(X4,X7,X49),X22))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X7),c_Set_OCollect(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X7),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)),X86)))),hAPP(c_COMBC(X4,X7,tc_HOL_Obool),X39))))),X105)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X49),hAPP(hAPP(c_COMBS(X4,tc_fun(X7,tc_HOL_Obool),X49),hAPP(hAPP(c_COMBB(tc_fun(X7,X49),tc_fun(tc_fun(X7,tc_HOL_Obool),X49),X4),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X49)),X22)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),c_Set_OCollect(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X105)))),X39)))),X86))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X86)))<=class_Groups_Ocomm__monoid__add(X49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__setsum__restrict)). 4.02/4.27 fof(fact_One__nat__def, axiom, c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_One__nat__def)). 4.02/4.27 fof(fact_min__max_Osup__Inf1__distrib, axiom, ![X9, X3, X4]:(class_Orderings_Olinorder(X4)=>((c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X4),X9))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3)))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X9),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X3))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__Inf1__distrib)). 4.02/4.27 fof(fact_min__max_Oinf__Sup1__distrib, axiom, ![X9, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X9),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X3))=c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X4),X9))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3)))))<=X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__Sup1__distrib)). 4.02/4.27 fof(fact_add__Max__commute, axiom, ![X28, X176, X4]:(class_Groups_Olinordered__ab__semigroup__add(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X176))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X176=>c_Big__Operators_Olinorder__class_OMax(X4,hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X4),X28))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X176)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X28),c_Big__Operators_Olinorder__class_OMax(X4,X176))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Max__commute)). 4.02/4.27 fof(fact_add__Min__commute, axiom, ![X28, X176, X4]:(class_Groups_Olinordered__ab__semigroup__add(X4)=>((X176!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>c_Big__Operators_Olinorder__class_OMin(X4,hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X4),X28))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X176)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X28),c_Big__Operators_Olinorder__class_OMin(X4,X176)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X176)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__Min__commute)). 4.02/4.27 fof(fact_inf__Sup1__distrib, axiom, ![X9, X3, X4]:(((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X9),c_Big__Operators_Olattice__class_OSup__fin(X4,X3))=c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X9))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3)))))<=X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Lattices_Odistrib__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__Sup1__distrib)). 4.02/4.27 fof(fact_sup__Inf1__distrib, axiom, ![X9, X3, X4]:(class_Lattices_Odistrib__lattice(X4)=>((X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X9),c_Big__Operators_Olattice__class_OInf__fin(X4,X3))=c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X9))))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__Inf1__distrib)). 4.02/4.27 fof(fact_reflcl__set__eq, axiom, ![X17, X9, X18, X4]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4)))),c_Product__Type_OPair(X4,X4)))),X18)),c_fequal),X9),X17))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),c_Relation_OId(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reflcl__set__eq)). 4.02/4.27 fof(fact_setsum__multicount__gen, axiom, ![X28, X39, X123, X7, X40, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X40))=>((![X19]:(hBOOL(hAPP(hAPP(c_member(X7),X19),X123))=>hAPP(X28,X19)=hAPP(c_Finite__Set_Ocard(X4),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X40))),hAPP(hAPP(c_COMBC(X4,X7,tc_HOL_Obool),X39),X19)))))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X28),X123)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_Nat_Onat,X4),c_Finite__Set_Ocard(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),c_Set_OCollect(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X123)))),X39)))),X40))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X123)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__multicount__gen)). 4.02/4.27 fof(fact_finite__image__set, axiom, ![X22, X7, X56, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_OCollect(X4),X56)))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBC(X7,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X7),c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj)),hAPP(hAPP(c_COMBC(X7,tc_fun(X4,X7),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X4,X7),tc_fun(X4,tc_HOL_Obool)),X7),c_COMBB(X7,tc_HOL_Obool,X4)),c_fequal)),X22)))),X56)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__image__set)). 4.02/4.27 fof(fact_setsum__multicount, axiom, ![X28, X39, X105, X7, X86, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X86))=>((![X19]:(hBOOL(hAPP(hAPP(c_member(X7),X19),X105))=>X28=hAPP(c_Finite__Set_Ocard(X4),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X86))),hAPP(hAPP(c_COMBC(X4,X7,tc_HOL_Obool),X39),X19)))))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_Nat_Onat,X4),c_Finite__Set_Ocard(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),c_Set_OCollect(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X105)))),X39)))),X86)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),hAPP(c_Finite__Set_Ocard(X7),X105)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X105)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__multicount)). 4.02/4.27 fof(fact_small__lazy__list_Osimps, axiom, ![X102, X4]:(class_Lazy__Sequence_Osmall__lazy(X4)=>c_Lazy__Sequence_Oappend(tc_List_Olist(X4),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X4))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X102)),hAPP(c_Lazy__Sequence_Obind(tc_prod(X4,tc_List_Olist(X4)),tc_List_Olist(X4),c_Lazy__Sequence_Oproduct(X4,tc_List_Olist(X4),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X102),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X102),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(X4,tc_List_Olist(X4),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_List_Olist(X4),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X4))),X4),hAPP(c_COMBB(tc_List_Olist(X4),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X4)),tc_List_Olist(X4)),c_Lazy__Sequence_Osingle(tc_List_Olist(X4)))),c_List_Olist_OCons(X4))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X4))))=c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X4),X102)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__lazy__list_Osimps)). 4.02/4.27 fof(fact_min__ext__compat, axiom, ![X86, X39, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X39),X86)),X39))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X4,X39)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X4,X86)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X4,X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__ext__compat)). 4.02/4.27 fof(fact_max__ext__compat, axiom, ![X86, X39, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X39),X86)),X39))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X4,X39)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X4,X86)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X4,X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ext__compat)). 4.02/4.27 fof(fact_setsum__image__gen, axiom, ![X22, X49, X76, X86, X4, X7]:(class_Groups_Ocomm__monoid__add(X7)=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),X86)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X49,X7),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),X7,X49),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X49),c_Set_OCollect(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X49),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)),X86)))),hAPP(c_COMBC(X4,X49,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X49,tc_fun(X49,tc_HOL_Obool),X4),c_fequal),X22)))))),hAPP(c_Set_Oimage(X4,X49,X22),X86))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X86)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__image__gen)). 4.02/4.27 fof(fact_map_Osimps_I1_J, axiom, ![X22, X4, X7]:c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Omap(X7,X4),X22),c_List_Olist_ONil(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map_Osimps_I1_J)). 4.02/4.27 fof(fact_card__less__Suc, axiom, ![X37, X54]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X54))=>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)),X54))),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,X37)))))=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)),X54))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X37)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__less__Suc)). 4.02/4.27 fof(fact_card__less__Suc2, axiom, ![X37, X54]:(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)),X54))),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,X37)))))=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)),X54))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X37))))<=~(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X54)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__less__Suc2)). 4.02/4.27 fof(fact_finite__lists__length__le, axiom, ![X20, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X4)),hAPP(c_Set_OCollect(tc_List_Olist(X4)),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X4)),c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool))),c_List_Oset(X4))),X3))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),X20)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__lists__length__le)). 4.02/4.27 fof(fact_setsum__cases, axiom, ![X76, X22, X56, X3, X4, X7]:((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),hAPP(hAPP(c_COMBS(X4,X7,X7),hAPP(hAPP(c_COMBS(X4,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X4),c_If(X7)),X56)),X22)),X76)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X4),X56)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OCollect(X4),X56)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Groups_Ocomm__monoid__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__cases)). 4.02/4.27 fof(fact_Diff__eq, axiom, ![X6, X3, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__eq)). 4.02/4.27 fof(fact_finite__lists__length__eq, axiom, ![X20, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X4)),hAPP(c_Set_OCollect(tc_List_Olist(X4)),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X4)),c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool))),c_List_Oset(X4))),X3))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),X20)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__lists__length__eq)). 4.02/4.27 fof(fact_wf__if__measure, axiom, ![X4, X76, X22, X56]:(![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X22,hAPP(X76,X19))),hAPP(X22,X19)))<=hBOOL(hAPP(X56,X19)))=>c_Wellfounded_Owf(X4,hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),X56))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,X4),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,X4)),c_fequal)),X76)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__if__measure)). 4.02/4.27 fof(fact_arith__series__general, axiom, ![X20, X102, X26, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Oone__class_Oone(X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBB(X4,X4,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X4),X26)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X4)),c_Nat_Osemiring__1__class_Oof__nat(X4))),X102))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X20)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X102))))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_arith__series__general)). 4.02/4.27 fof(fact_atLeast0LessThan, axiom, ![X20]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)=hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast0LessThan)). 4.02/4.27 fof(fact_listrel__subset, axiom, ![X3, X18, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X3))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool)),c_List_Olistrel(X4,X18)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olists(X4,X3)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_List_Olist(X4)),c_List_Olists(X4,X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__subset)). 4.02/4.27 fof(fact_less__eq__Suc__le__raw, axiom, ![X20]:hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20)=hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__Suc__le__raw)). 4.02/4.27 fof(fact_less, axiom, ![X64, X115, X17, X9]:(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),X9),X17)),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),X115),X64)),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),X9),X64)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X115),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less)). 4.02/4.27 fof(fact_le, axiom, ![X64, X115, X17, X9]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9),X64)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X115),X17)))<=>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),X9),X17)),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),X115),X64)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le)). 4.02/4.27 fof(fact_set__map__of__compr, axiom, ![X32, X7, X4]:(hAPP(c_List_Oset(tc_prod(X4,X7)),X32)=hAPP(c_Set_OCollect(tc_prod(X4,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_Option_Ooption(X7)),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X7),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_Option_Ooption(X7)),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBB(tc_Option_Ooption(X7),tc_HOL_Obool,X7)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X7),tc_fun(tc_Option_Ooption(X7),tc_HOL_Obool),X4),c_fequal),hAPP(c_Map_Omap__of(X4,X7),X32)))),c_Option_Ooption_OSome(X7))))<=hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(tc_prod(X4,X7),X4),c_Product__Type_Ofst(X4,X7)),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__map__of__compr)). 4.02/4.27 fof(fact_Nitpick_Osetsum_H__def, axiom, ![X22, X3, X4, X7]:(((c_Nitpick_Osetsum_H(X4,X7,X22,X3)=hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X4,X7),X22),c_Hilbert__Choice_OEps(tc_List_Olist(X4),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_List_Oset(X4))),X3))),c_List_Odistinct(X4)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))&(c_Groups_Ozero__class_Ozero(X7)=c_Nitpick_Osetsum_H(X4,X7,X22,X3)<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))))<=class_Groups_Ocomm__monoid__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Osetsum_H__def)). 4.02/4.27 fof(fact_Int__commute, axiom, ![X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X6),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__commute)). 4.02/4.27 fof(fact_minus__fold__remove, axiom, ![X6, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X6),X3)=hAPP(hAPP(c_Finite__Set_Ofold(X4,tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X6),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__fold__remove)). 4.02/4.27 fof(fact_fold__image__def, axiom, ![X76, X22, X7, X4]:c_Finite__Set_Ofold(X7,X4,hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X7),X22),X76))=hAPP(c_Finite__Set_Ofold__image(X4,X7,X22),X76), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__def)). 4.02/4.27 fof(fact_small_H_Opinduct, axiom, ![X56, X67, X70, X119]:((hBOOL(hAPP(hAPP(hAPP(X56,X119),X70),X67))<=![X160, X132, X42]:(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X160),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X132),X42))))=>(hBOOL(hAPP(hAPP(hAPP(X56,X160),X132),X42))<=((hAPP(X160,X42)=c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))=>hBOOL(hAPP(hAPP(hAPP(X56,X160),X132),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),X132),X42)))))))<=hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X119),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X70),X67))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small_H_Opinduct)). 4.02/4.27 fof(fact_Nitpick_Ocard_H__def, axiom, ![X3, X4]:((~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Nitpick_Ocard_H(X4,X3))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_Hilbert__Choice_OEps(tc_List_Olist(X4),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_List_Oset(X4))),X3))),c_List_Odistinct(X4))))=c_Nitpick_Ocard_H(X4,X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Ocard_H__def)). 4.02/4.27 fof(fact_setprod__gen__delta, axiom, ![X24, X25, X26, X86, X4, X7]:((((hBOOL(hAPP(hAPP(c_member(X4),X26),X86))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),hAPP(hAPP(c_COMBC(X4,X7,X7),hAPP(hAPP(c_COMBS(X4,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X4),c_If(X7)),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X26))),X25)),X24)),X86)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(X25,X26)),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X24),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X86)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))&(~(hBOOL(hAPP(hAPP(c_member(X4),X26),X86)))=>hAPP(hAPP(c_Power_Opower__class_Opower(X7),X24),hAPP(c_Finite__Set_Ocard(X4),X86))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),hAPP(hAPP(c_COMBC(X4,X7,X7),hAPP(hAPP(c_COMBS(X4,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X4),c_If(X7)),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X26))),X25)),X24)),X86)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X86)))<=class_Groups_Ocomm__monoid__mult(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__gen__delta)). 4.02/4.27 fof(fact_finite__Collect__bounded__ex, axiom, ![X112, X7, X56, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_OCollect(X4),X56)))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X7),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),X56))),X112)))))<=>![X34]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBC(X7,X4,tc_HOL_Obool),X112),X34))))<=hBOOL(hAPP(X56,X34))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Collect__bounded__ex)). 4.02/4.27 fof(fact_setsum__restrict__set, axiom, ![X6, X22, X3, X4, X7]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),hAPP(hAPP(c_COMBC(X4,X7,X7),hAPP(hAPP(c_COMBS(X4,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X4),c_If(X7)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X6))),X22)),c_Groups_Ozero__class_Ozero(X7))),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=class_Groups_Ocomm__monoid__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__restrict__set)). 4.02/4.27 fof(fact_transfer__nat__int__set__cong, axiom, ![X277, X56]:(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)))),X277))=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)))),X56))<=![X19]:((hBOOL(hAPP(X56,X19))<=>hBOOL(hAPP(X277,X19)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__cong)). 4.02/4.27 fof(fact_diff__nat__number__of, axiom, ![X64, X182]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X182))=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),X64),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X182)))),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))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X182),c_Int_OPls))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X182),c_Int_OPls))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X182))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__nat__number__of)). 4.02/4.27 fof(fact_vimage__if, axiom, ![X6, X7, X102, X3, X24, X4]:((((c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X7,X4,hAPP(hAPP(c_COMBC(X7,X4,X4),hAPP(hAPP(c_COMBC(X7,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X7),c_If(X4)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X6))),X24)),X102)),X3)<=hBOOL(hAPP(hAPP(c_member(X4),X102),X3)))&(~(hBOOL(hAPP(hAPP(c_member(X4),X102),X3)))=>hAPP(c_Set_Ovimage(X7,X4,hAPP(hAPP(c_COMBC(X7,X4,X4),hAPP(hAPP(c_COMBC(X7,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X7),c_If(X4)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X6))),X24)),X102)),X3)=X6))<=hBOOL(hAPP(hAPP(c_member(X4),X24),X3)))&(~(hBOOL(hAPP(hAPP(c_member(X4),X24),X3)))=>((hBOOL(hAPP(hAPP(c_member(X4),X102),X3))=>hAPP(c_Set_Ovimage(X7,X4,hAPP(hAPP(c_COMBC(X7,X4,X4),hAPP(hAPP(c_COMBC(X7,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X7),c_If(X4)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X6))),X24)),X102)),X3)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X6))&(~(hBOOL(hAPP(hAPP(c_member(X4),X102),X3)))=>c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X7,X4,hAPP(hAPP(c_COMBC(X7,X4,X4),hAPP(hAPP(c_COMBC(X7,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X7),c_If(X4)),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X6))),X24)),X102)),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__if)). 4.02/4.27 fof(fact_setsum__natinterval__difff, axiom, ![X22, X20, X21, X4]:(class_Groups_Oab__group__add(X4)=>((c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X4)),X22)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Nat_Onat),X22),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,X21,X20))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(X22,X21)),hAPP(X22,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X4)),X22)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Nat_Onat),X22),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,X21,X20))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__natinterval__difff)). 4.02/4.27 fof(fact_equiv__intrel__iff, axiom, ![X17, X9]:(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)),X17),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)),X9),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)),X9),X17)),c_Int_Ointrel))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__intrel__iff)). 4.02/4.27 fof(fact_zminus1__lemma, axiom, ![X18, X180, X25, X26]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26),X25),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X18),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X180)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X180)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X18),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),X25),X18)))))<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X26,X25),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X180),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zminus1__lemma)). 4.02/4.27 fof(fact_setprod__delta, axiom, ![X25, X26, X86, X4, X7]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X86))=>((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),hAPP(hAPP(c_COMBC(X4,X7,X7),hAPP(hAPP(c_COMBS(X4,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X4),c_If(X7)),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X26))),X25)),c_Groups_Oone__class_Oone(X7))),X86)=c_Groups_Oone__class_Oone(X7)<=~(hBOOL(hAPP(hAPP(c_member(X4),X26),X86))))&(hAPP(X25,X26)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),hAPP(hAPP(c_COMBC(X4,X7,X7),hAPP(hAPP(c_COMBS(X4,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X4),c_If(X7)),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X26))),X25)),c_Groups_Oone__class_Oone(X7))),X86)<=hBOOL(hAPP(hAPP(c_member(X4),X26),X86)))))<=class_Groups_Ocomm__monoid__mult(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__delta)). 4.02/4.27 fof(fact_setprod_OF__eq, axiom, ![X76, X3, X4, X7]:(((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X76),X3)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X76),c_Groups_Oone__class_Oone(X7)),X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))&(c_Groups_Oone__class_Oone(X7)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X76),X3)<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))))<=class_Groups_Ocomm__monoid__mult(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod_OF__eq)). 4.02/4.27 fof(fact_setsum__delta, axiom, ![X25, X26, X86, X4, X7]:((((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),hAPP(hAPP(c_COMBC(X4,X7,X7),hAPP(hAPP(c_COMBS(X4,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X4),c_If(X7)),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X26))),X25)),c_Groups_Ozero__class_Ozero(X7))),X86)=c_Groups_Ozero__class_Ozero(X7)<=~(hBOOL(hAPP(hAPP(c_member(X4),X26),X86))))&(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),hAPP(hAPP(c_COMBC(X4,X7,X7),hAPP(hAPP(c_COMBS(X4,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X4),c_If(X7)),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X26))),X25)),c_Groups_Ozero__class_Ozero(X7))),X86)=hAPP(X25,X26)<=hBOOL(hAPP(hAPP(c_member(X4),X26),X86))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X86)))<=class_Groups_Ocomm__monoid__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__delta)). 4.02/4.27 fof(fact_setsum_OF__eq, axiom, ![X76, X3, X4, X7]:(class_Groups_Ocomm__monoid__add(X7)=>((c_Groups_Ozero__class_Ozero(X7)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),X3)<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))))&(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),X3)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Oplus__class_Oplus(X7)),X76),c_Groups_Ozero__class_Ozero(X7)),X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum_OF__eq)). 4.02/4.27 fof(fact_divmod__nat__rel__add1__eq, axiom, ![X183, X184, X12, X185, X186, X10, X11]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10))=>hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11),X12),X10),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X186),X184)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X185),X183)),X10))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X185),X183),X10)))))<=hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X12,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X184),X183))))<=hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X11,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X186),X185)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__add1__eq)). 4.02/4.27 fof(fact_zadd1__lemma, axiom, ![X183, X184, X12, X185, X186, X10, X11]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X186),X185)))=>(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X184),X183)))=>(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11),X12),X10),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X186),X184)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X185),X183)),X10))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X185),X183),X10))))<=X10!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd1__lemma)). 4.02/4.27 fof(fact_sum__diff__distrib, axiom, ![X20, X56, X112]:(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)),X56)),X112)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20))=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),X56),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X112),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20)))<=![X19]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X112,X19)),hAPP(X56,X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__diff__distrib)). 4.02/4.27 fof(fact_UN__finite2__subset, axiom, ![X6, X28, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,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(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X6)))<=![X104]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X104)),X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X104),X28))),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__finite2__subset)). 4.02/4.27 fof(fact_concat__eq__concat__iff, axiom, ![X31, X32, X4]:(![X19]:(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X4),tc_List_Olist(X4),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_Nat_Onat),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X4),tc_Nat_Onat),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X4))))),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),X19))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),X19),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)))))=>(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),X31)=>(X32=X31<=>c_List_Oconcat(X4,X32)=c_List_Oconcat(X4,X31)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__eq__concat__iff)). 4.02/4.27 fof(fact_concat__injective, axiom, ![X31, X32, X4]:(c_List_Oconcat(X4,X31)=c_List_Oconcat(X4,X32)=>(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),X31)=>(![X19]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),X19),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31))))=>hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X4),tc_List_Olist(X4),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_Nat_Onat),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X4),tc_Nat_Onat),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X4))))),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),X19)))=>X32=X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__injective)). 4.02/4.27 fof(fact_zip__obtain__same__length, axiom, ![X56, X31, X7, X32, X4]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),hAPP(hAPP(c_List_Otake(X7),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31))),X31))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31))),X32))=>hBOOL(hAPP(X56,hAPP(hAPP(c_List_Ozip(X4,X7),hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31))),X32)),hAPP(hAPP(c_List_Otake(X7),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31))),X31)))))=>hBOOL(hAPP(X56,hAPP(hAPP(c_List_Ozip(X4,X7),X32),X31)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__obtain__same__length)). 4.02/4.27 fof(fact_inf__nat__def, axiom, c_Orderings_Oord__class_Omin(tc_Nat_Onat)=c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__nat__def)). 4.02/4.27 fof(fact_r__comp__rtrancl__eq, axiom, ![X18, X4]:hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X18),c_Transitive__Closure_Ortrancl(X4,X18))=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),c_Transitive__Closure_Ortrancl(X4,X18)),X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_r__comp__rtrancl__eq)). 4.02/4.27 fof(fact_card__Diff2__less, axiom, ![X17, X9, X3, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X4),X17),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X4),X3)))<=hBOOL(hAPP(hAPP(c_member(X4),X17),X3)))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff2__less)). 4.02/4.27 fof(fact_Diff__insert2, axiom, ![X6, X26, X3, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X6)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__insert2)). 4.02/4.27 fof(fact_diff__nat__eq__if, axiom, ![X16, X223]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X16)),hAPP(c_Int_Onat,X223))=hAPP(c_Int_Onat,X16)<=hBOOL(hAPP(c_Nat__Numeral_Oneg,X223)))&(~(hBOOL(hAPP(c_Nat__Numeral_Oneg,X223)))=>hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X16),X223)),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,X16)),hAPP(c_Int_Onat,X223)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__nat__eq__if)). 4.02/4.27 fof(fact_setsum__delta_H, axiom, ![X25, X26, X86, X4, X7]:(class_Groups_Ocomm__monoid__add(X7)=>(((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),hAPP(hAPP(c_COMBC(X4,X7,X7),hAPP(hAPP(c_COMBS(X4,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X4),c_If(X7)),hAPP(c_fequal,X26))),X25)),c_Groups_Ozero__class_Ozero(X7))),X86)=c_Groups_Ozero__class_Ozero(X7)<=~(hBOOL(hAPP(hAPP(c_member(X4),X26),X86))))&(hAPP(X25,X26)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),hAPP(hAPP(c_COMBC(X4,X7,X7),hAPP(hAPP(c_COMBS(X4,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X4),c_If(X7)),hAPP(c_fequal,X26))),X25)),c_Groups_Ozero__class_Ozero(X7))),X86)<=hBOOL(hAPP(hAPP(c_member(X4),X26),X86))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X86)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__delta_H)). 4.02/4.27 fof(fact_setprod__delta_H, axiom, ![X25, X26, X86, X4, X7]:((((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),hAPP(hAPP(c_COMBC(X4,X7,X7),hAPP(hAPP(c_COMBS(X4,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X4),c_If(X7)),hAPP(c_fequal,X26))),X25)),c_Groups_Oone__class_Oone(X7))),X86)=hAPP(X25,X26)<=hBOOL(hAPP(hAPP(c_member(X4),X26),X86)))&(~(hBOOL(hAPP(hAPP(c_member(X4),X26),X86)))=>c_Groups_Oone__class_Oone(X7)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),hAPP(hAPP(c_COMBC(X4,X7,X7),hAPP(hAPP(c_COMBS(X4,X7,tc_fun(X7,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X4),c_If(X7)),hAPP(c_fequal,X26))),X25)),c_Groups_Oone__class_Oone(X7))),X86)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X86)))<=class_Groups_Ocomm__monoid__mult(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__delta_H)). 4.02/4.27 fof(fact_eq__equiv__class__iff2, axiom, ![X17, X9, X18, X3, X4]:(c_Equiv__Relations_Oequiv(X4,X3,X18)=>(((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),X18))<=>hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),hAPP(hAPP(c_Set_Oinsert(X4),X17),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X18)=hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X18))<=hBOOL(hAPP(hAPP(c_member(X4),X17),X3)))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__equiv__class__iff2)). 4.02/4.27 fof(fact_equiv__class__eq__iff, axiom, ![X17, X9, X18, X3, X4]:(c_Equiv__Relations_Oequiv(X4,X3,X18)=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),X18))<=>((hBOOL(hAPP(hAPP(c_member(X4),X9),X3))&hBOOL(hAPP(hAPP(c_member(X4),X17),X3)))&hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X17),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__class__eq__iff)). 4.02/4.27 fof(fact_map__upd__upds__conv__if, axiom, ![X17, X22, X32, X31, X7, X9, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31)),X32))))=>c_Map_Omap__upds(X4,X7,X22,X32,X31)=c_Map_Omap__upds(X4,X7,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X22),X9),hAPP(c_Option_Ooption_OSome(X7),X17)),X32,X31))&(c_Map_Omap__upds(X4,X7,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X22),X9),hAPP(c_Option_Ooption_OSome(X7),X17)),X32,X31)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),c_Map_Omap__upds(X4,X7,X22,X32,X31)),X9),hAPP(c_Option_Ooption_OSome(X7),X17))<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31)),X32))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upd__upds__conv__if)). 4.02/4.27 fof(fact_map__upds__Cons, axiom, ![X108, X25, X109, X26, X21, X7, X4]:c_Map_Omap__upds(X4,X7,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X21),X26),hAPP(c_Option_Ooption_OSome(X7),X25)),X109,X108)=c_Map_Omap__upds(X4,X7,X21,hAPP(hAPP(c_List_Olist_OCons(X4),X26),X109),hAPP(hAPP(c_List_Olist_OCons(X7),X25),X108)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__Cons)). 4.02/4.27 fof(fact_lexord__take__index__conv, axiom, ![X18, X17, X9, X4]:((?[X42]:((hAPP(hAPP(c_List_Otake(X4),X42),X17)=hAPP(hAPP(c_List_Otake(X4),X42),X9)&hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(hAPP(c_List_Onth(X4),X9),X42)),hAPP(hAPP(c_List_Onth(X4),X17),X42))),X18)))&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(X4)),X9)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X17)))))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X9)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X17)))&X9=hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X9)),X17)))<=>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)),X9),X17)),c_List_Olexord(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__take__index__conv)). 4.02/4.27 fof(fact_setsum__ub__add__nat, axiom, ![X51, X22, X20, X21, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X21,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X51)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X21,X20))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X51)))))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__ub__add__nat)). 4.02/4.27 fof(fact_divmod__nat__if, axiom, ![X21, X20]:((hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21)=c_Divides_Odivmod__nat(X21,X20)<=(X20=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))))&(c_Divides_Odivmod__nat(X21,X20)=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),X21),X20),X20))<=~((X20=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__if)). 4.02/4.27 fof(fact_of__int, axiom, ![X38, X37, X4]:(class_Rings_Oring__1(X4)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X37)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X38))=hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X37),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_of__int)). 4.02/4.27 fof(fact_in__lex__prod, axiom, ![X40, X18, X181, X117, X25, X26, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X4,X7),tc_prod(X4,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X4,X7),tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X26),X25)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X117),X181))),c_Wellfounded_Olex__prod(X4,X7,X18,X40)))<=>((X117=X26&hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X25),X181)),X40)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X117)),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__lex__prod)). 4.02/4.27 fof(fact_o__apply, axiom, ![X9, X76, X22, X49, X4, X7]:hAPP(X22,hAPP(X76,X9))=hAPP(hAPP(c_Fun_Ocomp(X7,X4,X49,X22),X76),X9), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_o__apply)). 4.02/4.27 fof(fact_listrel1I, axiom, ![X31, X284, X285, X32, X18, X17, X9, X4]:((X32=hAPP(hAPP(c_List_Oappend(X4),X285),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X284))=>(X31=hAPP(hAPP(c_List_Oappend(X4),X285),hAPP(hAPP(c_List_Olist_OCons(X4),X17),X284))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)),c_List_Olistrel1(X4,X18)))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1I)). 4.02/4.27 fof(fact_Int__Collect__mono, axiom, ![X112, X56, X6, X3, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X4),X56))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X6),hAPP(c_Set_OCollect(X4),X112))))<=![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>(hBOOL(hAPP(X112,X19))<=hBOOL(hAPP(X56,X19)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Collect__mono)). 4.02/4.27 fof(fact_lists__IntI, axiom, ![X6, X3, X60, X4]:((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X60),c_List_Olists(X4,X6)))=>hBOOL(hAPP(c_List_Olistsp(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X6))),X60)))<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X60),c_List_Olists(X4,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__IntI)). 4.02/4.27 fof(fact_dropWhile__append1, axiom, ![X31, X56, X32, X9, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))=>(~(hBOOL(hAPP(X56,X9)))=>hAPP(hAPP(c_List_Oappend(X4),c_List_OdropWhile(X4,X56,X32)),X31)=c_List_OdropWhile(X4,X56,hAPP(hAPP(c_List_Oappend(X4),X32),X31)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__append1)). 4.02/4.27 fof(fact_distinct__concat, axiom, ![X32, X4]:(((![X146]:(![X258]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X258),hAPP(c_List_Oset(tc_List_Olist(X4)),X32)))=>(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X146)),hAPP(c_List_Oset(X4),X258))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=X146!=X258))<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X146),hAPP(c_List_Oset(tc_List_Olist(X4)),X32))))=>hBOOL(hAPP(c_List_Odistinct(X4),c_List_Oconcat(X4,X32))))<=![X146]:(hBOOL(hAPP(c_List_Odistinct(X4),X146))<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X146),hAPP(c_List_Oset(tc_List_Olist(X4)),X32)))))<=hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X4)),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__concat)). 4.02/4.27 fof(fact_UN__finite2__eq, axiom, ![X6, X28, X3, X4]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X3)<=![X104]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X104),X28))),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X104)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__finite2__eq)). 4.02/4.27 fof(fact_card__partition, axiom, ![X28, X8, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,tc_HOL_Obool)),X8))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X8)))=>(![X165]:(hAPP(c_Finite__Set_Ocard(X4),X165)=X28<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X165),X8)))=>(![X166]:(![X167]:((X167!=X166=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X166),X167))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X167),X8)))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X166),X8)))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),hAPP(c_Finite__Set_Ocard(tc_fun(X4,tc_HOL_Obool)),X8))=hAPP(c_Finite__Set_Ocard(X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X8)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__partition)). 4.02/4.27 fof(fact_finite__UnionD, axiom, ![X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X3)))=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,tc_HOL_Obool)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UnionD)). 4.02/4.27 fof(fact_listrel1__iff__update, axiom, ![X18, X31, X32, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)),c_List_Olistrel1(X4,X18)))<=>?[X34, X104]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(hAPP(c_List_Onth(X4),X32),X104)),X34)),X18))&hAPP(hAPP(c_List_Olist__update(X4,X32),X104),X34)=X31)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X104),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__iff__update)). 4.02/4.27 fof(fact_restrict__fun__upd, axiom, ![X17, X21, X7, X61, X9, X4]:((c_Map_Orestrict__map(X4,X7,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X21),X9),X17),X61)=c_Map_Orestrict__map(X4,X7,X21,X61)<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),X61))))&(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),c_Map_Orestrict__map(X4,X7,X21,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X61),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),X9),X17)=c_Map_Orestrict__map(X4,X7,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X21),X9),X17),X61)<=hBOOL(hAPP(hAPP(c_member(X4),X9),X61)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__fun__upd)). 4.02/4.27 fof(fact_fun__upd__restrict, axiom, ![X17, X9, X61, X21, X7, X4]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),c_Map_Orestrict__map(X4,X7,X21,X61)),X9),X17)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),c_Map_Orestrict__map(X4,X7,X21,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X61),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),X9),X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__restrict)). 4.02/4.27 fof(fact_wf__union__merge, axiom, ![X86, X39, X4]:(c_Wellfounded_Owf(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X39),X86))<=>c_Wellfounded_Owf(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X39),X39)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X86),X39))),X86))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__union__merge)). 4.02/4.27 fof(fact_Un__assoc, axiom, ![X8, X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)),X8)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X6),X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__assoc)). 4.02/4.27 fof(fact_Un__commute, axiom, ![X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X6),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__commute)). 4.02/4.27 fof(fact_append__listrel1I, axiom, ![X284, X285, X18, X31, X32, X4]:(((X285=X284&hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)),c_List_Olistrel1(X4,X18))))|(X31=X32&hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X285),X284)),c_List_Olistrel1(X4,X18)))))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Oappend(X4),X32),X285)),hAPP(hAPP(c_List_Oappend(X4),X31),X284))),c_List_Olistrel1(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__listrel1I)). 4.02/4.27 fof(fact_quotient__eq__iff, axiom, ![X17, X9, X203, X156, X18, X3, X4]:(c_Equiv__Relations_Oequiv(X4,X3,X18)=>((hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X203),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X3),X18)))=>(((X156=X203<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),X18)))<=hBOOL(hAPP(hAPP(c_member(X4),X17),X203)))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X156))))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X156),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X3),X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotient__eq__iff)). 4.02/4.27 fof(fact_Cons__in__lex, axiom, ![X18, X31, X17, X32, X9, X4]:(((X9=X17&hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)),c_List_Olex(X4,X18))))|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X31)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)&hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),X18))))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)),hAPP(hAPP(c_List_Olist_OCons(X4),X17),X31))),c_List_Olex(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__in__lex)). 4.02/4.27 fof(fact_lexord__cons__cons, axiom, ![X18, X17, X25, X9, X26, X4]:(((X26=X25&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)),X9),X17)),c_List_Olexord(X4,X18))))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),X18)))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X26),X9)),hAPP(hAPP(c_List_Olist_OCons(X4),X25),X17))),c_List_Olexord(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__cons__cons)). 4.02/4.27 fof(fact_dropWhile__append2, axiom, ![X31, X56, X32, X4]:(c_List_OdropWhile(X4,X56,X31)=c_List_OdropWhile(X4,X56,hAPP(hAPP(c_List_Oappend(X4),X32),X31))<=![X19]:(hBOOL(hAPP(X56,X19))<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__append2)). 4.02/4.27 fof(fact_divmod__nat__step, axiom, ![X2, X5]:((c_Divides_Odivmod__nat(X2,X5)=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),X5)),X5))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5),X5))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X2)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__step)). 4.02/4.27 fof(fact_divmod__nat__rel__def, axiom, ![X295, X20, X21]:(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21,X20),X295))<=>((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),X295)),X20)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X295))=X21&(X20=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),X295)))&(((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X295)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X295)),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),X295)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X295)),X20)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20))))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__def)). 4.02/4.27 fof(fact_less__eq__nat_Osimps_I1_J, axiom, ![X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__nat_Osimps_I1_J)). 4.02/4.27 fof(fact_lexord__lex, axiom, ![X18, X17, X9, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X9),X17)),c_List_Olexord(X4,X18)))&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X9)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X17))<=>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)),X9),X17)),c_List_Olex(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__lex)). 4.02/4.27 fof(fact_append__eq__append__conv__if, axiom, ![X266, X267, X268, X269, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X269)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X267)))=>(X268=hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X269)),X267)),X266)&hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X269)),X267)=X269))&((hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X267)),X269)),X268)=X266&X267=hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X267)),X269))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X269)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X267))))))<=>hAPP(hAPP(c_List_Oappend(X4),X267),X266)=hAPP(hAPP(c_List_Oappend(X4),X269),X268)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__eq__append__conv__if)). 4.02/4.27 fof(fact_the__inv__into__comp, axiom, ![X9, X3, X76, X49, X22, X7, X4]:((c_Fun_Oinj__on(X49,X4,X76,X3)=>(hAPP(c_Fun_Othe__inv__into(X49,X7,X3,hAPP(c_Fun_Ocomp(X4,X7,X49,X22),X76)),X9)=hAPP(hAPP(c_Fun_Ocomp(X4,X49,X7,c_Fun_Othe__inv__into(X49,X4,X3,X76)),c_Fun_Othe__inv__into(X4,X7,hAPP(c_Set_Oimage(X49,X4,X76),X3),X22)),X9)<=hBOOL(hAPP(hAPP(c_member(X7),X9),hAPP(c_Set_Oimage(X4,X7,X22),hAPP(c_Set_Oimage(X49,X4,X76),X3))))))<=c_Fun_Oinj__on(X4,X7,X22,hAPP(c_Set_Oimage(X49,X4,X76),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__into__comp)). 4.02/4.27 fof(fact_pigeonhole__infinite, axiom, ![X22, X7, X3, X4]:((?[X19]:(~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3))),hAPP(hAPP(c_COMBC(X4,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,tc_HOL_Obool),X4),c_fequal),X22)),hAPP(X22,X19)))))))&hBOOL(hAPP(hAPP(c_member(X4),X19),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_Oimage(X4,X7,X22),X3))))<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pigeonhole__infinite)). 4.02/4.27 fof(fact_length__drop, axiom, ![X45, X5, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),X5)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Odrop(X4),X5),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__drop)). 4.02/4.27 fof(fact_split__zdiv, axiom, ![X28, X20, X56]:(hBOOL(hAPP(X56,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20),X28)))<=>(((![X42]:(hBOOL(hAPP(X56,X42))<=?[X139]:((X20=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X28),X42)),X139)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X139),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),X139))))<=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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X28))=>![X42]:(?[X139]:((X20=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X28),X42)),X139)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),X28)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X139)))=>hBOOL(hAPP(X56,X42)))))&(X28=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>hBOOL(hAPP(X56,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__zdiv)). 4.02/4.27 fof(fact_split__zmod, axiom, ![X28, X20, X56]:(hBOOL(hAPP(X56,c_Divides_Odiv__class_Omod(tc_Int_Oint,X20,X28)))<=>(((hBOOL(hAPP(X56,X20))<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X28)&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>![X42, X139]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),X139))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X139),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),X28),X42)),X139)=X20)=>hBOOL(hAPP(X56,X139)))))&(![X42, X139]:(hBOOL(hAPP(X56,X139))<=((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),X28))&hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X28),X42)),X139)=X20)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X139))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X28))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__zmod)). 4.02/4.27 fof(fact_periodic__finite__ex, axiom, ![X56, X102]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X102))=>(![X19, X137]:(hBOOL(hAPP(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X137),X102))))<=>hBOOL(hAPP(X56,X19)))=>(?[X19]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X19),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X102)))&hBOOL(hAPP(X56,X19)))<=>?[X77]:hBOOL(hAPP(X56,X77))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_periodic__finite__ex)). 4.02/4.27 fof(fact_zmult__commute, axiom, ![X53, X29]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X53)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),X29), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__commute)). 4.02/4.27 fof(fact_small__lazy_H_Opinduct, axiom, ![X56, X70, X119]:(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),X119),X70)))=>(hBOOL(hAPP(hAPP(X56,X119),X70))<=![X132, 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),X132),X42)))=>(hBOOL(hAPP(hAPP(X56,X132),X42))<=(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X132),X42)))=>hBOOL(hAPP(hAPP(X56,X132),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X42),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__lazy_H_Opinduct)). 4.02/4.27 fof(fact_setsum__ivl__cong, axiom, ![X76, X22, X102, X25, X24, X26, X4, X7]:(((X25=X102=>(![X19]:((hAPP(X22,X19)=hAPP(X76,X19)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X19),X102)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X24),X19)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X24),X102))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X26),X25))))<=X26=X24)<=(class_Orderings_Oord(X4)&class_Groups_Ocomm__monoid__add(X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__ivl__cong)). 4.02/4.27 fof(fact_nat__intermed__int__val, axiom, ![X28, X22, X20, X21]:(![X42]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X20))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),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(X22,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X22,X42)))),c_Groups_Oone__class_Oone(tc_Int_Oint))))=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28),hAPP(X22,X20)))=>?[X42]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X42))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X20)))&X28=hAPP(X22,X42)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X22,X21)),X28)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__intermed__int__val)). 4.02/4.27 fof(fact_filter__eq__Cons__iff, axiom, ![X32, X9, X31, X56, X4]:(hAPP(c_List_Ofilter(X4,X56),X31)=hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)<=>?[X63, X218]:(((X31=hAPP(hAPP(c_List_Oappend(X4),X63),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X218))&hBOOL(hAPP(X56,X9)))&hAPP(c_List_Ofilter(X4,X56),X218)=X32)&![X19]:(~(hBOOL(hAPP(X56,X19)))<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X63)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__eq__Cons__iff)). 4.02/4.27 fof(fact_map__upds__twist, axiom, ![X108, X25, X21, X7, X109, X26, X4]:(c_Map_Omap__upds(X4,X7,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X21),X26),hAPP(c_Option_Ooption_OSome(X7),X25)),X109,X108)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),c_Map_Omap__upds(X4,X7,X21,X109,X108)),X26),hAPP(c_Option_Ooption_OSome(X7),X25))<=~(hBOOL(hAPP(hAPP(c_member(X4),X26),hAPP(c_List_Oset(X4),X109))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__twist)). 4.02/4.27 fof(fact_Collect__conv__if, axiom, ![X4, X26, X56]:((~(hBOOL(hAPP(X56,X26)))=>hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X26))),X56))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(hBOOL(hAPP(X56,X26))=>hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X26))),X56)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__conv__if)). 4.02/4.27 fof(fact_transpose__transpose, axiom, ![X32, X4]:(c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),X32)))=>c_List_OtakeWhile(tc_List_Olist(X4),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X4)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(X4),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X4))),X32)=c_List_Otranspose(X4,c_List_Otranspose(X4,X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__transpose)). 4.02/4.27 fof(fact_bset_I8_J, axiom, ![X6, X123, X61]:((![X19]:(![X114]:(![X124]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X124),X114)!=X19<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X124),X6)))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X114),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X61))))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),X61)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),X19))))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X123),c_Groups_Oone__class_Oone(tc_Int_Oint))),X6)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I8_J)). 4.02/4.27 fof(fact_rev__update, axiom, ![X43, X45, X4, X107]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))=>hAPP(c_List_Orev(X4),hAPP(hAPP(c_List_Olist__update(X4,X45),X107),X43))=hAPP(hAPP(c_List_Olist__update(X4,hAPP(c_List_Orev(X4),X45)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),X107)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__update)). 4.02/4.27 fof(fact_diff__diff__left, axiom, ![X107, X135, X46]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X46),X135)),X107)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X46),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X135),X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__diff__left)). 4.02/4.27 fof(fact_order__fun_I2_J, axiom, ![X76, X22, X4, X7]:(((hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X4),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(hAPP(c_COMBS(X4,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,tc_HOL_Obool),X4),c_fequal),X22)),X76))))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X7)),X22),X76)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,X7)),X22),X76)))<=(class_Orderings_Oorder(X7)&class_Enum_Oenum(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__fun_I2_J)). 4.02/4.27 fof(fact_upt__add__eq__append, axiom, ![X107, X135, X46]:(c_List_Oupt(X46,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X135),X107))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X46,X135)),c_List_Oupt(X135,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X135),X107)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__add__eq__append)). 4.02/4.27 fof(fact_New__DSequence_Oneg__decr__bind__def, axiom, ![X22, X9, X4, X7, X37]:((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X37=>hAPP(c_New__DSequence_Oneg__decr__bind(X7,X4,X9,X22),X37)=c_Lazy__Sequence_Ohit__bound(X4))&(hAPP(c_New__DSequence_Oneg__decr__bind(X7,X4,X9,X22),X37)=c_Lazy__Sequence_Ohb__bind(X7,X4,hAPP(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X37),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X7,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4))),X22),X37))<=X37!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Oneg__decr__bind__def)). 4.02/4.27 fof(fact_hb__bind__def, axiom, ![X22, X143, X4, X7]:c_Lazy__Sequence_Ohb__bind(X7,X4,X143,X22)=c_Lazy__Sequence_Ohb__flat(X4,c_Lazy__Sequence_Ohb__map(X7,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)),X22,X143)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hb__bind__def)). 4.02/4.27 fof(fact_image__minus__const__atLeastLessThan__nat, axiom, ![X9, X17, X24]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X17)))=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X17)))=>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)),X24)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9),X17)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X17))=>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)),X24)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9),X17)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X17))=>hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9),X24)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),X24))=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)),X24)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__minus__const__atLeastLessThan__nat)). 4.02/4.27 fof(fact_upto_Opinduct, axiom, ![X56, X70, X119]:(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),X119),X70)))=>(hBOOL(hAPP(hAPP(X56,X119),X70))<=![X42, X139]:((hBOOL(hAPP(hAPP(X56,X42),X139))<=(hBOOL(hAPP(hAPP(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X42),c_Groups_Oone__class_Oone(tc_Int_Oint))),X139))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X42),X139))))<=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),X139)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upto_Opinduct)). 4.02/4.27 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J, axiom, ![X6, X3]:((hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X3),X6)=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),X3)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X6)))<=c_Nat__Transfer_Onat__set(X6))<=c_Nat__Transfer_Onat__set(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J)). 4.02/4.27 fof(fact_image__Un, axiom, ![X6, X3, X22, X4, X7]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X4,X22),X3)),hAPP(c_Set_Oimage(X7,X4,X22),X6))=hAPP(c_Set_Oimage(X7,X4,X22),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Un)). 4.02/4.27 fof(fact_image__image, axiom, ![X3, X76, X49, X22, X4, X7]:hAPP(c_Set_Oimage(X7,X4,X22),hAPP(c_Set_Oimage(X49,X7,X76),X3))=hAPP(c_Set_Oimage(X49,X4,hAPP(hAPP(c_COMBB(X7,X4,X49),X22),X76)),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__image)). 4.02/4.27 fof(fact_nat__eq__add__iff2, axiom, ![X20, X21, X115, X38, X37]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X37),X38))=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X115)),X20)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X37),X115)),X21)<=>X21=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X38),X37)),X115)),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__eq__add__iff2)). 4.02/4.27 fof(fact_left__add__mult__distrib, axiom, ![X107, X135, X106, X46]: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),X46),X135)),X106)),X107)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X46),X106)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X135),X106)),X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_left__add__mult__distrib)). 4.02/4.27 fof(fact_sup__nat__def, axiom, c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)=c_Orderings_Oord__class_Omax(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__nat__def)). 4.02/4.27 fof(fact_dropWhile_Osimps_I2_J, axiom, ![X32, X4, X9, X56]:((c_List_OdropWhile(X4,X56,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32))=hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)<=~(hBOOL(hAPP(X56,X9))))&(c_List_OdropWhile(X4,X56,X32)=c_List_OdropWhile(X4,X56,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32))<=hBOOL(hAPP(X56,X9)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile_Osimps_I2_J)). 4.02/4.27 fof(fact_neq0__conv, axiom, ![X20]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X20<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neq0__conv)). 4.02/4.27 fof(fact_Cons__eq__filter__iff, axiom, ![X31, X56, X32, X9, X4]:(?[X63, X218]:(((X31=hAPP(hAPP(c_List_Oappend(X4),X63),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X218))&![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X63)))=>~(hBOOL(hAPP(X56,X19)))))&hBOOL(hAPP(X56,X9)))&hAPP(c_List_Ofilter(X4,X56),X218)=X32)<=>hAPP(c_List_Ofilter(X4,X56),X31)=hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__eq__filter__iff)). 4.02/4.27 fof(fact_nat0__intermed__int__val, axiom, ![X28, X22, X20]:(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X20))=>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(X22,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X22,X42)))),c_Groups_Oone__class_Oone(tc_Int_Oint))))=>((?[X42]:(hAPP(X22,X42)=X28&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X20)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28),hAPP(X22,X20))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X22,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat0__intermed__int__val)). 4.02/4.27 fof(fact_int__val__lemma, axiom, ![X28, X22, X20]:(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X20))=>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(X22,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X22,X42)))),c_Groups_Oone__class_Oone(tc_Int_Oint))))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X22,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X28))=>(?[X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X20))&hAPP(X22,X42)=X28)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28),hAPP(X22,X20)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__val__lemma)). 4.02/4.27 fof(fact_eq__add__iff1, axiom, ![X102, X25, X24, X207, X26, X4]:(class_Rings_Oring(X4)=>(X102=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X26),X25)),X207)),X24)<=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X207)),X24)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X25),X207)),X102))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__add__iff1)). 4.02/4.27 fof(fact_zmod__zmult2__eq, axiom, ![X12, X11, X10]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12),X10))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zmult2__eq)). 4.02/4.27 fof(fact_take__zip, axiom, ![X59, X45, X5, X7, X4]:hAPP(hAPP(c_List_Otake(tc_prod(X4,X7)),X5),hAPP(hAPP(c_List_Ozip(X4,X7),X45),X59))=hAPP(hAPP(c_List_Ozip(X4,X7),hAPP(hAPP(c_List_Otake(X4),X5),X45)),hAPP(hAPP(c_List_Otake(X7),X5),X59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__zip)). 4.02/4.27 fof(fact_transfer__nat__int__numerals_I2_J, axiom, c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__numerals_I2_J)). 4.02/4.27 fof(fact_nat__number__of__Pls, 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_nat__number__of__Pls)). 4.02/4.27 fof(fact_add__number__of__diff2, axiom, ![X53, X10, X1, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X53)))),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X10),hAPP(c_Int_Onumber__class_Onumber__of(X4),X53)))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__number__of__diff2)). 4.02/4.27 fof(fact_setsum__op__ivl__Suc, axiom, ![X22, X21, X20, X4]:(class_Groups_Ocomm__monoid__add(X4)=>((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X21),hAPP(c_Nat_OSuc,X20)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X21),X20))),hAPP(X22,X20))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X21))))&(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X21),hAPP(c_Nat_OSuc,X20)))=c_Groups_Ozero__class_Ozero(X4)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X21))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__op__ivl__Suc)). 4.02/4.27 fof(fact_split__pos__lemma, axiom, ![X20, X56, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X28))=>(![X42, X139]:(((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X28),X42)),X139)=X20&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),X28)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X139)))=>hBOOL(hAPP(hAPP(X56,X42),X139)))<=>hBOOL(hAPP(hAPP(X56,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20),X28)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20,X28))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__pos__lemma)). 4.02/4.27 fof(fact_split__neg__lemma, axiom, ![X20, X56, X28]:((hBOOL(hAPP(hAPP(X56,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20),X28)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20,X28)))<=>![X42, X139]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X139),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&X20=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X28),X42)),X139))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),X139)))=>hBOOL(hAPP(hAPP(X56,X42),X139))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__neg__lemma)). 4.02/4.27 fof(fact_ran__distinct, axiom, ![X314, X7, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(tc_prod(X4,X7),X4),c_Product__Type_Ofst(X4,X7)),X314)))=>c_Map_Oran(X4,X7,hAPP(c_Map_Omap__of(X4,X7),X314))=hAPP(c_Set_Oimage(tc_prod(X4,X7),X7,c_Product__Type_Osnd(X4,X7)),hAPP(c_List_Oset(tc_prod(X4,X7)),X314))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ran__distinct)). 4.02/4.27 fof(fact_snd__eq__Range, axiom, ![X39, X4, X7]:hAPP(c_Set_Oimage(tc_prod(X7,X4),X4,c_Product__Type_Osnd(X7,X4)),X39)=hAPP(c_Relation_ORange(X7,X4),X39), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__eq__Range)). 4.02/4.27 fof(fact_rtrancl__Int__subset, axiom, ![X18, X40, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X18)),X40))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X18)),X40)),X18)),X40)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Relation_OId(X4)),X40))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__Int__subset)). 4.02/4.27 fof(fact_map__sorted__distinct__set__unique, axiom, ![X31, X32, X22, X4, X7]:((c_Fun_Oinj__on(X4,X7,X22,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X32)),hAPP(c_List_Oset(X4),X31)))=>(((((hAPP(c_List_Oset(X4),X31)=hAPP(c_List_Oset(X4),X32)=>X32=X31)<=hBOOL(hAPP(c_List_Odistinct(X7),hAPP(hAPP(c_List_Omap(X4,X7),X22),X31))))<=c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Omap(X4,X7),X22),X31)))<=hBOOL(hAPP(c_List_Odistinct(X7),hAPP(hAPP(c_List_Omap(X4,X7),X22),X32))))<=c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Omap(X4,X7),X22),X32))))<=class_Orderings_Olinorder(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__sorted__distinct__set__unique)). 4.02/4.27 fof(fact_set__append, axiom, ![X31, X32, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X32)),hAPP(c_List_Oset(X4),X31))=hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Oappend(X4),X32),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__append)). 4.02/4.27 fof(fact_nat__number__of__add__left, axiom, ![X107, X131, X1]:((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),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131)),X107))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131)),X107))&(((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X131)))=>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),X131)),X107))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X107))&(~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X131))))=>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),X131))),X107)=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),X131)),X107))))<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of__add__left)). 4.02/4.27 fof(fact_div__pos__neg__1__number__of, axiom, ![X53]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X53)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X53)))))=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),X53))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__pos__neg__1__number__of)). 4.02/4.27 fof(fact_negateSnd__eq, axiom, ![X101, X14]:hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X14),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X101))=hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X14),X101)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negateSnd__eq)). 4.02/4.27 fof(fact_decr__lemma, axiom, ![X29, X13, X44]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X13),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),X13),X29))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X44))),X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X44))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_decr__lemma)). 4.02/4.27 fof(fact_dropWhile__eq__Cons__conv, axiom, ![X31, X17, X32, X56, X4]:(c_List_OdropWhile(X4,X56,X32)=hAPP(hAPP(c_List_Olist_OCons(X4),X17),X31)<=>(X32=hAPP(hAPP(c_List_Oappend(X4),c_List_OtakeWhile(X4,X56,X32)),hAPP(hAPP(c_List_Olist_OCons(X4),X17),X31))&~(hBOOL(hAPP(X56,X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__eq__Cons__conv)). 4.02/4.27 fof(fact_incr__lemma, axiom, ![X13, X29, X44]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X44))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13),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),X13),X29))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X44))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_incr__lemma)). 4.02/4.27 fof(fact_zip__same, axiom, ![X32, X25, X26, X4]:((X26=X25&hBOOL(hAPP(hAPP(c_member(X4),X26),hAPP(c_List_Oset(X4),X32))))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),hAPP(c_List_Oset(tc_prod(X4,X4)),hAPP(hAPP(c_List_Ozip(X4,X4),X32),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__same)). 4.02/4.27 fof(fact_mod__pos__neg__1__number__of, axiom, ![X53]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X53)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X53))=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),X53)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__neg__1__number__of)). 4.02/4.27 fof(fact_card__less, axiom, ![X37, X54]:(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)),X54))),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,X37)))))<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X54))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__less)). 4.02/4.27 fof(fact_finite__Collect__subsets, axiom, ![X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool))),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Collect__subsets)). 4.02/4.27 fof(fact_take__upt, axiom, ![X5, X2, X46]:(c_List_Oupt(X46,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X2))=hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X2),c_List_Oupt(X46,X5))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X2)),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__upt)). 4.02/4.27 fof(fact_takeWhile__eq__filter, axiom, ![X32, X56, X4]:(![X19]:(~(hBOOL(hAPP(X56,X19)))<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),c_List_OdropWhile(X4,X56,X32)))))=>c_List_OtakeWhile(X4,X56,X32)=hAPP(c_List_Ofilter(X4,X56),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__eq__filter)). 4.02/4.27 fof(fact_hd__rotate__conv__nth, axiom, ![X5, X4, X45]:(X45!=c_List_Olist_ONil(X4)=>hAPP(hAPP(c_List_Onth(X4),X45),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))=hAPP(c_List_Ohd(X4),hAPP(c_List_Orotate(X4,X5),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__rotate__conv__nth)). 4.02/4.27 fof(fact_map__of__eq__dom, axiom, ![X31, X32, X7, X4]:(hAPP(c_Map_Omap__of(X4,X7),X31)=hAPP(c_Map_Omap__of(X4,X7),X32)=>hAPP(c_Set_Oimage(tc_prod(X4,X7),X4,c_Product__Type_Ofst(X4,X7)),hAPP(c_List_Oset(tc_prod(X4,X7)),X32))=hAPP(c_Set_Oimage(tc_prod(X4,X7),X4,c_Product__Type_Ofst(X4,X7)),hAPP(c_List_Oset(tc_prod(X4,X7)),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__eq__dom)). 4.02/4.27 fof(fact_int__power__div__base, axiom, ![X107, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))=>(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X107),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X107),X2)),X107)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X107)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__power__div__base)). 4.02/4.27 fof(fact_setsum__reindex__cong, axiom, ![X48, X76, X6, X3, X22, X7, X4, X49]:(class_Groups_Ocomm__monoid__add(X49)=>(c_Fun_Oinj__on(X4,X7,X22,X3)=>((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X49),X76),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X49),X48),X6)<=![X27]:(hBOOL(hAPP(hAPP(c_member(X4),X27),X3))=>hAPP(X76,X27)=hAPP(X48,hAPP(X22,X27))))<=hAPP(c_Set_Oimage(X4,X7,X22),X3)=X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__reindex__cong)). 4.02/4.27 fof(fact_pick__same, axiom, ![X32, X4, X60]:(hAPP(c_Random_Opick(X4,hAPP(hAPP(c_List_Omap(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,X4)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X4),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X32)),hAPP(c_Code__Numeral_Oof__nat,X60))=hAPP(hAPP(c_List_Onth(X4),X32),X60)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X60),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pick__same)). 4.02/4.27 fof(fact_strong__setprod__reindex__cong, axiom, ![X48, X76, X6, X3, X22, X7, X4, X49]:(class_Groups_Ocomm__monoid__mult(X49)=>(c_Fun_Oinj__on(X4,X7,X22,X3)=>(X6=hAPP(c_Set_Oimage(X4,X7,X22),X3)=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X49),X48),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X49),X76),X3)<=![X19]:(hAPP(hAPP(c_Fun_Ocomp(X7,X49,X4,X48),X22),X19)=hAPP(X76,X19)<=hBOOL(hAPP(hAPP(c_member(X4),X19),X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_strong__setprod__reindex__cong)). 4.02/4.27 fof(fact_divmod__int__rel__div__eq, axiom, ![X316, X43, X297, X298]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X297),X43)),X316)=X298=>((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X297=>X43=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X298),X297))<=((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X297))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X316),X297))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X316))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X316),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X297),X316)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X297))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__div__eq)). 4.02/4.27 fof(fact_foldr__max__sorted, axiom, ![X17, X32, X4]:(class_Orderings_Olinorder(X4)=>(((hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_List_Onth(X4),X32),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X17)=c_List_Ofoldr(X4,X4,c_Orderings_Oord__class_Omax(X4),X32,X17)<=X32!=c_List_Olist_ONil(X4))&(X32=c_List_Olist_ONil(X4)=>X17=c_List_Ofoldr(X4,X4,c_Orderings_Oord__class_Omax(X4),X32,X17)))<=c_List_Olinorder__class_Osorted(X4,hAPP(c_List_Orev(X4),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldr__max__sorted)). 4.02/4.27 fof(fact_divmod__int__relI, axiom, ![X101, X14, X12, X11]:(X11=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X14)),X101)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X12))))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),X101)))))=>hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X12),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X14),X101))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__relI)). 4.02/4.27 fof(fact_listsp__conj__eq, axiom, ![X9, X6, X3, X4]:(hBOOL(hAPP(c_List_Olistsp(X4,hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),X3)),X6)),X9))<=>(hBOOL(hAPP(c_List_Olistsp(X4,X3),X9))&hBOOL(hAPP(c_List_Olistsp(X4,X6),X9)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp__conj__eq)). 4.02/4.27 fof(fact_foldl__foldr1__lemma, axiom, ![X32, X26, X4]:(class_Groups_Omonoid__add(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X26),c_List_Ofoldr(X4,X4,c_Groups_Oplus__class_Oplus(X4),X32,c_Groups_Ozero__class_Ozero(X4)))=hAPP(c_List_Ofoldl(X4,X4,c_Groups_Oplus__class_Oplus(X4),X26),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__foldr1__lemma)). 4.02/4.27 fof(fact_crossproduct__noteq, axiom, ![X102, X24, X25, X26, X4]:(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X25),X102))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X102)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X25),X24))<=>(X26!=X25&X24!=X102))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_crossproduct__noteq)). 4.02/4.27 fof(fact_nat__number__of__mult__left, axiom, ![X107, X131, X1]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),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),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131)),X107)))&(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),X131))),X107)=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),X131)),X107))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__number__of__mult__left)). 4.02/4.27 fof(fact_bset_I3_J, axiom, ![X6, X123, X61]:(((![X19]:(![X114]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X114),X6))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X114),X19)!=X123)<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X19),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X61))))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X123),X61)=X123)<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X123),c_Groups_Oone__class_Oone(tc_Int_Oint))),X6)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I3_J)). 4.02/4.27 fof(fact_setsum__shift__bounds__Suc__ivl, axiom, ![X20, X21, X22, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Nat_Onat),X22),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X21),X20))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X21)),hAPP(c_Nat_OSuc,X20)))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__bounds__Suc__ivl)). 4.02/4.27 fof(fact_setsum__lessThan__Suc, axiom, ![X20, X22, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20))),hAPP(X22,X20))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__lessThan__Suc)). 4.02/4.27 fof(fact_ivl__disj__un_I6_J, axiom, ![X115, X60, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X60),X115))=>c_SetInterval_Oord__class_OatLeastAtMost(X4,X60,X115)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X60),X115)),hAPP(hAPP(c_Set_Oinsert(X4),X115),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I6_J)). 4.02/4.27 fof(fact_Un__insert__right, axiom, ![X6, X26, X3, X4]:hAPP(hAPP(c_Set_Oinsert(X4),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__insert__right)). 4.02/4.27 fof(fact_Un__empty__right, axiom, ![X3, X4]:X3=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__empty__right)). 4.02/4.27 fof(fact_inf__INFI__fold__inf, axiom, ![X22, X6, X3, X4, X7]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X4),c_Lattices_Osemilattice__inf__class_Oinf(X7)),X22)),X6),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7),X3),X22)))<=class_Complete__Lattice_Ocomplete__lattice(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__INFI__fold__inf)). 4.02/4.27 fof(fact_sup__SUPR__fold__sup, axiom, ![X22, X6, X3, X4, X7]:(class_Complete__Lattice_Ocomplete__lattice(X7)=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X7),X3),X22))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X4),c_Lattices_Osemilattice__sup__class_Osup(X7)),X22)),X6),X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__SUPR__fold__sup)). 4.02/4.27 fof(fact_takeWhile__not__last, axiom, ![X4, X32]:((c_List_Obutlast(X4,X32)=c_List_OtakeWhile(X4,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),c_List_Olast(X4,X32))),X32)<=hBOOL(hAPP(c_List_Odistinct(X4),X32)))<=X32!=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__not__last)). 4.02/4.27 fof(fact_setsum__head, axiom, ![X56, X20, X21, X4]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(X56,X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X56),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X21,X20)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X56),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X21,X20))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20)))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__head)). 4.02/4.27 fof(fact_divmod__int__rel__mod__eq, axiom, ![X43, X296, X297, X298]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X297))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X43),X297))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X43))))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X297)))=>(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),X297),X43)))))=>(c_Divides_Odiv__class_Omod(tc_Int_Oint,X298,X297)=X43<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X297))<=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X297),X296)),X43)=X298), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__mod__eq)). 4.02/4.27 fof(fact_nth__map__upt, axiom, ![X22, X4, X21, X20, X37]:(hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X4),X22),c_List_Oupt(X21,X20))),X37)=hAPP(X22,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X37))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__map__upt)). 4.02/4.27 fof(fact_transfer__nat__int__sum__prod__cong_I2_J, axiom, ![X76, X22, X6, X3, X4]:((class_Groups_Ocomm__monoid__add(X4)&class_Groups_Ocomm__monoid__mult(X4))=>(X6=X3=>((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X4),X76),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X4),X22),X3)<=![X19]:(hAPP(X22,X19)=hAPP(X76,X19)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19))))<=c_Nat__Transfer_Onat__set(X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__sum__prod__cong_I2_J)). 4.02/4.27 fof(fact_transfer__nat__int__sum__prod__cong_I1_J, axiom, ![X76, X22, X6, X3, X4]:((X6=X3=>(c_Nat__Transfer_Onat__set(X6)=>(![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19))=>hAPP(X22,X19)=hAPP(X76,X19))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X4),X76),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X4),X22),X3))))<=(class_Groups_Ocomm__monoid__mult(X4)&class_Groups_Ocomm__monoid__add(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__sum__prod__cong_I1_J)). 4.02/4.27 fof(fact_setsum__nonneg__leq__bound, axiom, ![X37, X6, X22, X40, X4, X7]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X40))=>(((hBOOL(hAPP(hAPP(c_member(X4),X37),X40))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(X22,X37)),X6)))<=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X40)=X6)<=![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X40))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(X22,X42))))))<=class_Groups_Oordered__ab__group__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__nonneg__leq__bound)). 4.02/4.27 fof(fact_apsnd__eq__conv, axiom, ![X76, X9, X22, X4, X7, X49]:(hAPP(c_Product__Type_Oapsnd(X49,X7,X4,X76),X9)=hAPP(c_Product__Type_Oapsnd(X49,X7,X4,X22),X9)<=>hAPP(X22,hAPP(c_Product__Type_Osnd(X4,X49),X9))=hAPP(X76,hAPP(c_Product__Type_Osnd(X4,X49),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apsnd__eq__conv)). 4.02/4.27 fof(fact_apfst__eq__conv, axiom, ![X76, X9, X22, X7, X4, X49]:(hAPP(c_Product__Type_Oapfst(X49,X4,X7,X22),X9)=hAPP(c_Product__Type_Oapfst(X49,X4,X7,X76),X9)<=>hAPP(X22,hAPP(c_Product__Type_Ofst(X49,X7),X9))=hAPP(X76,hAPP(c_Product__Type_Ofst(X49,X7),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apfst__eq__conv)). 4.02/4.27 fof(fact_apfst__def, axiom, ![X22, X7, X49, X4]:c_Product__Type_Oapfst(X4,X49,X7,X22)=c_Product__Type_Omap__pair(X4,X49,X7,X7,X22,c_Fun_Oid(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apfst__def)). 4.02/4.27 fof(fact_ivl__disj__un_I3_J, axiom, ![X115, X60, X4]:(class_Orderings_Olinorder(X4)=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X60),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X60,X115))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X60),X115)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X60),X115)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I3_J)). 4.02/4.27 fof(fact_Un__insert__left, axiom, ![X8, X6, X26, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X26),X6)),X8)=hAPP(hAPP(c_Set_Oinsert(X4),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X6),X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__insert__left)). 4.02/4.27 fof(fact_Un__empty__left, axiom, ![X6, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X6)=X6, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__empty__left)). 4.02/4.27 fof(fact_Nil__eq__concat__conv, axiom, ![X134, X4]:(![X19]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X19),hAPP(c_List_Oset(tc_List_Olist(X4)),X134)))=>X19=c_List_Olist_ONil(X4))<=>c_List_Oconcat(X4,X134)=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nil__eq__concat__conv)). 4.02/4.27 fof(fact_incr__mult__lemma, axiom, ![X28, X56, X102]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X102))=>(![X19]:(hBOOL(hAPP(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),X102)))<=hBOOL(hAPP(X56,X19)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X28))=>![X19]:(hBOOL(hAPP(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X28),X102))))<=hBOOL(hAPP(X56,X19)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_incr__mult__lemma)). 4.02/4.27 fof(fact_concat__eq__Nil__conv, axiom, ![X134, X4]:(![X19]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X19),hAPP(c_List_Oset(tc_List_Olist(X4)),X134)))=>c_List_Olist_ONil(X4)=X19)<=>c_List_Oconcat(X4,X134)=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__eq__Nil__conv)). 4.02/4.27 fof(fact_aset_I4_J, axiom, ![X3, X123, X61]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))=>(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X123),X3))=>![X19]:((X19!=X123=>X123!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),X61))<=![X114]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X114),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X61)))=>![X124]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X124),X3))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X124),X114)!=X19))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I4_J)). 4.02/4.27 fof(fact_filter__in__sublist, axiom, ![X40, X32, X4]:(c_List_Osublist(X4,X32,X40)=hAPP(c_List_Ofilter(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),hAPP(c_List_Oset(X4),c_List_Osublist(X4,X32,X40)))),X32)<=hBOOL(hAPP(c_List_Odistinct(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__in__sublist)). 4.02/4.27 fof(fact_snd__image__times, axiom, ![X6, X7, X4, X3]:((X6=hAPP(c_Set_Oimage(tc_prod(X4,X7),X7,c_Product__Type_Osnd(X4,X7)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),X6)))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3)&(X3=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(c_Set_Oimage(tc_prod(X4,X7),X7,c_Product__Type_Osnd(X4,X7)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),X6)))=c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__image__times)). 4.02/4.27 fof(fact_bset_I4_J, axiom, ![X6, X123, X61]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))=>(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X123),X6))=>![X19]:(![X114]:(![X124]:(X19!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X124),X114)<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X124),X6)))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X114),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X61))))=>(X123!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),X61)<=X19!=X123)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I4_J)). 4.02/4.27 fof(fact_fst__image__times, axiom, ![X3, X7, X4, X6]:((X3=hAPP(c_Set_Oimage(tc_prod(X7,X4),X7,c_Product__Type_Ofst(X7,X4)),hAPP(hAPP(c_Product__Type_OSigma(X7,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X7),X6)))<=X6!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X6=>c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))=hAPP(c_Set_Oimage(tc_prod(X7,X4),X7,c_Product__Type_Ofst(X7,X4)),hAPP(hAPP(c_Product__Type_OSigma(X7,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X7),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__image__times)). 4.02/4.27 fof(fact_vimage__subsetD, axiom, ![X3, X6, X22, X4, X7]:(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_Oimage(X7,X4,X22),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X7,X4,X22),X6)),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),hAPP(c_Set_Oimage(X7,X4,X22),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__subsetD)). 4.02/4.27 fof(fact_atLeastatMost__psubset__iff, axiom, ![X102, X24, X25, X26, X4]:(class_Orderings_Oorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X26,X25)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X24,X102)))<=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),X25)))|((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X24),X26))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),X26))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X25),X102))))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),X102))))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X24),X102))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastatMost__psubset__iff)). 4.02/4.27 fof(fact_order__le__less, axiom, ![X17, X9, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X17))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X9),X17))|X17=X9))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__le__less)). 4.02/4.27 fof(fact_map__of__eq__None__iff, axiom, ![X9, X145, X4, X7]:(c_Option_Ooption_ONone(X4)=hAPP(hAPP(c_Map_Omap__of(X7,X4),X145),X9)<=>~(hBOOL(hAPP(hAPP(c_member(X7),X9),hAPP(c_Set_Oimage(tc_prod(X7,X4),X7,c_Product__Type_Ofst(X7,X4)),hAPP(c_List_Oset(tc_prod(X7,X4)),X145)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__eq__None__iff)). 4.02/4.27 fof(fact_ivl__disj__un_I5_J, axiom, ![X115, X60, X4]:(class_Orderings_Olinorder(X4)=>(c_SetInterval_Oord__class_OatLeastAtMost(X4,X60,X115)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X60),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X60,X115))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X60),X115)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I5_J)). 4.02/4.27 fof(fact_ivl__disj__un_I4_J, axiom, ![X115, X60, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X60),X115))=>c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X60,X115)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X60,X115)),hAPP(hAPP(c_Set_Oinsert(X4),X115),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I4_J)). 4.02/4.27 fof(fact_inj__on__iff__surj, axiom, ![X127, X7, X4, X3]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3=>(?[X238]:X3=hAPP(c_Set_Oimage(X7,X4,X238),X127)<=>?[X160]:(c_Fun_Oinj__on(X4,X7,X160,X3)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X7,X160),X3)),X127))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__iff__surj)). 4.02/4.27 fof(fact_SUPR__fold__sup, axiom, ![X22, X3, X4, X7]:((hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X4),c_Lattices_Osemilattice__sup__class_Osup(X7)),X22)),c_Orderings_Obot__class_Obot(X7)),X3)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X7),X3),X22)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Complete__Lattice_Ocomplete__lattice(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUPR__fold__sup)). 4.02/4.27 fof(fact_INFI__fold__inf, axiom, ![X22, X3, X4, X7]:(class_Complete__Lattice_Ocomplete__lattice(X7)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7),X3),X22)=hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X4),c_Lattices_Osemilattice__inf__class_Oinf(X7)),X22)),c_Orderings_Otop__class_Otop(X7)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INFI__fold__inf)). 4.02/4.27 fof(fact_setsum__atMost__Suc, axiom, ![X20, X22, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X20))),hAPP(X22,hAPP(c_Nat_OSuc,X20)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__atMost__Suc)). 4.02/4.27 fof(fact_atLeast0AtMost, axiom, ![X20]:hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X20)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast0AtMost)). 4.02/4.27 fof(fact_in__measure, axiom, ![X22, X17, X9, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),hAPP(c_Wellfounded_Omeasure(X4),X22)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X22,X9)),hAPP(X22,X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__measure)). 4.02/4.27 fof(fact_measure__def, axiom, ![X4]:c_Wellfounded_Omeasure(X4)=hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X4),c_Wellfounded_Oless__than), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_measure__def)). 4.02/4.27 fof(fact_split__div, axiom, ![X28, X20, X56]:(hBOOL(hAPP(X56,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20),X28)))<=>((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X28=>![X42, X139]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X139),X28))=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X42)),X139)=X20=>hBOOL(hAPP(X56,X42)))))&(hBOOL(hAPP(X56,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<=X28=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__div)). 4.02/4.27 fof(fact_sum__squares__le__zero__iff, axiom, ![X17, X9, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X9),X9)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X17),X17))),c_Groups_Ozero__class_Ozero(X4)))<=>(X9=c_Groups_Ozero__class_Ozero(X4)&c_Groups_Ozero__class_Ozero(X4)=X17))<=class_Rings_Olinordered__ring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__squares__le__zero__iff)). 4.02/4.27 fof(fact_setprod__reindex__cong, axiom, ![X48, X76, X6, X3, X22, X7, X4, X49]:(class_Groups_Ocomm__monoid__mult(X49)=>(((hAPP(c_Fun_Ocomp(X7,X49,X4,X48),X22)=X76=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X49),X48),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X49),X76),X3))<=X6=hAPP(c_Set_Oimage(X4,X7,X22),X3))<=c_Fun_Oinj__on(X4,X7,X22,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__reindex__cong)). 4.02/4.27 fof(fact_uminus__listsum__map, axiom, ![X32, X22, X7, X4]:(hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32)))=hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X7,X4),hAPP(c_Fun_Ocomp(X4,X4,X7,c_Groups_Ouminus__class_Ouminus(X4)),X22)),X32))<=class_Groups_Oab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_uminus__listsum__map)). 4.02/4.27 fof(fact_List_Omap_Ocompositionality, axiom, ![X224, X76, X49, X22, X4, X7]:hAPP(hAPP(c_List_Omap(X49,X4),hAPP(c_Fun_Ocomp(X7,X4,X49,X22),X76)),X224)=hAPP(hAPP(c_List_Omap(X7,X4),X22),hAPP(hAPP(c_List_Omap(X49,X7),X76),X224)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Omap_Ocompositionality)). 4.02/4.27 fof(fact_finite__less__ub, axiom, ![X115, X22]:(![X104]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X104),hAPP(X22,X104)))=>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)),X22)),X115))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__less__ub)). 4.02/4.27 fof(fact_setsum__eq__Suc0__iff, axiom, ![X22, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(?[X19]:((hBOOL(hAPP(hAPP(c_member(X4),X19),X3))&hAPP(X22,X19)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&![X114]:((X19!=X114=>hAPP(X22,X114)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=hBOOL(hAPP(hAPP(c_member(X4),X114),X3))))<=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X22),X3)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__eq__Suc0__iff)). 4.02/4.27 fof(fact_vimage__subsetI, axiom, ![X3, X6, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X7,X22),X6)),X3))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X6),hAPP(c_Set_Oimage(X4,X7,X22),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__subsetI)). 4.02/4.27 fof(fact_finite__conv__nat__seg__image, axiom, ![X3, X4]:(?[X104, X160]:hAPP(c_Set_Oimage(tc_Nat_Onat,X4,X160),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)),X104)))=X3<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__conv__nat__seg__image)). 4.02/4.27 fof(fact_zdiv__zminus2__eq__if, axiom, ![X11, X12]:(((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12)))&(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12))=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),X11),X12))),c_Groups_Oone__class_Oone(tc_Int_Oint))<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)))<=X12!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zminus2__eq__if)). 4.02/4.27 fof(fact_subsetD, axiom, ![X24, X6, X3, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X24),X6))<=hBOOL(hAPP(hAPP(c_member(X4),X24),X3)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subsetD)). 4.02/4.27 fof(fact_partition__set, axiom, ![X141, X142, X32, X56, X4]:(hAPP(c_List_Oset(X4),X32)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X142)),hAPP(c_List_Oset(X4),X141))<=c_List_Opartition(X4,X56,X32)=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X142),X141)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition__set)). 4.02/4.27 fof(fact_split__mod, axiom, ![X28, X20, X56]:(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X28=>![X42, X139]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X42)),X139)=X20=>hBOOL(hAPP(X56,X139)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X139),X28))))&(hBOOL(hAPP(X56,X20))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X28))<=>hBOOL(hAPP(X56,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20,X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__mod)). 4.02/4.27 fof(fact_ivl__disj__un_I2_J, axiom, ![X115, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X115)),hAPP(hAPP(c_Set_Oinsert(X4),X115),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=hAPP(c_SetInterval_Oord__class_OatMost(X4),X115)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I2_J)). 4.02/4.27 fof(fact_mod__nat__number__of, axiom, ![X131, X1]:((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),X131))=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))))&(((~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X131))))=>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),X131))=hAPP(c_Int_Onat,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),X131))))&(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),X131))=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),X131)))))<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__nat__number__of)). 4.02/4.27 fof(fact_transfer__nat__int__set__return__embed, axiom, ![X3]:(c_Nat__Transfer_Onat__set(X3)=>X3=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),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__return__embed)). 4.02/4.27 fof(fact_finite__fun__UNIVD1, axiom, ![X7, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,X7)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X4,X7),tc_HOL_Obool))))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))<=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(c_Finite__Set_Ocard(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__fun__UNIVD1)). 4.02/4.27 fof(fact_map__comp__Some__iff, axiom, ![X64, X28, X162, X163, X49, X4, X7]:(c_Map_Omap__comp(X7,X4,X49,X163,X162,X28)=hAPP(c_Option_Ooption_OSome(X4),X64)<=>?[X234]:(hAPP(c_Option_Ooption_OSome(X7),X234)=hAPP(X162,X28)&hAPP(c_Option_Ooption_OSome(X4),X64)=hAPP(X163,X234))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__comp__Some__iff)). 4.02/4.27 fof(fact_map__comp__def, axiom, ![X28, X76, X22, X49, X4, X7]:c_Map_Omap__comp(X7,X4,X49,X22,X76,X28)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X4),X7,c_Option_Ooption_ONone(X4),X22),hAPP(X76,X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__comp__def)). 4.02/4.27 fof(fact_Nat_Odiff__diff__eq, axiom, ![X5, X2, X107]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X107)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),X107))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),X5)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat_Odiff__diff__eq)). 4.02/4.27 fof(fact_div__nat__number__of, axiom, ![X131, X1]:((hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X131)))=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),X131))<=~(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),X1)))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__nat__number__of)). 4.02/4.27 fof(fact_foldl__foldr1, axiom, ![X32, X4]:(class_Groups_Omonoid__add(X4)=>hAPP(c_List_Ofoldl(X4,X4,c_Groups_Oplus__class_Oplus(X4),c_Groups_Ozero__class_Ozero(X4)),X32)=c_List_Ofoldr(X4,X4,c_Groups_Oplus__class_Oplus(X4),X32,c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__foldr1)). 4.02/4.27 fof(fact_dom__map__of__zip, axiom, ![X31, X7, X32, X4]:((hAPP(c_List_Oset(X4),X32)=c_Map_Odom(X4,X7,hAPP(c_Map_Omap__of(X4,X7),hAPP(hAPP(c_List_Ozip(X4,X7),X32),X31)))<=hBOOL(hAPP(c_List_Odistinct(X4),X32)))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__map__of__zip)). 4.02/4.27 fof(fact_vimage__mono, axiom, ![X22, X7, X6, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X7,X4,X22),X3)),hAPP(c_Set_Ovimage(X7,X4,X22),X6)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__mono)). 4.02/4.27 fof(fact_setsum__shift__lb__Suc0__0__upt, axiom, ![X28, X22, X4]:(class_Groups_Ocomm__monoid__add(X4)=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X28))<=c_Groups_Ozero__class_Ozero(X4)=hAPP(X22,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__lb__Suc0__0__upt)). 4.02/4.27 fof(fact_div__pos__pos__1__number__of, axiom, ![X53]:(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),X53)))=>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),X53)))=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),X53))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__pos__pos__1__number__of)). 4.02/4.27 fof(fact_mod__pos__pos__1__number__of, axiom, ![X53]:(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),X53))=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),X53)))<=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),X53)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__pos__1__number__of)). 4.02/4.27 fof(fact_setsum__shift__lb__Suc0__0, axiom, ![X28, X22]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X22),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X28))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X22),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28))<=hAPP(X22,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__lb__Suc0__0)). 4.02/4.27 fof(fact_ivl__disj__un_I1_J, axiom, ![X60, X4]:(class_Orderings_Olinorder(X4)=>hAPP(c_SetInterval_Oord__class_OatLeast(X4),X60)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X60),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X60))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I1_J)). 4.02/4.27 fof(fact_total__on__diff__Id, axiom, ![X18, X3, X4]:(c_Relation_Ototal__on(X4,X3,X18)<=>c_Relation_Ototal__on(X4,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),c_Relation_OId(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_total__on__diff__Id)). 4.02/4.27 fof(fact_nat__mult__distrib__neg, axiom, ![X157, X29]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29),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),X29))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X157)))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X157))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__distrib__neg)). 4.02/4.27 fof(fact_add__nat__number__of, axiom, ![X131, X1]:((((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),X131))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),c_Int_OPls)))&(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),X131))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X131))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),c_Int_OPls)))))<=~(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),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__nat__number__of)). 4.02/4.27 fof(fact_card__Pow, axiom, ![X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(X4),X3))=hAPP(c_Finite__Set_Ocard(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OPow(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Pow)). 4.02/4.27 fof(fact_upt__conv__Cons, axiom, ![X135, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X135))=>c_List_Oupt(X46,X135)=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X46),c_List_Oupt(hAPP(c_Nat_OSuc,X46),X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__conv__Cons)). 4.02/4.27 fof(fact_mult__0__right, axiom, ![X2]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__0__right)). 4.02/4.27 fof(fact_Nat_Oadd__0__right, axiom, ![X2]:X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat_Oadd__0__right)). 4.02/4.27 fof(fact_dropWhile__eq__Nil__conv, axiom, ![X32, X56, X4]:(c_List_Olist_ONil(X4)=c_List_OdropWhile(X4,X56,X32)<=>![X19]:(hBOOL(hAPP(X56,X19))<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__eq__Nil__conv)). 4.02/4.27 fof(fact_n__less__n__mult__m, axiom, ![X2, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X5))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X2)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_n__less__n__mult__m)). 4.02/4.27 fof(fact_n__less__m__mult__n, axiom, ![X2, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X5))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_n__less__m__mult__n)). 4.02/4.27 fof(fact_Powp__Pow__eq, axiom, ![X9, X3, X4]:(hBOOL(hAPP(c_Predicate_OPowp(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3)),X9))<=>hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X9),hAPP(c_Set_OPow(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Powp__Pow__eq)). 4.02/4.27 fof(fact_map__comp__None__iff, axiom, ![X28, X162, X163, X49, X4, X7]:(c_Option_Ooption_ONone(X4)=c_Map_Omap__comp(X7,X4,X49,X163,X162,X28)<=>(?[X234]:(hAPP(X162,X28)=hAPP(c_Option_Ooption_OSome(X7),X234)&c_Option_Ooption_ONone(X4)=hAPP(X163,X234))|hAPP(X162,X28)=c_Option_Ooption_ONone(X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__comp__None__iff)). 4.02/4.27 fof(fact_foldr__conv__foldl, axiom, ![X26, X32, X4]:(c_List_Ofoldr(X4,X4,c_Groups_Oplus__class_Oplus(X4),X32,X26)=hAPP(c_List_Ofoldl(X4,X4,c_Groups_Oplus__class_Oplus(X4),X26),X32)<=class_Groups_Oab__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldr__conv__foldl)). 4.02/4.27 fof(fact_sum__squares__eq__zero__iff, axiom, ![X17, X9, X4]:(class_Rings_Olinordered__ring__strict(X4)=>((X9=c_Groups_Ozero__class_Ozero(X4)&X17=c_Groups_Ozero__class_Ozero(X4))<=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X9),X9)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X17),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__squares__eq__zero__iff)). 4.02/4.27 fof(fact_acyclicP__converse, axiom, ![X18, X4]:(c_Wellfounded_Oacyclic(X4,hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),X18)))<=>c_Wellfounded_Oacyclic(X4,hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),c_Predicate_Oconversep(X4,X4,X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclicP__converse)). 4.02/4.27 fof(fact_nth__upt, axiom, ![X135, X107, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X107)),X135))=>hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X46,X135)),X107)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__upt)). 4.02/4.27 fof(fact_listsp__lists__eq, axiom, ![X9, X3, X4]:(hBOOL(hAPP(c_List_Olistsp(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3)),X9))<=>hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X9),c_List_Olists(X4,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp__lists__eq)). 4.02/4.27 fof(fact_one__less__mult, axiom, ![X2, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X5))=>(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),X5)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__less__mult)). 4.02/4.27 fof(fact_one__le__mult__iff, axiom, ![X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X20)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__le__mult__iff)). 4.02/4.27 fof(fact_IdE, axiom, ![X51, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X51),c_Relation_OId(X4)))=>~(![X19]:hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X19)!=X51)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_IdE)). 4.02/4.27 fof(fact_Id__on__eqI, axiom, ![X3, X4, X25, X26]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),c_Relation_OId__on(X4,X3)))<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3)))<=X26=X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__eqI)). 4.02/4.27 fof(fact_one__mod__nat__number__of, axiom, ![X131]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X131)))=>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),X131))=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X131))))=>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),X131)))=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),X131)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__mod__nat__number__of)). 4.02/4.27 fof(fact_rev__eq__Cons__iff, axiom, ![X31, X17, X32, X4]:(hAPP(hAPP(c_List_Olist_OCons(X4),X17),X31)=hAPP(c_List_Orev(X4),X32)<=>X32=hAPP(hAPP(c_List_Oappend(X4),hAPP(c_List_Orev(X4),X31)),hAPP(hAPP(c_List_Olist_OCons(X4),X17),c_List_Olist_ONil(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__eq__Cons__iff)). 4.02/4.27 fof(fact_rev_Osimps_I2_J, axiom, ![X45, X13, X4]:hAPP(hAPP(c_List_Oappend(X4),hAPP(c_List_Orev(X4),X45)),hAPP(hAPP(c_List_Olist_OCons(X4),X13),c_List_Olist_ONil(X4)))=hAPP(c_List_Orev(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev_Osimps_I2_J)). 4.02/4.27 fof(fact_mult__nat__number__of, axiom, ![X131, X1]:((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(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X131))<=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),X131))=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),X131))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__nat__number__of)). 4.02/4.27 fof(fact_image__atLeastZeroLessThan__int, axiom, ![X115]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X115))=>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,X115)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X115)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__atLeastZeroLessThan__int)). 4.02/4.27 fof(fact_interv__listsum__conv__setsum__set__int, axiom, ![X60, X28, X22, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X4),X22),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X28,X60)))=hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X4),X22),c_List_Oupto(X28,X60)))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_interv__listsum__conv__setsum__set__int)). 4.02/4.27 fof(fact_atLeastAtMost__upto, axiom, ![X38, X37]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X37,X38)=hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X37,X38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastAtMost__upto)). 4.02/4.27 fof(fact_zip__eq__conv, axiom, ![X30, X31, X7, X32, X4]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31)=>(X30=hAPP(hAPP(c_List_Ozip(X4,X7),X32),X31)<=>(hAPP(hAPP(c_List_Omap(tc_prod(X4,X7),X4),c_Product__Type_Ofst(X4,X7)),X30)=X32&hAPP(hAPP(c_List_Omap(tc_prod(X4,X7),X7),c_Product__Type_Osnd(X4,X7)),X30)=X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__eq__conv)). 4.02/4.27 fof(fact_inj__on__mapI, axiom, ![X3, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool),c_List_Oset(X4)),X3)))=>c_Fun_Oinj__on(tc_List_Olist(X4),tc_List_Olist(X7),hAPP(c_List_Omap(X4,X7),X22),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__mapI)). 4.02/4.27 fof(fact_Union__image__eq, axiom, ![X3, X6, X7, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),X6)=c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(c_Set_Oimage(X7,tc_fun(X4,tc_HOL_Obool),X6),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__image__eq)). 4.02/4.27 fof(fact_sorted_Osimps, axiom, ![X26, X4]:(((c_List_Olist_ONil(X4)=X26|?[X293, X19]:((X26=hAPP(hAPP(c_List_Olist_OCons(X4),X19),X293)&![X114]:(hBOOL(hAPP(hAPP(c_member(X4),X114),hAPP(c_List_Oset(X4),X293)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X19),X114))))&c_List_Olinorder__class_Osorted(X4,X293)))<=>c_List_Olinorder__class_Osorted(X4,X26))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted_Osimps)). 4.02/4.27 fof(fact_hd__dropWhile, axiom, ![X32, X56, X4]:(~(hBOOL(hAPP(X56,hAPP(c_List_Ohd(X4),c_List_OdropWhile(X4,X56,X32)))))<=c_List_Olist_ONil(X4)!=c_List_OdropWhile(X4,X56,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__dropWhile)). 4.02/4.27 fof(fact_SetInterval_Otransfer__int__nat__set__functions, axiom, ![X20, X21]:((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,X21),hAPP(c_Int_Onat,X20)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X21,X20)<=c_Nat__Transfer_Ois__nat(X20))<=c_Nat__Transfer_Ois__nat(X21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SetInterval_Otransfer__int__nat__set__functions)). 4.02/4.27 fof(fact_divide__eq__eq__number__of, axiom, ![X23, X24, X25, X4]:((hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X25),X24)=hAPP(c_Int_Onumber__class_Onumber__of(X4),X23)<=>((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X23)),X24)=X25<=c_Groups_Ozero__class_Ozero(X4)!=X24)&(c_Groups_Ozero__class_Ozero(X4)=hAPP(c_Int_Onumber__class_Onumber__of(X4),X23)<=X24=c_Groups_Ozero__class_Ozero(X4))))<=(class_Int_Onumber(X4)&class_Fields_Ofield__inverse__zero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__eq__eq__number__of)). 4.02/4.27 fof(fact_sum__eq__0__conv, axiom, ![X144, X21]:(hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X144)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=>(![X19]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X19),hAPP(c_List_Oset(tc_Nat_Onat),X144)))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X19)&c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__eq__0__conv)). 4.02/4.27 fof(fact_nat__add__distrib, axiom, ![X157, X29]:((hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X29),X157))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X29)),hAPP(c_Int_Onat,X157))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X157)))<=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_nat__add__distrib)). 4.02/4.27 fof(fact_add__nonneg__eq__0__iff, axiom, ![X17, X9, X4]:(class_Groups_Oordered__comm__monoid__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X9))=>((c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X9),X17)<=>(c_Groups_Ozero__class_Ozero(X4)=X9&c_Groups_Ozero__class_Ozero(X4)=X17))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__nonneg__eq__0__iff)). 4.02/4.27 fof(fact_div__mult__mult1__if, axiom, ![X12, X11, X10, X4]:(class_Divides_Osemiring__div(X4)=>((hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X11),X12)<=c_Groups_Ozero__class_Ozero(X4)!=X10)&(hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12))=c_Groups_Ozero__class_Ozero(X4)<=X10=c_Groups_Ozero__class_Ozero(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__mult1__if)). 4.02/4.27 fof(fact_Int__Collect, axiom, ![X56, X3, X9, X4]:((hBOOL(hAPP(X56,X9))&hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))<=>hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X4),X56))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Collect)). 4.02/4.27 fof(fact_code__numeral__decr, axiom, ![X107]:(hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X107=>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,X107)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X107)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral__decr)). 4.02/4.27 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)). 4.02/4.27 fof(fact_Code__Numeral_Oof__nat__code, axiom, c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral)=c_Code__Numeral_Oof__nat, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Code__Numeral_Oof__nat__code)). 4.02/4.27 fof(fact_eq__nat__number__of, axiom, ![X182, X64]:(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X182)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X182)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X64))))&(~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X64))))=>((hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X64)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<=hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X182))))&(X64=X182<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X182))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__nat__number__of)). 4.02/4.27 fof(fact_power__nat__number__of, axiom, ![X5, 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)),X5))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X5)<=~(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),X1)))=>hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__nat__number__of)). 4.02/4.27 fof(fact_inj__vimage__image__eq, axiom, ![X3, X22, X7, X4]:(hAPP(c_Set_Ovimage(X4,X7,X22),hAPP(c_Set_Oimage(X4,X7,X22),X3))=X3<=c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__vimage__image__eq)). 4.02/4.27 fof(fact_surj__image__vimage__eq, axiom, ![X3, X22, X4, X7]:(hAPP(c_Set_Oimage(X7,X4,X22),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=>X3=hAPP(c_Set_Oimage(X7,X4,X22),hAPP(c_Set_Ovimage(X7,X4,X22),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_surj__image__vimage__eq)). 4.02/4.27 fof(fact_finite__vimageI, axiom, ![X48, X7, X87, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X87))=>(c_Fun_Oinj__on(X7,X4,X48,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_Ovimage(X7,X4,X48),X87))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__vimageI)). 4.02/4.27 fof(fact_nat__diff__distrib, axiom, ![X29, X157]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X157))=>(hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X29),X157))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X29)),hAPP(c_Int_Onat,X157))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X157),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__diff__distrib)). 4.02/4.27 fof(fact_finite__vimageD, axiom, ![X87, X48, X7, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_Ovimage(X4,X7,X48),X87)))=>(hAPP(c_Set_Oimage(X4,X7,X48),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X87)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__vimageD)). 4.02/4.27 fof(fact_vimage__const, axiom, ![X7, X3, X24, X4]:((~(hBOOL(hAPP(hAPP(c_member(X4),X24),X3)))=>c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X7,X4,hAPP(c_COMBK(X4,X7),X24)),X3))&(hBOOL(hAPP(hAPP(c_member(X4),X24),X3))=>hAPP(c_Set_Ovimage(X7,X4,hAPP(c_COMBK(X4,X7),X24)),X3)=c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__const)). 4.02/4.27 fof(fact_vimage__singleton__eq, axiom, ![X25, X22, X7, X26, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X26),hAPP(c_Set_Ovimage(X4,X7,X22),hAPP(hAPP(c_Set_Oinsert(X7),X25),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))<=>hAPP(X22,X26)=X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__singleton__eq)). 4.02/4.27 fof(fact_vimageI2, axiom, ![X7, X3, X26, X22, X4]:(hBOOL(hAPP(hAPP(c_member(X7),X26),hAPP(c_Set_Ovimage(X7,X4,X22),X3)))<=hBOOL(hAPP(hAPP(c_member(X4),hAPP(X22,X26)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimageI2)). 4.02/4.27 fof(fact_vimageD, axiom, ![X3, X22, X7, X26, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X26),hAPP(c_Set_Ovimage(X4,X7,X22),X3)))=>hBOOL(hAPP(hAPP(c_member(X7),hAPP(X22,X26)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimageD)). 4.02/4.27 fof(fact_number__of__pred, axiom, ![X53, X4]:(class_Int_Onumber__ring(X4)=>hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_Opred(X53))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))),hAPP(c_Int_Onumber__class_Onumber__of(X4),X53))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__pred)). 4.02/4.27 fof(fact_nat__mod__distrib, axiom, ![X43, X13]:((hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X13,X43))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X13),hAPP(c_Int_Onat,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(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mod__distrib)). 4.02/4.27 fof(fact_eq__number__of__eq, axiom, ![X17, X9, X4]:((hAPP(c_Int_Onumber__class_Onumber__of(X4),X17)=hAPP(c_Int_Onumber__class_Onumber__of(X4),X9)<=>c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X17)))))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__number__of__eq)). 4.02/4.27 fof(fact_reflp__def, axiom, ![X18, X4]:(c_Relation_Orefl__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),X18)))<=>c_Predicate_Oreflp(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reflp__def)). 4.02/4.27 fof(fact_range__ex1__eq, axiom, ![X25, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>(hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_Set_Oimage(X4,X7,X22),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))<=>?[X19]:(hAPP(X22,X19)=X25&![X34]:(X34=X19<=X25=hAPP(X22,X34))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_range__ex1__eq)). 4.02/4.27 fof(fact_rangeI, axiom, ![X7, X9, X22, X4]:hBOOL(hAPP(hAPP(c_member(X4),hAPP(X22,X9)),hAPP(c_Set_Oimage(X7,X4,X22),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rangeI)). 4.02/4.27 fof(fact_inj__on__map__eq__map, axiom, ![X31, X32, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X32)),hAPP(c_List_Oset(X4),X31)))=>(X32=X31<=>hAPP(hAPP(c_List_Omap(X4,X7),X22),X31)=hAPP(hAPP(c_List_Omap(X4,X7),X22),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__map__eq__map)). 4.02/4.27 fof(fact_equal__fun__def, axiom, ![X76, X22, X4, X7]:((class_Enum_Oenum(X4)&class_HOL_Oequal(X7))=>(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X4,X7)),X22),X76))<=>![X19]:(hAPP(X22,X19)=hAPP(X76,X19)<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),c_Enum_Oenum__class_Oenum(X4))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equal__fun__def)). 4.02/4.27 fof(fact_in__enum, axiom, ![X9, X4]:(class_Enum_Oenum(X4)=>hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),c_Enum_Oenum__class_Oenum(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__enum)). 4.02/4.27 fof(fact_min__max_OInf__fin__set__fold, axiom, ![X32, X9, X4]:(c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)))=hAPP(c_List_Ofoldl(X4,X4,c_Orderings_Oord__class_Omin(X4),X9),X32)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin__set__fold)). 4.02/4.27 fof(fact_List_Oset_Osimps_I2_J, axiom, ![X32, X9, X4]:hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32))=hAPP(hAPP(c_Set_Oinsert(X4),X9),hAPP(c_List_Oset(X4),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Oset_Osimps_I2_J)). 4.02/4.27 fof(fact_min__max_OSup__fin__set__fold, axiom, ![X32, X9, X4]:(class_Orderings_Olinorder(X4)=>hAPP(c_List_Ofoldl(X4,X4,c_Orderings_Oord__class_Omax(X4),X9),X32)=c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin__set__fold)). 4.02/4.27 fof(fact_Suc__eq__plus1__left, axiom, ![X5]:hAPP(c_Nat_OSuc,X5)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__eq__plus1__left)). 4.02/4.27 fof(fact_of__int__of__nat, axiom, ![X107, X4]:(((hAPP(c_Int_Oring__1__class_Oof__int(X4),X107)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onat,X107))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X107),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))&(hAPP(c_Int_Oring__1__class_Oof__int(X4),X107)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X107))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X107),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__of__nat)). 4.02/4.27 fof(fact_rotate__length01, axiom, ![X5, X45, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=>hAPP(c_List_Orotate(X4,X5),X45)=X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__length01)). 4.02/4.27 fof(fact_map__comp__simps_I2_J, axiom, ![X163, X7, X49, X220, X4, X28, X162]:(hAPP(X162,X28)=hAPP(c_Option_Ooption_OSome(X4),X220)=>hAPP(X163,X220)=c_Map_Omap__comp(X4,X49,X7,X163,X162,X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__comp__simps_I2_J)). 4.02/4.27 fof(fact_div__pos__neg__trivial, axiom, ![X12, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11),X12)),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),X11),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__pos__neg__trivial)). 4.02/4.27 fof(fact_split__div__lemma, axiom, ![X21, X180, X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,X180))))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X180)),X21)))<=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21),X20)=X180)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__div__lemma)). 4.02/4.27 fof(fact_eq__special_I1_J, axiom, ![X17, X4]:((hAPP(c_Int_Onumber__class_Onumber__of(X4),X17)=c_Groups_Ozero__class_Ozero(X4)<=>c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X17)))))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__special_I1_J)). 4.02/4.27 fof(fact_eq__special_I3_J, axiom, ![X9, X4]:(class_Int_Onumber__ring(X4)=>(c_Groups_Ozero__class_Ozero(X4)=hAPP(c_Int_Onumber__class_Onumber__of(X4),X9)<=>c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__special_I3_J)). 4.02/4.27 fof(fact_minus__Pls, axiom, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)=c_Int_OPls, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__Pls)). 4.02/4.27 fof(fact_transfer__int__nat__set__relations_I2_J, axiom, ![X3, X9]:(((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X9)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X3)))<=>hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X9),X3)))<=c_Nat__Transfer_Onat__set(X3))<=c_Nat__Transfer_Ois__nat(X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__relations_I2_J)). 4.02/4.27 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J, axiom, ![X9, X3]:(c_Nat__Transfer_Onat__set(X3)=>(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X9),X3))=>c_Nat__Transfer_Ois__nat(X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J)). 4.02/4.27 fof(fact_Union__disjoint, axiom, ![X3, X8, X4]:(![X19]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X19),X8))=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X19),X3))<=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X8)),X3)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__disjoint)). 4.02/4.27 fof(fact_list__eq__iff__zip__eq, axiom, ![X4, X31, X32]:((![X19]:(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),c_fequal),X19))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X19),hAPP(c_List_Oset(tc_prod(X4,X4)),hAPP(hAPP(c_List_Ozip(X4,X4),X32),X31)))))&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X31)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))<=>X31=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__eq__iff__zip__eq)). 4.02/4.27 fof(fact_ospec, axiom, ![X9, X56, X3, X4]:((X3=hAPP(c_Option_Ooption_OSome(X4),X9)=>hBOOL(hAPP(X56,X9)))<=![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),c_Option_Oset(X4,X3)))=>hBOOL(hAPP(X56,X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ospec)). 4.02/4.27 fof(fact_Option_Oset_Osimps_I2_J, axiom, ![X9, X4]:c_Option_Oset(X4,hAPP(c_Option_Ooption_OSome(X4),X9))=hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Option_Oset_Osimps_I2_J)). 4.02/4.27 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J, axiom, ![X43, X13]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X43))=>hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X13,X43))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X13)),hAPP(c_Int_Onat,X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J)). 4.02/4.27 fof(fact_WT__bodies__def, axiom, (c_Com_OWT__bodies<=>![X19]:(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),X19))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),X19),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WT__bodies__def)). 4.02/4.27 fof(fact_distinct__rotate, axiom, ![X32, X20, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),hAPP(c_List_Orotate(X4,X20),X32)))<=>hBOOL(hAPP(c_List_Odistinct(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__rotate)). 4.02/4.27 fof(fact_append__eq__conv__conj, axiom, ![X30, X31, X32, X4]:((X32=hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)),X30)&X31=hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)),X30))<=>X30=hAPP(hAPP(c_List_Oappend(X4),X32),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__eq__conv__conj)). 4.02/4.27 fof(fact_last__upt, axiom, ![X135, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X135))=>c_List_Olast(tc_Nat_Onat,c_List_Oupt(X46,X135))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X135),c_Groups_Oone__class_Oone(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__upt)). 4.02/4.27 fof(fact_add__scale__eq__noteq, axiom, ![X44, X10, X12, X11, X101, X4]:(((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X101),X44))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X101),X10))<=(X12=X11&X10!=X44))<=c_Groups_Ozero__class_Ozero(X4)!=X101)<=class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__scale__eq__noteq)). 4.02/4.27 fof(fact_le__diff__conv2, axiom, ![X37, X38, X28]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),X28)),X38))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X37),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X38),X28))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__diff__conv2)). 4.02/4.27 fof(fact_add__leD2, axiom, ![X5, X107, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),X5))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X107)),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__leD2)). 4.02/4.27 fof(fact_sorted__same, axiom, ![X32, X76, X4]:(class_Orderings_Olinorder(X4)=>c_List_Olinorder__class_Osorted(X4,hAPP(c_List_Ofilter(X4,hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),hAPP(X76,X32))),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__same)). 4.02/4.27 fof(fact_rotate__id, axiom, ![X45, X4, X5]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45))=>X45=hAPP(c_List_Orotate(X4,X5),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__id)). 4.02/4.27 fof(fact_last__list__update, axiom, ![X13, X107, X4, X45]:(c_List_Olist_ONil(X4)!=X45=>((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X107=>X13=c_List_Olast(X4,hAPP(hAPP(c_List_Olist__update(X4,X45),X107),X13)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X107=>c_List_Olast(X4,X45)=c_List_Olast(X4,hAPP(hAPP(c_List_Olist__update(X4,X45),X107),X13))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__list__update)). 4.02/4.27 fof(fact_atLeastLessThanSuc, axiom, ![X20, X21]:((hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X20),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X21),X20))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X21),hAPP(c_Nat_OSuc,X20))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20)))&(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X21),hAPP(c_Nat_OSuc,X20))=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),X21),X20))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThanSuc)). 4.02/4.27 fof(fact_nat__one__le__power, axiom, ![X5, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X46))=>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),X46),X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__one__le__power)). 4.02/4.27 fof(fact_card__Suc__eq, axiom, ![X28, X3, X4]:(hAPP(c_Nat_OSuc,X28)=hAPP(c_Finite__Set_Ocard(X4),X3)<=>?[X78, X138]:((((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X138<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X28)&hAPP(c_Finite__Set_Ocard(X4),X138)=X28)&~(hBOOL(hAPP(hAPP(c_member(X4),X78),X138))))&X3=hAPP(hAPP(c_Set_Oinsert(X4),X78),X138))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Suc__eq)). 4.02/4.27 fof(fact_Inf__fin__set__fold, axiom, ![X32, X9, X4]:(c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)))=hAPP(c_List_Ofoldl(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4),X9),X32)<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin__set__fold)). 4.02/4.27 fof(fact_Sup__fin__set__fold, axiom, ![X32, X9, X4]:(class_Lattices_Olattice(X4)=>c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)))=hAPP(c_List_Ofoldl(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4),X9),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin__set__fold)). 4.02/4.27 fof(fact_Min__fin__set__fold, axiom, ![X32, X9, X4]:(hAPP(c_List_Ofoldl(X4,X4,c_Orderings_Oord__class_Omin(X4),X9),X32)=c_Big__Operators_Olinorder__class_OMin(X4,hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__fin__set__fold)). 4.02/4.27 fof(fact_Max__fin__set__fold, axiom, ![X32, X9, X4]:(class_Orderings_Olinorder(X4)=>hAPP(c_List_Ofoldl(X4,X4,c_Orderings_Oord__class_Omax(X4),X9),X32)=c_Big__Operators_Olinorder__class_OMax(X4,hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__fin__set__fold)). 4.02/4.27 fof(fact_nat__mult__distrib, axiom, ![X157, X29]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X29)),hAPP(c_Int_Onat,X157))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X157))<=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_nat__mult__distrib)). 4.02/4.27 fof(fact_nat__div__distrib, axiom, ![X43, X13]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X13)),hAPP(c_Int_Onat,X43))=hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X13),X43))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__div__distrib)). 4.02/4.27 fof(fact_of__nat__number__of__lemma, axiom, ![X1, X4]:(((hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Int_Onumber__class_Onumber__of(X4),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))))&(~(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(X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Ozero__class_Ozero(X4)))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__number__of__lemma)). 4.02/4.27 fof(fact_in__set__replicate, axiom, ![X17, X20, X9, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),c_List_Oreplicate(X4,X20,X17))))<=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X20&X9=X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__replicate)). 4.02/4.27 fof(fact_zmod__minus1, axiom, ![X12]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12),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_OMin),X12)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__minus1)). 4.02/4.27 fof(fact_snoc__eq__iff__butlast, axiom, ![X31, X9, X32, X4]:(((X31!=c_List_Olist_ONil(X4)&X9=c_List_Olast(X4,X31))&c_List_Obutlast(X4,X31)=X32)<=>X31=hAPP(hAPP(c_List_Oappend(X4),X32),hAPP(hAPP(c_List_Olist_OCons(X4),X9),c_List_Olist_ONil(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snoc__eq__iff__butlast)). 4.02/4.27 fof(fact_divmod__nat__base, axiom, ![X5, X2]:(c_Divides_Odivmod__nat(X2,X5)=hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__base)). 4.02/4.27 fof(fact_sum__squares__gt__zero__iff, axiom, ![X17, X9, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X9),X9)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X17),X17))))<=>(c_Groups_Ozero__class_Ozero(X4)!=X17|X9!=c_Groups_Ozero__class_Ozero(X4)))<=class_Rings_Olinordered__ring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__squares__gt__zero__iff)). 4.02/4.27 fof(fact_transfer__nat__int__list__return__embed, axiom, ![X47]:(c_List_Onat__list(X47)=>X47=c_List_Oembed__list(c_List_Oreturn__list(X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__list__return__embed)). 4.02/4.27 fof(fact_less__special_I3_J, axiom, ![X9, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X9)),c_Groups_Ozero__class_Ozero(X4))))<=(class_Rings_Olinordered__idom(X4)&class_Int_Onumber__ring(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__special_I3_J)). 4.02/4.27 fof(fact_le__special_I3_J, axiom, ![X9, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9),c_Int_OPls))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X9)),c_Groups_Ozero__class_Ozero(X4))))<=(class_Int_Onumber__ring(X4)&class_Rings_Olinordered__idom(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__special_I3_J)). 4.02/4.27 fof(fact_less__special_I1_J, axiom, ![X17, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X17))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X17))))<=(class_Int_Onumber__ring(X4)&class_Rings_Olinordered__idom(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__special_I1_J)). 4.02/4.27 fof(fact_le__special_I1_J, axiom, ![X17, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X17)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X17)))<=(class_Rings_Olinordered__idom(X4)&class_Int_Onumber__ring(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__special_I1_J)). 4.02/4.27 fof(fact_ex__least__nat__less, axiom, ![X20, X56]:(~(hBOOL(hAPP(X56,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=>(hBOOL(hAPP(X56,X20))=>?[X137]:((hBOOL(hAPP(X56,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X137),c_Groups_Oone__class_Oone(tc_Nat_Onat))))&![X42]:(~(hBOOL(hAPP(X56,X42)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X137))))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X137),X20))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__least__nat__less)). 4.02/4.27 fof(fact_wf, axiom, ![X4]:(class_Orderings_Owellorder(X4)=>c_Wellfounded_Owf(X4,hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf)). 4.02/4.27 fof(fact_norm__frac_Osimps, axiom, ![X26, X25]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))=>((~((X25=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X26=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X26),X25)),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),X26))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X25)))=c_Nitpick_Onorm__frac(X26,X25))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X26|X25=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))=c_Nitpick_Onorm__frac(X26,X25))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>c_Nitpick_Onorm__frac(X26,X25)=c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_norm__frac_Osimps)). 4.02/4.27 fof(fact_le__nat__number__of, axiom, ![X182, X64]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X64),c_Int_OPls))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X64),X182))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X182)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__nat__number__of)). 4.02/4.27 fof(fact_split__nat, axiom, ![X37, X56]:((![X104]:(hBOOL(hAPP(X56,X104))<=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X104)=X37)&(hBOOL(hAPP(X56,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))<=>hBOOL(hAPP(X56,hAPP(c_Int_Onat,X37)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__nat)). 4.02/4.27 fof(fact_of__nat__number__of__eq, axiom, ![X1, X4]:(((hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Int_Onumber__class_Onumber__of(X4),X1)<=~(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),X1)))=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Ozero__class_Ozero(X4)))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__number__of__eq)). 4.02/4.27 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J, axiom, ![X5, X13]:(hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X13),X5))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X13)),X5)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J)). 4.02/4.27 fof(fact_zless__nat__conj, axiom, ![X16, X23]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23),X16))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X23)),hAPP(c_Int_Onat,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__nat__conj)). 4.02/4.27 fof(fact_nat__less__eq__zless, axiom, ![X16, X23]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23),X16))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X23)),hAPP(c_Int_Onat,X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__less__eq__zless)). 4.02/4.27 fof(fact_wfP__acyclicP, axiom, ![X18, X4]:(c_Wellfounded_Oacyclic(X4,hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),X18)))<=c_Wellfounded_OwfP(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__acyclicP)). 4.02/4.27 fof(fact_wfP__def, axiom, ![X18, X4]:(c_Wellfounded_Owf(X4,hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),X18)))<=>c_Wellfounded_OwfP(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__def)). 4.02/4.27 fof(fact_Suc__nat__eq__nat__zadd1, axiom, ![X29]:(hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X29))=hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X29))<=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_Suc__nat__eq__nat__zadd1)). 4.02/4.27 fof(fact_hd__upt, axiom, ![X135, X46]:(X46=hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X46,X135))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__upt)). 4.02/4.27 fof(fact_card_Oneutral, axiom, ![X3, X4]:((hAPP(c_Finite__Set_Ocard(X4),X3)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=(?[X19]:hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Oone__class_Oone(tc_Nat_Onat)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card_Oneutral)). 4.02/4.27 fof(fact_card__def, axiom, ![X3, X4]:((hAPP(c_Finite__Set_Ocard(X4),X3)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X4),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X4),X3)<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__def)). 4.02/4.27 fof(fact_disjoint__iff__not__equal, axiom, ![X6, X3, X4]:(![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>![X114]:(hBOOL(hAPP(hAPP(c_member(X4),X114),X6))=>X19!=X114))<=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_disjoint__iff__not__equal)). 4.02/4.27 fof(fact_divide__eq__eq, axiom, ![X26, X24, X25, X4]:(class_Fields_Ofield__inverse__zero(X4)=>(((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24)=X25<=X24!=c_Groups_Ozero__class_Ozero(X4))&(X26=c_Groups_Ozero__class_Ozero(X4)<=c_Groups_Ozero__class_Ozero(X4)=X24))<=>X26=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X25),X24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__eq__eq)). 4.02/4.27 fof(fact_div__eq__minus1, axiom, ![X12]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X12)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__eq__minus1)). 4.02/4.27 fof(fact_nat__less__iff, axiom, ![X21, X23]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X23)),X21))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__less__iff)). 4.02/4.27 fof(fact_Ints__double__eq__0__iff, axiom, ![X26, X4]:(class_Int_Oring__char__0(X4)=>((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X26),X26)=c_Groups_Ozero__class_Ozero(X4)<=>X26=c_Groups_Ozero__class_Ozero(X4))<=hBOOL(hAPP(hAPP(c_member(X4),X26),c_Int_Oring__1__class_OInts(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__double__eq__0__iff)). 4.02/4.27 fof(fact_nonzero__eq__divide__eq, axiom, ![X25, X26, X24, X4]:(class_Rings_Odivision__ring(X4)=>((X26=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X25),X24)<=>X25=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24))<=c_Groups_Ozero__class_Ozero(X4)!=X24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__eq__divide__eq)). 4.02/4.27 fof(fact_zle__diff1__eq, axiom, ![X16, X23]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X16),c_Groups_Oone__class_Oone(tc_Int_Oint))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__diff1__eq)). 4.02/4.27 fof(fact_divide__eq__imp, axiom, ![X11, X12, X10, X4]:((X10!=c_Groups_Ozero__class_Ozero(X4)=>(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X10)=X11<=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)=X12))<=class_Rings_Odivision__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__eq__imp)). 4.02/4.27 fof(fact_remove1__filter__not, axiom, ![X32, X4, X9, X56]:(hAPP(c_List_Ofilter(X4,X56),X32)=c_List_Oremove1(X4,X9,hAPP(c_List_Ofilter(X4,X56),X32))<=~(hBOOL(hAPP(X56,X9)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__filter__not)). 4.02/4.27 fof(fact_filter__remove1, axiom, ![X32, X9, X112, X4]:hAPP(c_List_Ofilter(X4,X112),c_List_Oremove1(X4,X9,X32))=c_List_Oremove1(X4,X9,hAPP(c_List_Ofilter(X4,X112),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__remove1)). 4.02/4.27 fof(fact_Nats__number__of, axiom, ![X23, X4]:(class_Int_Onumber__ring(X4)=>(hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X23)),c_Nat_Osemiring__1__class_ONats(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nats__number__of)). 4.02/4.27 fof(fact_zero__less__zpower__abs__iff, axiom, ![X20, X9]:(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),X9)),X20)))<=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X20|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__zpower__abs__iff)). 4.02/4.27 fof(fact_comp__equivI, axiom, ![X3, X18, X4]:((hAPP(c_Relation_ODomain(X4,X4),X18)=X3=>c_Equiv__Relations_Oequiv(X4,X3,X18))<=X18=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(c_Relation_Oconverse(X4,X4),X18)),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comp__equivI)). 4.02/4.27 fof(fact_abs__le__zero__iff, axiom, ![X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X26)),c_Groups_Ozero__class_Ozero(X4)))<=>c_Groups_Ozero__class_Ozero(X4)=X26)<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__le__zero__iff)). 4.02/4.27 fof(fact_pair__in__Id__conv, axiom, ![X25, X26, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),c_Relation_OId(X4)))<=>X26=X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__in__Id__conv)). 4.02/4.27 fof(fact_square__eq__iff, axiom, ![X25, X26, X4]:(class_Rings_Oidom(X4)=>((hAPP(c_Groups_Ouminus__class_Ouminus(X4),X25)=X26|X26=X25)<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X26)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X25),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_square__eq__iff)). 4.02/4.27 fof(fact_one__less__nat__eq, axiom, ![X16]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X16))<=>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,X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__less__nat__eq)). 4.02/4.27 fof(fact_zsgn__def, axiom, ![X46]:((c_Groups_Osgn__class_Osgn(tc_Int_Oint,X46)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X46)&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X46=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X46)))=>c_Groups_Osgn__class_Osgn(tc_Int_Oint,X46)=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,X46)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X46)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zsgn__def)). 4.02/4.27 fof(fact_add__is__1, axiom, ![X20, X21]:(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20)<=>((X21=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&X20=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X20&c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X21))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__is__1)). 4.02/4.27 fof(fact_less__eq__nat_Osimps_I2_J, axiom, ![X20, X21]:(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21)),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__nat_Osimps_I2_J)). 4.02/4.27 fof(fact_finite__sorted__distinct__unique, axiom, ![X3, X4]:((?[X19]:(((hAPP(c_List_Oset(X4),X19)=X3&c_List_Olinorder__class_Osorted(X4,X19))&hBOOL(hAPP(c_List_Odistinct(X4),X19)))&![X34]:(((X3=hAPP(c_List_Oset(X4),X34)&hBOOL(hAPP(c_List_Odistinct(X4),X34)))&c_List_Olinorder__class_Osorted(X4,X34))=>X19=X34))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__sorted__distinct__unique)). 4.02/4.27 fof(fact_finite__set, axiom, ![X32, X4]:hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_List_Oset(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__set)). 4.02/4.27 fof(fact_nat__le__eq__zle, axiom, ![X16, X23]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X23)),hAPP(c_Int_Onat,X16)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__le__eq__zle)). 4.02/4.27 fof(fact_upt__eq__Nil__conv, axiom, ![X38, X37]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X38),X37))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X38)<=>c_List_Oupt(X37,X38)=c_List_Olist_ONil(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__eq__Nil__conv)). 4.02/4.27 fof(fact_le__iff__pred__less, axiom, ![X60, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X28)),X60))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28),X60))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__iff__pred__less)). 4.02/4.27 fof(fact_divmod__nat__eq, axiom, ![X200, X5, X2]:(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X5),X200))=>X200=c_Divides_Odivmod__nat(X2,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__eq)). 4.02/4.27 fof(fact_upt__rec, axiom, ![X135, X46]:((c_List_Oupt(X46,X135)=c_List_Olist_ONil(tc_Nat_Onat)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X135))))&(hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X46),c_List_Oupt(hAPP(c_Nat_OSuc,X46),X135))=c_List_Oupt(X46,X135)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X135)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upt__rec)). 4.02/4.27 fof(fact_of__nat__nat, axiom, ![X29, X4]:(class_Rings_Oring__1(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29))=>hAPP(c_Int_Oring__1__class_Oof__int(X4),X29)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Int_Onat,X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__nat)). 4.02/4.27 fof(fact_square__eq__1__iff, axiom, ![X9, X4]:(((X9=hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))|c_Groups_Oone__class_Oone(X4)=X9)<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X9),X9)=c_Groups_Oone__class_Oone(X4))<=class_Rings_Oring__1__no__zero__divisors(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_square__eq__1__iff)). 4.02/4.27 fof(fact_code__numeral__not__eq__zero, axiom, ![X37]:(X37!=hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral__not__eq__zero)). 4.02/4.27 fof(fact_divide__Numeral0, axiom, ![X13, X4]:((class_Fields_Ofield__inverse__zero(X4)&class_Int_Onumber__ring(X4))=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__Numeral0)). 4.02/4.27 fof(fact_power__eq__0__iff, axiom, ![X20, X26, X4]:((((class_Rings_Omult__zero(X4)&class_Rings_Ono__zero__divisors(X4))&class_Rings_Ozero__neq__one(X4))&class_Power_Opower(X4))=>((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X20&c_Groups_Ozero__class_Ozero(X4)=X26)<=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),X26),X20)=c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__eq__0__iff)). 4.02/4.27 fof(fact_zmult__eq__1__iff, axiom, ![X20, X21]:(c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X20)<=>((hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X21&hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X20)|(X20=c_Groups_Oone__class_Oone(tc_Int_Oint)&X21=c_Groups_Oone__class_Oone(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__eq__1__iff)). 4.02/4.27 fof(fact_nat__power__eq__Suc__0__iff, axiom, ![X21, X9]:((hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X9|X21=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X9),X21)=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)). 4.02/4.27 fof(fact_eq__neg__iff__add__eq__0, axiom, ![X25, X26, X4]:((c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X26),X25)<=>X26=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X25))<=class_Groups_Ogroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__neg__iff__add__eq__0)). 4.02/4.27 fof(fact_zero__less__nat__eq, axiom, ![X16]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X16)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__nat__eq)). 4.02/4.27 fof(fact_int__nat__eq, axiom, ![X29]:((X29=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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)),X29)))=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X29))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__nat__eq)). 4.02/4.27 fof(fact_transfer__nat__int__relations_I1_J, axiom, ![X17, X9]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17))=>(X17=X9<=>hAPP(c_Int_Onat,X9)=hAPP(c_Int_Onat,X17)))<=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_transfer__nat__int__relations_I1_J)). 4.02/4.27 fof(fact_eq__divide__eq__number__of1, axiom, ![X23, X25, X26, X4]:((hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X25),hAPP(c_Int_Onumber__class_Onumber__of(X4),X23))=X26<=>((c_Groups_Ozero__class_Ozero(X4)!=hAPP(c_Int_Onumber__class_Onumber__of(X4),X23)=>X25=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),hAPP(c_Int_Onumber__class_Onumber__of(X4),X23)))&(X26=c_Groups_Ozero__class_Ozero(X4)<=hAPP(c_Int_Onumber__class_Onumber__of(X4),X23)=c_Groups_Ozero__class_Ozero(X4))))<=(class_Fields_Ofield__inverse__zero(X4)&class_Int_Onumber(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__divide__eq__number__of1)). 4.02/4.27 fof(fact_length__remdups__eq, axiom, ![X32, X4]:(c_List_Oremdups(X4,X32)=X32<=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Oremdups(X4,X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__remdups__eq)). 4.02/4.27 fof(fact_length__remdups__card__conv, axiom, ![X32, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Oremdups(X4,X32))=hAPP(c_Finite__Set_Ocard(X4),hAPP(c_List_Oset(X4),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__remdups__card__conv)). 4.02/4.27 fof(fact_less__code__numeral__code, axiom, ![X21, X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X21))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X20)),hAPP(c_Code__Numeral_Oof__nat,X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__code__numeral__code)). 4.02/4.27 fof(fact_less__eq__code__numeral__code, axiom, ![X21, X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X20)),hAPP(c_Code__Numeral_Oof__nat,X21)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),X21))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__code__numeral__code)). 4.02/4.27 fof(fact_Collect__empty__eq, axiom, ![X56, X4]:(hAPP(c_Set_OCollect(X4),X56)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=>![X19]:~(hBOOL(hAPP(X56,X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Collect__empty__eq)). 4.02/4.27 fof(fact_empty__Collect__eq, axiom, ![X56, X4]:(![X19]:~(hBOOL(hAPP(X56,X19)))<=>hAPP(c_Set_OCollect(X4),X56)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__Collect__eq)). 4.02/4.27 fof(fact_not__less__eq__eq, axiom, ![X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),X21))<=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__less__eq__eq)). 4.02/4.27 fof(fact_add__numeral__0, axiom, ![X11, X4]:(class_Int_Onumber__ring(X4)=>X11=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OPls)),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__numeral__0)). 4.02/4.27 fof(fact_add__numeral__0__right, axiom, ![X11, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OPls))=X11<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__numeral__0__right)). 4.02/4.27 fof(fact_zless__nat__eq__int__zless, axiom, ![X16, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Int_Onat,X16)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__nat__eq__int__zless)). 4.02/4.27 fof(fact_split__div_H, axiom, ![X20, X21, X56]:((?[X103]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,X103))))&hBOOL(hAPP(X56,X103)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X103)),X21)))|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X20&hBOOL(hAPP(X56,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))<=>hBOOL(hAPP(X56,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__div_H)). 4.02/4.27 fof(fact_all__nat, axiom, ![X56]:(![X77]:hBOOL(hAPP(X56,X77))<=>![X19]:(hBOOL(hAPP(X56,hAPP(c_Int_Onat,X19)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__nat)). 4.02/4.27 fof(fact_ex__nat, axiom, ![X56]:(?[X77]:hBOOL(hAPP(X56,X77))<=>?[X19]:(hBOOL(hAPP(X56,hAPP(c_Int_Onat,X19)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__nat)). 4.02/4.27 fof(fact_mult__eq__0__iff, axiom, ![X25, X26, X4]:((c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X25)<=>(X25=c_Groups_Ozero__class_Ozero(X4)|c_Groups_Ozero__class_Ozero(X4)=X26))<=class_Rings_Oring__no__zero__divisors(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__eq__0__iff)). 4.02/4.27 fof(fact_diff__eq__diff__eq, axiom, ![X102, X24, X25, X26, X4]:(class_Groups_Oab__group__add(X4)=>(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X26),X25)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X24),X102)=>(X24=X102<=>X26=X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__eq__diff__eq)). 4.02/4.27 fof(fact_double__zero__sym, axiom, ![X26, X4]:((c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X26),X26)<=>c_Groups_Ozero__class_Ozero(X4)=X26)<=class_Groups_Olinordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__zero__sym)). 4.02/4.27 fof(fact_nat__eq__iff2, axiom, ![X23, X21]:(hAPP(c_Int_Onat,X23)=X21<=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23)))=>X21=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)),X23))=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21)=X23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__eq__iff2)). 4.02/4.27 fof(fact_add__0__iff, axiom, ![X26, X25, X4]:(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X25),X26)=X25<=>X26=c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__0__iff)). 4.02/4.27 fof(fact_int__nat__number__of, axiom, ![X1]:((~(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(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))&(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))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__nat__number__of)). 4.02/4.27 fof(fact_eq__iff__diff__eq__0, axiom, ![X25, X26, X4]:((X26=X25<=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X26),X25)=c_Groups_Ozero__class_Ozero(X4))<=class_Groups_Oab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__iff__diff__eq__0)). 4.02/4.27 fof(fact_minus__equation__iff, axiom, ![X25, X26, X4]:(class_Groups_Ogroup__add(X4)=>(X25=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26)<=>X26=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__equation__iff)). 4.02/4.27 fof(fact_zero__less__abs__iff, axiom, ![X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Groups_Oabs__class_Oabs(X4),X26)))<=>c_Groups_Ozero__class_Ozero(X4)!=X26)<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__abs__iff)). 4.02/4.27 fof(fact_not__neg__nat, axiom, ![X29]:(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X29))=X29<=~(hBOOL(hAPP(c_Nat__Numeral_Oneg,X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__neg__nat)). 4.02/4.27 fof(fact_less__Suc0, axiom, ![X20]:(X20=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Suc0)). 4.02/4.27 fof(fact_nat__0__iff, axiom, ![X37]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X37),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>hAPP(c_Int_Onat,X37)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__0__iff)). 4.02/4.27 fof(fact_iszero__Numeral0, axiom, ![X4]:(c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OPls))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_iszero__Numeral0)). 4.02/4.27 fof(fact_eq__number__of__0, axiom, ![X64]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X64),c_Int_OPls))<=>hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X64)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__number__of__0)). 4.02/4.27 fof(fact_neg__imp__number__of__eq__0, axiom, ![X1]:(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)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__imp__number__of__eq__0)). 4.02/4.27 fof(fact_of__int__eq__0__iff, axiom, ![X16, X4]:(class_Int_Oring__char__0(X4)=>(X16=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<=>c_Groups_Ozero__class_Ozero(X4)=hAPP(c_Int_Oring__1__class_Oof__int(X4),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__eq__0__iff)). 4.02/4.27 fof(fact_neg__equal__zero, axiom, ![X26, X4]:(class_Groups_Olinordered__ab__group__add(X4)=>(X26=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26)<=>c_Groups_Ozero__class_Ozero(X4)=X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__equal__zero)). 4.02/4.27 fof(fact_sgn__0__0, axiom, ![X26, X4]:(class_Rings_Olinordered__idom(X4)=>(X26=c_Groups_Ozero__class_Ozero(X4)<=>c_Groups_Osgn__class_Osgn(X4,X26)=c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__0__0)). 4.02/4.27 fof(fact_order__less__imp__not__eq, axiom, ![X43, X13, X4]:(class_Orderings_Oorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),X43))=>X43!=X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__imp__not__eq)). 4.02/4.27 fof(fact_linorder__neq__iff, axiom, ![X17, X9, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X17),X9))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X9),X17)))<=>X9!=X17)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__neq__iff)). 4.02/4.27 fof(fact_semiring__norm_I112_J, axiom, ![X4]:(class_Int_Onumber__ring(X4)=>c_Groups_Ozero__class_Ozero(X4)=hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OPls)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_semiring__norm_I112_J)). 4.02/4.27 fof(fact_iszero__def, axiom, ![X16, X4]:((c_Groups_Ozero__class_Ozero(X4)=X16<=>c_Int_Oiszero(X4,X16))<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_iszero__def)). 4.02/4.27 fof(fact_Code__Numeral_Oof__nat__inject, axiom, ![X21, X20]:(hAPP(c_Code__Numeral_Oof__nat,X21)=hAPP(c_Code__Numeral_Oof__nat,X20)<=>X20=X21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Code__Numeral_Oof__nat__inject)). 4.02/4.27 fof(fact_WT__bodiesD, axiom, ![X12, X189]:(c_Com_OWT__bodies=>(hAPP(c_Com_Obody,X189)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X12)=>hBOOL(hAPP(c_Com_OWT,X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WT__bodiesD)). 4.02/4.27 fof(fact_max__ext_Osimps, axiom, ![X39, X67, X70, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X70),X67)),c_Wellfounded_Omax__ext(X4,X39)))<=>(((![X19]:(?[X114]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X114)),X39))&hBOOL(hAPP(hAPP(c_member(X4),X114),X67)))<=hBOOL(hAPP(hAPP(c_member(X4),X19),X70)))&X67!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X67)))&hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ext_Osimps)). 4.02/4.27 fof(fact_conversep__noteq, axiom, ![X17, X9, X4]:(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4,X4,hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot)),c_fequal)),X9),X17))<=>X9!=X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conversep__noteq)). 4.02/4.27 fof(fact_max__extp_Oequations, axiom, ![X67, X70, X39, X4]:((((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X67))&![X19]:(?[X114]:(hBOOL(hAPP(hAPP(c_member(X4),X114),X67))&hBOOL(hAPP(hAPP(X39,X19),X114)))<=hBOOL(hAPP(hAPP(c_member(X4),X19),X70))))&X67!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X70)))<=>c_Wellfounded_Omax__extp(X4,X39,X70,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__extp_Oequations)). 4.02/4.27 fof(fact_zless__le, axiom, ![X23, X16]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16),X23))<=>(X16!=X23&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16),X23)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__le)). 4.02/4.27 fof(fact_eq__int__code_I5_J, axiom, ~(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I5_J)). 4.02/4.27 fof(fact_eq__int__code_I2_J, axiom, ~(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__code_I2_J)). 4.02/4.27 fof(fact_rel__simps_I3_J, axiom, ~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I3_J)). 4.02/4.27 fof(fact_rel__simps_I20_J, axiom, ~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I20_J)). 4.02/4.27 fof(fact_single__stateE, axiom, (![X199]:~(![X198]:X198=X199)<=c_Hoare__Mirabelle_Ostate__not__singleton), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__stateE)). 4.02/4.27 fof(fact_state__not__singleton__def, axiom, (?[X198, X199]:X199!=X198<=>c_Hoare__Mirabelle_Ostate__not__singleton), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_state__not__singleton__def)). 4.02/4.27 fof(conj_4, conjecture, hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_4)). 4.02/4.27 fof(fact_mult, axiom, ![X64, X115, X17, X9]: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),X9),X115)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X64))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9),X64)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X115)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X9),X17)),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),X115),X64)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult)). 4.02/4.27 fof(fact_dom__if, axiom, ![X76, X22, X56, X7, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X7,X22)),hAPP(c_Set_OCollect(X4),X56))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X7,X76)),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),X56))))=c_Map_Odom(X4,X7,hAPP(hAPP(c_COMBS(X4,tc_Option_Ooption(X7),tc_Option_Ooption(X7)),hAPP(hAPP(c_COMBS(X4,tc_Option_Ooption(X7),tc_fun(tc_Option_Ooption(X7),tc_Option_Ooption(X7))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X7),tc_fun(tc_Option_Ooption(X7),tc_Option_Ooption(X7))),X4),c_If(tc_Option_Ooption(X7))),X56)),X22)),X76)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__if)). 4.02/4.27 fof(fact_if__image__distrib, axiom, ![X86, X76, X22, X56, X4, X7]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X4,X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X86),hAPP(c_Set_OCollect(X7),X56)))),hAPP(c_Set_Oimage(X7,X4,X76),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X86),hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7),c_fNot),X56)))))=hAPP(c_Set_Oimage(X7,X4,hAPP(hAPP(c_COMBS(X7,X4,X4),hAPP(hAPP(c_COMBS(X7,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X7),c_If(X4)),X56)),X22)),X76)),X86), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_if__image__distrib)). 4.02/4.27 fof(fact_arith__series__nat, axiom, ![X20, X102, X26]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X102))))=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),X26)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X102))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_arith__series__nat)). 4.02/4.27 fof(fact_length__sublist, axiom, ![X41, X32, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Osublist(X4,X32,X41))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__sublist)). 4.02/4.27 fof(fact_map__pair__surj__on, axiom, ![X125, X6, X76, X49, X126, X127, X3, X22, X4, X7]:(hAPP(c_Set_Oimage(X7,X4,X22),X3)=X127=>(hAPP(c_Set_Oimage(tc_prod(X7,X126),tc_prod(X4,X49),c_Product__Type_Omap__pair(X7,X4,X126,X49,X22,X76)),hAPP(hAPP(c_Product__Type_OSigma(X7,X126),X3),hAPP(c_COMBK(tc_fun(X126,tc_HOL_Obool),X7),X6)))=hAPP(hAPP(c_Product__Type_OSigma(X4,X49),X127),hAPP(c_COMBK(tc_fun(X49,tc_HOL_Obool),X4),X125))<=X125=hAPP(c_Set_Oimage(X126,X49,X76),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__surj__on)). 4.02/4.27 fof(fact_dropWhile__map, axiom, ![X32, X22, X7, X56, X4]:hAPP(hAPP(c_List_Omap(X7,X4),X22),c_List_OdropWhile(X7,hAPP(c_Fun_Ocomp(X4,tc_HOL_Obool,X7,X56),X22),X32))=c_List_OdropWhile(X4,X56,hAPP(hAPP(c_List_Omap(X7,X4),X22),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dropWhile__map)). 4.02/4.27 fof(fact_Image__singleton, axiom, ![X26, X18, X4, X7]:hAPP(c_Relation_OImage(X7,X4,X18),hAPP(hAPP(c_Set_Oinsert(X7),X26),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X7,X4),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X7,X4),tc_fun(tc_fun(tc_prod(X7,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X7,X4))),hAPP(c_Product__Type_OPair(X7,X4),X26))),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__singleton)). 4.02/4.27 fof(fact_UN__le__add__shift, axiom, ![X28, X54, X20, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X20)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool),tc_Nat_Onat),X54),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X28)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X28,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X28))),X54), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__le__add__shift)). 4.02/4.27 fof(fact_foldr__map, axiom, ![X26, X32, X22, X49, X76, X4, X7]:c_List_Ofoldr(X49,X4,hAPP(c_Fun_Ocomp(X7,tc_fun(X4,X4),X49,X76),X22),X32,X26)=c_List_Ofoldr(X7,X4,X76,hAPP(hAPP(c_List_Omap(X49,X7),X22),X32),X26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldr__map)). 4.02/4.27 fof(fact_map__concat, axiom, ![X32, X22, X4, X7]:hAPP(hAPP(c_List_Omap(X7,X4),X22),c_List_Oconcat(X7,X32))=c_List_Oconcat(X4,hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_List_Olist(X4)),hAPP(c_List_Omap(X7,X4),X22)),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__concat)). 4.02/4.27 fof(fact_foldr_Osimps_I2_J, axiom, ![X26, X32, X9, X22, X4, X7]:c_List_Ofoldr(X7,X4,X22,hAPP(hAPP(c_List_Olist_OCons(X7),X9),X32),X26)=hAPP(hAPP(X22,X9),c_List_Ofoldr(X7,X4,X22,X32,X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldr_Osimps_I2_J)). 4.02/4.27 fof(fact_zadd__zmult__distrib2, axiom, ![X216, X217, X53]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X217),X216))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),X217)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),X216)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__zmult__distrib2)). 4.02/4.27 fof(fact_apsnd__apfst, axiom, ![X9, X76, X126, X22, X4, X7, X49]:hAPP(c_Product__Type_Oapsnd(X49,X7,X4,X22),hAPP(c_Product__Type_Oapfst(X126,X4,X49,X76),X9))=hAPP(hAPP(c_Product__Type_OPair(X4,X7),hAPP(X76,hAPP(c_Product__Type_Ofst(X126,X49),X9))),hAPP(X22,hAPP(c_Product__Type_Osnd(X126,X49),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apsnd__apfst)). 4.02/4.27 fof(fact_apfst__apsnd, axiom, ![X9, X76, X126, X22, X7, X4, X49]:hAPP(c_Product__Type_Oapfst(X49,X4,X7,X22),hAPP(c_Product__Type_Oapsnd(X126,X7,X49,X76),X9))=hAPP(hAPP(c_Product__Type_OPair(X4,X7),hAPP(X22,hAPP(c_Product__Type_Ofst(X49,X126),X9))),hAPP(X76,hAPP(c_Product__Type_Osnd(X49,X126),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apfst__apsnd)). 4.02/4.27 fof(fact_apsnd__apfst__commute, axiom, ![X51, X76, X126, X22, X4, X7, X49]:hAPP(c_Product__Type_Oapfst(X126,X4,X7,X76),hAPP(c_Product__Type_Oapsnd(X49,X7,X126,X22),X51))=hAPP(c_Product__Type_Oapsnd(X49,X7,X4,X22),hAPP(c_Product__Type_Oapfst(X126,X4,X49,X76),X51)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apsnd__apfst__commute)). 4.02/4.27 fof(fact_set__Cons__sing__Nil, axiom, ![X3, X4]:hAPP(c_Set_Oimage(X4,tc_List_Olist(X4),hAPP(hAPP(c_COMBC(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)),c_List_Olist_ONil(X4))),X3)=c_List_Oset__Cons(X4,X3,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__Cons__sing__Nil)). 4.02/4.27 fof(fact_apsnd__compose, axiom, ![X9, X76, X126, X22, X4, X7, X49]:hAPP(c_Product__Type_Oapsnd(X49,X7,X4,X22),hAPP(c_Product__Type_Oapsnd(X126,X49,X4,X76),X9))=hAPP(c_Product__Type_Oapsnd(X126,X7,X4,hAPP(c_Fun_Ocomp(X49,X7,X126,X22),X76)),X9), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apsnd__compose)). 4.02/4.27 fof(fact_apfst__compose, axiom, ![X9, X76, X126, X22, X7, X4, X49]:hAPP(c_Product__Type_Oapfst(X49,X4,X7,X22),hAPP(c_Product__Type_Oapfst(X126,X49,X7,X76),X9))=hAPP(c_Product__Type_Oapfst(X126,X4,X7,hAPP(c_Fun_Ocomp(X49,X4,X126,X22),X76)),X9), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apfst__compose)). 4.02/4.27 fof(fact_rotate__map, axiom, ![X32, X22, X7, X20, X4]:hAPP(c_List_Orotate(X4,X20),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32))=hAPP(hAPP(c_List_Omap(X7,X4),X22),hAPP(c_List_Orotate(X7,X20),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__map)). 4.02/4.27 fof(fact_dom__fun__upd, axiom, ![X9, X22, X7, X4, X17]:((c_Option_Ooption_ONone(X4)=X17=>c_Map_Odom(X7,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X4)),X22),X9),X17))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),c_Map_Odom(X7,X4,X22)),hAPP(hAPP(c_Set_Oinsert(X7),X9),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))&(X17!=c_Option_Ooption_ONone(X4)=>c_Map_Odom(X7,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X4)),X22),X9),X17))=hAPP(hAPP(c_Set_Oinsert(X7),X9),c_Map_Odom(X7,X4,X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__fun__upd)). 4.02/4.27 fof(fact_length__concat, axiom, ![X134, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Oconcat(X4,X134))=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),X134)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__concat)). 4.02/4.27 fof(fact_list_Osize_I2_J, axiom, ![X224, X26, X228, X4]:c_List_Olist_Olist__size(X4,X228,hAPP(hAPP(c_List_Olist_OCons(X4),X26),X224))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X228,X26)),c_List_Olist_Olist__size(X4,X228,X224))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osize_I2_J)). 4.02/4.27 fof(fact_lazy__sequence_Osize_I2_J, axiom, ![X118, X26, X228, X4]:hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X4,X228),c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X26,X118))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X228,X26)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X4,X228),X118))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Osize_I2_J)). 4.02/4.27 fof(fact_Range__Collect__split, axiom, ![X56, X4, X7]:hAPP(c_Relation_ORange(X7,X4),hAPP(c_Set_OCollect(tc_prod(X7,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X4,tc_HOL_Obool),X56)))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X7)),hAPP(c_COMBC(X7,X4,tc_HOL_Obool),X56))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Collect__split)). 4.02/4.27 fof(fact_Field__Union, axiom, ![X39, X4]:hAPP(c_Relation_OField(X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),X39))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),c_Relation_OField(X4)),X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__Union)). 4.02/4.27 fof(fact_com_Osize_I13_J, axiom, ![X73, X74, X75]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X74)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X73))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X75,X74,X73)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I13_J)). 4.02/4.27 fof(fact_Pow__def, axiom, ![X3, X4]:hAPP(c_Set_OPow(X4),X3)=hAPP(c_Set_OCollect(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool))),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__def)). 4.02/4.27 fof(fact_vimage__compose, axiom, ![X9, X22, X76, X49, X7, X4]:hAPP(c_Set_Ovimage(X4,X7,hAPP(c_Fun_Ocomp(X49,X7,X4,X76),X22)),X9)=hAPP(c_Set_Ovimage(X4,X49,X22),hAPP(c_Set_Ovimage(X49,X7,X76),X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__compose)). 4.02/4.27 fof(fact_vimage__Compl, axiom, ![X3, X22, X7, X4]:hAPP(c_Set_Ovimage(X4,X7,X22),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X7,X22),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Compl)). 4.02/4.27 fof(fact_divmod__nat__div__mod, axiom, ![X5, X2]:hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X5)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5))=c_Divides_Odivmod__nat(X2,X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__div__mod)). 4.02/4.27 fof(fact_com_Osize_I5_J, axiom, ![X73, X74, X75]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X74)),c_Com_Ocom_Ocom__size(X73))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X75,X74,X73)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I5_J)). 4.02/4.27 fof(fact_image__vimage__eq, axiom, ![X3, X22, X4, X7]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(c_Set_Oimage(X7,X4,X22),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))=hAPP(c_Set_Oimage(X7,X4,X22),hAPP(c_Set_Ovimage(X7,X4,X22),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__vimage__eq)). 4.02/4.27 fof(fact_anamorph_Osimps, axiom, ![X9, X22, X4, X7, X28]:((hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X7,X4,X22),X28),X9)=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),X7),c_List_Olist_ONil(X4)),X9)<=X28=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X28=>hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X7,X4,X22),X28),X9)=hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X4),X7),tc_prod(X4,X7),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),X7),c_List_Olist_ONil(X4)),X9),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_prod(tc_List_Olist(X4),X7)),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_prod(tc_List_Olist(X4),X7)),tc_fun(X7,tc_prod(tc_List_Olist(X4),X7))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X4),X7),tc_prod(tc_List_Olist(X4),X7)),tc_fun(tc_fun(X7,tc_prod(tc_List_Olist(X4),X7)),tc_fun(X7,tc_prod(tc_List_Olist(X4),X7))),X4),c_COMBB(tc_prod(tc_List_Olist(X4),X7),tc_prod(tc_List_Olist(X4),X7),X7)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_fun(X7,tc_prod(tc_List_Olist(X4),X7))),tc_fun(tc_prod(tc_List_Olist(X4),X7),tc_prod(tc_List_Olist(X4),X7)),X4),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X4),X7,tc_prod(tc_List_Olist(X4),X7))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_List_Olist(X4),tc_fun(X7,tc_prod(tc_List_Olist(X4),X7))),X4),hAPP(c_COMBB(tc_List_Olist(X4),tc_fun(X7,tc_prod(tc_List_Olist(X4),X7)),tc_List_Olist(X4)),c_Product__Type_OPair(tc_List_Olist(X4),X7))),c_List_Olist_OCons(X4))))),hAPP(c_Lazy__Sequence_Oanamorph(X7,X4,X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X28),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(X22,X9)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_anamorph_Osimps)). 4.02/4.27 fof(fact_relpow_Osimps_I1_J, axiom, ![X39, X4]:hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X39)=c_Relation_OId(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_relpow_Osimps_I1_J)). 4.02/4.27 fof(fact_lenlex__conv, axiom, ![X18, X4]:c_List_Olenlex(X4,X18)=hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X4),tc_List_Olist(X4),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBS(tc_List_Olist(X4),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X4)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_Nat_Onat),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X4),tc_Nat_Onat),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X4))))),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBS(tc_List_Olist(X4),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X4)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_Nat_Onat),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X4),tc_Nat_Onat),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X4))))),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_fun(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBC(tc_List_Olist(X4),tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),tc_fun(tc_List_Olist(X4),tc_fun(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X4)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X4)),c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))))),c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4))))),c_List_Olex(X4,X18)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lenlex__conv)). 4.02/4.27 fof(fact_set__Cons__def, axiom, ![X230, X3, X4]:c_List_Oset__Cons(X4,X3,X230)=hAPP(c_Set_OCollect(tc_List_Olist(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X4)),c_HOL_OEx(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool),tc_List_Olist(X4)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(tc_List_Olist(X4)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool))),tc_fun(tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool))),tc_List_Olist(X4)),c_COMBS(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X4,tc_fun(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool))),tc_List_Olist(X4)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),X4),c_COMBS(tc_List_Olist(X4),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X4)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_List_Olist(X4))),tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_List_Olist(X4))),tc_fun(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool))),tc_List_Olist(X4)),c_COMBB(tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_List_Olist(X4),tc_HOL_Obool),X4)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBB(tc_List_Olist(X4),tc_HOL_Obool,tc_List_Olist(X4))),c_fequal))),c_List_Olist_OCons(X4)))))),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X4))),X230)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__Cons__def)). 4.02/4.27 fof(fact_rel__comp__def, axiom, ![X40, X18, X7, X49, X4]:hAPP(c_Set_OCollect(tc_prod(X4,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X49,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_COMBB(tc_fun(X49,tc_HOL_Obool),tc_HOL_Obool,X7),c_HOL_OEx(X49))),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_fun(X49,tc_HOL_Obool)),tc_fun(X7,tc_fun(X49,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X49,tc_HOL_Obool),tc_fun(X49,tc_HOL_Obool)),tc_fun(tc_fun(X7,tc_fun(X49,tc_HOL_Obool)),tc_fun(X7,tc_fun(X49,tc_HOL_Obool))),X4),c_COMBB(tc_fun(X49,tc_HOL_Obool),tc_fun(X49,tc_HOL_Obool),X7)),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X49,tc_HOL_Obool),tc_fun(X49,tc_HOL_Obool)),X4),c_COMBS(X49,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_HOL_Obool),tc_fun(X49,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X49),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X49),tc_HOL_Obool),tc_fun(X49,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_fun(tc_fun(tc_prod(X4,X49),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X49),tc_HOL_Obool),tc_fun(X49,tc_HOL_Obool)),X4),c_COMBC(X49,tc_fun(tc_prod(X4,X49),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_prod(X4,X49)),tc_fun(X49,tc_fun(tc_fun(tc_prod(X4,X49),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X49),tc_fun(tc_fun(tc_prod(X4,X49),tc_HOL_Obool),tc_HOL_Obool),X49),c_member(tc_prod(X4,X49)))),c_Product__Type_OPair(X4,X49)))),X18))))),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X49,X7),tc_HOL_Obool),tc_fun(X49,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_fun(tc_fun(tc_prod(X49,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X49,X7),tc_HOL_Obool),tc_fun(X49,tc_HOL_Obool)),X7),c_COMBC(X49,tc_fun(tc_prod(X49,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_prod(X49,X7)),tc_fun(X49,tc_fun(tc_fun(tc_prod(X49,X7),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X49,X7),tc_fun(tc_fun(tc_prod(X49,X7),tc_HOL_Obool),tc_HOL_Obool),X49),c_member(tc_prod(X49,X7)))),hAPP(c_COMBC(X49,X7,tc_prod(X49,X7)),c_Product__Type_OPair(X49,X7))))),X40)))))=hAPP(hAPP(c_Relation_Orel__comp(X4,X49,X7),X18),X40), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__def)). 4.02/4.27 fof(fact_Pow__Compl, axiom, ![X3, X4]:hAPP(c_Set_OCollect(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X4,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),c_COMBS(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X4,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X4,tc_HOL_Obool)),hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X3)),c_Set_OPow(X4)))))=hAPP(c_Set_OPow(X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__Compl)). 4.02/4.27 fof(fact_lexn_Osimps_I2_J, axiom, ![X20, X18, X4]:hAPP(c_List_Olexn(X4,X18),hAPP(c_Nat_OSuc,X20))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X4,tc_List_Olist(X4)),tc_prod(X4,tc_List_Olist(X4))),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),c_Product__Type_Omap__pair(tc_prod(X4,tc_List_Olist(X4)),tc_List_Olist(X4),tc_prod(X4,tc_List_Olist(X4)),tc_List_Olist(X4),hAPP(c_Product__Type_Oprod_Oprod__case(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)))),c_Wellfounded_Olex__prod(X4,tc_List_Olist(X4),X18,hAPP(c_List_Olexn(X4,X18),X20)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X4),tc_List_Olist(X4),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),tc_List_Olist(X4)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),hAPP(c_Nat_OSuc,X20))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),hAPP(c_Nat_OSuc,X20)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexn_Osimps_I2_J)). 4.02/4.27 fof(fact_set__zip, axiom, ![X31, X32, X7, X4]:hAPP(c_Set_OCollect(tc_prod(X4,X7)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X4,X7)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X4,X7),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X4,X7)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(X4,X7)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(X4,X7),tc_fun(tc_Nat_Onat,tc_prod(X4,X7)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X4,X7)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X4,X7)),c_COMBB(tc_prod(X4,X7),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X7,tc_prod(X4,X7)),hAPP(hAPP(c_COMBB(X4,tc_fun(X7,tc_prod(X4,X7)),tc_Nat_Onat),c_Product__Type_OPair(X4,X7)),hAPP(c_List_Onth(X4),X32))),hAPP(c_List_Onth(X7),X31)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31))))))=hAPP(c_List_Oset(tc_prod(X4,X7)),hAPP(hAPP(c_List_Ozip(X4,X7),X32),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__zip)). 4.02/4.27 fof(fact_map__add__map__of__foldr, axiom, ![X113, X21, X7, X4]:c_List_Ofoldr(tc_prod(X4,X7),tc_fun(X4,tc_Option_Ooption(X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_fun(tc_fun(X4,tc_Option_Ooption(X7)),tc_fun(X4,tc_Option_Ooption(X7)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_Option_Ooption(X7)),tc_fun(X7,tc_fun(tc_fun(X4,tc_Option_Ooption(X7)),tc_fun(X4,tc_Option_Ooption(X7))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X7),tc_fun(tc_fun(X4,tc_Option_Ooption(X7)),tc_fun(X4,tc_Option_Ooption(X7)))),tc_fun(tc_fun(X7,tc_Option_Ooption(X7)),tc_fun(X7,tc_fun(tc_fun(X4,tc_Option_Ooption(X7)),tc_fun(X4,tc_Option_Ooption(X7))))),X4),c_COMBB(tc_Option_Ooption(X7),tc_fun(tc_fun(X4,tc_Option_Ooption(X7)),tc_fun(X4,tc_Option_Ooption(X7))),X7)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_Option_Ooption(X7)),tc_fun(tc_Option_Ooption(X7),tc_fun(X4,tc_Option_Ooption(X7)))),tc_fun(tc_Option_Ooption(X7),tc_fun(tc_fun(X4,tc_Option_Ooption(X7)),tc_fun(X4,tc_Option_Ooption(X7)))),X4),c_COMBC(tc_fun(X4,tc_Option_Ooption(X7)),tc_Option_Ooption(X7),tc_fun(X4,tc_Option_Ooption(X7)))),hAPP(c_COMBC(tc_fun(X4,tc_Option_Ooption(X7)),X4,tc_fun(tc_Option_Ooption(X7),tc_fun(X4,tc_Option_Ooption(X7)))),c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)))))),c_Option_Ooption_OSome(X7))),X113,X21)=c_Map_Omap__add(X4,X7,X21,hAPP(c_Map_Omap__of(X4,X7),X113)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__map__of__foldr)). 4.02/4.27 fof(fact_divmod__int__rel__def, axiom, ![X25, X26]: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,X26))),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),X25)))))),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)),X25))),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)),X25))))),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)),X25)))),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),X25))),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(X26,X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__def)). 4.02/4.27 fof(fact_set__sublist, axiom, ![X41, X32, X4]:hAPP(c_List_Oset(X4),c_List_Osublist(X4,X32,X41))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X4),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_Nat_Onat,X4),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X4),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X4),X32))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X41))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__sublist)). 4.02/4.27 fof(fact_inv__image__def, axiom, ![X22, X18, X4, X7]:hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X7,X7)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X7,X7),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X7,X7)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X7),tc_fun(X4,tc_prod(X7,X7))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X7,X7)),tc_fun(tc_fun(X4,X7),tc_fun(X4,tc_prod(X7,X7))),X4),c_COMBB(X7,tc_prod(X7,X7),X4)),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,tc_prod(X7,X7)),X4),c_Product__Type_OPair(X7,X7)),X22))),X22)))),X18)))=hAPP(hAPP(c_Relation_Oinv__image(X7,X4),X18),X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inv__image__def)). 4.02/4.27 fof(fact_lazy__sequence__size__code, axiom, ![X143, X40, X4]:hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X4,X40),X143)=hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X4,tc_Lazy__Sequence_Olazy__sequence(X4)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X4,tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat),hAPP(hAPP(c_COMBC(X4,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat)),X4),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X4),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X4)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat)),X4),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X4))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X40))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X4,X40))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X4),X143)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence__size__code)). 4.02/4.27 fof(fact_seq__case, axiom, ![X143, X76, X22, X7, X4]:hAPP(c_Option_Ooption_Ooption__case(X4,tc_prod(X7,tc_Lazy__Sequence_Olazy__sequence(X7)),X22,hAPP(c_Product__Type_Oprod_Oprod__case(X7,tc_Lazy__Sequence_Olazy__sequence(X7),X4),X76)),hAPP(c_Lazy__Sequence_Oyield(X7),X143))=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X4,X7,X22,X76,X143), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_seq__case)). 4.02/4.27 fof(fact_set__conv__nth, axiom, ![X32, X4]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X4),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_Nat_Onat,X4),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X4),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X4),c_COMBB(X4,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X4),X32))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))))=hAPP(c_List_Oset(X4),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__conv__nth)). 4.02/4.27 fof(fact_finite__psubset__def, axiom, ![X4]:hAPP(c_Set_OCollect(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),c_COMBS(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X4))))=c_Wellfounded_Ofinite__psubset(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__psubset__def)). 4.02/4.27 fof(fact_converse__def, axiom, ![X18, X4, X7]:hAPP(c_Set_OCollect(tc_prod(X4,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X7,X4),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X4),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBC(X7,tc_fun(tc_prod(X7,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X7,X4)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X7,X4),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X7,X4),tc_fun(tc_fun(tc_prod(X7,X4),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X7,X4)))),hAPP(c_COMBC(X7,X4,tc_prod(X7,X4)),c_Product__Type_OPair(X7,X4))))),X18)))=hAPP(c_Relation_Oconverse(X7,X4),X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__def)). 4.02/4.27 fof(fact_nat__def, axiom, ![X16]:hAPP(c_Int_Onat,X16)=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,X16)),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)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__def)). 4.02/4.27 fof(fact_INTER__def, axiom, ![X6, X3, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X3),X6)=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OAll(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_COMBS(X7,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fimplies),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X3)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_fun(X4,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X7,tc_fun(X4,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X7)),c_member(X4))),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INTER__def)). 4.02/4.27 fof(fact_quotient__def, axiom, ![X18, X3, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X4),c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X4),c_Relation_OImage(X4,X4,X18)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X3),X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotient__def)). 4.02/4.27 fof(fact_image__eq__UN, axiom, ![X3, X22, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X7,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X7),c_Set_Oinsert(X4)),X22)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=hAPP(c_Set_Oimage(X7,X4,X22),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__eq__UN)). 4.02/4.27 fof(fact_set__n__lists, axiom, ![X32, X20, X4]:hAPP(c_List_Oset(tc_List_Olist(X4)),c_Enum_On__lists(X4,X20,X32))=hAPP(c_Set_OCollect(tc_List_Olist(X4)),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),X20))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X4)),c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool))),c_List_Oset(X4))),hAPP(c_List_Oset(X4),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__n__lists)). 4.02/4.27 fof(fact_zip__map__map, axiom, ![X31, X76, X126, X32, X22, X49, X7, X4]:hAPP(hAPP(c_List_Omap(tc_prod(X49,X126),tc_prod(X4,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X49,X126,tc_prod(X4,X7)),hAPP(hAPP(c_COMBC(X49,tc_fun(X126,X7),tc_fun(X126,tc_prod(X4,X7))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(tc_fun(X126,X7),tc_fun(X126,tc_prod(X4,X7))),X49),c_COMBB(X7,tc_prod(X4,X7),X126)),hAPP(hAPP(c_COMBB(X4,tc_fun(X7,tc_prod(X4,X7)),X49),c_Product__Type_OPair(X4,X7)),X22))),X76))),hAPP(hAPP(c_List_Ozip(X49,X126),X32),X31))=hAPP(hAPP(c_List_Ozip(X4,X7),hAPP(hAPP(c_List_Omap(X49,X4),X22),X32)),hAPP(hAPP(c_List_Omap(X126,X7),X76),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__map__map)). 4.02/4.27 fof(fact_map__pair__def, axiom, ![X76, X22, X126, X7, X49, X4]:hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_prod(X49,X126)),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,X126),tc_fun(X7,tc_prod(X49,X126))),hAPP(hAPP(c_COMBB(tc_fun(X126,tc_prod(X49,X126)),tc_fun(tc_fun(X7,X126),tc_fun(X7,tc_prod(X49,X126))),X4),c_COMBB(X126,tc_prod(X49,X126),X7)),hAPP(hAPP(c_COMBB(X49,tc_fun(X126,tc_prod(X49,X126)),X4),c_Product__Type_OPair(X49,X126)),X22))),X76))=c_Product__Type_Omap__pair(X4,X49,X7,X126,X22,X76), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__def)). 4.02/4.27 fof(fact_add, axiom, ![X64, X115, X17, X9]: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),X9),X115)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X64))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))=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),X9),X17)),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),X115),X64)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add)). 4.02/4.27 fof(fact_n__lists_Osimps_I2_J, axiom, ![X32, X20, X4]:c_Enum_On__lists(X4,hAPP(c_Nat_OSuc,X20),X32)=c_List_Oconcat(tc_List_Olist(X4),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_List_Olist(X4)),tc_fun(tc_List_Olist(X4),tc_List_Olist(tc_List_Olist(X4))),tc_List_Olist(X4)),c_List_Omap(X4,tc_List_Olist(X4))),hAPP(c_COMBC(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)))),X32)),c_Enum_On__lists(X4,X20,X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_n__lists_Osimps_I2_J)). 4.02/4.27 fof(fact_dom__override__on, axiom, ![X3, X76, X22, X7, X4]:c_Map_Odom(X4,X7,c_Fun_Ooverride__on(X4,tc_Option_Ooption(X7),X22,X76,X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X7,X22)),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),c_Map_Odom(X4,X7,X76)))))),hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),c_Map_Odom(X4,X7,X76))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__override__on)). 4.02/4.27 fof(fact_Id__on__def, axiom, ![X3, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X4),c_Set_Oinsert(tc_prod(X4,X4))),hAPP(hAPP(c_COMBS(X4,X4,tc_prod(X4,X4)),c_Product__Type_OPair(X4,X4)),c_COMBI(X4)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))))=c_Relation_OId__on(X4,X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__def)). 4.02/4.27 fof(fact_transfer__int__nat__numerals_I3_J, axiom, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(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_OBit0(c_Int_OBit1(c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__numerals_I3_J)). 4.02/4.27 fof(fact_Eps__split__eq, axiom, ![X17, X9, X7, X4]:hAPP(hAPP(c_Product__Type_OPair(X4,X7),X9),X17)=c_Hilbert__Choice_OEps(tc_prod(X4,X7),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(c_fequal,X9)))),hAPP(c_fequal,X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Eps__split__eq)). 4.02/4.27 fof(fact_UN__UN__finite__eq, axiom, ![X3, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X3))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__UN__finite__eq)). 4.02/4.27 fof(fact_UN__extend__simps_I9_J, axiom, ![X8, X6, X49, X3, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X49,tc_HOL_Obool)),X3),X6)),X8)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X7,tc_fun(X49,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_HOL_Obool),tc_fun(tc_fun(X49,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),X7),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,tc_fun(X4,tc_HOL_Obool))),X6)),X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__extend__simps_I9_J)). 4.02/4.27 fof(fact_sublist__Cons, axiom, ![X3, X60, X9, X4]:hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X4)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)),hAPP(hAPP(c_List_Olist_OCons(X4),X9),c_List_Olist_ONil(X4))),c_List_Olist_ONil(X4))),c_List_Osublist(X4,X60,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)),X3))))=c_List_Osublist(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X60),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__Cons)). 4.02/4.27 fof(fact_lists__Int__eq, axiom, ![X6, X3, X4]:c_List_Olistsp(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X3)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X6)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X4))),c_List_Olists(X4,X3))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X4))),c_List_Olists(X4,X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__Int__eq)). 4.02/4.27 fof(fact_Un__Int__crazy, axiom, ![X8, X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X6),X8))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X8),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X6),X8))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X8),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Int__crazy)). 4.02/4.27 fof(fact_Int__assoc, axiom, ![X8, X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X6),X8))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)),X8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__assoc)). 4.02/4.27 fof(fact_transfer__int__nat__numerals_I4_J, axiom, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__numerals_I4_J)). 4.02/4.27 fof(fact_lenlex__def, axiom, ![X18, X4]:c_List_Olenlex(X4,X18)=hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X4)),tc_List_Olist(X4)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X4),c_Wellfounded_Oless__than,c_List_Olex(X4,X18))),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_List_Olist(X4),tc_prod(tc_Nat_Onat,tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X4),tc_prod(tc_Nat_Onat,tc_List_Olist(X4))),tc_List_Olist(X4)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X4))),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),c_COMBI(tc_List_Olist(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lenlex__def)). 4.02/4.27 fof(fact_mlex__prod__def, axiom, ![X39, X22, X4]:hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X4),X4),c_Wellfounded_Olex__prod(tc_Nat_Onat,X4,c_Wellfounded_Oless__than,X39)),hAPP(hAPP(c_COMBS(X4,X4,tc_prod(tc_Nat_Onat,X4)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X4,tc_prod(tc_Nat_Onat,X4)),X4),c_Product__Type_OPair(tc_Nat_Onat,X4)),X22)),c_COMBI(X4)))=c_Wellfounded_Omlex__prod(X4,X22,X39), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mlex__prod__def)). 4.02/4.27 fof(fact_sublist__append, axiom, ![X3, X252, X60, X4]:hAPP(hAPP(c_List_Oappend(X4),c_List_Osublist(X4,X60,X3)),c_List_Osublist(X4,X252,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X60)))),X3))))=c_List_Osublist(X4,hAPP(hAPP(c_List_Oappend(X4),X60),X252),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__append)). 4.02/4.27 fof(fact_size__code, axiom, ![X143, X4]:hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X4)),X143)=hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X4,tc_Lazy__Sequence_Olazy__sequence(X4)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X4,tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat),X4),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X4),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X4)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X4)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(c_Lazy__Sequence_Oyield(X4),X143)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_size__code)). 4.02/4.27 fof(fact_minus, axiom, ![X17, X9]: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),X17),X9)),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),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),X9),X17)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus)). 4.02/4.27 fof(fact_select__def, axiom, ![X32, X4]:c_Random_Oselect(X4,X32)=hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))),hAPP(hAPP(c_COMBB(X4,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X4),X32)),c_Code__Numeral_Onat__of))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__def)). 4.02/4.27 fof(fact_length__filter__conv__card, axiom, ![X32, X51, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Ofilter(X4,X51),X32))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))),hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,tc_Nat_Onat),X51),hAPP(c_List_Onth(X4),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__filter__conv__card)). 4.02/4.27 fof(fact_vimage__Times, axiom, ![X6, X3, X22, X49, X7, X4]:hAPP(c_Set_Ovimage(X4,tc_prod(X7,X49),X22),hAPP(hAPP(c_Product__Type_OSigma(X7,X49),X3),hAPP(c_COMBK(tc_fun(X49,tc_HOL_Obool),X7),X6)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X7,hAPP(c_Fun_Ocomp(tc_prod(X7,X49),X7,X4,c_Product__Type_Ofst(X7,X49)),X22)),X3)),hAPP(c_Set_Ovimage(X4,X49,hAPP(c_Fun_Ocomp(tc_prod(X7,X49),X49,X4,c_Product__Type_Osnd(X7,X49)),X22)),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Times)). 4.02/4.27 fof(fact_map__filter__def, axiom, ![X32, X22, X4, X7]:hAPP(hAPP(c_List_Omap(X7,X4),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X4),X4,X7,c_Option_Othe(X4)),X22)),hAPP(c_List_Ofilter(X7,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7),c_fNot),hAPP(hAPP(c_COMBC(X7,tc_Option_Ooption(X4),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X4),tc_fun(tc_Option_Ooption(X4),tc_HOL_Obool),X7),c_fequal),X22)),c_Option_Ooption_ONone(X4)))),X32))=c_List_Omap__filter(X7,X4,X22,X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__filter__def)). 4.02/4.27 fof(fact_UN__simps_I2_J, axiom, ![X6, X3, X7, X4, X8]:((c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool))),X3)),X6))<=X8=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X8=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool))),X3)),X6))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),X3)),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I2_J)). 4.02/4.27 fof(fact_ran__def, axiom, ![X21, X4, X7]:c_Map_Oran(X7,X4,X21)=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X7)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X4),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_COMBC(X7,tc_Option_Ooption(X4),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X4),tc_fun(tc_Option_Ooption(X4),tc_HOL_Obool),X7),c_fequal),X21))),c_Option_Ooption_OSome(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ran__def)). 4.02/4.27 fof(fact_concat__map__singleton, axiom, ![X32, X22, X7, X4]:c_List_Oconcat(X4,hAPP(hAPP(c_List_Omap(X7,tc_List_Olist(X4)),hAPP(hAPP(c_COMBC(X7,tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_COMBB(X4,tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),X7),c_List_Olist_OCons(X4)),X22)),c_List_Olist_ONil(X4))),X32))=hAPP(hAPP(c_List_Omap(X7,X4),X22),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__map__singleton)). 4.02/4.27 fof(fact_listrel__Cons, axiom, ![X32, X9, X18, X4]:hAPP(c_Relation_OImage(tc_List_Olist(X4),tc_List_Olist(X4),c_List_Olistrel(X4,X18)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X4),tc_HOL_Obool))))=c_List_Oset__Cons(X4,hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X4),tc_List_Olist(X4),c_List_Olistrel(X4,X18)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X4)),X32),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X4),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Cons)). 4.02/4.27 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, axiom, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J)). 4.02/4.27 fof(fact_card__UNIV__bool, axiom, hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__UNIV__bool)). 4.02/4.27 fof(fact_int__ge__less__than2__def, axiom, ![X102]:c_Int_Oint__ge__less__than2(X102)=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),X102)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__ge__less__than2__def)). 4.02/4.27 fof(fact_zdiv__zadd1__eq, axiom, ![X10, X12, X11]: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),X11),X10)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X10))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X10)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X10))),X10))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11),X12)),X10), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zadd1__eq)). 4.02/4.27 fof(fact_div__add1__eq, axiom, ![X10, X12, X11]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11),X12)),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X11),X10)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X12),X10))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X11,X10)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10))),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__add1__eq)). 4.02/4.27 fof(fact_rotate__rev, axiom, ![X45, X5, X4]:hAPP(c_List_Orotate(X4,X5),hAPP(c_List_Orev(X4),X45))=hAPP(c_List_Orev(X4),hAPP(c_List_Orotate(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__rev)). 4.02/4.27 fof(fact_insert__Collect, axiom, ![X56, X26, X4]:hAPP(hAPP(c_Set_Oinsert(X4),X26),hAPP(c_Set_OCollect(X4),X56))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X26)))),X56)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__Collect)). 4.02/4.27 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, axiom, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J)). 4.02/4.27 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J, axiom, c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J)). 4.02/4.27 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J, axiom, ![X56]: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),X56),c_Int_Onat))))=hAPP(c_Set_OCollect(tc_Nat_Onat),X56), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J)). 4.02/4.27 fof(fact_set__filter, axiom, ![X32, X56, X4]:hAPP(c_List_Oset(X4),hAPP(c_List_Ofilter(X4,X56),X32))=hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),hAPP(c_List_Oset(X4),X32)))),X56)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__filter)). 4.02/4.27 fof(fact_rotate__drop__take, axiom, ![X45, X5, X4]:hAPP(c_List_Orotate(X4,X5),X45)=hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Odrop(X4),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45))),X45)),hAPP(hAPP(c_List_Otake(X4),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45))),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__drop__take)). 4.02/4.27 fof(fact_zadd__left__commute, axiom, ![X29, X43, X13]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X43),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13),X29))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X43),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__left__commute)). 4.02/4.27 fof(fact_nat, axiom, ![X17, X9]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9),X17)=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),X9),X17)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat)). 4.02/4.27 fof(fact_The__split, axiom, ![X56, X7, X4]:c_HOL_OThe(tc_prod(X4,X7),hAPP(hAPP(c_COMBS(tc_prod(X4,X7),X7,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X4,tc_fun(X7,tc_HOL_Obool),tc_prod(X4,X7)),X56),c_Product__Type_Ofst(X4,X7))),c_Product__Type_Osnd(X4,X7)))=c_HOL_OThe(tc_prod(X4,X7),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_HOL_Obool),X56)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_The__split)). 4.02/4.27 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J, axiom, ![X56]: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),X56),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)))),X56)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J)). 4.02/4.27 fof(fact_singleton__quotient, axiom, ![X18, X9, X4]:hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X18)=hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_singleton__quotient)). 4.02/4.27 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J, axiom, c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J)). 4.02/4.27 fof(fact_int__def, axiom, ![X21]: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),X21),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__def)). 4.02/4.27 fof(fact_rev__map, axiom, ![X32, X22, X7, X4]:hAPP(c_List_Orev(X4),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32))=hAPP(hAPP(c_List_Omap(X7,X4),X22),hAPP(c_List_Orev(X7),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__map)). 4.02/4.27 fof(fact_Field__insert, axiom, ![X18, X25, X26, X4]:hAPP(c_Relation_OField(X4),hAPP(hAPP(c_Set_Oinsert(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),X18))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X26),hAPP(hAPP(c_Set_Oinsert(X4),X25),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),hAPP(c_Relation_OField(X4),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__insert)). 4.02/4.27 fof(fact_eq__Abs__Integ, axiom, ![X16]:~(![X19, X34]:X16!=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),X19),X34)),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)). 4.02/4.27 fof(fact_rotate__rotate, axiom, ![X45, X5, X2, X4]:hAPP(c_List_Orotate(X4,X2),hAPP(c_List_Orotate(X4,X5),X45))=hAPP(c_List_Orotate(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X5)),X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__rotate)). 4.02/4.27 fof(fact_the__elem__def, axiom, ![X156, X4]:c_HOL_OThe(X4,hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool,X4),hAPP(c_fequal,X156)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=c_Set_Othe__elem(X4,X156), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__elem__def)). 4.02/4.27 fof(fact_O__assoc, axiom, ![X105, X86, X39, X126, X7, X49, X4]:hAPP(hAPP(c_Relation_Orel__comp(X4,X49,X7),hAPP(hAPP(c_Relation_Orel__comp(X4,X126,X49),X39),X86)),X105)=hAPP(hAPP(c_Relation_Orel__comp(X4,X126,X7),X39),hAPP(hAPP(c_Relation_Orel__comp(X126,X49,X7),X86),X105)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_O__assoc)). 4.02/4.27 fof(fact_sum__length__filter__compl, axiom, ![X32, X56, X4]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Ofilter(X4,X56),X32))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Ofilter(X4,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),X56)),X32)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__length__filter__compl)). 4.02/4.27 fof(fact_length__append, axiom, ![X59, X45, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Oappend(X4),X45),X59))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__append)). 4.02/4.27 fof(fact_finite__M__bounded__by__nat, axiom, ![X37, X56]: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),X56)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X37))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__M__bounded__by__nat)). 4.02/4.27 fof(fact_vimage__UN, axiom, ![X6, X3, X49, X22, X7, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X49),c_Set_Ovimage(X4,X7,X22)),X6))=hAPP(c_Set_Ovimage(X4,X7,X22),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,tc_fun(X7,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__UN)). 4.02/4.27 fof(fact_Diff__Un, axiom, ![X8, X6, X3, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X6),X8))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Un)). 4.02/4.27 fof(fact_vimage__INT, axiom, ![X6, X3, X49, X22, X7, X4]:hAPP(c_Set_Ovimage(X4,X7,X22),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X49,tc_fun(X7,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X49,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X49),c_Set_Ovimage(X4,X7,X22)),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__INT)). 4.02/4.27 fof(fact_UN__simps_I3_J, axiom, ![X6, X3, X7, X4, X8]:((hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3)),X6))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),X6))<=X8!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3)),X6))=c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))<=X8=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I3_J)). 4.02/4.27 fof(fact_Diff__Int__distrib, axiom, ![X6, X3, X8, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X8),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X8),X6))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Int__distrib)). 4.02/4.27 fof(fact_lexord__append__rightI, axiom, ![X18, X9, X4, X17]:(?[X78, X36]:X17=hAPP(hAPP(c_List_Olist_OCons(X4),X78),X36)=>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)),X9),hAPP(hAPP(c_List_Oappend(X4),X9),X17))),c_List_Olexord(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__append__rightI)). 4.02/4.27 fof(fact_filter__concat, axiom, ![X32, X51, X4]:c_List_Oconcat(X4,hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Ofilter(X4,X51)),X32))=hAPP(c_List_Ofilter(X4,X51),c_List_Oconcat(X4,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__concat)). 4.02/4.27 fof(fact_Int__eq__Inter, axiom, ![X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)=c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__eq__Inter)). 4.02/4.27 fof(fact_Un__eq__Union, axiom, ![X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)=c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__eq__Union)). 4.02/4.27 fof(fact_UN__simps_I1_J, axiom, ![X6, X26, X7, X4, X8]:((hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_Set_Oinsert(X7),X26)),X6))=hAPP(hAPP(c_Set_Oinsert(X7),X26),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),X6))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X8)&(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_Set_Oinsert(X7),X26)),X6))=c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))<=X8=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I1_J)). 4.02/4.27 fof(fact_prod__size__simp, axiom, ![X51, X76, X22, X7, X4]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X22,hAPP(c_Product__Type_Ofst(X4,X7),X51))),hAPP(X76,hAPP(c_Product__Type_Osnd(X4,X7),X51)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Product__Type_Oprod_Oprod__size(X4,X7,X22,X76,X51), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_prod__size__simp)). 4.02/4.27 fof(fact_lexord__Nil__left, axiom, ![X18, X17, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_ONil(X4)),X17)),c_List_Olexord(X4,X18)))<=>?[X27, X19]:hAPP(hAPP(c_List_Olist_OCons(X4),X27),X19)=X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__Nil__left)). 4.02/4.27 fof(fact_map__append, axiom, ![X31, X32, X22, X4, X7]:hAPP(hAPP(c_List_Omap(X7,X4),X22),hAPP(hAPP(c_List_Oappend(X7),X32),X31))=hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32)),hAPP(hAPP(c_List_Omap(X7,X4),X22),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__append)). 4.02/4.27 fof(fact_pdivmod__def, axiom, ![X47, X107]: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),X107)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X47))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X107),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X47)))=c_Divides_Opdivmod(X107,X47), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pdivmod__def)). 4.02/4.27 fof(fact_divmod__int__mod__div, axiom, ![X14, X15]:c_Divides_Odivmod__int(X15,X14)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X15),X14)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__mod__div)). 4.02/4.27 fof(fact_listrel__Nil, axiom, ![X18, X4]:hAPP(c_Relation_OImage(tc_List_Olist(X4),tc_List_Olist(X4),c_List_Olistrel(X4,X18)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X4),tc_HOL_Obool))))=hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X4),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Nil)). 4.02/4.27 fof(fact_rev__rev__ident, axiom, ![X45, X4]:X45=hAPP(c_List_Orev(X4),hAPP(c_List_Orev(X4),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__rev__ident)). 4.02/4.27 fof(fact_mod__mult2__eq, axiom, ![X10, X12, X11]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X11),X12),X10))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X11,X12))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult2__eq)). 4.02/4.27 fof(fact_rotate__conv__mod, axiom, ![X45, X5, X4]:hAPP(c_List_Orotate(X4,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45))),X45)=hAPP(c_List_Orotate(X4,X5),X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__conv__mod)). 4.02/4.27 fof(fact_max__Suc2, axiom, ![X20, X21]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X21),hAPP(c_Nat_OSuc,X20))=c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X20),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)),X20)),X21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__Suc2)). 4.02/4.27 fof(fact_Union__Un__distrib, axiom, ![X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X3)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X6))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__Un__distrib)). 4.02/4.27 fof(fact_Union__insert, axiom, ![X6, X26, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X26),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X6))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),X26),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__insert)). 4.02/4.27 fof(fact_Inter__Un__distrib, axiom, ![X6, X3, X4]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X3)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__Un__distrib)). 4.02/4.27 fof(fact_Inter__insert, axiom, ![X6, X26, X4]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),X26),X6))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X26),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__insert)). 4.02/4.27 fof(fact_Compl__Un, axiom, ![X6, X3, X4]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__Un)). 4.02/4.27 fof(fact_vimage__Int, axiom, ![X6, X3, X22, X7, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X7,X22),X3)),hAPP(c_Set_Ovimage(X4,X7,X22),X6))=hAPP(c_Set_Ovimage(X4,X7,X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Int)). 4.02/4.27 fof(fact_vimage__Un, axiom, ![X6, X3, X22, X7, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X7,X22),X3)),hAPP(c_Set_Ovimage(X4,X7,X22),X6))=hAPP(c_Set_Ovimage(X4,X7,X22),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Un)). 4.02/4.27 fof(fact_vimage__Diff, axiom, ![X6, X3, X22, X7, X4]:hAPP(c_Set_Ovimage(X4,X7,X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X4,X7,X22),X3)),hAPP(c_Set_Ovimage(X4,X7,X22),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Diff)). 4.02/4.27 fof(fact_min__Suc2, axiom, ![X20, X21]: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)),X20)),X21)=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X21),hAPP(c_Nat_OSuc,X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__Suc2)). 4.02/4.27 fof(fact_rel__pow__commute, axiom, ![X20, X39, X4]:hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X20),X39)),X39)=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X39),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X20),X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__commute)). 4.02/4.27 fof(fact_relpow_Osimps_I2_J, axiom, ![X39, X20, X4]:hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),hAPP(c_Nat_OSuc,X20)),X39)=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X20),X39)),X39), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_relpow_Osimps_I2_J)). 4.02/4.27 fof(fact_image__Pow__surj, axiom, ![X6, X3, X22, X4, X7]:(X6=hAPP(c_Set_Oimage(X7,X4,X22),X3)=>hAPP(c_Set_OPow(X4),X6)=hAPP(c_Set_Oimage(tc_fun(X7,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),c_Set_Oimage(X7,X4,X22)),hAPP(c_Set_OPow(X7),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Pow__surj)). 4.02/4.27 fof(fact_dom__eq__singleton__conv, axiom, ![X9, X22, X7, X4]:(c_Map_Odom(X4,X7,X22)=hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=>?[X133]:X22=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),hAPP(c_COMBK(tc_Option_Ooption(X7),X4),c_Option_Ooption_ONone(X7))),X9),hAPP(c_Option_Ooption_OSome(X7),X133))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__eq__singleton__conv)). 4.02/4.27 fof(fact_New__DSequence_Oneg__bind__def, axiom, ![X37, X22, X9, X4, X7]:c_Lazy__Sequence_Ohb__bind(X7,X4,hAPP(X9,X37),hAPP(hAPP(c_COMBC(X7,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4))),X22),X37))=hAPP(c_New__DSequence_Oneg__bind(X7,X4,X9,X22),X37), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Oneg__bind__def)). 4.02/4.27 fof(fact_length__map, axiom, ![X32, X22, X7, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__map)). 4.02/4.27 fof(fact_refl__reflcl, axiom, ![X18, X4]:c_Relation_Orefl__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),c_Relation_OId(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__reflcl)). 4.02/4.27 fof(fact_vimage__Union, axiom, ![X3, X22, X7, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X7,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),c_Set_Ovimage(X4,X7,X22))=hAPP(c_Set_Ovimage(X4,X7,X22),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__Union)). 4.02/4.27 fof(fact_length__zip, axiom, ![X59, X45, X7, X4]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X59))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X4,X7))),hAPP(hAPP(c_List_Ozip(X4,X7),X45),X59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__zip)). 4.02/4.27 fof(fact_Domain__Collect__split, axiom, ![X56, X7, X4]:hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X4),c_HOL_OEx(X7)),X56))=hAPP(c_Relation_ODomain(X4,X7),hAPP(c_Set_OCollect(tc_prod(X4,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_HOL_Obool),X56))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Collect__split)). 4.02/4.27 fof(fact_set__concat, axiom, ![X32, X4]:hAPP(c_List_Oset(X4),c_List_Oconcat(X4,X32))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X4)),X32)),c_List_Oset(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__concat)). 4.02/4.27 fof(fact_transfer__int__nat__set__return__embed, axiom, ![X3]: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)),X3))=X3, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__return__embed)). 4.02/4.27 fof(fact_greaterThan__Suc, axiom, ![X28]:hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X28))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X28)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X28)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThan__Suc)). 4.02/4.27 fof(fact_rotate__Suc, axiom, ![X45, X5, X4]:hAPP(c_List_Orotate(X4,hAPP(c_Nat_OSuc,X5)),X45)=hAPP(c_List_Orotate1(X4),hAPP(c_List_Orotate(X4,X5),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__Suc)). 4.02/4.27 fof(fact_finite__dom__map__of, axiom, ![X60, X7, X4]:hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Map_Odom(X4,X7,hAPP(c_Map_Omap__of(X4,X7),X60)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__dom__map__of)). 4.02/4.27 fof(fact_map__of__Cons__code_I2_J, axiom, ![X318, X1, X49, X7, X107, X47]:((X107!=X47=>hAPP(hAPP(c_Map_Omap__of(X7,X49),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X7,X49)),hAPP(hAPP(c_Product__Type_OPair(X7,X49),X47),X1)),X318)),X107)=hAPP(hAPP(c_Map_Omap__of(X7,X49),X318),X107))&(X47=X107=>hAPP(c_Option_Ooption_OSome(X49),X1)=hAPP(hAPP(c_Map_Omap__of(X7,X49),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X7,X49)),hAPP(hAPP(c_Product__Type_OPair(X7,X49),X47),X1)),X318)),X107))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__Cons__code_I2_J)). 4.02/4.27 fof(fact_Pow__empty, axiom, ![X4]:hAPP(c_Set_OPow(X4),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__empty)). 4.02/4.27 fof(fact_UN__extend__simps_I1_J, axiom, ![X6, X26, X7, X4, X8]:((X8=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Set_Oinsert(X7),X26),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),X6))=hAPP(hAPP(c_Set_Oinsert(X7),X26),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))&(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X8=>hAPP(hAPP(c_Set_Oinsert(X7),X26),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_Set_Oinsert(X7),X26)),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__extend__simps_I1_J)). 4.02/4.27 fof(fact_zip__replicate, axiom, ![X43, X135, X13, X46, X7, X4]:c_List_Oreplicate(tc_prod(X4,X7),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X46),X135),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X13),X43))=hAPP(hAPP(c_List_Ozip(X4,X7),c_List_Oreplicate(X4,X46,X13)),c_List_Oreplicate(X7,X135,X43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__replicate)). 4.02/4.27 fof(fact_rtrancl__r__diff__Id, axiom, ![X18, X4]:c_Transitive__Closure_Ortrancl(X4,X18)=c_Transitive__Closure_Ortrancl(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),c_Relation_OId(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__r__diff__Id)). 4.02/4.27 fof(fact_rtrancl__reflcl__absorb, axiom, ![X39, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X39)),c_Relation_OId(X4))=c_Transitive__Closure_Ortrancl(X4,X39), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__reflcl__absorb)). 4.02/4.27 fof(fact_atLeast__Suc, axiom, ![X28]:hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X28))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X28)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X28),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast__Suc)). 4.02/4.27 fof(fact_atLeast__Suc__greaterThan, axiom, ![X28]:hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X28)=hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast__Suc__greaterThan)). 4.02/4.27 fof(fact_max__Suc1, axiom, ![X21, X20]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),X21)=c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X20),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),X20)),X21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__Suc1)). 4.02/4.27 fof(fact_takeWhile__dropWhile__id, axiom, ![X32, X56, X4]:hAPP(hAPP(c_List_Oappend(X4),c_List_OtakeWhile(X4,X56,X32)),c_List_OdropWhile(X4,X56,X32))=X32, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__dropWhile__id)). 4.02/4.27 fof(fact_map__nth, axiom, ![X32, X4]:X32=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X4),hAPP(c_List_Onth(X4),X32)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__nth)). 4.02/4.27 fof(fact_min__diff, axiom, ![X5, X46, X2]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X46)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),X46))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X2),X5)),X46), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__diff)). 4.02/4.27 fof(fact_UN__constant, axiom, ![X24, X7, X4, X3]:((hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X3),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),X24))=X24<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3)&(X3=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X3),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),X24)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__constant)). 4.02/4.27 fof(fact_min__Suc1, axiom, ![X21, X20]: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),X20)),X21)=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),X21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__Suc1)). 4.02/4.27 fof(fact_list_Osize_I4_J, axiom, ![X302, X11, X4]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X302)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X11),X302)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osize_I4_J)). 4.02/4.27 fof(fact_list__size__conv__listsum, axiom, ![X32, X22, X4]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X4,tc_Nat_Onat),X22),X32))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))=c_List_Olist_Olist__size(X4,X22,X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__size__conv__listsum)). 4.02/4.27 fof(fact_map__replicate__trivial, axiom, ![X37, X9, X4]:c_List_Oreplicate(X4,X37,X9)=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X4),hAPP(c_COMBK(X4,tc_Nat_Onat),X9)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__replicate__trivial)). 4.02/4.27 fof(fact_irrefl__diff__Id, axiom, ![X18, X4]:c_Relation_Oirrefl(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),c_Relation_OId(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_irrefl__diff__Id)). 4.02/4.27 fof(fact_pair__box_Osize_I1_J, axiom, ![X25, X26, X227, X228, X7, X4]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X228,X26)),hAPP(X227,X25))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Nitpick_Opair__box_Opair__box__size(X4,X7,X228,X227,c_Nitpick_Opair__box_OPairBox(X4,X7,X26,X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__box_Osize_I1_J)). 4.02/4.27 fof(fact_UN__extend__simps_I2_J, axiom, ![X6, X3, X7, X4, X8]:((X6=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),X3)),X6)<=X8=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X8=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),X3)),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool))),X3)),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__extend__simps_I2_J)). 4.02/4.27 fof(fact_UN__extend__simps_I3_J, axiom, ![X6, X3, X7, X4, X8]:((X3=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),X6))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X8)&(X8!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3)),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__extend__simps_I3_J)). 4.02/4.27 fof(fact_INT__extend__simps_I4_J, axiom, ![X6, X3, X7, X4, X8]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X3)),X6))<=X8!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(X3=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X8),X6))<=X8=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__extend__simps_I4_J)). 4.02/4.27 fof(fact_Suc__diff__diff, axiom, ![X107, X5, X2]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X5)),hAPP(c_Nat_OSuc,X107))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5)),X107), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__diff__diff)). 4.02/4.27 fof(fact_Times__empty, axiom, ![X6, X3, X7, X4]:((X3=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))=X6)<=>hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),X6))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X7),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Times__empty)). 4.02/4.27 fof(fact_image__vimage__subset, axiom, ![X3, X22, X7, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X4,X22),hAPP(c_Set_Ovimage(X7,X4,X22),X3))),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__vimage__subset)). 4.02/4.27 fof(fact_length__splice, axiom, ![X59, X45, X4]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X59))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Osplice(X4,X45,X59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__splice)). 4.02/4.27 fof(fact_vimage__UNIV, axiom, ![X22, X7, X4]:hAPP(c_Set_Ovimage(X4,X7,X22),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__UNIV)). 4.02/4.27 fof(fact_vimage__empty, axiom, ![X22, X7, X4]:c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X4,X7,X22),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__empty)). 4.02/4.27 fof(fact_vimage__id, axiom, ![X3, X4]:hAPP(c_Set_Ovimage(X4,X4,c_Fun_Oid(X4)),X3)=X3, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__id)). 4.02/4.27 fof(fact_vimage__ident, axiom, ![X203, X4]:X203=hAPP(c_Set_Ovimage(X4,X4,c_COMBI(X4)),X203), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_vimage__ident)). 4.02/4.27 fof(fact_drop__upt, axiom, ![X135, X46, X2]:c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X2),X135)=hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X2),c_List_Oupt(X46,X135)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__upt)). 4.02/4.27 fof(fact_card_Oempty, axiom, ![X4]:hAPP(c_Finite__Set_Ocard(X4),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card_Oempty)). 4.02/4.27 fof(fact_empty__iff, axiom, ![X24, X4]:~(hBOOL(hAPP(hAPP(c_member(X4),X24),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__iff)). 4.02/4.27 fof(fact_length__rotate, axiom, ![X45, X5, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Orotate(X4,X5),X45))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__rotate)). 4.02/4.27 fof(fact_map__comp__empty_I2_J, axiom, ![X9, X21, X49, X4, X7]:c_Map_Omap__comp(X7,X4,X49,hAPP(c_COMBK(tc_Option_Ooption(X4),X7),c_Option_Ooption_ONone(X4)),X21,X9)=c_Option_Ooption_ONone(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__comp__empty_I2_J)). 4.02/4.27 fof(fact_concat__replicate__trivial, axiom, ![X46, X4]:c_List_Oconcat(X4,c_List_Oreplicate(tc_List_Olist(X4),X46,c_List_Olist_ONil(X4)))=c_List_Olist_ONil(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_concat__replicate__trivial)). 4.02/4.27 fof(fact_zmod__zdiv__equality, axiom, ![X12, X11]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12))=X11, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zdiv__equality)). 4.02/4.27 fof(fact_one__div__nat__number__of, axiom, ![X131]: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),X131)))=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),X131)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__div__nat__number__of)). 4.02/4.27 fof(fact_lessThan__Suc__eq__insert__0, axiom, ![X20]:hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20))=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),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__Suc__eq__insert__0)). 4.02/4.27 fof(fact_nat__mult__div__cancel__disj, axiom, ![X5, X2, X107]:((hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X5))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X5)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X107)&(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),X107),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X5))<=X107=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__div__cancel__disj)). 4.02/4.27 fof(fact_mult__0, axiom, ![X5]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__0)). 4.02/4.27 fof(fact_Nitpick_Oint__gcd__def, axiom, ![X43, X13]:hAPP(hAPP(c_Nitpick_Oint__gcd,X13),X43)=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),X13)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Oint__gcd__def)). 4.02/4.27 fof(fact_converse__Id, axiom, ![X4]:hAPP(c_Relation_Oconverse(X4,X4),c_Relation_OId(X4))=c_Relation_OId(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__Id)). 4.02/4.27 fof(fact_length__sublists, axiom, ![X45, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),c_Enum_Osublists(X4,X45))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__sublists)). 4.02/4.27 fof(fact_Divides_Omod__div__equality_H, axiom, ![X5, X2]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X5)),X5))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Omod__div__equality_H)). 4.02/4.27 fof(fact_nat__mult__commute, axiom, ![X5, X2]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__commute)). 4.02/4.27 fof(fact_zmod__zdiv__equality_H, axiom, ![X5, X2]:c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X5)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X5)),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zdiv__equality_H)). 4.02/4.27 fof(fact_set__rotate, axiom, ![X32, X20, X4]:hAPP(c_List_Oset(X4),hAPP(c_List_Orotate(X4,X20),X32))=hAPP(c_List_Oset(X4),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__rotate)). 4.02/4.27 fof(fact_take__take, axiom, ![X45, X2, X5, X4]:hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X5),X2)),X45)=hAPP(hAPP(c_List_Otake(X4),X5),hAPP(hAPP(c_List_Otake(X4),X2),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__take)). 4.02/4.27 fof(fact_some__eq__trivial, axiom, ![X9, X4]:c_Hilbert__Choice_OEps(X4,hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X9))=X9, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_some__eq__trivial)). 4.02/4.27 fof(fact_lazy__sequence_Osize_I4_J, axiom, ![X260, X11, X4]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X4)),X260)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X4)),c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X11,X260)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Osize_I4_J)). 4.02/4.27 fof(fact_lists__empty, axiom, ![X4]:hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)))=c_List_Olists(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__empty)). 4.02/4.27 fof(fact_fold1Set__sing, axiom, ![X25, X26, X22, X4]:(X26=X25<=>hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,X22,hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1Set__sing)). 4.02/4.27 fof(fact_listset_Osimps_I1_J, axiom, ![X4]:c_List_Olistset(X4,c_List_Olist_ONil(tc_fun(X4,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X4),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listset_Osimps_I1_J)). 4.02/4.27 fof(fact_Id__O__R, axiom, ![X39, X7, X4]:X39=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X7),c_Relation_OId(X4)),X39), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__O__R)). 4.02/4.27 fof(fact_R__O__Id, axiom, ![X39, X7, X4]:X39=hAPP(hAPP(c_Relation_Orel__comp(X4,X7,X7),X39),c_Relation_OId(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_R__O__Id)). 4.02/4.27 fof(fact_nat__seg__image__imp__finite, axiom, ![X20, X22, X4, X3]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))<=hAPP(c_Set_Oimage(tc_Nat_Onat,X4,X22),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)),X20)))=X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__seg__image__imp__finite)). 4.02/4.27 fof(fact_in__set__conv__decomp, axiom, ![X32, X9, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))<=>?[X146, X258]:X32=hAPP(hAPP(c_List_Oappend(X4),X146),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X258))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__conv__decomp)). 4.02/4.27 fof(fact_butlast__list__update, axiom, ![X13, X45, X4, X107]:((hAPP(hAPP(c_List_Olist__update(X4,c_List_Obutlast(X4,X45)),X107),X13)=c_List_Obutlast(X4,hAPP(hAPP(c_List_Olist__update(X4,X45),X107),X13))<=X107!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X107=>c_List_Obutlast(X4,X45)=c_List_Obutlast(X4,hAPP(hAPP(c_List_Olist__update(X4,X45),X107),X13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast__list__update)). 4.02/4.27 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J, axiom, ![X20]: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),X20)))=hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SetInterval_Otransfer__nat__int__set__functions_I1_J)). 4.02/4.27 fof(fact_Plus__eq__empty__conv, axiom, ![X6, X3, X7, X4]:((X3=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))&c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))=X6)<=>c_Sum__Type_OPlus(X4,X7,X3,X6)=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X4,X7),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Plus__eq__empty__conv)). 4.02/4.27 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)). 4.02/4.27 fof(fact_finite__Collect__less__nat, axiom, ![X28]: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)),X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Collect__less__nat)). 4.02/4.27 fof(fact_finite__Collect__le__nat, axiom, ![X28]: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)),X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Collect__le__nat)). 4.02/4.27 fof(fact_one__code__numeral__code, axiom, c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__code__numeral__code)). 4.02/4.27 fof(fact_rev__singleton__conv, axiom, ![X9, X32, X4]:(X32=hAPP(hAPP(c_List_Olist_OCons(X4),X9),c_List_Olist_ONil(X4))<=>hAPP(c_List_Orev(X4),X32)=hAPP(hAPP(c_List_Olist_OCons(X4),X9),c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__singleton__conv)). 4.02/4.27 fof(fact_div__nat__def, axiom, ![X5, X2]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X5)=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X2,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__nat__def)). 4.02/4.27 fof(fact_atLeastLessThan__upto, axiom, ![X38, X37]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X37),X38)=hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X37,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X38),c_Groups_Oone__class_Oone(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__upto)). 4.02/4.27 fof(fact_length__upt, axiom, ![X135, X46]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X46,X135))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X135),X46), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__upt)). 4.02/4.27 fof(fact_take__replicate, axiom, ![X13, X107, X46, X4]:hAPP(hAPP(c_List_Otake(X4),X46),c_List_Oreplicate(X4,X107,X13))=c_List_Oreplicate(X4,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X46),X107),X13), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__replicate)). 4.02/4.27 fof(fact_Image__Id, axiom, ![X3, X4]:hAPP(c_Relation_OImage(X4,X4,c_Relation_OId(X4)),X3)=X3, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__Id)). 4.02/4.27 fof(fact_mod__nat__def, axiom, ![X5, X2]:hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X2,X5))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__nat__def)). 4.02/4.27 fof(fact_divmod__nat__zero, axiom, ![X2]:hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=c_Divides_Odivmod__nat(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__zero)). 4.02/4.27 fof(fact_option_Osize_I2_J, axiom, ![X26, X228, X4]:c_Option_Ooption_Ooption__size(X4,X228,hAPP(c_Option_Ooption_OSome(X4),X26))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X228,X26)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Osize_I2_J)). 4.02/4.27 fof(fact_minus__code__numeral__def, axiom, ![X2, X5]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X5)),hAPP(c_Code__Numeral_Onat__of,X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X5),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__code__numeral__def)). 4.02/4.27 fof(fact_div__code__numeral__def, axiom, ![X2, X5]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X5)),hAPP(c_Code__Numeral_Onat__of,X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X5),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__code__numeral__def)). 4.02/4.27 fof(fact_times__code__numeral__def, axiom, ![X2, X5]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X5),X2)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X5)),hAPP(c_Code__Numeral_Onat__of,X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_times__code__numeral__def)). 4.02/4.27 fof(fact_plus__code__numeral__def, axiom, ![X2, X5]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X5),X2)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X5)),hAPP(c_Code__Numeral_Onat__of,X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_plus__code__numeral__def)). 4.02/4.27 fof(fact_wfP__empty, axiom, ![X4]:c_Wellfounded_OwfP(X4,hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBK(tc_HOL_Obool,X4),c_fFalse))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__empty)). 4.02/4.27 fof(fact_com_Osize_I11_J, axiom, ![X120, X75, X121]:hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X121,X75,X120))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X120)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I11_J)). 4.02/4.27 fof(fact_atMost__Suc, axiom, ![X28]:hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X28))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X28)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atMost__Suc)). 4.02/4.27 fof(fact_zless__iff__Suc__zadd, axiom, ![X16, X23]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23),X16))<=>?[X104]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X104)))=X16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__iff__Suc__zadd)). 4.02/4.27 fof(fact_min__Suc__Suc, axiom, ![X5, X2]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Nat_OSuc,X5))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X2),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__Suc__Suc)). 4.02/4.27 fof(fact_times__code__numeral__code, axiom, ![X2, X5]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X5)),hAPP(c_Code__Numeral_Oof__nat,X2))=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_times__code__numeral__code)). 4.02/4.27 fof(fact_max__Suc__Suc, axiom, ![X5, X2]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Nat_OSuc,X5))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X2),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__Suc__Suc)). 4.02/4.27 fof(fact_plus__code__numeral__code, axiom, ![X2, X5]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X5)),hAPP(c_Code__Numeral_Oof__nat,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_plus__code__numeral__code)). 4.02/4.27 fof(fact_zless__add1__eq, axiom, ![X16, X23]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16),c_Groups_Oone__class_Oone(tc_Int_Oint))))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23),X16))|X23=X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__add1__eq)). 4.02/4.27 fof(fact_quotient__is__empty2, axiom, ![X18, X3, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X3<=>hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X3),X18)=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotient__is__empty2)). 4.02/4.27 fof(fact_divmod__nat__rel__divmod__nat, axiom, ![X5, X2]:hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X5),c_Divides_Odivmod__nat(X2,X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__divmod__nat)). 4.02/4.27 fof(fact_card__atLeastLessThan__int, axiom, ![X115, X60]:hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X60),X115))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X115),X60)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__atLeastLessThan__int)). 4.02/4.27 fof(fact_zle__iff__zadd, axiom, ![X16, X23]:(?[X104]:X16=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X104))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__iff__zadd)). 4.02/4.27 fof(fact_mult__Min, axiom, ![X107]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X107)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X107), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Min)). 4.02/4.27 fof(fact_fold__def, axiom, ![X3, X16, X22, X4, X7]:hAPP(hAPP(c_Finite__Set_Ofold(X7,X4,X22),X16),X3)=c_HOL_OThe(X4,c_Finite__Set_Ofold__graph(X7,X4,X22,X16,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__def)). 4.02/4.27 fof(fact_mod__code__numeral__def, axiom, ![X2, X5]:hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X5),hAPP(c_Code__Numeral_Onat__of,X2)))=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X5,X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__code__numeral__def)). 4.02/4.27 fof(fact_com_Osize_I14_J, axiom, ![X120, X75]:hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X75,X120))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X120)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I14_J)). 4.02/4.27 fof(fact_subtract__code__numeral__code, axiom, ![X2, X5]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),X2))=hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X5)),hAPP(c_Code__Numeral_Oof__nat,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subtract__code__numeral__code)). 4.02/4.27 fof(fact_card__atLeastAtMost, axiom, ![X115, X60]:hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X60,X115))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X115)),X60), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__atLeastAtMost)). 4.02/4.27 fof(fact_single__valued__Id, axiom, ![X4]:c_Relation_Osingle__valued(X4,X4,c_Relation_OId(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__Id)). 4.02/4.27 fof(fact_zabs__less__one__iff, axiom, ![X16]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X16)),c_Groups_Oone__class_Oone(tc_Int_Oint)))<=>X16=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zabs__less__one__iff)). 4.02/4.27 fof(fact_pdivmod__posDivAlg, axiom, ![X107, X47]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X47=>c_Divides_Opdivmod(X107,X47)=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),X107)))&(X47!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X107),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X47))=c_Divides_Opdivmod(X107,X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pdivmod__posDivAlg)). 4.02/4.27 fof(fact_lessThan__Suc, axiom, ![X28]:hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X28))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X28),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__Suc)). 4.02/4.27 fof(fact_apfst__id, axiom, ![X7, X4]:c_Fun_Oid(tc_prod(X4,X7))=c_Product__Type_Oapfst(X4,X4,X7,c_Fun_Oid(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_apfst__id)). 4.02/4.27 fof(fact_nat_Osize_I2_J, axiom, ![X219]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X219)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X219)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat_Osize_I2_J)). 4.02/4.27 fof(fact_com_Osize_I3_J, axiom, ![X120, X75, X121]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X120)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X121,X75,X120)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I3_J)). 4.02/4.27 fof(fact_less__iff__Suc__add, axiom, ![X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))<=>?[X137]:hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X137))=X20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__iff__Suc__add)). 4.02/4.27 fof(fact_dom__eq__empty__conv, axiom, ![X22, X7, X4]:(hAPP(c_COMBK(tc_Option_Ooption(X7),X4),c_Option_Ooption_ONone(X7))=X22<=>c_Map_Odom(X4,X7,X22)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__eq__empty__conv)). 4.02/4.27 fof(fact_iterate_Osimps, axiom, ![X9, X22, X4, X7, X28]:((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X28=>hAPP(c_Product__Type_OPair(X7,X4),X9)=hAPP(c_Random_Oiterate(X7,X4,X28,X22),X9))&(hAPP(c_Random_Oiterate(X7,X4,X28,X22),X9)=hAPP(hAPP(c_Product__Type_Oscomp(X4,X7,X4,tc_prod(X7,X4)),hAPP(X22,X9)),c_Random_Oiterate(X7,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X28),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X22))<=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_iterate_Osimps)). 4.02/4.27 fof(fact_empty__is__image, axiom, ![X3, X22, X7, X4]:(hAPP(c_Set_Oimage(X7,X4,X22),X3)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=>X3=c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__is__image)). 4.02/4.27 fof(fact_butlast_Osimps_I2_J, axiom, ![X13, X4, X45]:((X45=c_List_Olist_ONil(X4)=>c_List_Obutlast(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45))=c_List_Olist_ONil(X4))&(c_List_Olist_ONil(X4)!=X45=>hAPP(hAPP(c_List_Olist_OCons(X4),X13),c_List_Obutlast(X4,X45))=c_List_Obutlast(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast_Osimps_I2_J)). 4.02/4.27 fof(fact_Domain__empty__iff, axiom, ![X18, X7, X4]:(X18=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X7),tc_HOL_Obool))<=>hAPP(c_Relation_ODomain(X4,X7),X18)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__empty__iff)). 4.02/4.27 fof(fact_Range__empty__iff, axiom, ![X18, X4, X7]:(X18=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X4),tc_HOL_Obool))<=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Relation_ORange(X7,X4),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__empty__iff)). 4.02/4.27 fof(fact_remove1_Osimps_I2_J, axiom, ![X45, X4, X43, X13]:((X43=X13=>X45=c_List_Oremove1(X4,X13,hAPP(hAPP(c_List_Olist_OCons(X4),X43),X45)))&(X13!=X43=>hAPP(hAPP(c_List_Olist_OCons(X4),X43),c_List_Oremove1(X4,X13,X45))=c_List_Oremove1(X4,X13,hAPP(hAPP(c_List_Olist_OCons(X4),X43),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1_Osimps_I2_J)). 4.02/4.27 fof(fact_distinct__upt, axiom, ![X135, X46]:hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X46,X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__upt)). 4.02/4.27 fof(fact_sublist__upt__eq__take, axiom, ![X20, X60, X4]:c_List_Osublist(X4,X60,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X20))=hAPP(hAPP(c_List_Otake(X4),X20),X60), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__upt__eq__take)). 4.02/4.27 fof(fact_power__Suc__0, axiom, ![X5]:hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__Suc__0)). 4.02/4.27 fof(fact_zdiv__minus1__right, axiom, ![X11]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__minus1__right)). 4.02/4.27 fof(fact_zmod__eq__0__iff, axiom, ![X102, X21]:(?[X103]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X102),X103)=X21<=>c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X102)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__eq__0__iff)). 4.02/4.27 fof(fact_mod__eq__0__iff, axiom, ![X102, X21]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21,X102)<=>?[X103]:X21=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X102),X103)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__eq__0__iff)). 4.02/4.27 fof(fact_last__ConsL, axiom, ![X13, X4, X45]:(X13=c_List_Olast(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45))<=X45=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__ConsL)). 4.02/4.27 fof(fact_com_Osize_I6_J, axiom, ![X120, X75]:c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X75,X120))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X120)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I6_J)). 4.02/4.27 fof(fact_New__DSequence_Opos__decr__bind__def, axiom, ![X22, X9, X4, X7, X37]:((hAPP(c_New__DSequence_Opos__decr__bind(X7,X4,X9,X22),X37)=c_Lazy__Sequence_Oempty(X4)<=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X37)&(X37!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=>hAPP(c_Lazy__Sequence_Obind(X7,X4,hAPP(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X37),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X7,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4)),X22),X37))=hAPP(c_New__DSequence_Opos__decr__bind(X7,X4,X9,X22),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__decr__bind__def)). 4.02/4.27 fof(fact_sorted__upt, axiom, ![X135, X46]:c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X46,X135)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__upt)). 4.02/4.27 fof(fact_nat__zminus__int, axiom, ![X5]: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),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__zminus__int)). 4.02/4.27 fof(fact_fold1__def, axiom, ![X3, X22, X4]:c_HOL_OThe(X4,c_Finite__Set_Ofold1Set(X4,X22,X3))=hAPP(c_Finite__Set_Ofold1(X4,X22),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__def)). 4.02/4.27 fof(fact_wf__measure, axiom, ![X22, X4]:c_Wellfounded_Owf(X4,hAPP(c_Wellfounded_Omeasure(X4),X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__measure)). 4.02/4.27 fof(fact_power__eq__if, axiom, ![X15, X2]:((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))<=X2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15),X2)=c_Groups_Oone__class_Oone(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__eq__if)). 4.02/4.27 fof(fact_div__1, axiom, ![X2]:X2=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__1)). 4.02/4.27 fof(fact_zmod__minus1__right, axiom, ![X11]:c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))=c_Groups_Ozero__class_Ozero(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__minus1__right)). 4.02/4.27 fof(fact_mod__1, axiom, ![X2]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__1)). 4.02/4.27 fof(fact_list__all2__Nil2, axiom, ![X32, X56, X7, X4]:(c_List_Olist__all2(X4,X7,X56,X32,c_List_Olist_ONil(X7))<=>c_List_Olist_ONil(X4)=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__Nil2)). 4.02/4.27 fof(fact_insert__code, axiom, ![X9, X3, X17, X4]:(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X4),X17),X3),X9))<=>(hBOOL(hAPP(X3,X9))|X9=X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__code)). 4.02/4.27 fof(fact_eq__mem, axiom, ![X17, X9, X4]:(X9=X17<=>hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_fequal,X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__mem)). 4.02/4.27 fof(fact_min__0L, axiom, ![X5]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__0L)). 4.02/4.27 fof(fact_min__0R, axiom, ![X5]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X5),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__0R)). 4.02/4.27 fof(fact_nat__int, axiom, ![X5]:X5=hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__int)). 4.02/4.27 fof(fact_list__all2__eq, axiom, ![X4, X31, X32]:(c_List_Olist__all2(X4,X4,c_fequal,X32,X31)<=>X31=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__eq)). 4.02/4.27 fof(fact_max__0L, axiom, ![X5]:X5=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__0L)). 4.02/4.27 fof(fact_max__0R, axiom, ![X5]:X5=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X5),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__0R)). 4.02/4.27 fof(fact_diff__bin__simps_I1_J, axiom, ![X107]:X107=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X107),c_Int_OPls), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__bin__simps_I1_J)). 4.02/4.27 fof(fact_mult__Pls, axiom, ![X53]:c_Int_OPls=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X53), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Pls)). 4.02/4.27 fof(fact_nat__gcd_Osimps, axiom, ![X13, X43]:((X43=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>c_Nitpick_Onat__gcd(X13,X43)=X13)&(c_Nitpick_Onat__gcd(X13,X43)=c_Nitpick_Onat__gcd(X43,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X13,X43))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__gcd_Osimps)). 4.02/4.27 fof(fact_inc__shift__def, axiom, ![X107, X1]:((c_Random_Oinc__shift(X1,X107)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)<=X107=X1)&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X107),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=c_Random_Oinc__shift(X1,X107)<=X107!=X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inc__shift__def)). 4.02/4.27 fof(help_c__fequal__2, axiom, ![X17, X9]:(hBOOL(hAPP(hAPP(c_fequal,X9),X17))|X17!=X9), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fequal__2)). 4.02/4.27 fof(fact_the__sym__eq__trivial, axiom, ![X9, X4]:c_HOL_OThe(X4,hAPP(c_fequal,X9))=X9, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__sym__eq__trivial)). 4.02/4.27 fof(fact_nat__of__of__nat, axiom, ![X5]:X5=hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__of__of__nat)). 4.02/4.27 fof(fact_of__nat__nat__of, axiom, ![X107]:X107=hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__nat__of)). 4.02/4.27 fof(fact_inf__Int__eq2, axiom, ![X17, X9, X86, X39, X7, X4]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBC(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X7),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X4,X7)))),c_Product__Type_OPair(X4,X7)))),X39)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBC(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X7),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X4,X7)))),c_Product__Type_OPair(X4,X7)))),X86)),X9),X17))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X9),X17)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X39),X86)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__Int__eq2)). 4.02/4.27 fof(fact_sup__Un__eq2, axiom, ![X17, X9, X86, X39, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X9),X17)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X39),X86)))<=>hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBC(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X7),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X4,X7)))),c_Product__Type_OPair(X4,X7)))),X39)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBC(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X7),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X4,X7)))),c_Product__Type_OPair(X4,X7)))),X86)),X9),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__Un__eq2)). 4.02/4.27 fof(fact_pred__comp__rel__comp__eq, axiom, ![X17, X9, X40, X18, X49, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X49)),hAPP(hAPP(c_Product__Type_OPair(X4,X49),X9),X17)),hAPP(hAPP(c_Relation_Orel__comp(X4,X7,X49),X18),X40)))<=>hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X4,X7,X49,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBC(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X7),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X4,X7)))),c_Product__Type_OPair(X4,X7)))),X18),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_fun(X49,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_fun(tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_fun(X49,tc_HOL_Obool)),X7),c_COMBC(X49,tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_prod(X7,X49)),tc_fun(X49,tc_fun(tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X49),tc_fun(tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_HOL_Obool),X49),c_member(tc_prod(X7,X49)))),c_Product__Type_OPair(X7,X49)))),X40)),X9),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__comp__rel__comp__eq)). 4.02/4.27 fof(fact_pred__subset__eq2, axiom, ![X86, X39, X7, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBC(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X7),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X4,X7)))),c_Product__Type_OPair(X4,X7)))),X39)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBC(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X7),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X4,X7)))),c_Product__Type_OPair(X4,X7)))),X86)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X39),X86))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__subset__eq2)). 4.02/4.27 fof(fact_INF__INT__eq2, axiom, ![X17, X9, X18, X49, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X49)),hAPP(hAPP(c_Product__Type_OPair(X7,X49),X9),X17)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(tc_prod(X7,X49),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X18)))<=>hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_fun(X49,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_fun(X7,tc_fun(X49,tc_HOL_Obool)),X4),hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_fun(X49,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_fun(tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_fun(X49,tc_HOL_Obool)),X7),c_COMBC(X49,tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_prod(X7,X49)),tc_fun(X49,tc_fun(tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X49),tc_fun(tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_HOL_Obool),X49),c_member(tc_prod(X7,X49)))),c_Product__Type_OPair(X7,X49))))),X18)),X9),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__INT__eq2)). 4.02/4.27 fof(fact_SUP__UN__eq2, axiom, ![X17, X9, X18, X49, X7, X4]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_fun(X49,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_fun(X7,tc_fun(X49,tc_HOL_Obool)),X4),hAPP(c_COMBC(X7,tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_fun(X49,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_fun(tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_fun(X49,tc_HOL_Obool)),X7),c_COMBC(X49,tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_prod(X7,X49)),tc_fun(X49,tc_fun(tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_HOL_Obool)),X7),hAPP(c_COMBB(tc_prod(X7,X49),tc_fun(tc_fun(tc_prod(X7,X49),tc_HOL_Obool),tc_HOL_Obool),X49),c_member(tc_prod(X7,X49)))),c_Product__Type_OPair(X7,X49))))),X18)),X9),X17))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X49)),hAPP(hAPP(c_Product__Type_OPair(X7,X49),X9),X17)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(tc_prod(X7,X49),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__UN__eq2)). 4.02/4.27 fof(fact_listrel__iff__zip, axiom, ![X18, X31, X32, X4]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X31)&![X19]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X19),hAPP(c_List_Oset(tc_prod(X4,X4)),hAPP(hAPP(c_List_Ozip(X4,X4),X32),X31))))=>hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4)))),c_Product__Type_OPair(X4,X4)))),X18)),X19))))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)),c_List_Olistrel(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__iff__zip)). 4.02/4.27 fof(fact_conversep__converse__eq, axiom, ![X17, X9, X18, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X4),X9),X17)),hAPP(c_Relation_Oconverse(X4,X7),X18)))<=>hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4,X7,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBC(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X7),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X4,X7)))),c_Product__Type_OPair(X4,X7)))),X18)),X9),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conversep__converse__eq)). 4.02/4.27 fof(fact_max__extp__max__ext__eq, axiom, ![X154, X9, X39, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X9),X154)),c_Wellfounded_Omax__ext(X4,X39)))<=>c_Wellfounded_Omax__extp(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4)))),c_Product__Type_OPair(X4,X4)))),X39),X9,X154)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__extp__max__ext__eq)). 4.02/4.27 fof(fact_listrelp__listrel__eq, axiom, ![X154, X9, X18, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X9),X154)),c_List_Olistrel(X4,X18)))<=>c_List_Olistrelp(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4)))),c_Product__Type_OPair(X4,X4)))),X18),X9,X154)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrelp__listrel__eq)). 4.02/4.27 fof(fact_RangeP__Range__eq, axiom, ![X9, X18, X7, X4]:(hBOOL(hAPP(c_Predicate_ORangeP(X4,X7,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBC(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X7),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X4,X7)))),c_Product__Type_OPair(X4,X7)))),X18)),X9))<=>hBOOL(hAPP(hAPP(c_member(X7),X9),hAPP(c_Relation_ORange(X4,X7),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_RangeP__Range__eq)). 4.02/4.27 fof(fact_DomainP__Domain__eq, axiom, ![X9, X18, X7, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_Relation_ODomain(X4,X7),X18)))<=>hBOOL(hAPP(c_Predicate_ODomainP(X4,X7,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBC(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X7),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X4,X7)))),c_Product__Type_OPair(X4,X7)))),X18)),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DomainP__Domain__eq)). 4.02/4.27 fof(fact_accp__acc__eq, axiom, ![X9, X18, X4]:(hBOOL(hAPP(c_Wellfounded_Oaccp(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4)))),c_Product__Type_OPair(X4,X4)))),X18)),X9))<=>hBOOL(hAPP(hAPP(c_member(X4),X9),c_Wellfounded_Oacc(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_accp__acc__eq)). 4.02/4.27 fof(fact_equivp__equiv, axiom, ![X3, X4]:(c_Equiv__Relations_Oequiv(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),X3)<=>c_Equiv__Relations_Oequivp(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4)))),c_Product__Type_OPair(X4,X4)))),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivp__equiv)). 4.02/4.27 fof(fact_wfP__wf__eq, axiom, ![X18, X4]:(c_Wellfounded_OwfP(X4,hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X4,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X4),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X4,X4)))),c_Product__Type_OPair(X4,X4)))),X18))<=>c_Wellfounded_Owf(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__wf__eq)). 4.02/4.27 fof(fact_pred__equals__eq2, axiom, ![X86, X39, X7, X4]:(hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBC(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X7),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X4,X7)))),c_Product__Type_OPair(X4,X7)))),X86)=hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_COMBC(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_prod(X4,X7),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_HOL_Obool),X7),c_member(tc_prod(X4,X7)))),c_Product__Type_OPair(X4,X7)))),X39)<=>X86=X39), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__equals__eq2)). 4.02/4.27 fof(fact_fold__image__Sigma, axiom, ![X76, X6, X7, X3, X4, X49]:(class_Groups_Ocomm__monoid__mult(X49)=>((hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X49,X4,c_Groups_Otimes__class_Otimes(X49)),hAPP(hAPP(c_COMBS(X4,tc_fun(X7,tc_HOL_Obool),X49),hAPP(hAPP(c_COMBC(X4,X49,tc_fun(tc_fun(X7,tc_HOL_Obool),X49)),hAPP(hAPP(c_COMBB(tc_fun(X7,X49),tc_fun(X49,tc_fun(tc_fun(X7,tc_HOL_Obool),X49)),X4),c_Finite__Set_Ofold__image(X49,X7,c_Groups_Otimes__class_Otimes(X49))),X76)),c_Groups_Oone__class_Oone(X49))),X6)),c_Groups_Oone__class_Oone(X49)),X3)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X49,tc_prod(X4,X7),c_Groups_Otimes__class_Otimes(X49)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,X49),X76)),c_Groups_Oone__class_Oone(X49)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),X6))<=![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(X6,X19)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__Sigma)). 4.02/4.27 fof(fact_setsum__product, axiom, ![X6, X76, X49, X3, X22, X7, X4]:(class_Rings_Osemiring__0(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),hAPP(hAPP(c_COMBC(X7,tc_fun(X49,tc_HOL_Obool),X4),hAPP(hAPP(c_COMBB(tc_fun(X49,X4),tc_fun(tc_fun(X49,tc_HOL_Obool),X4),X7),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X49,X4)),hAPP(hAPP(c_COMBC(X7,tc_fun(X49,X4),tc_fun(X49,X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,X4),tc_fun(tc_fun(X49,X4),tc_fun(X49,X4)),X7),c_COMBB(X4,X4,X49)),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X7),c_Groups_Otimes__class_Otimes(X4)),X22))),X76))),X6)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),X22),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X49,X4),X76),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__product)). 4.02/4.27 fof(fact_quotient__diff1, axiom, ![X26, X3, X18, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X26),X3))=>hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X18)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X3),X18)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X18)))<=c_Fun_Oinj__on(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X4),c_Equiv__Relations_Oquotient(X4)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X18),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotient__diff1)). 4.02/4.27 fof(fact_wmax__insertI, axiom, ![X230, X9, X229, X17]:(((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)),X230),X229)),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)),X9),X230)),X229)),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)),X9),X17)),c_FunDef_Opair__leq)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X17),X229))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wmax__insertI)). 4.02/4.27 fof(fact_smax__insertI, axiom, ![X156, X9, X203, X17]:(((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)),X156),X203)),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)),X9),X156)),X203)),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)),X9),X17)),c_FunDef_Opair__less)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X17),X203))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_smax__insertI)). 4.02/4.27 fof(fact_smin__insertI, axiom, ![X229, X17, X230, X9]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X9),X230))=>(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)),X9),X17)),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)),X230),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X17),X229))),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)),X230),X229)),c_FunDef_Omin__strict))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_smin__insertI)). 4.02/4.27 fof(fact_wmin__insertI, axiom, ![X229, X17, X230, X9]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X9),X230))=>((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)),X230),X229)),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)),X230),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X17),X229))),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)),X9),X17)),c_FunDef_Opair__leq)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wmin__insertI)). 4.02/4.27 fof(fact_UN__equiv__class2, axiom, ![X67, X70, X22, X49, X83, X254, X7, X84, X255, X4]:(((((hBOOL(hAPP(hAPP(c_member(X7),X67),X254))=>hAPP(hAPP(X22,X70),X67)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X49,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X84),hAPP(hAPP(c_Set_Oinsert(X4),X70),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X49,tc_HOL_Obool)),tc_fun(X49,tc_HOL_Obool),X4),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X49,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X7,X83),hAPP(hAPP(c_Set_Oinsert(X7),X67),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))),X22)))<=hBOOL(hAPP(hAPP(c_member(X4),X70),X255)))<=c_Equiv__Relations_Ocongruent2(X4,X7,tc_fun(X49,tc_HOL_Obool),X84,X83,X22))<=c_Equiv__Relations_Oequiv(X7,X254,X83))<=c_Equiv__Relations_Oequiv(X4,X255,X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__equiv__class2)). 4.02/4.27 fof(fact_UN__equiv__class__type2, axiom, ![X6, X299, X300, X22, X49, X83, X254, X7, X84, X255, X4]:((((hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X300),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X255),X84)))=>(hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X299),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X254),X83)))=>(hBOOL(hAPP(hAPP(c_member(tc_fun(X49,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X49,tc_HOL_Obool)),X300),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X49,tc_HOL_Obool)),tc_fun(X49,tc_HOL_Obool),X4),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X49,tc_HOL_Obool)),X299)),X22))),X6))<=![X77]:(hBOOL(hAPP(hAPP(c_member(X4),X77),X255))=>![X301]:(hBOOL(hAPP(hAPP(c_member(X7),X301),X254))=>hBOOL(hAPP(hAPP(c_member(tc_fun(X49,tc_HOL_Obool)),hAPP(hAPP(X22,X77),X301)),X6)))))))<=c_Equiv__Relations_Ocongruent2(X4,X7,tc_fun(X49,tc_HOL_Obool),X84,X83,X22))<=c_Equiv__Relations_Oequiv(X7,X254,X83))<=c_Equiv__Relations_Oequiv(X4,X255,X84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__equiv__class__type2)). 4.02/4.27 fof(fact_small__prod__def, axiom, ![X102, X22, X4, X7]:((class_Smallcheck_Osmall(X7)&class_Smallcheck_Osmall(X4))=>hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(X4,X7)),X22),X102)=hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(X4),hAPP(hAPP(c_COMBC(X4,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X4),c_Smallcheck_Osmall__class_Osmall(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X4),hAPP(c_COMBB(tc_prod(X4,X7),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),X7),X22)),c_Product__Type_OPair(X4,X7)))),X102)),X102)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__prod__def)). 4.02/4.27 fof(fact_setsum__Sigma, axiom, ![X22, X6, X7, X3, X4, X49]:(class_Groups_Ocomm__monoid__add(X49)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(X6,X19))))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X49),hAPP(hAPP(c_COMBS(X4,tc_fun(X7,tc_HOL_Obool),X49),hAPP(hAPP(c_COMBB(tc_fun(X7,X49),tc_fun(tc_fun(X7,tc_HOL_Obool),X49),X4),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X49)),X22)),X6)),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X4,X7),X49),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,X49),X22)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Sigma)). 4.02/4.27 fof(fact_enum__fun__def, axiom, ![X7, X4]:(hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_fun(X4,X7)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_Option_Ooption(X7)),tc_fun(X4,X7),tc_List_Olist(X7)),c_Fun_Ocomp(tc_Option_Ooption(X7),X7,X4,c_Option_Othe(X7))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X4,X7)),tc_fun(X4,tc_Option_Ooption(X7)),tc_List_Olist(X7)),c_Map_Omap__of(X4,X7)),hAPP(c_List_Ozip(X4,X7),c_Enum_Oenum__class_Oenum(X4))))),c_Enum_On__lists(X7,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_Enum_Oenum__class_Oenum(X4)),c_Enum_Oenum__class_Oenum(X7)))=c_Enum_Oenum__class_Oenum(tc_fun(X4,X7))<=(class_Enum_Oenum(X7)&class_Enum_Oenum(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__fun__def)). 4.02/4.27 fof(fact_enum__ex__fun__def, axiom, ![X56, X4, X7]:((hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X4,X7)),X56))<=>c_Enum_Oex__n__lists(X7,hAPP(hAPP(c_COMBB(tc_fun(X4,X7),tc_HOL_Obool,tc_List_Olist(X7)),X56),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_Option_Ooption(X7)),tc_fun(X4,X7),tc_List_Olist(X7)),c_Fun_Ocomp(tc_Option_Ooption(X7),X7,X4,c_Option_Othe(X7))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X4,X7)),tc_fun(X4,tc_Option_Ooption(X7)),tc_List_Olist(X7)),c_Map_Omap__of(X4,X7)),hAPP(c_List_Ozip(X4,X7),c_Enum_Oenum__class_Oenum(X4))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_Enum_Oenum__class_Oenum(X4))))<=(class_Enum_Oenum(X4)&class_Enum_Oenum(X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__ex__fun__def)). 4.02/4.27 fof(fact_enum__all__fun__def, axiom, ![X56, X4, X7]:((c_Enum_Oall__n__lists(X7,hAPP(hAPP(c_COMBB(tc_fun(X4,X7),tc_HOL_Obool,tc_List_Olist(X7)),X56),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_Option_Ooption(X7)),tc_fun(X4,X7),tc_List_Olist(X7)),c_Fun_Ocomp(tc_Option_Ooption(X7),X7,X4,c_Option_Othe(X7))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X4,X7)),tc_fun(X4,tc_Option_Ooption(X7)),tc_List_Olist(X7)),c_Map_Omap__of(X4,X7)),hAPP(c_List_Ozip(X4,X7),c_Enum_Oenum__class_Oenum(X4))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_Enum_Oenum__class_Oenum(X4)))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X4,X7)),X56)))<=(class_Enum_Oenum(X4)&class_Enum_Oenum(X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__all__fun__def)). 4.02/4.27 fof(fact_fold__image__Un__one, axiom, ![X22, X105, X86, X4, X7]:(class_Groups_Ocomm__monoid__mult(X7)=>(((![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X86),X105)))=>c_Groups_Oone__class_Oone(X7)=hAPP(X22,X19))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X22),c_Groups_Oone__class_Oone(X7)),X86)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X22),c_Groups_Oone__class_Oone(X7)),X105))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X22),c_Groups_Oone__class_Oone(X7)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X86),X105)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X105)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X86)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__Un__one)). 4.02/4.27 fof(fact_max__ext__additive, axiom, ![X61, X8, X39, X6, X3, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),X6)),c_Wellfounded_Omax__ext(X4,X39)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X8),X61)),c_Wellfounded_Omax__ext(X4,X39)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X8)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X6),X61))),c_Wellfounded_Omax__ext(X4,X39))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ext__additive)). 4.02/4.27 fof(fact_fold__image__Un__Int, axiom, ![X76, X6, X3, X4, X7]:(((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X76),c_Groups_Oone__class_Oone(X7)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X76),c_Groups_Oone__class_Oone(X7)),X6))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X76),c_Groups_Oone__class_Oone(X7)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X76),c_Groups_Oone__class_Oone(X7)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Groups_Ocomm__monoid__mult(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__Un__Int)). 4.02/4.27 fof(fact_fold__image__distrib, axiom, ![X48, X76, X3, X4, X7]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X76),c_Groups_Oone__class_Oone(X7)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X48),c_Groups_Oone__class_Oone(X7)),X3))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),hAPP(hAPP(c_COMBS(X4,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X4),c_Groups_Otimes__class_Otimes(X7)),X76)),X48)),c_Groups_Oone__class_Oone(X7)),X3))<=class_Groups_Ocomm__monoid__mult(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__distrib)). 4.02/4.27 fof(fact_setprod__Un, axiom, ![X22, X6, X3, X4, X7]:(class_Fields_Ofield(X7)=>(((![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))=>c_Groups_Ozero__class_Ozero(X7)!=hAPP(X22,X19))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),X6))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__Un)). 4.02/4.27 fof(fact_setprod__cartesian__product, axiom, ![X3, X6, X22, X49, X7, X4]:(class_Groups_Ocomm__monoid__mult(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X4),hAPP(hAPP(c_COMBC(X7,tc_fun(X49,tc_HOL_Obool),X4),hAPP(hAPP(c_COMBB(tc_fun(X49,X4),tc_fun(tc_fun(X49,tc_HOL_Obool),X4),X7),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X49,X4)),X22)),X6)),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X7,X49),X4),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X49,X4),X22)),hAPP(hAPP(c_Product__Type_OSigma(X7,X49),X3),hAPP(c_COMBK(tc_fun(X49,tc_HOL_Obool),X7),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__cartesian__product)). 4.02/4.27 fof(fact_setsum__cartesian__product, axiom, ![X3, X6, X22, X49, X7, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),hAPP(hAPP(c_COMBC(X7,tc_fun(X49,tc_HOL_Obool),X4),hAPP(hAPP(c_COMBB(tc_fun(X49,X4),tc_fun(tc_fun(X49,tc_HOL_Obool),X4),X7),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X49,X4)),X22)),X6)),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X7,X49),X4),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X49,X4),X22)),hAPP(hAPP(c_Product__Type_OSigma(X7,X49),X3),hAPP(c_COMBK(tc_fun(X49,tc_HOL_Obool),X7),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__cartesian__product)). 4.02/4.27 fof(fact_reduction__pair__def, axiom, ![X56, X4]:((c_Wellfounded_Owf(X4,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X56))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X56)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X56))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X56))))<=>c_FunDef_Oreduction__pair(X4,X56)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reduction__pair__def)). 4.02/4.27 fof(fact_setprod__Sigma, axiom, ![X22, X6, X7, X3, X4, X49]:(class_Groups_Ocomm__monoid__mult(X49)=>((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X4,X7),X49),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,X49),X22)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),X6))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X49),hAPP(hAPP(c_COMBS(X4,tc_fun(X7,tc_HOL_Obool),X49),hAPP(hAPP(c_COMBB(tc_fun(X7,X49),tc_fun(tc_fun(X7,tc_HOL_Obool),X49),X4),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X49)),X22)),X6)),X3)<=![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(X6,X19)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__Sigma)). 4.02/4.27 fof(fact_congruent__def, axiom, ![X22, X18, X7, X4]:(c_Equiv__Relations_Ocongruent(X4,X7,X18,X22)<=>![X19]:(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,X7),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X4,X7),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(X7,tc_HOL_Obool,X4)),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,tc_HOL_Obool),X4),c_fequal),X22))),X22)),X19))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X19),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_congruent__def)). 4.02/4.27 fof(fact_lexord__append__leftD, axiom, ![X18, X64, X115, X9, X4]:((![X27]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X27),X27)),X18)))=>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)),X115),X64)),c_List_Olexord(X4,X18))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Oappend(X4),X9),X115)),hAPP(hAPP(c_List_Oappend(X4),X9),X64))),c_List_Olexord(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__append__leftD)). 4.02/4.27 fof(fact_rel__comp__subset__Sigma, axiom, ![X8, X40, X49, X6, X3, X18, X7, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X49),tc_HOL_Obool)),X40),hAPP(hAPP(c_Product__Type_OSigma(X7,X49),X6),hAPP(c_COMBK(tc_fun(X49,tc_HOL_Obool),X7),X8))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X49),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X7,X49),X18),X40)),hAPP(hAPP(c_Product__Type_OSigma(X4,X49),X3),hAPP(c_COMBK(tc_fun(X49,tc_HOL_Obool),X4),X8)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X18),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__subset__Sigma)). 4.02/4.27 fof(fact_image__eq__fold__image, axiom, ![X22, X7, X3, X4]:(hAPP(c_Set_Oimage(X4,X7,X22),X3)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X7,tc_HOL_Obool),X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X7,tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_Set_Oinsert(X7)),X22)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__eq__fold__image)). 4.02/4.27 fof(fact_setsum__commute, axiom, ![X3, X6, X22, X49, X7, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X49,X4),hAPP(hAPP(c_COMBC(X49,tc_fun(X7,tc_HOL_Obool),X4),hAPP(hAPP(c_COMBB(tc_fun(X7,X4),tc_fun(tc_fun(X7,tc_HOL_Obool),X4),X49),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4)),hAPP(c_COMBC(X7,X49,X4),X22))),X3)),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),hAPP(hAPP(c_COMBC(X7,tc_fun(X49,tc_HOL_Obool),X4),hAPP(hAPP(c_COMBB(tc_fun(X49,X4),tc_fun(tc_fun(X49,tc_HOL_Obool),X4),X7),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X49,X4)),X22)),X6)),X3)<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__commute)). 4.02/4.27 fof(fact_map__of__zip__upd, axiom, ![X16, X17, X9, X30, X32, X7, X31, X4]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X31)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X32)=>(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X30)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X32)=>(~(hBOOL(hAPP(hAPP(c_member(X7),X9),hAPP(c_List_Oset(X7),X32))))=>(hAPP(c_Map_Omap__of(X7,X4),hAPP(hAPP(c_List_Ozip(X7,X4),X32),X31))=hAPP(c_Map_Omap__of(X7,X4),hAPP(hAPP(c_List_Ozip(X7,X4),X32),X30))<=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X4)),hAPP(c_Map_Omap__of(X7,X4),hAPP(hAPP(c_List_Ozip(X7,X4),X32),X31))),X9),hAPP(c_Option_Ooption_OSome(X4),X17))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X4)),hAPP(c_Map_Omap__of(X7,X4),hAPP(hAPP(c_List_Ozip(X7,X4),X32),X30))),X9),hAPP(c_Option_Ooption_OSome(X4),X16)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__zip__upd)). 4.02/4.27 fof(fact_INT__simps_I1_J, axiom, ![X6, X3, X7, X4, X8]:((c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool))),X3)),X6))<=X8=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X8=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X8),X3)),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool))),X3)),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__simps_I1_J)). 4.02/4.27 fof(fact_transpose__column, axiom, ![X37, X32, X4]:(c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),X32)))=>(hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),X4),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_Nat_Onat,X4),c_List_Onth(X4)),X37)),hAPP(c_List_Ofilter(tc_List_Olist(X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X4)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37)),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),c_List_Otranspose(X4,X32)))=hAPP(hAPP(c_List_Onth(tc_List_Olist(X4)),X32),X37)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__column)). 4.02/4.27 fof(fact_single__valued__confluent, axiom, ![X16, X17, X9, X18, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),c_Transitive__Closure_Ortrancl(X4,X18)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X16)),c_Transitive__Closure_Ortrancl(X4,X18)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X17),X16)),c_Transitive__Closure_Ortrancl(X4,X18)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X16),X17)),c_Transitive__Closure_Ortrancl(X4,X18))))))<=c_Relation_Osingle__valued(X4,X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__confluent)). 4.02/4.27 fof(fact_INT__extend__simps_I3_J, axiom, ![X6, X3, X7, X4, X8]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))),X6)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X8),X3)),X6)<=X8=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(X8!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X8),X3)),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBC(X4,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool))),X3)),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__extend__simps_I3_J)). 4.02/4.27 fof(fact_map__of__mapk__SomeI, axiom, ![X9, X28, X123, X49, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>(hAPP(hAPP(c_Map_Omap__of(X4,X49),X123),X28)=hAPP(c_Option_Ooption_OSome(X49),X9)=>hAPP(c_Option_Ooption_OSome(X49),X9)=hAPP(hAPP(c_Map_Omap__of(X7,X49),hAPP(hAPP(c_List_Omap(tc_prod(X4,X49),tc_prod(X7,X49)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X49,tc_prod(X7,X49)),hAPP(hAPP(c_COMBB(X7,tc_fun(X49,tc_prod(X7,X49)),X4),c_Product__Type_OPair(X7,X49)),X22))),X123)),hAPP(X22,X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__mapk__SomeI)). 4.02/4.27 fof(fact_nth__nth__transpose__sorted, axiom, ![X38, X37, X32, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),c_List_Otranspose(X4,X32))))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X38),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),hAPP(c_List_Ofilter(tc_List_Olist(X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X4)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37)),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),X32))))=>hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Onth(tc_List_Olist(X4)),c_List_Otranspose(X4,X32)),X37)),X38)=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Onth(tc_List_Olist(X4)),X32),X38)),X37)))<=c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__nth__transpose__sorted)). 4.02/4.27 fof(fact_congruent2__implies__congruent__UN, axiom, ![X26, X22, X49, X83, X254, X7, X84, X255, X4]:(c_Equiv__Relations_Oequiv(X4,X255,X84)=>(((c_Equiv__Relations_Ocongruent(X4,tc_fun(X49,tc_HOL_Obool),X84,hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(X49,tc_HOL_Obool)),tc_fun(X49,tc_HOL_Obool),X4),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X49,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X7,X83),hAPP(hAPP(c_Set_Oinsert(X7),X26),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))),X22))<=hBOOL(hAPP(hAPP(c_member(X7),X26),X254)))<=c_Equiv__Relations_Ocongruent2(X4,X7,tc_fun(X49,tc_HOL_Obool),X84,X83,X22))<=c_Equiv__Relations_Oequiv(X7,X254,X83))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_congruent2__implies__congruent__UN)). 4.02/4.27 fof(fact_map__upds__append1, axiom, ![X9, X21, X31, X7, X32, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31)))=>c_Map_Omap__upds(X4,X7,X21,hAPP(hAPP(c_List_Oappend(X4),X32),hAPP(hAPP(c_List_Olist_OCons(X4),X9),c_List_Olist_ONil(X4))),X31)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),c_Map_Omap__upds(X4,X7,X21,X32,X31)),X9),hAPP(c_Option_Ooption_OSome(X7),hAPP(hAPP(c_List_Onth(X7),X31),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__append1)). 4.02/4.27 fof(fact_rtrancl__listrel1__ConsI2, axiom, ![X31, X32, X18, X17, X9, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),c_Transitive__Closure_Ortrancl(X4,X18)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)),hAPP(hAPP(c_List_Olist_OCons(X4),X17),X31))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X18))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X18)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__listrel1__ConsI2)). 4.02/4.27 fof(fact_listsum__subtractf, axiom, ![X32, X76, X22, X7, X4]:(hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X7,X4),hAPP(hAPP(c_COMBS(X7,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X7),c_Groups_Ominus__class_Ominus(X4)),X22)),X76)),X32))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32))),hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X7,X4),X76),X32)))<=class_Groups_Oab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__subtractf)). 4.02/4.27 fof(fact_listsum__addf, axiom, ![X32, X76, X22, X7, X4]:(hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X7,X4),hAPP(hAPP(c_COMBS(X7,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X7),c_Groups_Oplus__class_Oplus(X4)),X22)),X76)),X32))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32))),hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X7,X4),X76),X32)))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__addf)). 4.02/4.27 fof(fact_setprod_Ounion__inter__neutral, axiom, ![X76, X6, X3, X4, X7]:(class_Groups_Ocomm__monoid__mult(X7)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X76),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X76),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X76),X6))<=![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))=>hAPP(X76,X19)=c_Groups_Oone__class_Oone(X7)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod_Ounion__inter__neutral)). 4.02/4.27 fof(fact_setprod__Un__one, axiom, ![X22, X105, X86, X4, X7]:(class_Groups_Ocomm__monoid__mult(X7)=>(((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X86),X105))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),X86)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),X105))<=![X19]:(hAPP(X22,X19)=c_Groups_Oone__class_Oone(X7)<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X86),X105)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X105)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X86)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__Un__one)). 4.02/4.27 fof(fact_setsum__Un__zero, axiom, ![X22, X105, X86, X4, X7]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X86))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X105))=>(![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X86),X105)))=>c_Groups_Ozero__class_Ozero(X7)=hAPP(X22,X19))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X86),X105))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X86)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X105)))))<=class_Groups_Ocomm__monoid__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Un__zero)). 4.02/4.27 fof(fact_setsum_Ounion__inter__neutral, axiom, ![X76, X6, X3, X4, X7]:(class_Groups_Ocomm__monoid__add(X7)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))=>c_Groups_Ozero__class_Ozero(X7)=hAPP(X76,X19))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum_Ounion__inter__neutral)). 4.02/4.27 fof(fact_image__INT, axiom, ![X38, X6, X3, X49, X8, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,X8)=>((hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X49,tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X49),c_Set_Oimage(X4,X7,X22)),X6))=hAPP(c_Set_Oimage(X4,X7,X22),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X49,tc_fun(X4,tc_HOL_Obool)),X3),X6))<=hBOOL(hAPP(hAPP(c_member(X49),X38),X3)))<=![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(X6,X19)),X8))<=hBOOL(hAPP(hAPP(c_member(X49),X19),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__INT)). 4.02/4.27 fof(fact_rtrancl__Un__separatorE, axiom, ![X112, X56, X25, X26, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),c_Transitive__Closure_Ortrancl(X4,X56)))<=![X19]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X19)),c_Transitive__Closure_Ortrancl(X4,X56)))=>![X34]:(X34=X19<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X34)),X112)))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),c_Transitive__Closure_Ortrancl(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X56),X112))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__Un__separatorE)). 4.02/4.27 fof(fact_rtrancl__Un__separator__converseE, axiom, ![X112, X56, X25, X26, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),c_Transitive__Closure_Ortrancl(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X56),X112))))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),c_Transitive__Closure_Ortrancl(X4,X56)))<=![X19]:(![X34]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X34),X19)),X112))=>X19=X34)<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X25)),c_Transitive__Closure_Ortrancl(X4,X56)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__Un__separator__converseE)). 4.02/4.27 fof(fact_nth__transpose, axiom, ![X32, X4, X37]:(hAPP(hAPP(c_List_Onth(tc_List_Olist(X4)),c_List_Otranspose(X4,X32)),X37)=hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),X4),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_Nat_Onat,X4),c_List_Onth(X4)),X37)),hAPP(c_List_Ofilter(tc_List_Olist(X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X4)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37)),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),X32))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),c_List_Otranspose(X4,X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__transpose)). 4.02/4.27 fof(fact_lexord__linear, axiom, ![X17, X9, X18, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X9),X17)),c_List_Olexord(X4,X18)))|X17=X9|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)),X17),X9)),c_List_Olexord(X4,X18))))<=![X27, X78]:(X27=X78|hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X78),X27)),X18))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X27),X78)),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__linear)). 4.02/4.27 fof(fact_divmod__nat__rel__mult1__eq, axiom, ![X11, X101, X14, X10, X12]:(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X12,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X14),X101)))=>(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X12),X10),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X14)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X101)),X10))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X101),X10))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__mult1__eq)). 4.02/4.27 fof(fact_snoc__listrel1__snoc__iff, axiom, ![X18, X17, X31, X9, X32, X4]:(((X31=X32&hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),X18)))|(X9=X17&hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)),c_List_Olistrel1(X4,X18)))))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Oappend(X4),X32),hAPP(hAPP(c_List_Olist_OCons(X4),X9),c_List_Olist_ONil(X4)))),hAPP(hAPP(c_List_Oappend(X4),X31),hAPP(hAPP(c_List_Olist_OCons(X4),X17),c_List_Olist_ONil(X4))))),c_List_Olistrel1(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snoc__listrel1__snoc__iff)). 4.02/4.27 fof(fact_folding__image__simple_Ounion__inter__neutral, axiom, ![X6, X3, X87, X76, X16, X22, X7, X4]:(c_Finite__Set_Ofolding__image__simple(X4,X7,X22,X16,X76,X87)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X6))=>(hAPP(hAPP(X22,hAPP(X87,X3)),hAPP(X87,X6))=hAPP(X87,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3),X6))<=![X19]:(X16=hAPP(X76,X19)<=hBOOL(hAPP(hAPP(c_member(X7),X19),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X3),X6)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Ounion__inter__neutral)). 4.02/4.27 fof(fact_min__max_OSup__fin_Ounion__inter, axiom, ![X6, X3, X4]:(class_Orderings_Olinorder(X4)=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X3)),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X6))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Ounion__inter)). 4.02/4.27 fof(fact_zmult1__lemma, axiom, ![X11, X101, X14, X10, X12]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12,X10),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X14),X101)))=>(X10!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X12),X10),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X14)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X101)),X10))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X101),X10)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult1__lemma)). 4.02/4.27 fof(fact_fold__Un__disjoint, axiom, ![X76, X6, X3, X4, X7]:((((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)=>hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X76),c_Groups_Oone__class_Oone(X7)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X76),c_Groups_Oone__class_Oone(X7)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X76),c_Groups_Oone__class_Oone(X7)),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Groups_Ocomm__monoid__mult(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__Un__disjoint)). 4.02/4.27 fof(fact_smax__emptyI, axiom, ![X203]:((X203!=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))),X203)),c_FunDef_Omax__strict)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X203))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_smax__emptyI)). 4.02/4.27 fof(fact_min__max_OInf__fin_Ounion__inter, axiom, ![X6, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>(hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X3)),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X6))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Ounion__inter)). 4.02/4.27 fof(fact_setsum__Un, axiom, ![X22, X6, X3, X4, X7]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X6))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Groups_Oab__group__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Un)). 4.02/4.27 fof(fact_max__ext_Ointros, axiom, ![X39, X203, X156, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X203))=>((![X19]:(?[X114]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X114)),X39))&hBOOL(hAPP(hAPP(c_member(X4),X114),X203)))<=hBOOL(hAPP(hAPP(c_member(X4),X19),X156)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X156),X203)),c_Wellfounded_Omax__ext(X4,X39))))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X203))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X156))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ext_Ointros)). 4.02/4.27 fof(fact_same__fstI, axiom, ![X4, X39, X17, X85, X7, X9, X56]:(hBOOL(hAPP(X56,X9))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X4,X7),tc_prod(X4,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X4,X7),tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X9),X85)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X9),X17))),c_Recdef_Osame__fst(X4,X7,X56,X39)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X85),X17)),hAPP(X39,X9))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_same__fstI)). 4.02/4.27 fof(fact_rel__pow__Suc__I2, axiom, ![X20, X16, X39, X17, X9, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X16)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),hAPP(c_Nat_OSuc,X20)),X39)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X17),X16)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X20),X39))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__Suc__I2)). 4.02/4.27 fof(fact_rel__pow__Suc__I, axiom, ![X16, X39, X20, X17, X9, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X17),X16)),X39))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X16)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),hAPP(c_Nat_OSuc,X20)),X39))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X20),X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__Suc__I)). 4.02/4.27 fof(fact_setsum__shift__bounds__nat__ivl, axiom, ![X20, X28, X21, X22, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Nat_Onat),X22),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X28))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X21),X20))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X28)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X28)))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__bounds__nat__ivl)). 4.02/4.27 fof(fact_setprod__Un__Int, axiom, ![X76, X6, X3, X4, X7]:(class_Groups_Ocomm__monoid__mult(X7)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X76),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X76),X6))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X76),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X76),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__Un__Int)). 4.02/4.27 fof(fact_setsum__Un__Int, axiom, ![X76, X6, X3, X4, X7]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),X6))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))))<=class_Groups_Ocomm__monoid__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Un__Int)). 4.02/4.27 fof(fact_transpose__column__length, axiom, ![X37, X32, X4]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),hAPP(c_List_Ofilter(tc_List_Olist(X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X4)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37)),c_Nat_Osize__class_Osize(tc_List_Olist(X4)))),c_List_Otranspose(X4,X32)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X4)),X32),X37))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),X32))))<=c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__column__length)). 4.02/4.27 fof(fact_setsum__Un__nat, axiom, ![X22, X6, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X22),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X22),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X22),X6))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Un__nat)). 4.02/4.27 fof(fact_foldl__apply, axiom, ![X40, X76, X48, X22, X7, X49, X32, X4]:(![X19]:(hAPP(c_Fun_Ocomp(X49,X49,X7,hAPP(X22,X19)),X48)=hAPP(c_Fun_Ocomp(X7,X49,X7,X48),hAPP(X76,X19))<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32))))=>hAPP(X48,hAPP(c_List_Ofoldl(X7,X4,hAPP(c_COMBC(X4,X7,X7),X76),X40),X32))=hAPP(c_List_Ofoldl(X49,X4,hAPP(c_COMBC(X4,X49,X49),X22),hAPP(X48,X40)),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__apply)). 4.02/4.27 fof(fact_listrel_OCons, axiom, ![X31, X32, X18, X17, X9, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)),c_List_Olistrel(X4,X18)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)),hAPP(hAPP(c_List_Olist_OCons(X4),X17),X31))),c_List_Olistrel(X4,X18))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel_OCons)). 4.02/4.27 fof(fact_rtrancl__listrel1__ConsI1, axiom, ![X9, X18, X31, X32, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X31))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X18))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__listrel1__ConsI1)). 4.02/4.27 fof(fact_equiv__class__subset, axiom, ![X25, X26, X18, X3, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),X18))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X25),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))<=c_Equiv__Relations_Oequiv(X4,X3,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__class__subset)). 4.02/4.27 fof(fact_setsum__shift__bounds__cl__nat__ivl, axiom, ![X20, X28, X21, X22, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Nat_Onat),X22),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X28))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X21,X20))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X28),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__bounds__cl__nat__ivl)). 4.02/4.27 fof(fact_rel__pow__E2, axiom, ![X39, X20, X16, X9, X4]:((~(![X34, X50]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X34)),X39))=>~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X34),X16)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X50),X39)))))<=hAPP(c_Nat_OSuc,X50)=X20))<=(X20=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>X9!=X16))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X16)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X20),X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__E2)). 4.02/4.27 fof(fact_lexord__append__left__rightI, axiom, ![X17, X9, X115, X18, X25, X26, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),X18))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Oappend(X4),X115),hAPP(hAPP(c_List_Olist_OCons(X4),X26),X9))),hAPP(hAPP(c_List_Oappend(X4),X115),hAPP(hAPP(c_List_Olist_OCons(X4),X25),X17)))),c_List_Olexord(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__append__left__rightI)). 4.02/4.27 fof(fact_rel__pow__E, axiom, ![X39, X20, X16, X9, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X16)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X20),X39)))=>(~(![X34, X50]:((~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X34),X16)),X39)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X34)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X50),X39))))<=hAPP(c_Nat_OSuc,X50)=X20))<=(X20=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>X16!=X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__E)). 4.02/4.27 fof(fact_card__quotient__disjoint, axiom, ![X18, X3, X4]:((c_Fun_Oinj__on(X4,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X4),c_Equiv__Relations_Oquotient(X4)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X18),X3)=>hAPP(c_Finite__Set_Ocard(X4),X3)=hAPP(c_Finite__Set_Ocard(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X3),X18)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__quotient__disjoint)). 4.02/4.27 fof(fact_INF__INT__eq, axiom, ![X9, X18, X7, X4]:(hBOOL(hAPP(hAPP(c_member(X7),X9),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X18)))<=>hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7))),X18)),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__INT__eq)). 4.02/4.27 fof(fact_SUP__UN__eq, axiom, ![X9, X18, X7, X4]:(hBOOL(hAPP(hAPP(c_member(X7),X9),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X18)))<=>hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7))),X18)),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__UN__eq)). 4.02/4.27 fof(fact_setprod__dividef, axiom, ![X76, X22, X3, X4, X7]:(class_Fields_Ofield__inverse__zero(X7)=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),hAPP(hAPP(c_COMBS(X4,X7,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,X7),X4),c_Rings_Oinverse__class_Odivide(X7)),X22)),X76)),X3)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X76),X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__dividef)). 4.02/4.27 fof(fact_Sup__fin_Ounion__inter, axiom, ![X6, X3, X4]:(class_Lattices_Olattice(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))),c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),c_Big__Operators_Olattice__class_OSup__fin(X4,X3)),c_Big__Operators_Olattice__class_OSup__fin(X4,X6))<=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Ounion__inter)). 4.02/4.27 fof(fact_Min_Ounion__inter, axiom, ![X6, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>(hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))),c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olinorder__class_OMin(X4,X3)),c_Big__Operators_Olinorder__class_OMin(X4,X6))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Ounion__inter)). 4.02/4.27 fof(fact_Max_Ounion__inter, axiom, ![X6, X3, X4]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))),c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olinorder__class_OMax(X4,X3)),c_Big__Operators_Olinorder__class_OMax(X4,X6))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Ounion__inter)). 4.02/4.27 fof(fact_Inf__fin_Ounion__inter, axiom, ![X6, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),c_Big__Operators_Olattice__class_OInf__fin(X4,X3)),c_Big__Operators_Olattice__class_OInf__fin(X4,X6))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))),c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Ounion__inter)). 4.02/4.27 fof(fact_setsum__mono3, axiom, ![X22, X3, X6, X4, X7]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X6)))<=![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(X22,X19)))<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X6),X3))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))<=(class_Groups_Oordered__ab__semigroup__add(X7)&class_Groups_Ocomm__monoid__add(X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__mono3)). 4.02/4.27 fof(fact_enum__all__prod__def, axiom, ![X56, X4, X7]:((hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X4),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X4),c_Enum_Oenum__class_Oenum__all(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_COMBB(tc_prod(X4,X7),tc_HOL_Obool,X7),X56)),c_Product__Type_OPair(X4,X7)))))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X4,X7)),X56)))<=(class_Enum_Oenum(X4)&class_Enum_Oenum(X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__all__prod__def)). 4.02/4.27 fof(fact_min__max_OInf__fin_Oremove, axiom, ![X9, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_member(X4),X9),X3))=>((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X9),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X3))&(c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X3)=X9<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oremove)). 4.02/4.27 fof(fact_divmod__nat__rel__mult2__eq, axiom, ![X10, X101, X14, X12, X11]:(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X11,X12),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X14),X101)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10))=>hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X10)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X14),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X14,X10))),X101))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__mult2__eq)). 4.02/4.27 fof(fact_Times__subset__cancel2, axiom, ![X6, X3, X7, X8, X9, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X3),X6))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X4),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X7,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X7),X8))),hAPP(hAPP(c_Product__Type_OSigma(X7,X4),X6),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X7),X8)))))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Times__subset__cancel2)). 4.02/4.27 fof(fact_enum__ex__prod__def, axiom, ![X56, X4, X7]:((hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X4),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool,X4),c_Enum_Oenum__class_Oenum__ex(X7)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_COMBB(tc_prod(X4,X7),tc_HOL_Obool,X7),X56)),c_Product__Type_OPair(X4,X7)))))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X4,X7)),X56)))<=(class_Enum_Oenum(X4)&class_Enum_Oenum(X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__ex__prod__def)). 4.02/4.27 fof(fact_fold__graph_H_Oequations_I2_J, axiom, ![X65, X70, X67, X66, X69, X7, X4]:((?[X19, X34]:((hAPP(hAPP(X69,X19),X34)=hAPP(hAPP(X69,X70),X65)&c_Nitpick_Ofold__graph_H(X4,X7,X69,X66,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X67),hAPP(hAPP(c_Set_Oinsert(X4),X19),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X34))&hBOOL(hAPP(hAPP(c_member(X4),X19),X67)))|(X67=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))&hAPP(hAPP(X69,X70),X65)=X66))<=>c_Nitpick_Ofold__graph_H(X4,X7,X69,X66,X67,hAPP(hAPP(X69,X70),X65))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph_H_Oequations_I2_J)). 4.02/4.27 fof(fact_min__max_OSup__fin_Oremove, axiom, ![X9, X3, X4]:(class_Orderings_Olinorder(X4)=>((((c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X3)=X9<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X3)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X9),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oremove)). 4.02/4.27 fof(fact_setsum__mono2, axiom, ![X22, X3, X6, X4, X7]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>((![X78]:(hBOOL(hAPP(hAPP(c_member(X4),X78),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X6),X3)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(X22,X78))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X6))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))))<=class_Groups_Oordered__comm__monoid__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__mono2)). 4.02/4.27 fof(fact_smin__emptyI, axiom, ![X156]:(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)),X156),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))<=X156!=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)). 4.02/4.27 fof(fact_zmult2__lemma, axiom, ![X10, X101, X14, X12, X11]:(((hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X10)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),c_Divides_Odiv__class_Omod(tc_Int_Oint,X14,X10))),X101))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10)))<=X12!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X12),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X14),X101)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult2__lemma)). 4.02/4.27 fof(fact_fold__graph__permute__diff, axiom, ![X26, X9, X3, X25, X4]:(((hBOOL(hAPP(hAPP(c_member(X4),X26),X3))=>(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X4,c_Groups_Otimes__class_Otimes(X4),X26,hAPP(hAPP(c_Set_Oinsert(X4),X25),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),X9))<=~(hBOOL(hAPP(hAPP(c_member(X4),X25),X3)))))<=hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X4,c_Groups_Otimes__class_Otimes(X4),X25,X3),X9)))<=class_Groups_Oab__semigroup__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph__permute__diff)). 4.02/4.27 fof(fact_wmax__emptyI, axiom, ![X156]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X156))=>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))),X156)),c_FunDef_Omax__weak))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wmax__emptyI)). 4.02/4.27 fof(fact_min__max_OInf__fin_Oinsert__remove, axiom, ![X9, X3, X4]:(class_Orderings_Olinorder(X4)=>(((c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=X9<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))&(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X9),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oinsert__remove)). 4.02/4.27 fof(fact_Cons__listrel1__Cons, axiom, ![X18, X31, X17, X32, X9, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)),hAPP(hAPP(c_List_Olist_OCons(X4),X17),X31))),c_List_Olistrel1(X4,X18)))<=>((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),X18))&X31=X32)|(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)),c_List_Olistrel1(X4,X18)))&X17=X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__listrel1__Cons)). 4.02/4.27 fof(fact_setprod__timesf, axiom, ![X3, X76, X22, X7, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X4),hAPP(hAPP(c_COMBS(X7,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X7),c_Groups_Otimes__class_Otimes(X4)),X22)),X76)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X4),X22),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X4),X76),X3))<=class_Groups_Ocomm__monoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__timesf)). 4.02/4.27 fof(fact_min__max_OSup__fin_Oinsert__remove, axiom, ![X9, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X9),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))&(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=X9)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oinsert__remove)). 4.02/4.27 fof(fact_zdiv__mono2__neg__lemma, axiom, ![X212, X213, X110, X101, X14, X12]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X14)),X101)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X110),X213)),X212)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X212))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X110),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X213),X14)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X110)))))<=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),X110),X213)),X212)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono2__neg__lemma)). 4.02/4.27 fof(fact_zdiv__mono2__lemma, axiom, ![X212, X213, X110, X101, X14, X12]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X14)),X101)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X110),X213)),X212)=>(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),X110),X213)),X212)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X212),X110))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X110),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14),X213)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X110))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono2__lemma)). 4.02/4.27 fof(fact_listrel__iff__nth, axiom, ![X18, X31, X32, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)),c_List_Olistrel(X4,X18)))<=>(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X31)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)&![X104]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X104),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(hAPP(c_List_Onth(X4),X32),X104)),hAPP(hAPP(c_List_Onth(X4),X31),X104))),X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__iff__nth)). 4.02/4.27 fof(fact_setsum__subtractf, axiom, ![X3, X76, X22, X7, X4]:(class_Groups_Oab__group__add(X4)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),hAPP(hAPP(c_COMBS(X7,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X7),c_Groups_Ominus__class_Ominus(X4)),X22)),X76)),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),X22),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),X76),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__subtractf)). 4.02/4.27 fof(fact_prod__fun__imageE, axiom, ![X39, X76, X22, X126, X49, X24, X7, X4]:(~(![X19, X34]:(X24=hAPP(hAPP(c_Product__Type_OPair(X4,X7),hAPP(X22,X19)),hAPP(X76,X34))=>~(hBOOL(hAPP(hAPP(c_member(tc_prod(X49,X126)),hAPP(hAPP(c_Product__Type_OPair(X49,X126),X19),X34)),X39)))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),X24),hAPP(c_Set_Oimage(tc_prod(X49,X126),tc_prod(X4,X7),c_Product__Type_Omap__pair(X49,X4,X126,X7,X22,X76)),X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_prod__fun__imageE)). 4.02/4.27 fof(fact_map__of__eqI, axiom, ![X31, X32, X7, X4]:((hAPP(c_Map_Omap__of(X4,X7),X32)=hAPP(c_Map_Omap__of(X4,X7),X31)<=![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Omap(tc_prod(X4,X7),X4),c_Product__Type_Ofst(X4,X7)),X32))))=>hAPP(hAPP(c_Map_Omap__of(X4,X7),X31),X19)=hAPP(hAPP(c_Map_Omap__of(X4,X7),X32),X19)))<=hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Omap(tc_prod(X4,X7),X4),c_Product__Type_Ofst(X4,X7)),X31))=hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Omap(tc_prod(X4,X7),X4),c_Product__Type_Ofst(X4,X7)),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__eqI)). 4.02/4.27 fof(fact_setsum__addf, axiom, ![X3, X76, X22, X7, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),hAPP(hAPP(c_COMBS(X7,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X7),c_Groups_Oplus__class_Oplus(X4)),X22)),X76)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),X22),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),X76),X3))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__addf)). 4.02/4.27 fof(fact_folding__one_Oremove, axiom, ![X9, X3, X87, X22, X4]:(((((X9=hAPP(X87,X3)<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))&(hAPP(hAPP(X22,X9),hAPP(X87,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(X87,X3)<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=c_Finite__Set_Ofolding__one(X4,X22,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oremove)). 4.02/4.27 fof(fact_folding_Ocommute__left__comp_H_H, axiom, ![X76, X49, X6, X3, X87, X22, X7, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hAPP(c_Fun_Ocomp(X7,X7,X49,hAPP(X87,X6)),hAPP(c_Fun_Ocomp(X7,X7,X49,hAPP(X87,X3)),X76))=hAPP(c_Fun_Ocomp(X7,X7,X49,hAPP(X87,X3)),hAPP(c_Fun_Ocomp(X7,X7,X49,hAPP(X87,X6)),X76))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))))<=c_Finite__Set_Ofolding(X4,X7,X22,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__left__comp_H_H)). 4.02/4.27 fof(fact_folding__one_Oinsert__remove, axiom, ![X9, X3, X87, X22, X4]:(c_Finite__Set_Ofolding__one(X4,X22,X87)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>hAPP(hAPP(X22,X9),hAPP(X87,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(X87,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(X87,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=X9)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oinsert__remove)). 4.02/4.27 fof(fact_inj__on__Un, axiom, ![X6, X3, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))<=>((c_Fun_Oinj__on(X4,X7,X22,X3)&c_Fun_Oinj__on(X4,X7,X22,X6))&c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X7,X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6))),hAPP(c_Set_Oimage(X4,X7,X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X6),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__Un)). 4.02/4.27 fof(fact_UN__equiv__class__inject, axiom, ![X203, X156, X22, X7, X18, X3, X4]:((c_Equiv__Relations_Ocongruent(X4,tc_fun(X7,tc_HOL_Obool),X18,X22)=>(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X156),X22)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X203),X22)=>((hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X203),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X3),X18)))=>(X203=X156<=![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>![X34]:((hAPP(X22,X34)=hAPP(X22,X19)=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X34)),X18)))<=hBOOL(hAPP(hAPP(c_member(X4),X34),X3))))))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X156),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X3),X18))))))<=c_Equiv__Relations_Oequiv(X4,X3,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__equiv__class__inject)). 4.02/4.27 fof(fact_Max_Oremove, axiom, ![X9, X3, X4]:(((hBOOL(hAPP(hAPP(c_member(X4),X9),X3))=>((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X9),c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMax(X4,X3))&(X9=c_Big__Operators_Olinorder__class_OMax(X4,X3)<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Oremove)). 4.02/4.27 fof(fact_UN__equiv__class__type, axiom, ![X6, X156, X22, X7, X18, X3, X4]:((c_Equiv__Relations_Ocongruent(X4,tc_fun(X7,tc_HOL_Obool),X18,X22)=>(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X156),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X3),X18)))=>(![X19]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),hAPP(X22,X19)),X6))<=hBOOL(hAPP(hAPP(c_member(X4),X19),X3)))=>hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X156),X22)),X6)))))<=c_Equiv__Relations_Oequiv(X4,X3,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__equiv__class__type)). 4.02/4.27 fof(fact_setsum__reindex__nonzero, axiom, ![X7, X48, X22, X86, X4, X49]:(((![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X86))=>![X34]:((X34!=X19=>(hAPP(X48,hAPP(X22,X19))=c_Groups_Ozero__class_Ozero(X49)<=hAPP(X22,X34)=hAPP(X22,X19)))<=hBOOL(hAPP(hAPP(c_member(X4),X34),X86))))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X49),hAPP(c_Fun_Ocomp(X7,X49,X4,X48),X22)),X86)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X49),X48),hAPP(c_Set_Oimage(X4,X7,X22),X86)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X86)))<=class_Groups_Ocomm__monoid__add(X49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__reindex__nonzero)). 4.02/4.27 fof(fact_Min_Oremove, axiom, ![X9, X3, X4]:(((((c_Big__Operators_Olinorder__class_OMin(X4,X3)=X9<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))&(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X9),c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMin(X4,X3)))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Oremove)). 4.02/4.27 fof(fact_Inf__fin_Oremove, axiom, ![X9, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>c_Big__Operators_Olattice__class_OInf__fin(X4,X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X9),c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))&(c_Big__Operators_Olattice__class_OInf__fin(X4,X3)=X9<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3))))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oremove)). 4.02/4.27 fof(fact_Sup__fin_Oremove, axiom, ![X9, X3, X4]:(class_Lattices_Olattice(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_member(X4),X9),X3))=>((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>X9=c_Big__Operators_Olattice__class_OSup__fin(X4,X3))&(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>c_Big__Operators_Olattice__class_OSup__fin(X4,X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X9),c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oremove)). 4.02/4.27 fof(fact_total__on__def, axiom, ![X18, X3, X4]:(c_Relation_Ototal__on(X4,X3,X18)<=>![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>![X114]:((X19!=X114=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X114)),X18))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X114),X19)),X18))))<=hBOOL(hAPP(hAPP(c_member(X4),X114),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_total__on__def)). 4.02/4.27 fof(fact_folding__one_Ounion__inter, axiom, ![X6, X3, X87, X22, X4]:(c_Finite__Set_Ofolding__one(X4,X22,X87)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((hAPP(hAPP(X22,hAPP(X87,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))),hAPP(X87,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))=hAPP(hAPP(X22,hAPP(X87,X3)),hAPP(X87,X6))<=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Ounion__inter)). 4.02/4.27 fof(fact_pair__leqI2, axiom, ![X123, X40, X25, X26]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26),X25))=>(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),X26),X40)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X25),X123))),c_FunDef_Opair__leq))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X40),X123)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__leqI2)). 4.02/4.27 fof(fact_list__all2__map2, axiom, ![X108, X22, X49, X109, X56, X7, X4]:(c_List_Olist__all2(X4,X7,X56,X109,hAPP(hAPP(c_List_Omap(X49,X7),X22),X108))<=>c_List_Olist__all2(X4,X49,hAPP(hAPP(c_COMBC(X4,tc_fun(X49,X7),tc_fun(X49,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X49,X7),tc_fun(X49,tc_HOL_Obool)),X4),c_COMBB(X7,tc_HOL_Obool,X49)),X56)),X22),X109,X108)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__map2)). 4.02/4.27 fof(fact_Image__INT__eq, axiom, ![X6, X49, X3, X18, X7, X4]:((c_Orderings_Obot__class_Obot(tc_fun(X49,tc_HOL_Obool))!=X3=>hAPP(c_Relation_OImage(X7,X4,X18),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X49,tc_fun(X7,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X49,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X49),c_Relation_OImage(X7,X4,X18)),X6)))<=c_Relation_Osingle__valued(X4,X7,hAPP(c_Relation_Oconverse(X7,X4),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__INT__eq)). 4.02/4.27 fof(fact_Inf__fin_Oinsert__remove, axiom, ![X9, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=X9)&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X9),c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oinsert__remove)). 4.02/4.27 fof(fact_pair__lessI2, axiom, ![X123, X40, X25, X26]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X40),X123))=>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),X26),X40)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X25),X123))),c_FunDef_Opair__less)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__lessI2)). 4.02/4.27 fof(fact_abs__diff__triangle__ineq, axiom, ![X44, X10, X12, X11, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X44)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X10))),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X44)))))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__diff__triangle__ineq)). 4.02/4.27 fof(fact_intrel__iff, axiom, ![X64, X115, X17, X9]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9),X64)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X115),X17)<=>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),X9),X17)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X115),X64))),c_Int_Ointrel))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_intrel__iff)). 4.02/4.27 fof(fact_INT__simps_I2_J, axiom, ![X6, X3, X7, X4, X8]:((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X8),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X3)),X6))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X8)&(X8=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X3)),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__simps_I2_J)). 4.02/4.27 fof(fact_Sigma__mono, axiom, ![X61, X6, X7, X8, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X8))=>(![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(X6,X19)),hAPP(X61,X19))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),X6)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X8),X61))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__mono)). 4.02/4.27 fof(fact_equiv__class__eq, axiom, ![X25, X26, X18, X3, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),X18))=>hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X25),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))<=c_Equiv__Relations_Oequiv(X4,X3,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__class__eq)). 4.02/4.27 fof(fact_Sup__fin_Oinsert__remove, axiom, ![X9, X3, X4]:(class_Lattices_Olattice(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((X9=c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))&(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X9),c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oinsert__remove)). 4.02/4.27 fof(fact_lexord__append__leftI, axiom, ![X9, X18, X64, X115, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X115),X64)),c_List_Olexord(X4,X18)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Oappend(X4),X9),X115)),hAPP(hAPP(c_List_Oappend(X4),X9),X64))),c_List_Olexord(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__append__leftI)). 4.02/4.27 fof(fact_listrel1I2, axiom, ![X9, X18, X31, X32, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X31))),c_List_Olistrel1(X4,X18)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)),c_List_Olistrel1(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1I2)). 4.02/4.27 fof(fact_card__Diff__insert, axiom, ![X6, X26, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6))),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),X6)))<=~(hBOOL(hAPP(hAPP(c_member(X4),X26),X6))))<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff__insert)). 4.02/4.27 fof(fact_reduction__pair__lemma, axiom, ![X86, X39, X56, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X86),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X56)))=>(c_Wellfounded_Owf(X4,X86)=>c_Wellfounded_Owf(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X39),X86))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X39),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X56))))<=c_FunDef_Oreduction__pair(X4,X56)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reduction__pair__lemma)). 4.02/4.27 fof(fact_fun__upd__None__restrict, axiom, ![X21, X7, X61, X9, X4]:((~(hBOOL(hAPP(hAPP(c_member(X4),X9),X61)))=>c_Map_Orestrict__map(X4,X7,X21,X61)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),c_Map_Orestrict__map(X4,X7,X21,X61)),X9),c_Option_Ooption_ONone(X7)))&(c_Map_Orestrict__map(X4,X7,X21,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X61),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),c_Map_Orestrict__map(X4,X7,X21,X61)),X9),c_Option_Ooption_ONone(X7))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X61)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__None__restrict)). 4.02/4.27 fof(fact_Max_Oinsert__remove, axiom, ![X9, X3, X4]:((((X9=c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))&(c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X9),c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Oinsert__remove)). 4.02/4.27 fof(fact_listsum__mono, axiom, ![X76, X22, X32, X4, X7]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X4,X7),X22),X32))),hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X4,X7),X76),X32))))<=![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(X22,X19)),hAPP(X76,X19)))))<=(class_Groups_Oordered__ab__semigroup__add(X7)&class_Groups_Omonoid__add(X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__mono)). 4.02/4.27 fof(fact_map__pair__imageI, axiom, ![X76, X22, X126, X49, X39, X25, X26, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X49,X126)),hAPP(hAPP(c_Product__Type_OPair(X49,X126),hAPP(X22,X26)),hAPP(X76,X25))),hAPP(c_Set_Oimage(tc_prod(X4,X7),tc_prod(X49,X126),c_Product__Type_Omap__pair(X4,X49,X7,X126,X22,X76)),X39)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X26),X25)),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__imageI)). 4.02/4.27 fof(fact_select__weight__member, axiom, ![X40, X32, X4]:(hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Product__Type_Ofst(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X4,X32),X40))),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X4),X4),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X4)),X32))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X4),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X4)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__weight__member)). 4.02/4.27 fof(fact_folding_Ocommute__left__comp_H, axiom, ![X76, X9, X49, X3, X87, X22, X7, X4]:((hAPP(c_Fun_Ocomp(X7,X7,X49,hAPP(X22,X9)),hAPP(c_Fun_Ocomp(X7,X7,X49,hAPP(X87,X3)),X76))=hAPP(c_Fun_Ocomp(X7,X7,X49,hAPP(X87,X3)),hAPP(c_Fun_Ocomp(X7,X7,X49,hAPP(X22,X9)),X76))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=c_Finite__Set_Ofolding(X4,X7,X22,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__left__comp_H)). 4.02/4.27 fof(fact_fun__left__comm_Ofold__graph__insertE__aux, axiom, ![X26, X17, X3, X16, X22, X7, X4]:((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X7,X22,X16,X3),X17))=>(hBOOL(hAPP(hAPP(c_member(X4),X26),X3))=>?[X291]:(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X7,X22,X16,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X291))&hAPP(hAPP(X22,X26),X291)=X17)))<=c_Finite__Set_Ofun__left__comm(X4,X7,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__graph__insertE__aux)). 4.02/4.27 fof(fact_rel__compI, axiom, ![X40, X24, X49, X18, X25, X26, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X26),X25)),X18))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X49)),hAPP(hAPP(c_Product__Type_OPair(X4,X49),X26),X24)),hAPP(hAPP(c_Relation_Orel__comp(X4,X7,X49),X18),X40)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X49)),hAPP(hAPP(c_Product__Type_OPair(X7,X49),X25),X24)),X40)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__compI)). 4.02/4.27 fof(fact_Min_Oinsert__remove, axiom, ![X9, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X9),c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))&(X9=c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Oinsert__remove)). 4.02/4.27 fof(fact_fold__image__insert, axiom, ![X16, X76, X26, X3, X4, X7]:(class_Groups_Oab__semigroup__mult(X7)=>((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(X76,X26)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X76),X16),X3))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X76),X16),hAPP(hAPP(c_Set_Oinsert(X4),X26),X3))<=~(hBOOL(hAPP(hAPP(c_member(X4),X26),X3))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__insert)). 4.02/4.27 fof(fact_card__SigmaI, axiom, ![X6, X7, X3, X4]:((hAPP(c_Finite__Set_Ocard(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),X6))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_Nat_Onat,X4),c_Finite__Set_Ocard(X7)),X6)),X3)<=![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(X6,X19)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__SigmaI)). 4.02/4.27 fof(fact_folding_Ounion__inter, axiom, ![X6, X3, X87, X22, X7, X4]:(c_Finite__Set_Ofolding(X4,X7,X22,X87)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X87,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))),hAPP(X87,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))=hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X87,X3)),hAPP(X87,X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ounion__inter)). 4.02/4.27 fof(fact_add__frac__eq, axiom, ![X53, X13, X29, X43, X4]:(((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X53),X29))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X13),X29)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X53),X43))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X43),X29))<=c_Groups_Ozero__class_Ozero(X4)!=X29)<=c_Groups_Ozero__class_Ozero(X4)!=X43)<=class_Fields_Ofield(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__frac__eq)). 4.02/4.27 fof(fact_fold__image__cong, axiom, ![X16, X48, X76, X3, X4, X7]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(![X19]:(hAPP(X48,X19)=hAPP(X76,X19)<=hBOOL(hAPP(hAPP(c_member(X4),X19),X3)))=>hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X48),X16),X3)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X76),X16),X3)))<=class_Groups_Oab__semigroup__mult(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__cong)). 4.02/4.27 fof(fact_fun__left__comm_Ofold__insert__remove, axiom, ![X9, X16, X3, X22, X7, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),X16),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=hAPP(hAPP(X22,X9),hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),X16),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))<=c_Finite__Set_Ofun__left__comm(X4,X7,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__insert__remove)). 4.02/4.27 fof(fact_fun__left__comm_Ofold__rec, axiom, ![X16, X9, X3, X22, X7, X4]:(c_Finite__Set_Ofun__left__comm(X4,X7,X22)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),X16),X3)=hAPP(hAPP(X22,X9),hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),X16),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__rec)). 4.02/4.27 fof(fact_diff__frac__eq, axiom, ![X53, X13, X29, X43, X4]:(class_Fields_Ofield(X4)=>(c_Groups_Ozero__class_Ozero(X4)!=X43=>(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X53),X29))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X13),X29)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X53),X43))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X43),X29))<=X29!=c_Groups_Ozero__class_Ozero(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__frac__eq)). 4.02/4.27 fof(fact_pair__leqI1, axiom, ![X123, X40, X25, X26]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),X25))=>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),X26),X40)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X25),X123))),c_FunDef_Opair__leq))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__leqI1)). 4.02/4.27 fof(fact_pair__lessI1, axiom, ![X123, X40, X25, X26]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),X25))=>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),X26),X40)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X25),X123))),c_FunDef_Opair__less))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__lessI1)). 4.02/4.27 fof(fact_setprod_Oinsert__remove, axiom, ![X9, X76, X3, X4, X7]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(X76,X9)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X76),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X76),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Groups_Ocomm__monoid__mult(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod_Oinsert__remove)). 4.02/4.27 fof(fact_inj__on__image__set__diff, axiom, ![X6, X3, X8, X22, X7, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X8))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X8))=>hAPP(c_Set_Oimage(X4,X7,X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X7,X22),X3)),hAPP(c_Set_Oimage(X4,X7,X22),X6))))<=c_Fun_Oinj__on(X4,X7,X22,X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__image__set__diff)). 4.02/4.27 fof(fact_inj__on__image__Int, axiom, ![X6, X3, X8, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,X8)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X8))=>(hAPP(c_Set_Oimage(X4,X7,X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X7,X22),X3)),hAPP(c_Set_Oimage(X4,X7,X22),X6))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X8))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__image__Int)). 4.02/4.27 fof(fact_setsum_Oinsert__remove, axiom, ![X9, X76, X3, X4, X7]:(class_Groups_Ocomm__monoid__add(X7)=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(X76,X9)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum_Oinsert__remove)). 4.02/4.27 fof(fact_setsum__strict__mono, axiom, ![X76, X22, X3, X4, X7]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3=>(![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(X22,X19)),hAPP(X76,X19))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),X3))))))<=(class_Groups_Ocomm__monoid__add(X7)&class_Groups_Oordered__cancel__ab__semigroup__add(X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__strict__mono)). 4.02/4.27 fof(fact_inj__on__insert, axiom, ![X3, X26, X22, X7, X4]:((c_Fun_Oinj__on(X4,X7,X22,X3)&~(hBOOL(hAPP(hAPP(c_member(X7),hAPP(X22,X26)),hAPP(c_Set_Oimage(X4,X7,X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))))<=>c_Fun_Oinj__on(X4,X7,X22,hAPP(hAPP(c_Set_Oinsert(X4),X26),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__insert)). 4.02/4.27 fof(fact_folding__image_Odistrib, axiom, ![X48, X76, X3, X87, X16, X22, X7, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3))=>hAPP(hAPP(X87,hAPP(hAPP(c_COMBS(X7,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X7),X22),X76)),X48)),X3)=hAPP(hAPP(X22,hAPP(hAPP(X87,X76),X3)),hAPP(hAPP(X87,X48),X3)))<=c_Finite__Set_Ofolding__image(X4,X7,X22,X16,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image_Odistrib)). 4.02/4.27 fof(fact_rel__pow__Suc__E2, axiom, ![X39, X20, X16, X9, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X16)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),hAPP(c_Nat_OSuc,X20)),X39)))=>~(![X34]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X34)),X39))=>~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X34),X16)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X20),X39))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__Suc__E2)). 4.02/4.27 fof(fact_rel__pow__Suc__D2, axiom, ![X39, X20, X16, X9, X4]:(?[X34]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X34)),X39))&hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X34),X16)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X20),X39))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X16)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),hAPP(c_Nat_OSuc,X20)),X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__Suc__D2)). 4.02/4.27 fof(fact_rel__pow__Suc__E, axiom, ![X39, X20, X16, X9, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X16)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),hAPP(c_Nat_OSuc,X20)),X39)))=>~(![X34]:(~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X34),X16)),X39)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X34)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X20),X39)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__Suc__E)). 4.02/4.27 fof(fact_setprod_Oremove, axiom, ![X76, X9, X3, X4, X7]:(class_Groups_Ocomm__monoid__mult(X7)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X76),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(X76,X9)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X76),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod_Oremove)). 4.02/4.27 fof(fact_setsum__diff1_H, axiom, ![X22, X26, X3, X4, X7]:(((hBOOL(hAPP(hAPP(c_member(X4),X26),X3))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(X22,X26)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Groups_Ocomm__monoid__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff1_H)). 4.02/4.27 fof(fact_map__of__map__keys, axiom, ![X21, X7, X32, X4]:(hAPP(c_List_Oset(X4),X32)=c_Map_Odom(X4,X7,X21)=>X21=hAPP(c_Map_Omap__of(X4,X7),hAPP(hAPP(c_List_Omap(X4,tc_prod(X4,X7)),hAPP(hAPP(c_COMBS(X4,X7,tc_prod(X4,X7)),c_Product__Type_OPair(X4,X7)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X7),X7,X4),c_Option_Othe(X7)),X21))),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__map__keys)). 4.02/4.27 fof(fact_fold__image__reindex, axiom, ![X16, X76, X48, X7, X3, X4, X49]:(((hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X49,X4,c_Groups_Otimes__class_Otimes(X49)),hAPP(c_Fun_Ocomp(X7,X49,X4,X76),X48)),X16),X3)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X49,X7,c_Groups_Otimes__class_Otimes(X49)),X76),X16),hAPP(c_Set_Oimage(X4,X7,X48),X3))<=c_Fun_Oinj__on(X4,X7,X48,X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Groups_Oab__semigroup__mult(X49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__reindex)). 4.02/4.27 fof(fact_fun__upd__image, axiom, ![X17, X22, X7, X3, X9, X4]:((hAPP(c_Set_Oimage(X4,X7,X22),X3)=hAPP(c_Set_Oimage(X4,X7,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X7),X22),X9),X17)),X3)<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3))))&(hAPP(c_Set_Oimage(X4,X7,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X7),X22),X9),X17)),X3)=hAPP(hAPP(c_Set_Oinsert(X7),X17),hAPP(c_Set_Oimage(X4,X7,X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__image)). 4.02/4.27 fof(fact_nat__diff__add__eq1, axiom, ![X5, X2, X106, X46, X135]:(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),X46),X135)),X106)),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),X46),X106)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X135),X106)),X5))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X135),X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__diff__add__eq1)). 4.02/4.27 fof(fact_nat__diff__add__eq2, axiom, ![X5, X2, X106, X135, X46]:(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),X46),X106)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X135),X106)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(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(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X135),X46)),X106)),X5))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__diff__add__eq2)). 4.02/4.27 fof(fact_listsum__mult__const, axiom, ![X32, X24, X22, X7, X4]:(class_Rings_Osemiring__0(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32))),X24)=hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X7,X4),hAPP(hAPP(c_COMBC(X7,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X7),c_Groups_Otimes__class_Otimes(X4)),X22)),X24)),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__mult__const)). 4.02/4.27 fof(fact_listrel__Cons2, axiom, ![X18, X31, X17, X32, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),hAPP(hAPP(c_List_Olist_OCons(X4),X17),X31))),c_List_Olistrel(X4,X18)))=>~(![X19, X293]:(X32=hAPP(hAPP(c_List_Olist_OCons(X4),X19),X293)=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X17)),X18))=>~(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)),X293),X31)),c_List_Olistrel(X4,X18)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Cons2)). 4.02/4.27 fof(fact_nth__zip, axiom, ![X59, X7, X45, X4, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))=>(hAPP(hAPP(c_Product__Type_OPair(X4,X7),hAPP(hAPP(c_List_Onth(X4),X45),X46)),hAPP(hAPP(c_List_Onth(X7),X59),X46))=hAPP(hAPP(c_List_Onth(tc_prod(X4,X7)),hAPP(hAPP(c_List_Ozip(X4,X7),X45),X59)),X46)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X59))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__zip)). 4.02/4.27 fof(fact_listrel__Cons1, axiom, ![X18, X32, X31, X17, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X17),X31)),X32)),c_List_Olistrel(X4,X18)))=>~(![X34, X146]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X17),X34)),X18))=>~(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)),X31),X146)),c_List_Olistrel(X4,X18)))))<=X32=hAPP(hAPP(c_List_Olist_OCons(X4),X34),X146)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Cons1)). 4.02/4.27 fof(fact_INF__commute, axiom, ![X22, X6, X49, X3, X7, X4]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,X4),X3),hAPP(hAPP(c_COMBB(tc_fun(X49,X4),X4,X7),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X49,X4),X6)),X22))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X49,X4),X6),hAPP(hAPP(c_COMBB(tc_fun(X7,X4),X4,X49),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,X4),X3)),hAPP(c_COMBC(X7,X49,X4),X22)))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__commute)). 4.02/4.27 fof(fact_SUP__commute, axiom, ![X22, X6, X49, X3, X7, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X4),X3),hAPP(hAPP(c_COMBB(tc_fun(X49,X4),X4,X7),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,X4),X6)),X22))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,X4),X6),hAPP(hAPP(c_COMBB(tc_fun(X7,X4),X4,X49),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X4),X3)),hAPP(c_COMBC(X7,X49,X4),X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__commute)). 4.02/4.27 fof(fact_measures__lesseq, axiom, ![X278, X4, X17, X9, X22]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X22),X278))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),c_List_Omeasures(X4,X278))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X22,X9)),hAPP(X22,X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_measures__lesseq)). 4.02/4.27 fof(fact_listrel1I1, axiom, ![X32, X18, X17, X9, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),X18))=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)),hAPP(hAPP(c_List_Olist_OCons(X4),X17),X32))),c_List_Olistrel1(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1I1)). 4.02/4.27 fof(fact_UN__insert__distrib, axiom, ![X6, X26, X7, X3, X115, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X115),X3))=>hAPP(hAPP(c_Set_Oinsert(X7),X26),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_Set_Oinsert(X7),X26)),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__insert__distrib)). 4.02/4.27 fof(fact_pick__member, axiom, ![X32, X4, X37]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X37),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X4),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X4)),X32))))=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Random_Opick(X4,X32),X37)),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X4),X4),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X4)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pick__member)). 4.02/4.27 fof(fact_eq__equiv__class, axiom, ![X3, X25, X26, X18, X4]:(((hBOOL(hAPP(hAPP(c_member(X4),X25),X3))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),X18)))<=c_Equiv__Relations_Oequiv(X4,X3,X18))<=hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X25),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__equiv__class)). 4.02/4.27 fof(fact_listsum__map__filter, axiom, ![X22, X56, X32, X4, X7]:((![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32)))=>(hAPP(X22,X19)=c_Groups_Ozero__class_Ozero(X7)<=~(hBOOL(hAPP(X56,X19)))))=>hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X4,X7),X22),X32))=hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X4,X7),X22),hAPP(c_List_Ofilter(X4,X56),X32))))<=class_Groups_Omonoid__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__map__filter)). 4.02/4.27 fof(fact_setprod__diff1, axiom, ![X26, X22, X3, X4, X7]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),X3)<=~(hBOOL(hAPP(hAPP(c_member(X4),X26),X3))))&(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),X3)),hAPP(X22,X26))<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3))))<=hAPP(X22,X26)!=c_Groups_Ozero__class_Ozero(X7)))<=class_Fields_Ofield(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__diff1)). 4.02/4.27 fof(fact_distinct__list__update, axiom, ![X37, X26, X32, X4]:((hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Olist__update(X4,X32),X37),X26)))<=~(hBOOL(hAPP(hAPP(c_member(X4),X26),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X32)),hAPP(hAPP(c_Set_Oinsert(X4),hAPP(hAPP(c_List_Onth(X4),X32),X37)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))))<=hBOOL(hAPP(c_List_Odistinct(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__list__update)). 4.02/4.27 fof(fact_setsum__diff1__ring, axiom, ![X22, X26, X3, X4, X7]:(class_Rings_Oring(X7)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X3)),hAPP(X22,X26))<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff1__ring)). 4.02/4.27 fof(fact_card__Un__Int, axiom, ![X6, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X3)),hAPP(c_Finite__Set_Ocard(X4),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Un__Int)). 4.02/4.27 fof(fact_folding_Ocommute__left__comp, axiom, ![X76, X9, X17, X49, X87, X22, X7, X4]:(c_Finite__Set_Ofolding(X4,X7,X22,X87)=>hAPP(c_Fun_Ocomp(X7,X7,X49,hAPP(X22,X9)),hAPP(c_Fun_Ocomp(X7,X7,X49,hAPP(X22,X17)),X76))=hAPP(c_Fun_Ocomp(X7,X7,X49,hAPP(X22,X17)),hAPP(c_Fun_Ocomp(X7,X7,X49,hAPP(X22,X9)),X76))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__left__comp)). 4.02/4.27 fof(fact_folding__image__simple_Ounion__inter, axiom, ![X6, X3, X87, X76, X16, X22, X7, X4]:(((hAPP(hAPP(X22,hAPP(X87,X3)),hAPP(X87,X6))=hAPP(hAPP(X22,hAPP(X87,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3),X6))),hAPP(X87,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X3),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3)))<=c_Finite__Set_Ofolding__image__simple(X4,X7,X22,X16,X76,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Ounion__inter)). 4.02/4.27 fof(fact_rtrancl__trans, axiom, ![X24, X18, X25, X26, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),c_Transitive__Closure_Ortrancl(X4,X18)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X24)),c_Transitive__Closure_Ortrancl(X4,X18)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X25),X24)),c_Transitive__Closure_Ortrancl(X4,X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__trans)). 4.02/4.27 fof(fact_setsum__diff1, axiom, ![X22, X26, X3, X4, X7]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X3)<=~(hBOOL(hAPP(hAPP(c_member(X4),X26),X3))))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X3)),hAPP(X22,X26))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3)))))<=class_Groups_Oab__group__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff1)). 4.02/4.27 fof(fact_folding_Oinsert__remove, axiom, ![X9, X3, X87, X22, X7, X4]:(c_Finite__Set_Ofolding(X4,X7,X22,X87)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(X87,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X87,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),hAPP(X22,X9)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Oinsert__remove)). 4.02/4.27 fof(fact_surj__Compl__image__subset, axiom, ![X3, X22, X4, X7]:(hAPP(c_Set_Oimage(X7,X4,X22),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X4,X22),X3))),hAPP(c_Set_Oimage(X7,X4,X22),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_surj__Compl__image__subset)). 4.02/4.27 fof(fact_geometric__sum, axiom, ![X20, X9, X4]:(class_Fields_Ofield(X4)=>(c_Groups_Oone__class_Oone(X4)!=X9=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X9),X20)),c_Groups_Oone__class_Oone(X4))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X9),c_Groups_Oone__class_Oone(X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(c_Power_Opower__class_Opower(X4),X9)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_geometric__sum)). 4.02/4.27 fof(fact_in__measures_I2_J, axiom, ![X278, X22, X17, X9, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X22),X278))))<=>((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),c_List_Omeasures(X4,X278)))&hAPP(X22,X9)=hAPP(X22,X17))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X22,X9)),hAPP(X22,X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__measures_I2_J)). 4.02/4.27 fof(fact_convex__bound__lt, axiom, ![X1, X106, X43, X11, X13, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X43),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X106))=>((c_Groups_Oone__class_Oone(X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X106),X1)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X106),X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X43))),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X1))))))<=class_Rings_Olinordered__semiring__1__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_convex__bound__lt)). 4.02/4.27 fof(fact_convex__bound__le, axiom, ![X1, X106, X43, X11, X13, X4]:(class_Rings_Olinordered__semiring__1(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X43),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X106))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X1))=>(c_Groups_Oone__class_Oone(X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X106),X1)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X106),X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X1),X43))),X11)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_convex__bound__le)). 4.02/4.27 fof(fact_folding_Oremove, axiom, ![X9, X3, X87, X22, X7, X4]:(c_Finite__Set_Ofolding(X4,X7,X22,X87)=>((hBOOL(hAPP(hAPP(c_member(X4),X9),X3))=>hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X87,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),hAPP(X22,X9))=hAPP(X87,X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Oremove)). 4.02/4.27 fof(fact_insort__left__comm, axiom, ![X32, X17, X9, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X17),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X9),X32))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X9),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X17),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__left__comm)). 4.02/4.27 fof(fact_setprod__mono__one__right, axiom, ![X22, X86, X105, X4, X7]:(class_Groups_Ocomm__monoid__mult(X7)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X105))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X86),X105))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),X86)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),X105)<=![X19]:(hAPP(X22,X19)=c_Groups_Oone__class_Oone(X7)<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X105),X86)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__mono__one__right)). 4.02/4.27 fof(fact_setprod__mono__one__left, axiom, ![X22, X86, X105, X4, X7]:(class_Groups_Ocomm__monoid__mult(X7)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X86),X105))=>(![X19]:(c_Groups_Oone__class_Oone(X7)=hAPP(X22,X19)<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X105),X86))))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),X105)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),X86)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X105)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__mono__one__left)). 4.02/4.27 fof(fact_setsum__mono__zero__left, axiom, ![X22, X86, X105, X4, X7]:(class_Groups_Ocomm__monoid__add(X7)=>(((![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X105),X86)))=>hAPP(X22,X19)=c_Groups_Ozero__class_Ozero(X7))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X105)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X86))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X86),X105)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X105)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__mono__zero__left)). 4.02/4.27 fof(fact_setsum__mono__zero__right, axiom, ![X22, X86, X105, X4, X7]:((((![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X105),X86)))=>c_Groups_Ozero__class_Ozero(X7)=hAPP(X22,X19))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X105)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X86))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X86),X105)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X105)))<=class_Groups_Ocomm__monoid__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__mono__zero__right)). 4.02/4.27 fof(fact_sorted__list__of__set__insert, axiom, ![X9, X3, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>c_List_Olinorder__class_Osorted__list__of__set(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X9),c_List_Olinorder__class_Osorted__list__of__set(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set__insert)). 4.02/4.27 fof(fact_sequence__trans, axiom, ![X28, X37, X18, X22, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(X22,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),X28))),hAPP(X22,X37))),c_Transitive__Closure_Ortrancl(X4,X18)))<=![X42]:hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(X22,hAPP(c_Nat_OSuc,X42))),hAPP(X22,X42))),c_Transitive__Closure_Ortrancl(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sequence__trans)). 4.02/4.27 fof(fact_folding__image__simple_Oinsert__remove, axiom, ![X9, X3, X87, X76, X16, X22, X7, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3))=>hAPP(X87,hAPP(hAPP(c_Set_Oinsert(X7),X9),X3))=hAPP(hAPP(X22,hAPP(X76,X9)),hAPP(X87,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X7),X9),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))))))<=c_Finite__Set_Ofolding__image__simple(X4,X7,X22,X16,X76,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Oinsert__remove)). 4.02/4.27 fof(fact_Image__subset__eq, axiom, ![X6, X3, X18, X7, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X4,X18),X3)),X6))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X7,hAPP(c_Relation_Oconverse(X7,X4),X18)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X6)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__subset__eq)). 4.02/4.27 fof(fact_insert__partition, axiom, ![X87, X9, X4]:((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X9),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X87))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=![X19]:(![X114]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X114),hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),X9),X87)))=>(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X19),X114)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=X19!=X114))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X19),hAPP(hAPP(c_Set_Oinsert(tc_fun(X4,tc_HOL_Obool)),X9),X87)))))<=~(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X9),X87)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__partition)). 4.02/4.27 fof(fact_setsum__diff__nat__ivl, axiom, ![X22, X51, X20, X21, X4]:(class_Groups_Oab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),X51))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X21),X51))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X21),X20)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X20),X51))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff__nat__ivl)). 4.02/4.27 fof(fact_folding__image__simple_Oremove, axiom, ![X9, X3, X87, X76, X16, X22, X7, X4]:(c_Finite__Set_Ofolding__image__simple(X4,X7,X22,X16,X76,X87)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3))=>(hBOOL(hAPP(hAPP(c_member(X7),X9),X3))=>hAPP(hAPP(X22,hAPP(X76,X9)),hAPP(X87,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X7),X9),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))=hAPP(X87,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Oremove)). 4.02/4.27 fof(fact_subset__equiv__class, axiom, ![X26, X25, X18, X3, X4]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),X18))<=hBOOL(hAPP(hAPP(c_member(X4),X25),X3)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X25),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))<=c_Equiv__Relations_Oequiv(X4,X3,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__equiv__class)). 4.02/4.27 fof(fact_converse__rtrancl__into__rtrancl, axiom, ![X24, X18, X25, X26, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X25),X24)),c_Transitive__Closure_Ortrancl(X4,X18)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X24)),c_Transitive__Closure_Ortrancl(X4,X18))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__rtrancl__into__rtrancl)). 4.02/4.27 fof(fact_rtrancl_Ortrancl__into__rtrancl, axiom, ![X24, X18, X25, X26, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),c_Transitive__Closure_Ortrancl(X4,X18)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X25),X24)),X18))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X24)),c_Transitive__Closure_Ortrancl(X4,X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl_Ortrancl__into__rtrancl)). 4.02/4.27 fof(fact_setsum__add__nat__ivl, axiom, ![X22, X51, X20, X21, X4]:(class_Groups_Ocomm__monoid__add(X4)=>((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X21),X51))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X21),X20))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X20),X51)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),X51)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__add__nat__ivl)). 4.02/4.27 fof(fact_finite__range__updI, axiom, ![X25, X26, X22, X7, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X4)),hAPP(c_Set_Oimage(X7,tc_Option_Ooption(X4),X22),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))))=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X4)),hAPP(c_Set_Oimage(X7,tc_Option_Ooption(X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X4)),X22),X26),hAPP(c_Option_Ooption_OSome(X4),X25))),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__range__updI)). 4.02/4.27 fof(fact_insort__key__left__comm, axiom, ![X32, X7, X17, X9, X22, X4]:(class_Orderings_Olinorder(X4)=>(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X4,X22),X9),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X4,X22),X17),X32))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X4,X22),X17),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X4,X22),X9),X32))<=hAPP(X22,X9)!=hAPP(X22,X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__key__left__comm)). 4.02/4.27 fof(fact_aset_I6_J, axiom, ![X3, X123, X61]:((![X19]:(![X114]:(![X124]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X124),X3))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X124),X114)!=X19)<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X114),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X61))))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),X61)),X123))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19),X123))))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X123),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)),X61))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I6_J)). 4.02/4.27 fof(fact_hom__fold1__commute, axiom, ![X176, X48, X4]:(class_Lattices_Oab__semigroup__idem__mult(X4)=>(![X19, X34]:hAPP(X48,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X19),X34))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(X48,X19)),hAPP(X48,X34))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X176))=>(X176!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(X48,hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),X176))=hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),hAPP(c_Set_Oimage(X4,X4,X48),X176)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hom__fold1__commute)). 4.02/4.27 fof(fact_setprod_Ounion__disjoint, axiom, ![X76, X6, X3, X4, X7]:(class_Groups_Ocomm__monoid__mult(X7)=>(((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X76),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X76),X6))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X76),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod_Ounion__disjoint)). 4.02/4.27 fof(fact_inj__image__Compl__subset, axiom, ![X3, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X7,X22),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X3))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X7,X22),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__image__Compl__subset)). 4.02/4.27 fof(fact_setsum__Un__disjoint, axiom, ![X76, X6, X3, X4, X7]:(class_Groups_Ocomm__monoid__add(X7)=>(((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X76),X6))<=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__Un__disjoint)). 4.02/4.27 fof(fact_equiv__class__nondisjoint, axiom, ![X25, X26, X9, X18, X3, X4]:(c_Equiv__Relations_Oequiv(X4,X3,X18)=>(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X25),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__class__nondisjoint)). 4.02/4.27 fof(fact_setsum__diff1__nat, axiom, ![X22, X3, X26, X4]:((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X22),X3)<=~(hBOOL(hAPP(hAPP(c_member(X4),X26),X3))))&(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X22),X3)),hAPP(X22,X26))<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff1__nat)). 4.02/4.27 fof(fact_ball__Un, axiom, ![X56, X6, X3, X4]:((![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(X56,X19)))&![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X6))=>hBOOL(hAPP(X56,X19))))<=>![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)))=>hBOOL(hAPP(X56,X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ball__Un)). 4.02/4.27 fof(fact_nat__less__add__iff1, axiom, ![X20, X21, X115, X37, X38]:((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),X37),X38)),X115)),X21)),X20))<=>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),X37),X115)),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X115)),X20))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X38),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__less__add__iff1)). 4.02/4.27 fof(fact_nat__le__add__iff1, axiom, ![X20, X21, X115, X37, X38]:((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),X37),X115)),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X115)),X20)))<=>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),X37),X38)),X115)),X21)),X20)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X38),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__le__add__iff1)). 4.02/4.27 fof(fact_nat__less__add__iff2, axiom, ![X20, X21, X115, X38, X37]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X37),X38))=>(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),X37),X115)),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X115)),X20)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X38),X37)),X115)),X20))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__less__add__iff2)). 4.02/4.27 fof(fact_rel__comp__mono, axiom, ![X40, X271, X49, X18, X214, X7, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X49),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X7,X49),X214),X271)),hAPP(hAPP(c_Relation_Orel__comp(X4,X7,X49),X18),X40)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X49),tc_HOL_Obool)),X271),X40)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X214),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__mono)). 4.02/4.27 fof(fact_nat__le__add__iff2, axiom, ![X20, X21, X115, X38, X37]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X38),X37)),X115)),X20)))<=>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),X37),X115)),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),X115)),X20))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X37),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__le__add__iff2)). 4.02/4.27 fof(fact_list__update__append, axiom, ![X13, X59, X45, X4, X5]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45))))=>hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Oappend(X4),X45),X59)),X5),X13)=hAPP(hAPP(c_List_Oappend(X4),X45),hAPP(hAPP(c_List_Olist__update(X4,X59),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45))),X13)))&(hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Oappend(X4),X45),X59)),X5),X13)=hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Olist__update(X4,X45),X5),X13)),X59)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__append)). 4.02/4.27 fof(fact_setsum__bounded, axiom, ![X211, X22, X3, X4, X7]:((class_Groups_Oordered__ab__semigroup__add(X7)&class_Rings_Osemiring__1(X7))=>(![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(X22,X42)),X211)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7),hAPP(c_Finite__Set_Ocard(X4),X3))),X211))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__bounded)). 4.02/4.27 fof(fact_zip__append, axiom, ![X304, X59, X282, X7, X45, X4]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X282)=>(hAPP(hAPP(c_List_Ozip(X4,X7),hAPP(hAPP(c_List_Oappend(X4),X45),X59)),hAPP(hAPP(c_List_Oappend(X7),X282),X304))=hAPP(hAPP(c_List_Oappend(tc_prod(X4,X7)),hAPP(hAPP(c_List_Ozip(X4,X7),X45),X282)),hAPP(hAPP(c_List_Ozip(X4,X7),X59),X304))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X59)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X304))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__append)). 4.02/4.27 fof(fact_card_Ounion__inter__neutral, axiom, ![X6, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X3)),hAPP(c_Finite__Set_Ocard(X4),X6))=hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))<=(?[X19]:hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))=>c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card_Ounion__inter__neutral)). 4.02/4.27 fof(fact_less__add__iff1, axiom, ![X102, X25, X24, X207, X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X207)),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X25),X207)),X102)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X26),X25)),X207)),X24)),X102)))<=class_Rings_Oordered__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__add__iff1)). 4.02/4.27 fof(fact_le__add__iff1, axiom, ![X102, X25, X24, X207, X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X26),X25)),X207)),X24)),X102))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X207)),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X25),X207)),X102))))<=class_Rings_Oordered__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__add__iff1)). 4.02/4.27 fof(fact_less__add__iff2, axiom, ![X102, X25, X24, X207, X26, X4]:(class_Rings_Oordered__ring(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X25),X26)),X207)),X102)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X207)),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X25),X207)),X102))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__add__iff2)). 4.02/4.27 fof(fact_folding__one_Oclosed, axiom, ![X3, X87, X22, X4]:((((hBOOL(hAPP(hAPP(c_member(X4),hAPP(X87,X3)),X3))<=![X19, X34]:hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(X22,X19),X34)),hAPP(hAPP(c_Set_Oinsert(X4),X19),hAPP(hAPP(c_Set_Oinsert(X4),X34),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))<=X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=c_Finite__Set_Ofolding__one(X4,X22,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oclosed)). 4.02/4.27 fof(fact_le__add__iff2, axiom, ![X102, X25, X24, X207, X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X24),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X25),X26)),X207)),X102)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X207)),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X25),X207)),X102))))<=class_Rings_Oordered__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__add__iff2)). 4.02/4.27 fof(fact_restrict__map__upds, axiom, ![X21, X61, X31, X7, X32, X4]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=>(c_Map_Omap__upds(X4,X7,c_Map_Orestrict__map(X4,X7,X21,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X61),hAPP(c_List_Oset(X4),X32))),X32,X31)=c_Map_Orestrict__map(X4,X7,c_Map_Omap__upds(X4,X7,X21,X32,X31),X61)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X32)),X61)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__map__upds)). 4.02/4.27 fof(fact_fun__upd__twist, axiom, ![X102, X25, X21, X7, X4, X24, X26]:(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X7),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X7),X21),X26),X25)),X24),X102)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X7),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X7),X21),X24),X102)),X26),X25)<=X26!=X24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__twist)). 4.02/4.27 fof(fact_rtrancl__listrel1__if__listrel, axiom, ![X18, X31, X32, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X18))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)),c_List_Olistrel(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__listrel1__if__listrel)). 4.02/4.27 fof(fact_map__add__upd__left, axiom, ![X245, X246, X247, X7, X21, X4]:(c_Map_Omap__add(X4,X7,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X246),X21),hAPP(c_Option_Ooption_OSome(X7),X245)),X247)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),c_Map_Omap__add(X4,X7,X246,X247)),X21),hAPP(c_Option_Ooption_OSome(X7),X245))<=~(hBOOL(hAPP(hAPP(c_member(X4),X21),c_Map_Odom(X4,X7,X247))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__upd__left)). 4.02/4.27 fof(fact_UN__equiv__class, axiom, ![X26, X22, X7, X18, X3, X4]:(c_Equiv__Relations_Oequiv(X4,X3,X18)=>((hAPP(X22,X26)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X22)<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3)))<=c_Equiv__Relations_Ocongruent(X4,tc_fun(X7,tc_HOL_Obool),X18,X22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__equiv__class)). 4.02/4.27 fof(fact_fold__sup__le__sup, axiom, ![X24, X25, X3, X4]:(class_Lattices_Osemilattice__sup(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4)),X24),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X25),X24)))<=![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X19),X25)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__sup__le__sup)). 4.02/4.27 fof(fact_min__max_Ofold__sup__le__sup, axiom, ![X24, X25, X3, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X19),X25))<=hBOOL(hAPP(hAPP(c_member(X4),X19),X3)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omax(X4)),X24),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X25),X24)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofold__sup__le__sup)). 4.02/4.27 fof(fact_min__max_Oinf__le__fold__inf, axiom, ![X24, X25, X3, X4]:(class_Orderings_Olinorder(X4)=>((![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),X19)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X25),X24)),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omin(X4)),X24),X3))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__le__fold__inf)). 4.02/4.27 fof(fact_inf__le__fold__inf, axiom, ![X24, X25, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),X19)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X25),X24)),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X24),X3)))))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__le__fold__inf)). 4.02/4.27 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J, axiom, ![X6, X3]:(c_Nat__Transfer_Onat__set(X3)=>(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X3),X6)=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),X3)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X6)))<=c_Nat__Transfer_Onat__set(X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J)). 4.02/4.27 fof(fact_insort__key_Osimps_I2_J, axiom, ![X31, X7, X17, X9, X22, X4]:(((hAPP(hAPP(c_List_Olist_OCons(X7),X17),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X4,X22),X9),X31))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X4,X22),X9),hAPP(hAPP(c_List_Olist_OCons(X7),X17),X31))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(X22,X9)),hAPP(X22,X17)))))&(hAPP(hAPP(c_List_Olist_OCons(X7),X9),hAPP(hAPP(c_List_Olist_OCons(X7),X17),X31))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X4,X22),X9),hAPP(hAPP(c_List_Olist_OCons(X7),X17),X31))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(X22,X9)),hAPP(X22,X17)))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__key_Osimps_I2_J)). 4.02/4.27 fof(fact_map__pair__surj, axiom, ![X76, X49, X126, X22, X4, X7]:((c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X4,X49),tc_HOL_Obool))=hAPP(c_Set_Oimage(tc_prod(X7,X126),tc_prod(X4,X49),c_Product__Type_Omap__pair(X7,X4,X126,X49,X22,X76)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X7,X126),tc_HOL_Obool)))<=hAPP(c_Set_Oimage(X126,X49,X76),c_Orderings_Otop__class_Otop(tc_fun(X126,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X49,tc_HOL_Obool)))<=hAPP(c_Set_Oimage(X7,X4,X22),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__surj)). 4.02/4.27 fof(fact_ball__UN, axiom, ![X56, X6, X3, X7, X4]:(![X19]:(hBOOL(hAPP(hAPP(c_member(X7),X19),X3))=>![X114]:(hBOOL(hAPP(hAPP(c_member(X4),X114),hAPP(X6,X19)))=>hBOOL(hAPP(X56,X114))))<=>![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),X6)))=>hBOOL(hAPP(X56,X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ball__UN)). 4.02/4.27 fof(fact_setsum__cl__ivl__Suc, axiom, ![X22, X21, X20, X4]:(((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),X21)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X21,hAPP(c_Nat_OSuc,X20)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X21,X20))),hAPP(X22,hAPP(c_Nat_OSuc,X20))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),X21))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X21,hAPP(c_Nat_OSuc,X20)))=c_Groups_Ozero__class_Ozero(X4)))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__cl__ivl__Suc)). 4.02/4.27 fof(fact_list__all2I, axiom, ![X56, X25, X26, X7, X4]:(![X19]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),X19),hAPP(c_List_Oset(tc_prod(X4,X7)),hAPP(hAPP(c_List_Ozip(X4,X7),X26),X25))))=>hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_HOL_Obool),X56),X19)))=>(c_List_Olist__all2(X4,X7,X56,X26,X25)<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X26)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2I)). 4.02/4.27 fof(fact_list__all2__def, axiom, ![X31, X32, X56, X7, X4]:(c_List_Olist__all2(X4,X7,X56,X32,X31)<=>(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)&![X19]:(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_HOL_Obool),X56),X19))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),X19),hAPP(c_List_Oset(tc_prod(X4,X7)),hAPP(hAPP(c_List_Ozip(X4,X7),X32),X31))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__def)). 4.02/4.27 fof(fact_sorted__map__same, axiom, ![X32, X76, X22, X7, X4]:(class_Orderings_Olinorder(X4)=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X7,X4),X22),hAPP(c_List_Ofilter(X7,hAPP(hAPP(c_COMBC(X7,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,tc_HOL_Obool),X7),c_fequal),X22)),hAPP(X76,X32))),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__map__same)). 4.02/4.27 fof(fact_norm__frac_Opinduct, axiom, ![X56, X70, X119]:((![X27, X78]:(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),X27),X78)))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X78),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hBOOL(hAPP(hAPP(X56,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X27)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X78))))=>hBOOL(hAPP(hAPP(X56,X27),X78))))=>hBOOL(hAPP(hAPP(X56,X119),X70)))<=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),X119),X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_norm__frac_Opinduct)). 4.02/4.27 fof(fact_fold1__Un, axiom, ![X6, X3, X4]:(class_Groups_Oab__semigroup__mult(X4)=>(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>((hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),X3)),hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),X6))<=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=X6!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__Un)). 4.02/4.27 fof(fact_fold1__in, axiom, ![X3, X4]:(class_Groups_Oab__semigroup__mult(X4)=>(((![X19, X34]:hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X19),X34)),hAPP(hAPP(c_Set_Oinsert(X4),X19),hAPP(hAPP(c_Set_Oinsert(X4),X34),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),X3)),X3)))<=X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__in)). 4.02/4.27 fof(fact_setsum__diff, axiom, ![X22, X6, X3, X4, X7]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X6))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X3))))<=class_Groups_Oab__group__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff)). 4.02/4.27 fof(fact_map__of__inject__set, axiom, ![X31, X32, X7, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(tc_prod(X4,X7),X4),c_Product__Type_Ofst(X4,X7)),X32)))=>((hAPP(c_List_Oset(tc_prod(X4,X7)),X31)=hAPP(c_List_Oset(tc_prod(X4,X7)),X32)<=>hAPP(c_Map_Omap__of(X4,X7),X31)=hAPP(c_Map_Omap__of(X4,X7),X32))<=hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(tc_prod(X4,X7),X4),c_Product__Type_Ofst(X4,X7)),X31))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__inject__set)). 4.02/4.27 fof(fact_fun__left__comm_Ofold__insert, axiom, ![X16, X9, X3, X22, X7, X4]:(((hAPP(hAPP(X22,X9),hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),X16),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),X16),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=c_Finite__Set_Ofun__left__comm(X4,X7,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__insert)). 4.02/4.27 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)). 4.02/4.27 fof(fact_gauss__sum, axiom, ![X20, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X20)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X20)),c_Groups_Oone__class_Oone(X4)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Oone__class_Oone(X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),c_Nat_Osemiring__1__class_Oof__nat(X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X20)))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_gauss__sum)). 4.02/4.27 fof(fact_subset__insert__iff, axiom, ![X6, X9, X3, X4]:(((~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X6))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__insert__iff)). 4.02/4.27 fof(fact_aset_I5_J, axiom, ![X3, X123, X61]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))=>(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X123),X3))=>![X19]:(![X114]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X114),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X61)))=>![X124]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X124),X3))=>X19!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X124),X114)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),X61)),X123))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19),X123)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I5_J)). 4.02/4.27 fof(fact_bset_I7_J, axiom, ![X6, X123, X61]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))=>(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X123),X6))=>![X19]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),X61)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),X19)))<=![X114]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X114),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X61)))=>![X124]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X124),X114)!=X19<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X124),X6))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I7_J)). 4.02/4.27 fof(fact_min__max_OSup__fin_Ohom__commute, axiom, ![X176, X48, X4]:((![X19, X34]:hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(X48,X19)),hAPP(X48,X34))=hAPP(X48,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X19),X34))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X176))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X176=>c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(c_Set_Oimage(X4,X4,X48),X176))=hAPP(X48,c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X176)))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Ohom__commute)). 4.02/4.27 fof(fact_min__max_OInf__fin_Ohom__commute, axiom, ![X176, X48, X4]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X176))=>(X176!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(c_Set_Oimage(X4,X4,X48),X176))=hAPP(X48,c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X176))))<=![X19, X34]:hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(X48,X19)),hAPP(X48,X34))=hAPP(X48,hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X19),X34)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Ohom__commute)). 4.02/4.27 fof(fact_setsum__diff__nat, axiom, ![X22, X3, X6, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X22),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X22),X6))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__diff__nat)). 4.02/4.27 fof(fact_map__of__filter__in, axiom, ![X56, X16, X28, X32, X4, X7]:((hBOOL(hAPP(hAPP(X56,X28),X16))=>hAPP(c_Option_Ooption_OSome(X4),X16)=hAPP(hAPP(c_Map_Omap__of(X7,X4),hAPP(c_List_Ofilter(tc_prod(X7,X4),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X4,tc_HOL_Obool),X56)),X32)),X28))<=hAPP(c_Option_Ooption_OSome(X4),X16)=hAPP(hAPP(c_Map_Omap__of(X7,X4),X32),X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__filter__in)). 4.02/4.27 fof(fact_map__of__zip__enum__inject, axiom, ![X31, X32, X4, X7]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),c_Enum_Oenum__class_Oenum(X7))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=>((X32=X31<=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X4),X4,X7,c_Option_Othe(X4)),hAPP(c_Map_Omap__of(X7,X4),hAPP(hAPP(c_List_Ozip(X7,X4),c_Enum_Oenum__class_Oenum(X7)),X32)))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X4),X4,X7,c_Option_Othe(X4)),hAPP(c_Map_Omap__of(X7,X4),hAPP(hAPP(c_List_Ozip(X7,X4),c_Enum_Oenum__class_Oenum(X7)),X31))))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),c_Enum_Oenum__class_Oenum(X7))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X31)))<=(class_Enum_Oenum(X7)&class_Enum_Oenum(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__zip__enum__inject)). 4.02/4.27 fof(fact_take__hd__drop, axiom, ![X45, X4, X5]:(hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Otake(X4),X5),X45)),hAPP(hAPP(c_List_Olist_OCons(X4),hAPP(c_List_Ohd(X4),hAPP(hAPP(c_List_Odrop(X4),X5),X45))),c_List_Olist_ONil(X4)))=hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_OSuc,X5)),X45)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__hd__drop)). 4.02/4.27 fof(fact_zmult2__lemma__aux4, axiom, ![X14, X12, X101, X10]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X12))=>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),X12),c_Divides_Odiv__class_Omod(tc_Int_Oint,X14,X10))),X101)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X10))))<=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_zmult2__lemma__aux4)). 4.02/4.27 fof(fact_zmult2__lemma__aux1, axiom, ![X14, X101, X12, X10]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),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),X12),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),c_Divides_Odiv__class_Omod(tc_Int_Oint,X14,X10))),X101))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),X101)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult2__lemma__aux1)). 4.02/4.27 fof(fact_setsum__left__distrib, axiom, ![X18, X3, X22, X7, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),hAPP(hAPP(c_COMBC(X7,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X7),c_Groups_Otimes__class_Otimes(X4)),X22)),X18)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),X22),X3)),X18)<=class_Rings_Osemiring__0(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__left__distrib)). 4.02/4.27 fof(fact_take__add, axiom, ![X45, X4, X135, X46]:(hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X135)),X45)=hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Otake(X4),X46),X45)),hAPP(hAPP(c_List_Otake(X4),X135),hAPP(hAPP(c_List_Odrop(X4),X46),X45)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X135)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__add)). 4.02/4.27 fof(fact_bex__Un, axiom, ![X56, X6, X3, X4]:((?[X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))&hBOOL(hAPP(X56,X19)))|?[X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X6))&hBOOL(hAPP(X56,X19))))<=>?[X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)))&hBOOL(hAPP(X56,X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bex__Un)). 4.02/4.27 fof(fact_rel__compE, axiom, ![X40, X18, X49, X313, X7, X4]:(~(![X19, X34, X36]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X49)),hAPP(hAPP(c_Product__Type_OPair(X4,X49),X19),X34)),X18))=>~(hBOOL(hAPP(hAPP(c_member(tc_prod(X49,X7)),hAPP(hAPP(c_Product__Type_OPair(X49,X7),X34),X36)),X40))))<=hAPP(hAPP(c_Product__Type_OPair(X4,X7),X19),X36)=X313))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),X313),hAPP(hAPP(c_Relation_Orel__comp(X4,X49,X7),X18),X40)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__compE)). 4.02/4.27 fof(fact_min__max_OInf__fin_Oclosed, axiom, ![X3, X4]:((((![X19, X34]:hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X19),X34)),hAPP(hAPP(c_Set_Oinsert(X4),X19),hAPP(hAPP(c_Set_Oinsert(X4),X34),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=>hBOOL(hAPP(hAPP(c_member(X4),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X3)),X3)))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oclosed)). 4.02/4.27 fof(fact_min__max_OSup__fin_Oclosed, axiom, ![X3, X4]:((((hBOOL(hAPP(hAPP(c_member(X4),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X3)),X3))<=![X19, X34]:hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X19),X34)),hAPP(hAPP(c_Set_Oinsert(X4),X19),hAPP(hAPP(c_Set_Oinsert(X4),X34),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oclosed)). 4.02/4.27 fof(fact_in__finite__psubset, axiom, ![X6, X3, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X3),X6))&hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),X6)),c_Wellfounded_Ofinite__psubset(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__finite__psubset)). 4.02/4.27 fof(fact_right__diff__distrib__number__of, axiom, ![X10, X12, X1, X7]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1)),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1)),X10))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X12),X10))<=(class_Rings_Oring(X7)&class_Int_Onumber(X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_right__diff__distrib__number__of)). 4.02/4.27 fof(fact_card__Diff1__less, axiom, ![X9, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X4),X3)))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff1__less)). 4.02/4.27 fof(fact_right__distrib__number__of, axiom, ![X10, X12, X1, X7]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1)),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1)),X10))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X12),X10))<=(class_Int_Onumber(X7)&class_Rings_Osemiring(X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_right__distrib__number__of)). 4.02/4.27 fof(fact_nat__gcd_Opinduct, axiom, ![X56, X70, X119]:((hBOOL(hAPP(hAPP(X56,X119),X70))<=![X19, X34]:(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X34=>hBOOL(hAPP(hAPP(X56,X34),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X34))))=>hBOOL(hAPP(hAPP(X56,X19),X34)))<=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),X19),X34)))))<=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),X119),X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__gcd_Opinduct)). 4.02/4.27 fof(fact_setsum__divide__distrib, axiom, ![X18, X3, X22, X7, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),hAPP(hAPP(c_COMBC(X7,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X7),c_Rings_Oinverse__class_Odivide(X4)),X22)),X18)),X3)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),X22),X3)),X18)<=class_Fields_Ofield(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__divide__distrib)). 4.02/4.27 fof(fact_small_H_Osimps, axiom, ![X22, X37, X102]:((c_Smallcheck_Osmall_H(X22,X102,X37)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X22,X102,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X37),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X22,X37))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X102),X37))))&(c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))=c_Smallcheck_Osmall_H(X22,X102,X37)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X102),X37)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small_H_Osimps)). 4.02/4.27 fof(fact_fun__left__comm_Ofold__insert2, axiom, ![X16, X9, X3, X22, X7, X4]:(c_Finite__Set_Ofun__left__comm(X4,X7,X22)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))=>hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),hAPP(hAPP(X22,X9),X16)),X3)=hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),X16),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__insert2)). 4.02/4.27 fof(fact_card__Diff__subset__Int, axiom, ![X6, X3, X4]:(hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X3)),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff__subset__Int)). 4.02/4.27 fof(fact_in__inv__image, axiom, ![X22, X18, X7, X17, X9, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),hAPP(hAPP(c_Relation_Oinv__image(X7,X4),X18),X22)))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),hAPP(X22,X9)),hAPP(X22,X17))),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__inv__image)). 4.02/4.27 fof(fact_folding_Ounion, axiom, ![X6, X3, X87, X22, X7, X4]:(c_Finite__Set_Ofolding(X4,X7,X22,X87)=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)=>hAPP(X87,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X87,X3)),hAPP(X87,X6))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ounion)). 4.02/4.27 fof(fact_card__Diff__singleton__if, axiom, ![X9, X3, X4]:(((~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))=>hAPP(c_Finite__Set_Ocard(X4),X3)=hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff__singleton__if)). 4.02/4.27 fof(fact_refl__on__INTER, axiom, ![X18, X3, X7, X86, X4]:(![X19]:(c_Relation_Orefl__on(X7,hAPP(X3,X19),hAPP(X18,X19))<=hBOOL(hAPP(hAPP(c_member(X4),X19),X86)))=>c_Relation_Orefl__on(X7,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X86),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),X86),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__INTER)). 4.02/4.27 fof(fact_transfer__int__nat__sum__prod2_I2_J, axiom, ![X22, X3, X4]:(![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>c_Nat__Transfer_Ois__nat(hAPP(X22,X19)))=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X4),c_Int_Onat),X22)),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,tc_Int_Oint),X22),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__sum__prod2_I2_J)). 4.02/4.27 fof(fact_transfer__int__nat__sum__prod2_I1_J, axiom, ![X22, X3, X4]:(![X19]:(c_Nat__Transfer_Ois__nat(hAPP(X22,X19))<=hBOOL(hAPP(hAPP(c_member(X4),X19),X3)))=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X4),c_Int_Onat),X22)),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Int_Oint),X22),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__sum__prod2_I1_J)). 4.02/4.27 fof(fact_listrel1E, axiom, ![X18, X31, X32, X4]:(~(![X19, X34]:(![X63, X218]:(hAPP(hAPP(c_List_Oappend(X4),X63),hAPP(hAPP(c_List_Olist_OCons(X4),X19),X218))=X32=>X31!=hAPP(hAPP(c_List_Oappend(X4),X63),hAPP(hAPP(c_List_Olist_OCons(X4),X34),X218)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X34)),X18))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)),c_List_Olistrel1(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1E)). 4.02/4.27 fof(fact_folding__one_Ounion__disjoint, axiom, ![X6, X3, X87, X22, X4]:(((X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X6=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)=>hAPP(X87,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(X22,hAPP(X87,X3)),hAPP(X87,X6))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=c_Finite__Set_Ofolding__one(X4,X22,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Ounion__disjoint)). 4.02/4.27 fof(fact_insort__key__remove1, axiom, ![X22, X32, X26, X4, X7]:(class_Orderings_Olinorder(X7)=>(((hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X7,X22),X26),c_List_Oremove1(X4,X26,X32))=X32<=X26=hAPP(c_List_Ohd(X4),hAPP(c_List_Ofilter(X4,hAPP(hAPP(c_COMBB(X7,tc_HOL_Obool,X4),hAPP(c_fequal,hAPP(X22,X26))),X22)),X32)))<=c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Omap(X4,X7),X22),X32)))<=hBOOL(hAPP(hAPP(c_member(X4),X26),hAPP(c_List_Oset(X4),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__key__remove1)). 4.02/4.27 fof(fact_filter__insort, axiom, ![X9, X56, X32, X22, X7, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X7,X4),X22),X32))=>(hBOOL(hAPP(X56,X9))=>hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X4,X22),X9),hAPP(c_List_Ofilter(X7,X56),X32))=hAPP(c_List_Ofilter(X7,X56),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X4,X22),X9),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__insort)). 4.02/4.27 fof(fact_min__max_OSup__fin_Ounion__idem, axiom, ![X6, X3, X4]:(((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X6=>c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X3)),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X6)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Ounion__idem)). 4.02/4.27 fof(fact_folding__image__simple_Ounion__disjoint, axiom, ![X6, X3, X87, X76, X16, X22, X7, X4]:((((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X3),X6)=c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))=>hAPP(hAPP(X22,hAPP(X87,X3)),hAPP(X87,X6))=hAPP(X87,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3)))<=c_Finite__Set_Ofolding__image__simple(X4,X7,X22,X16,X76,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Ounion__disjoint)). 4.02/4.27 fof(fact_min__max_OInf__fin_Ounion__idem, axiom, ![X6, X3, X4]:((((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>(c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X3)),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X6))<=X6!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Ounion__idem)). 4.02/4.27 fof(fact_listsum__map__remove1, axiom, ![X22, X32, X9, X4, X7]:((hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X4,X7),X22),X32))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(X22,X9)),hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X4,X7),X22),c_List_Oremove1(X4,X9,X32))))<=hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32))))<=class_Groups_Ocomm__monoid__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__map__remove1)). 4.02/4.27 fof(fact_Inf__fin_Oclosed, axiom, ![X3, X4]:((((![X19, X34]:hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X19),X34)),hAPP(hAPP(c_Set_Oinsert(X4),X19),hAPP(hAPP(c_Set_Oinsert(X4),X34),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=>hBOOL(hAPP(hAPP(c_member(X4),c_Big__Operators_Olattice__class_OInf__fin(X4,X3)),X3)))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oclosed)). 4.02/4.27 fof(fact_Sup__fin_Oclosed, axiom, ![X3, X4]:(class_Lattices_Olattice(X4)=>((X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>(hBOOL(hAPP(hAPP(c_member(X4),c_Big__Operators_Olattice__class_OSup__fin(X4,X3)),X3))<=![X19, X34]:hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X19),X34)),hAPP(hAPP(c_Set_Oinsert(X4),X19),hAPP(hAPP(c_Set_Oinsert(X4),X34),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oclosed)). 4.02/4.27 fof(fact_Diff__mono, axiom, ![X6, X61, X8, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X8))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X8),X61)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X61),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__mono)). 4.02/4.27 fof(fact_trancl__subset__Sigma__aux, axiom, ![X3, X18, X25, X26, X4]:(((hBOOL(hAPP(hAPP(c_member(X4),X26),X3))|X25=X26)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X3)))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),c_Transitive__Closure_Ortrancl(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trancl__subset__Sigma__aux)). 4.02/4.27 fof(fact_mem__splitI2, axiom, ![X24, X16, X49, X7, X4, X51]:(![X27, X78]:(hAPP(hAPP(c_Product__Type_OPair(X4,X7),X27),X78)=X51=>hBOOL(hAPP(hAPP(c_member(X49),X16),hAPP(hAPP(X24,X27),X78))))=>hBOOL(hAPP(hAPP(c_member(X49),X16),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_fun(X49,tc_HOL_Obool)),X24),X51)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mem__splitI2)). 4.02/4.27 fof(fact_left__distrib__number__of, axiom, ![X1, X12, X11, X7]:((class_Rings_Osemiring(X7)&class_Int_Onumber(X7))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X11),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X11),X12)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_left__distrib__number__of)). 4.02/4.27 fof(fact_Int__mono, axiom, ![X61, X6, X8, X3, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X8),X61)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X61)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__mono)). 4.02/4.27 fof(fact_Un__mono, axiom, ![X61, X6, X8, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X8))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X61))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X8),X61))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__mono)). 4.02/4.27 fof(fact_combine__common__factor, axiom, ![X10, X12, X122, X11, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),X122)),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X122)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X122)),X10))<=class_Rings_Osemiring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_combine__common__factor)). 4.02/4.27 fof(fact_inj__on__INTER, axiom, ![X3, X22, X49, X7, X4, X41]:((c_Fun_Oinj__on(X7,X49,X22,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X41),X3))<=![X42]:(c_Fun_Oinj__on(X7,X49,X22,hAPP(X3,X42))<=hBOOL(hAPP(hAPP(c_member(X4),X42),X41))))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X41), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__INTER)). 4.02/4.27 fof(fact_left__diff__distrib__number__of, axiom, ![X1, X12, X11, X7]:((class_Rings_Oring(X7)&class_Int_Onumber(X7))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X11),X12)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X11),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X12),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_left__diff__distrib__number__of)). 4.02/4.27 fof(fact_bset_I6_J, axiom, ![X123, X6, X61]:(![X19]:(![X114]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X114),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X61)))=>![X124]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X124),X114)!=X19<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X124),X6))))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19),X123))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),X61)),X123))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I6_J)). 4.02/4.27 fof(fact_length__takeWhile__less__P__nth, axiom, ![X32, X4, X56, X38]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X38),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X56,X32))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X38),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))))<=![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X38))=>hBOOL(hAPP(X56,hAPP(hAPP(c_List_Onth(X4),X32),X42))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__takeWhile__less__P__nth)). 4.02/4.27 fof(fact_measures__less, axiom, ![X278, X4, X17, X9, X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X22,X9)),hAPP(X22,X17)))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X22),X278))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_measures__less)). 4.02/4.27 fof(fact_bset_I5_J, axiom, ![X123, X6, X61]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))=>![X19]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19),X123))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),X61)),X123)))<=![X114]:(![X124]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X124),X6))=>X19!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X124),X114))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X114),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X61)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bset_I5_J)). 4.02/4.27 fof(fact_aset_I8_J, axiom, ![X123, X3, X61]:(![X19]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),X19))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),X61))))<=![X114]:(![X124]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X124),X3))=>X19!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X124),X114))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X114),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X61)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I8_J)). 4.02/4.27 fof(fact_aset_I7_J, axiom, ![X123, X3, X61]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))=>![X19]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),X19))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),X61))))<=![X114]:(![X124]:(X19!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X124),X114)<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X124),X3)))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X114),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X61)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I7_J)). 4.02/4.27 fof(fact_Image__Int__eq, axiom, ![X6, X3, X39, X7, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X4,X39),X3)),hAPP(c_Relation_OImage(X7,X4,X39),X6))=hAPP(c_Relation_OImage(X7,X4,X39),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X3),X6))<=c_Relation_Osingle__valued(X4,X7,hAPP(c_Relation_Oconverse(X7,X4),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__Int__eq)). 4.02/4.27 fof(fact_map__pair__inj__on, axiom, ![X6, X76, X126, X49, X3, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,X3)=>(c_Fun_Oinj__on(X49,X126,X76,X6)=>c_Fun_Oinj__on(tc_prod(X4,X49),tc_prod(X7,X126),c_Product__Type_Omap__pair(X4,X7,X49,X126,X22,X76),hAPP(hAPP(c_Product__Type_OSigma(X4,X49),X3),hAPP(c_COMBK(tc_fun(X49,tc_HOL_Obool),X4),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__inj__on)). 4.02/4.27 fof(fact_finite__range__map__of__map__add, axiom, ![X60, X22, X7, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X4)),hAPP(c_Set_Oimage(X7,tc_Option_Ooption(X4),c_Map_Omap__add(X7,X4,X22,hAPP(c_Map_Omap__of(X7,X4),X60))),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X4)),hAPP(c_Set_Oimage(X7,tc_Option_Ooption(X4),X22),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__range__map__of__map__add)). 4.02/4.27 fof(fact_setsum__head__upt__Suc, axiom, ![X22, X20, X21, X4]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(X22,X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X21)),X20)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X21),X20))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20)))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__head__upt__Suc)). 4.02/4.27 fof(fact_id__take__nth__drop, axiom, ![X45, X4, X46]:(hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Otake(X4),X46),X45)),hAPP(hAPP(c_List_Olist_OCons(X4),hAPP(hAPP(c_List_Onth(X4),X45),X46)),hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_OSuc,X46)),X45)))=X45<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_id__take__nth__drop)). 4.02/4.27 fof(fact_map__of__zip__is__Some, axiom, ![X9, X31, X7, X32, X4]:((?[X34]:hAPP(c_Option_Ooption_OSome(X7),X34)=hAPP(hAPP(c_Map_Omap__of(X4,X7),hAPP(hAPP(c_List_Ozip(X4,X7),X32),X31)),X9)<=>hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32))))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__zip__is__Some)). 4.02/4.27 fof(fact_listsum__const__mult, axiom, ![X32, X22, X24, X7, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X24),hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32)))=hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X7,X4),hAPP(hAPP(c_COMBB(X4,X4,X7),hAPP(c_Groups_Otimes__class_Otimes(X4),X24)),X22)),X32))<=class_Rings_Osemiring__0(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__const__mult)). 4.02/4.27 fof(fact_mlex__leq, axiom, ![X39, X4, X17, X9, X22]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X22,X9)),hAPP(X22,X17)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),c_Wellfounded_Omlex__prod(X4,X22,X39)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mlex__leq)). 4.02/4.27 fof(fact_setsum__abs, axiom, ![X3, X22, X7, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),X22),X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),hAPP(hAPP(c_COMBB(X4,X4,X7),c_Groups_Oabs__class_Oabs(X4)),X22)),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__abs)). 4.02/4.27 fof(fact_filter__equals__takeWhile__sorted__rev, axiom, ![X123, X32, X22, X7, X4]:((c_List_Olinorder__class_Osorted(X4,hAPP(c_List_Orev(X4),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32)))=>hAPP(c_List_Ofilter(X7,hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,X7),hAPP(c_Orderings_Oord__class_Oless(X4),X123)),X22)),X32)=c_List_OtakeWhile(X7,hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,X7),hAPP(c_Orderings_Oord__class_Oless(X4),X123)),X22),X32))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__equals__takeWhile__sorted__rev)). 4.02/4.27 fof(fact_folding_Ocommute__comp_H_H, axiom, ![X6, X3, X87, X22, X7, X4]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X87,X6)),hAPP(X87,X3))=hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X87,X3)),hAPP(X87,X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=c_Finite__Set_Ofolding(X4,X7,X22,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__comp_H_H)). 4.02/4.27 fof(fact_fold__graph__insert__swap, axiom, ![X16, X17, X3, X25, X4]:(class_Groups_Oab__semigroup__mult(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X4,c_Groups_Otimes__class_Otimes(X4),X25,X3),X17))=>(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X4,c_Groups_Otimes__class_Otimes(X4),X16,hAPP(hAPP(c_Set_Oinsert(X4),X25),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X16),X17)))<=~(hBOOL(hAPP(hAPP(c_member(X4),X25),X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph__insert__swap)). 4.02/4.27 fof(fact_INFI__set__fold, axiom, ![X22, X32, X7, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>hAPP(c_List_Ofoldl(X4,X7,hAPP(c_COMBC(X7,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X7),c_Lattices_Osemilattice__inf__class_Oinf(X4)),X22)),c_Orderings_Otop__class_Otop(X4)),X32)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,X4),hAPP(c_List_Oset(X7),X32)),X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INFI__set__fold)). 4.02/4.27 fof(fact_SUPR__set__fold, axiom, ![X22, X32, X7, X4]:(hAPP(c_List_Ofoldl(X4,X7,hAPP(c_COMBC(X7,X4,X4),hAPP(hAPP(c_COMBB(X4,tc_fun(X4,X4),X7),c_Lattices_Osemilattice__sup__class_Osup(X4)),X22)),c_Orderings_Obot__class_Obot(X4)),X32)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X4),hAPP(c_List_Oset(X7),X32)),X22)<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUPR__set__fold)). 4.02/4.27 fof(fact_quotient__disj, axiom, ![X203, X156, X18, X3, X4]:(c_Equiv__Relations_Oequiv(X4,X3,X18)=>(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X156),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X3),X18)))=>(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X203),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X3),X18)))=>(X203=X156|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X156),X203)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotient__disj)). 4.02/4.27 fof(fact_map__le__imp__upd__le, axiom, ![X17, X9, X162, X163, X7, X4]:(c_Map_Omap__le(X4,X7,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X163),X9),c_Option_Ooption_ONone(X7)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X162),X9),hAPP(c_Option_Ooption_OSome(X7),X17)))<=c_Map_Omap__le(X4,X7,X163,X162)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__le__imp__upd__le)). 4.02/4.27 fof(fact_quotientI, axiom, ![X18, X3, X9, X4]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X3),X18)))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotientI)). 4.02/4.27 fof(fact_union__comp__emptyL, axiom, ![X6, X8, X3, X4]:(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X3),X8)=>(hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X3),X6)),X8)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))<=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X6),X8)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_union__comp__emptyL)). 4.02/4.27 fof(fact_union__comp__emptyR, axiom, ![X8, X6, X3, X4]:(hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X3),X6)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))=>(hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X6),X8))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))<=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X3),X8)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_union__comp__emptyR)). 4.02/4.27 fof(fact_fold1__Un2, axiom, ![X6, X3, X4]:(class_Lattices_Oab__semigroup__idem__mult(X4)=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3=>((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),X3)),hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),X6))=hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))<=X6!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__Un2)). 4.02/4.27 fof(fact_UN__finite__subset, axiom, ![X8, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X3)),X8))<=![X104]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X104)),X3)),X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__finite__subset)). 4.02/4.27 fof(fact_fun__left__comm__idem_Ofold__insert__idem, axiom, ![X9, X16, X3, X22, X7, X4]:(c_Finite__Set_Ofun__left__comm__idem(X4,X7,X22)=>(hAPP(hAPP(X22,X9),hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),X16),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),X16),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofold__insert__idem)). 4.02/4.27 fof(fact_fun__left__comm__idem_Ofold__insert__idem2, axiom, ![X9, X16, X3, X22, X7, X4]:(c_Finite__Set_Ofun__left__comm__idem(X4,X7,X22)=>(hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),X16),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),hAPP(hAPP(X22,X9),X16)),X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofold__insert__idem2)). 4.02/4.27 fof(fact_congruent2D, axiom, ![X79, X80, X81, X82, X22, X83, X84, X49, X7, X4]:(c_Equiv__Relations_Ocongruent2(X4,X7,X49,X84,X83,X22)=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X82),X81)),X84))=>(hAPP(hAPP(X22,X82),X80)=hAPP(hAPP(X22,X81),X79)<=hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X80),X79)),X83))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_congruent2D)). 4.02/4.27 fof(fact_acyclic__insert, axiom, ![X18, X9, X17, X4]:((c_Wellfounded_Oacyclic(X4,X18)&~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),c_Transitive__Closure_Ortrancl(X4,X18)))))<=>c_Wellfounded_Oacyclic(X4,hAPP(hAPP(c_Set_Oinsert(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X17),X9)),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclic__insert)). 4.02/4.27 fof(fact_wf__insert, axiom, ![X18, X9, X17, X4]:((~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),c_Transitive__Closure_Ortrancl(X4,X18))))&c_Wellfounded_Owf(X4,X18))<=>c_Wellfounded_Owf(X4,hAPP(hAPP(c_Set_Oinsert(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X17),X9)),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__insert)). 4.02/4.27 fof(fact_atLeastLessThan__add__Un, axiom, ![X28, X38, X37]:(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,X37),X38)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X38),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X38),X28)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X37),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X38),X28))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X37),X38))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__add__Un)). 4.02/4.27 fof(fact_upd__conv__take__nth__drop, axiom, ![X11, X45, X4, X46]:(hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Otake(X4),X46),X45)),hAPP(hAPP(c_List_Olist_OCons(X4),X11),hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_OSuc,X46)),X45)))=hAPP(hAPP(c_List_Olist__update(X4,X45),X46),X11)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upd__conv__take__nth__drop)). 4.02/4.27 fof(fact_take__Suc__conv__app__nth, axiom, ![X45, X4, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))=>hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_OSuc,X46)),X45)=hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Otake(X4),X46),X45)),hAPP(hAPP(c_List_Olist_OCons(X4),hAPP(hAPP(c_List_Onth(X4),X45),X46)),c_List_Olist_ONil(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Suc__conv__app__nth)). 4.02/4.27 fof(fact_abs__mult__less, axiom, ![X44, X12, X10, X11, X4]:(class_Rings_Olinordered__idom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),hAPP(c_Groups_Oabs__class_Oabs(X4),X12))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X44)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)),X44)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__mult__less)). 4.02/4.27 fof(fact_transfer__int__nat__sum__prod_I2_J, axiom, ![X22, X3, X4]:((c_Nat__Transfer_Onat__set(X3)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBB(tc_Int_Oint,X4,tc_Nat_Onat),X22),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,X4),X22),X3))<=(class_Groups_Ocomm__monoid__mult(X4)&class_Groups_Ocomm__monoid__add(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__sum__prod_I2_J)). 4.02/4.27 fof(fact_strict__below__fold1__iff, axiom, ![X9, X3, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X9),hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X3)))<=>![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X9),X19))<=hBOOL(hAPP(hAPP(c_member(X4),X19),X3))))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_strict__below__fold1__iff)). 4.02/4.27 fof(fact_transfer__int__nat__sum__prod_I1_J, axiom, ![X22, X3, X4]:((class_Groups_Ocomm__monoid__add(X4)&class_Groups_Ocomm__monoid__mult(X4))=>(c_Nat__Transfer_Onat__set(X3)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X4),X22),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBB(tc_Int_Oint,X4,tc_Nat_Onat),X22),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__sum__prod_I1_J)). 4.02/4.27 fof(fact_below__fold1__iff, axiom, ![X9, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),hAPP(c_Finite__Set_Ofold1(X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X3)))<=>![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X19))))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_below__fold1__iff)). 4.02/4.27 fof(fact_min__max_Obelow__fold1__iff, axiom, ![X9, X3, X4]:(class_Orderings_Olinorder(X4)=>(((![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X19)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X3))))<=X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Obelow__fold1__iff)). 4.02/4.27 fof(fact_lexord__irreflexive, axiom, ![X17, X18, X4]:(![X19]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X19)),X18)))=>~(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)),X17),X17)),c_List_Olexord(X4,X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__irreflexive)). 4.02/4.27 fof(fact_zmult2__lemma__aux2, axiom, ![X14, X101, X12, X10]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),c_Divides_Odiv__class_Omod(tc_Int_Oint,X14,X10))),X101)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),X101)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult2__lemma__aux2)). 4.02/4.27 fof(fact_zmult2__lemma__aux3, axiom, ![X14, X12, X101, X10]:(((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),X12),c_Divides_Odiv__class_Omod(tc_Int_Oint,X14,X10))),X101)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult2__lemma__aux3)). 4.02/4.27 fof(fact_pair__imageI, axiom, ![X22, X49, X3, X25, X26, X7, X4]:(hBOOL(hAPP(hAPP(c_member(X49),hAPP(hAPP(X22,X26),X25)),hAPP(c_Set_Oimage(tc_prod(X4,X7),X49,hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,X49),X22)),X3)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X26),X25)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__imageI)). 4.02/4.27 fof(fact_image__Int, axiom, ![X6, X3, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X7,X22),X3)),hAPP(c_Set_Oimage(X4,X7,X22),X6))=hAPP(c_Set_Oimage(X4,X7,X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Int)). 4.02/4.27 fof(fact_image__set__diff, axiom, ![X6, X3, X22, X7, X4]:(hAPP(c_Set_Oimage(X4,X7,X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X7,X22),X3)),hAPP(c_Set_Oimage(X4,X7,X22),X6))<=c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__set__diff)). 4.02/4.27 fof(fact_card__Diff1__le, axiom, ![X9, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X4),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff1__le)). 4.02/4.27 fof(fact_mod__lemma, axiom, ![X14, X12, X101, X10]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X14,X10))),X101)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X101),X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__lemma)). 4.02/4.27 fof(fact_min__max_Odistrib__inf__le, axiom, ![X29, X43, X13, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),X43)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),X29))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X43),X29))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Odistrib__inf__le)). 4.02/4.27 fof(fact_distrib__inf__le, axiom, ![X29, X43, X13, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X29))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X43),X29))))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distrib__inf__le)). 4.02/4.27 fof(fact_min__max_Odistrib__sup__le, axiom, ![X29, X43, X13, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X43),X29))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),X43)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),X29))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Odistrib__sup__le)). 4.02/4.27 fof(fact_distrib__sup__le, axiom, ![X29, X43, X13, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X43),X29))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X29))))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distrib__sup__le)). 4.02/4.27 fof(fact_Un__Int__assoc__eq, axiom, ![X8, X6, X3, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)),X8)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X6),X8))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X8),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Int__assoc__eq)). 4.02/4.27 fof(fact_sorted__list__of__set__remove, axiom, ![X9, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>c_List_Olinorder__class_Osorted__list__of__set(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=c_List_Oremove1(X4,X9,c_List_Olinorder__class_Osorted__list__of__set(X4,X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set__remove)). 4.02/4.27 fof(fact_reduction__pairI, axiom, ![X86, X39, X4]:((c_FunDef_Oreduction__pair(X4,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X39),X86))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X39),X86)),X39)))<=c_Wellfounded_Owf(X4,X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reduction__pairI)). 4.02/4.27 fof(fact_folding_Oinsert, axiom, ![X9, X3, X87, X22, X7, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X87,X3)),hAPP(X22,X9))=hAPP(X87,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))))<=c_Finite__Set_Ofolding(X4,X7,X22,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Oinsert)). 4.02/4.27 fof(fact_card__insert, axiom, ![X9, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__insert)). 4.02/4.27 fof(fact_UN__subset__iff, axiom, ![X6, X3, X41, X7, X4]:(![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(X3,X19)),X6))<=hBOOL(hAPP(hAPP(c_member(X7),X19),X41)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X41),X3)),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__subset__iff)). 4.02/4.27 fof(fact_comp__surj, axiom, ![X76, X49, X22, X4, X7]:((hAPP(c_Set_Oimage(X7,X49,hAPP(c_Fun_Ocomp(X4,X49,X7,X76),X22)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X49,tc_HOL_Obool))<=c_Orderings_Otop__class_Otop(tc_fun(X49,tc_HOL_Obool))=hAPP(c_Set_Oimage(X4,X49,X76),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))<=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_Oimage(X7,X4,X22),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comp__surj)). 4.02/4.27 fof(fact_INT__subset__iff, axiom, ![X3, X41, X7, X6, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X41),X3)))<=>![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),hAPP(X3,X19)))<=hBOOL(hAPP(hAPP(c_member(X7),X19),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__subset__iff)). 4.02/4.27 fof(fact_card__Suc__Diff1, axiom, ![X9, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X4),X3)<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Suc__Diff1)). 4.02/4.27 fof(fact_takeWhile__eq__take__P__nth, axiom, ![X56, X32, X4, X20]:((hAPP(hAPP(c_List_Otake(X4),X20),X32)=c_List_OtakeWhile(X4,X56,X32)<=(~(hBOOL(hAPP(X56,hAPP(hAPP(c_List_Onth(X4),X32),X20))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))))<=![X42]:((hBOOL(hAPP(X56,hAPP(hAPP(c_List_Onth(X4),X32),X42)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__eq__take__P__nth)). 4.02/4.27 fof(fact_insort__insert__insort__key, axiom, ![X32, X7, X9, X22, X4]:(class_Orderings_Olinorder(X4)=>(~(hBOOL(hAPP(hAPP(c_member(X4),hAPP(X22,X9)),hAPP(c_Set_Oimage(X7,X4,X22),hAPP(c_List_Oset(X7),X32)))))=>hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X4,X22),X9),X32)=c_List_Olinorder__class_Oinsort__insert__key(X7,X4,X22,X9,X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__insert__insort__key)). 4.02/4.27 fof(fact_listsum__update__nat, axiom, ![X5, X309, X107]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X309)))=>hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X309),X107),X5))=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),X309)),X5)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X309),X107))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__update__nat)). 4.02/4.27 fof(fact_fold1Set_Oequations, axiom, ![X69, X67, X70, X22, X4]:(hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,X22,hAPP(hAPP(c_Set_Oinsert(X4),X70),X67)),X69))<=>?[X27, X195]:((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X4,X22,X27,X195),X69))&~(hBOOL(hAPP(hAPP(c_member(X4),X27),X195))))&hAPP(hAPP(c_Set_Oinsert(X4),X70),X67)=hAPP(hAPP(c_Set_Oinsert(X4),X27),X195))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1Set_Oequations)). 4.02/4.27 fof(fact_Diff1__fold__graph, axiom, ![X17, X9, X3, X16, X22, X7, X4]:(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X7,X22,X16,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X17))=>(hBOOL(hAPP(hAPP(c_member(X4),X9),X3))=>hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X7,X22,X16,X3),hAPP(hAPP(X22,X9),X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff1__fold__graph)). 4.02/4.27 fof(fact_order__fun_I1_J, axiom, ![X76, X22, X4, X7]:((class_Orderings_Oorder(X7)&class_Enum_Oenum(X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X7)),X22),X76))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X4),hAPP(hAPP(c_COMBS(X4,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X7,tc_fun(X7,tc_HOL_Obool),X4),c_Orderings_Oord__class_Oless__eq(X7)),X22)),X76))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__fun_I1_J)). 4.02/4.27 fof(fact_finite__range__imageI, axiom, ![X22, X49, X76, X7, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_Oimage(X7,X4,X76),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X49),hAPP(c_Set_Oimage(X7,X49,hAPP(hAPP(c_COMBB(X4,X49,X7),X22),X76)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__range__imageI)). 4.02/4.27 fof(fact_mem__splitE, axiom, ![X51, X24, X49, X7, X16, X4]:(~(![X19, X34]:(~(hBOOL(hAPP(hAPP(c_member(X4),X16),hAPP(hAPP(X24,X19),X34))))<=hAPP(hAPP(c_Product__Type_OPair(X7,X49),X19),X34)=X51))<=hBOOL(hAPP(hAPP(c_member(X4),X16),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X49,tc_fun(X4,tc_HOL_Obool)),X24),X51)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mem__splitE)). 4.02/4.27 fof(fact_folding__idem_Ounion__idem, axiom, ![X6, X3, X87, X22, X7, X4]:(c_Finite__Set_Ofolding__idem(X4,X7,X22,X87)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X87,X3)),hAPP(X87,X6))=hAPP(X87,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Ounion__idem)). 4.02/4.27 fof(fact_fold1__antimono, axiom, ![X6, X3, X4]:((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X6)),hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X3))))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__antimono)). 4.02/4.27 fof(fact_append__eq__append__conv2, axiom, ![X62, X30, X31, X32, X4]:(?[X63]:((hAPP(hAPP(c_List_Oappend(X4),X32),X63)=X30&X31=hAPP(hAPP(c_List_Oappend(X4),X63),X62))|(hAPP(hAPP(c_List_Oappend(X4),X30),X63)=X32&X62=hAPP(hAPP(c_List_Oappend(X4),X63),X31)))<=>hAPP(hAPP(c_List_Oappend(X4),X30),X62)=hAPP(hAPP(c_List_Oappend(X4),X32),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__eq__append__conv2)). 4.02/4.27 fof(fact_aset_I3_J, axiom, ![X3, X123, X61]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X123),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3))=>(![X19]:(![X114]:(X123!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X114),X19)<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X114),X3)))<=hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X19),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X61))))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X123),X61)=X123))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X61))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_aset_I3_J)). 4.02/4.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, axiom, ![X244, X89, X90, X91, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X91),X89)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X90),X244))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X91),X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X89),X244))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J)). 4.02/4.27 fof(fact_frac__less2, axiom, ![X29, X53, X43, X13, X4]:(class_Fields_Olinordered__field(X4)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X53))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X29)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X43),X53)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X53),X29))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X43)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_frac__less2)). 4.02/4.27 fof(fact_frac__less, axiom, ![X29, X53, X43, X13, X4]:(class_Fields_Olinordered__field(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X13))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),X43))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X53))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X53),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X29)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X43),X53)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_frac__less)). 4.02/4.27 fof(fact_mult__strict__mono, axiom, ![X44, X10, X12, X11, X4]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X44)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X10),X44)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12)))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__strict__mono)). 4.02/4.27 fof(fact_mult__strict__mono_H, axiom, ![X44, X10, X12, X11, X4]:(class_Rings_Olinordered__semiring__strict(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X44)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X10),X44))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__strict__mono_H)). 4.02/4.27 fof(fact_wfP__SUP, axiom, ![X4, X18, X7]:((c_Wellfounded_OwfP(X7,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_fun(X7,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X18))<=![X42, X139]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),c_Predicate_ODomainP(X7,X7,hAPP(X18,X42))),c_Predicate_ORangeP(X7,X7,hAPP(X18,X139)))=c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))<=hAPP(X18,X42)!=hAPP(X18,X139)))<=![X42]:c_Wellfounded_OwfP(X7,hAPP(X18,X42))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__SUP)). 4.02/4.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, axiom, ![X44, X10, X12, X11, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X44))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X44))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J)). 4.02/4.27 fof(fact_mult__le__less__imp__less, axiom, ![X44, X10, X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12))=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X44))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X10),X44))))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__less__imp__less)). 4.02/4.27 fof(fact_mult__less__le__imp__less, axiom, ![X44, X10, X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X44)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),X44))))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__le__imp__less)). 4.02/4.27 fof(fact_frac__le, axiom, ![X29, X53, X43, X13, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X13))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X43))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X29)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X43),X53)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X53),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X53)))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_frac__le)). 4.02/4.27 fof(fact_mult__mono_H, axiom, ![X44, X10, X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),X44))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X44)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))))<=class_Rings_Oordered__semiring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__mono_H)). 4.02/4.27 fof(fact_folding__one__idem_Ohom__commute, axiom, ![X176, X48, X87, X22, X4]:(c_Finite__Set_Ofolding__one__idem(X4,X22,X87)=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X176))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X176=>hAPP(X48,hAPP(X87,X176))=hAPP(X87,hAPP(c_Set_Oimage(X4,X4,X48),X176))))<=![X19, X34]:hAPP(X48,hAPP(hAPP(X22,X19),X34))=hAPP(hAPP(X22,hAPP(X48,X19)),hAPP(X48,X34)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Ohom__commute)). 4.02/4.27 fof(fact_converseE, axiom, ![X18, X287, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),X287),hAPP(c_Relation_Oconverse(X7,X4),X18)))=>~(![X19, X34]:(hAPP(hAPP(c_Product__Type_OPair(X4,X7),X34),X19)=X287=>~(hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X4),X19),X34)),X18)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converseE)). 4.02/4.27 fof(fact_mult__mono, axiom, ![X44, X10, X12, X11, X4]:(class_Rings_Oordered__semiring(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12))=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X44))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),X44))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__mono)). 4.02/4.27 fof(fact_pick_Osimps, axiom, ![X45, X13, X4, X46]:((hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X4),X13)=hAPP(c_Random_Opick(X4,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X4)),X13),X45)),X46)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X46),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X4),X13))))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X46),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X4),X13))))=>hAPP(c_Random_Opick(X4,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X4)),X13),X45)),X46)=hAPP(c_Random_Opick(X4,X45),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X46),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X4),X13))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pick_Osimps)). 4.02/4.27 fof(fact_fold__image__1, axiom, ![X22, X86, X4, X7]:(class_Groups_Ocomm__monoid__mult(X7)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X86))=>(c_Groups_Oone__class_Oone(X7)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X7,X4,c_Groups_Otimes__class_Otimes(X7)),X22),c_Groups_Oone__class_Oone(X7)),X86)<=![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X86))=>hAPP(X22,X19)=c_Groups_Oone__class_Oone(X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__1)). 4.02/4.27 fof(fact_setsum__reindex, axiom, ![X48, X6, X22, X7, X4, X49]:((c_Fun_Oinj__on(X4,X7,X22,X6)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X49),hAPP(c_Fun_Ocomp(X7,X49,X4,X48),X22)),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X49),X48),hAPP(c_Set_Oimage(X4,X7,X22),X6)))<=class_Groups_Ocomm__monoid__add(X49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__reindex)). 4.02/4.27 fof(fact_Int__insert__right__if1, axiom, ![X6, X3, X26, X4]:(hAPP(hAPP(c_Set_Oinsert(X4),X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),X6))<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__insert__right__if1)). 4.02/4.27 fof(fact_abs__setsum__abs, axiom, ![X3, X22, X7, X4]:(hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),hAPP(hAPP(c_COMBB(X4,X4,X7),c_Groups_Oabs__class_Oabs(X4)),X22)),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),hAPP(hAPP(c_COMBB(X4,X4,X7),c_Groups_Oabs__class_Oabs(X4)),X22)),X3)<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__setsum__abs)). 4.02/4.27 fof(fact_folding__one__idem_Ounion__idem, axiom, ![X6, X3, X87, X22, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X6=>hAPP(hAPP(X22,hAPP(X87,X3)),hAPP(X87,X6))=hAPP(X87,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))))<=c_Finite__Set_Ofolding__one__idem(X4,X22,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Ounion__idem)). 4.02/4.27 fof(fact_unique__quotient__lemma, axiom, ![X101, X14, X212, X213, X12]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X213),X14)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X212),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X212)))<=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),X12),X213)),X212)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X14)),X101)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_unique__quotient__lemma)). 4.02/4.27 fof(fact_unique__quotient__lemma__neg, axiom, ![X101, X14, X212, X213, X12]:(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),X12),X213)),X212)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X14)),X101)))=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14),X213))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),X212)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),X101)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_unique__quotient__lemma__neg)). 4.02/4.27 fof(fact_nth__take__lemma, axiom, ![X59, X45, X4, X107]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X59)))=>(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X107))=>hAPP(hAPP(c_List_Onth(X4),X45),X42)=hAPP(hAPP(c_List_Onth(X4),X59),X42))=>hAPP(hAPP(c_List_Otake(X4),X107),X45)=hAPP(hAPP(c_List_Otake(X4),X107),X59)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__take__lemma)). 4.02/4.27 fof(fact_card__bij__eq, axiom, ![X76, X6, X3, X22, X7, X4]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X4,X76),X6)),X3))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hAPP(c_Finite__Set_Ocard(X4),X3)=hAPP(c_Finite__Set_Ocard(X7),X6)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X6)))))<=c_Fun_Oinj__on(X7,X4,X76,X6))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X7,X22),X3)),X6)))<=c_Fun_Oinj__on(X4,X7,X22,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__bij__eq)). 4.02/4.27 fof(fact_div__mod__equality, axiom, ![X10, X12, X11, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X11),X12)),X12)),c_Divides_Odiv__class_Omod(X4,X11,X12))),X10)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mod__equality)). 4.02/4.27 fof(fact_div__mod__equality2, axiom, ![X10, X11, X12, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X11),X12))),c_Divides_Odiv__class_Omod(X4,X11,X12))),X10)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mod__equality2)). 4.02/4.27 fof(fact_diff__card__le__card__Diff, axiom, ![X3, X6, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X3)),hAPP(c_Finite__Set_Ocard(X4),X6))),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__card__le__card__Diff)). 4.02/4.27 fof(fact_min__max_OInf__fin_Osubset__idem, axiom, ![X6, X3, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X6)),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X3))=c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X3)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X3)))<=X6!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Osubset__idem)). 4.02/4.27 fof(fact_min__max_OSup__fin_Osubset__idem, axiom, ![X6, X3, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(X6!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>(hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X6)),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X3))=c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X3)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Osubset__idem)). 4.02/4.27 fof(fact_Image__subset, axiom, ![X8, X6, X3, X18, X7, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X18),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),X6))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X7,X18),X8)),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__subset)). 4.02/4.27 fof(fact_Cons__acc__listrel1I, axiom, ![X32, X18, X9, X4]:((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X32),c_Wellfounded_Oacc(tc_List_Olist(X4),c_List_Olistrel1(X4,X18))))=>hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)),c_Wellfounded_Oacc(tc_List_Olist(X4),c_List_Olistrel1(X4,X18)))))<=hBOOL(hAPP(hAPP(c_member(X4),X9),c_Wellfounded_Oacc(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__acc__listrel1I)). 4.02/4.27 fof(fact_card__Un__disjoint, axiom, ![X6, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X3)),hAPP(c_Finite__Set_Ocard(X4),X6))=hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Un__disjoint)). 4.02/4.27 fof(fact_nth__append, axiom, ![X59, X45, X4, X5]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45))))=>hAPP(hAPP(c_List_Onth(X4),X59),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Oappend(X4),X45),X59)),X5))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))=>hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Oappend(X4),X45),X59)),X5)=hAPP(hAPP(c_List_Onth(X4),X45),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__append)). 4.02/4.27 fof(fact_transfer__nat__int__sum__prod_I2_J, axiom, ![X3, X22, X4]:((class_Groups_Ocomm__monoid__mult(X4)&class_Groups_Ocomm__monoid__add(X4))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Int_Oint),X22),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,X4),X22),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__sum__prod_I2_J)). 4.02/4.27 fof(fact_mod__diff__cong, axiom, ![X110, X12, X111, X10, X11, X4]:(class_Divides_Oring__div(X4)=>(c_Divides_Odiv__class_Omod(X4,X111,X10)=c_Divides_Odiv__class_Omod(X4,X11,X10)=>(c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X12),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X111),X110),X10)<=c_Divides_Odiv__class_Omod(X4,X12,X10)=c_Divides_Odiv__class_Omod(X4,X110,X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__diff__cong)). 4.02/4.27 fof(fact_sorted__rev__nth__mono, axiom, ![X135, X46, X45, X4]:(class_Orderings_Olinorder(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),X135))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_List_Onth(X4),X45),X135)),hAPP(hAPP(c_List_Onth(X4),X45),X46)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X135),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))))<=c_List_Olinorder__class_Osorted(X4,hAPP(c_List_Orev(X4),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__rev__nth__mono)). 4.02/4.27 fof(fact_transfer__nat__int__sum__prod_I1_J, axiom, ![X3, X22, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Int_Oint),X22),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,X4),X22),X3)<=(class_Groups_Ocomm__monoid__mult(X4)&class_Groups_Ocomm__monoid__add(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__sum__prod_I1_J)). 4.02/4.27 fof(fact_folding__image__simple__idem_Ounion__idem, axiom, ![X6, X3, X87, X76, X16, X22, X7, X4]:(((hAPP(hAPP(X22,hAPP(X87,X3)),hAPP(X87,X6))=hAPP(X87,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3),X6))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3)))<=c_Finite__Set_Ofolding__image__simple__idem(X4,X7,X22,X16,X76,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple__idem_Ounion__idem)). 4.02/4.27 fof(fact_Image__mono, axiom, ![X3, X127, X18, X214, X7, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X214),X18))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X127),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X7,X214),X127)),hAPP(c_Relation_OImage(X4,X7,X18),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__mono)). 4.02/4.27 fof(fact_setsum__shift__bounds__cl__Suc__ivl, axiom, ![X20, X21, X22, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,tc_Nat_Onat),X22),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X21,X20))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),X22),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X21),hAPP(c_Nat_OSuc,X20)))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__shift__bounds__cl__Suc__ivl)). 4.02/4.27 fof(fact_mod__mult__cong, axiom, ![X110, X12, X111, X10, X11, X4]:((c_Divides_Odiv__class_Omod(X4,X111,X10)=c_Divides_Odiv__class_Omod(X4,X11,X10)=>(c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X111),X110),X10)<=c_Divides_Odiv__class_Omod(X4,X110,X10)=c_Divides_Odiv__class_Omod(X4,X12,X10)))<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__cong)). 4.02/4.27 fof(fact_divide__strict__left__mono, axiom, ![X10, X11, X12, X4]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X10),X11)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X10),X12))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11)))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__strict__left__mono)). 4.02/4.27 fof(fact_divide__left__mono, axiom, ![X10, X11, X12, X4]:(class_Fields_Olinordered__field(X4)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X10),X11)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X10),X12))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__left__mono)). 4.02/4.27 fof(fact_divide__strict__left__mono__neg, axiom, ![X10, X12, X11, X4]:(class_Fields_Olinordered__field(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X10),X11)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X10),X12))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X10),c_Groups_Ozero__class_Ozero(X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__strict__left__mono__neg)). 4.02/4.27 fof(fact_equiv__class__self, axiom, ![X26, X18, X3, X4]:(c_Equiv__Relations_Oequiv(X4,X3,X18)=>(hBOOL(hAPP(hAPP(c_member(X4),X26),hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__class__self)). 4.02/4.27 fof(fact_mod__add__cong, axiom, ![X110, X12, X111, X10, X11, X4]:(class_Divides_Osemiring__div(X4)=>((c_Divides_Odiv__class_Omod(X4,X110,X10)=c_Divides_Odiv__class_Omod(X4,X12,X10)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X111),X110),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12),X10))<=c_Divides_Odiv__class_Omod(X4,X11,X10)=c_Divides_Odiv__class_Omod(X4,X111,X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__cong)). 4.02/4.27 fof(fact_length__filter__less, axiom, ![X56, X32, X9, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Ofilter(X4,X56),X32))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))<=~(hBOOL(hAPP(X56,X9))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__filter__less)). 4.02/4.27 fof(fact_UN__absorb, axiom, ![X3, X7, X41, X28, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X28),X41))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),hAPP(X3,X28)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X41),X3))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X41),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__absorb)). 4.02/4.27 fof(fact_INT__absorb, axiom, ![X3, X7, X41, X28, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X28),X41))=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X41),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),hAPP(X3,X28)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X41),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__absorb)). 4.02/4.27 fof(fact_folding_Ocommute__comp_H, axiom, ![X9, X3, X87, X22, X7, X4]:(c_Finite__Set_Ofolding(X4,X7,X22,X87)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X87,X3)),hAPP(X22,X9))=hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X22,X9)),hAPP(X87,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__comp_H)). 4.02/4.27 fof(fact_inj__on__iff__card__le, axiom, ![X6, X7, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X3)),hAPP(c_Finite__Set_Ocard(X7),X6)))<=>?[X160]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X7,X160),X3)),X6))&c_Fun_Oinj__on(X4,X7,X160,X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__iff__card__le)). 4.02/4.27 fof(fact_list__update__append1, axiom, ![X13, X59, X45, X4, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))=>hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Olist__update(X4,X45),X46),X13)),X59)=hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Oappend(X4),X45),X59)),X46),X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__append1)). 4.02/4.27 fof(fact_decr__mult__lemma, axiom, ![X28, X56, X102]:((![X19]:(hBOOL(hAPP(X56,X19))=>hBOOL(hAPP(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),X102))))=>(![X19]:(hBOOL(hAPP(X56,X19))=>hBOOL(hAPP(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X28),X102)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X28))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X102))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_decr__mult__lemma)). 4.02/4.27 fof(fact_list__size__pointwise, axiom, ![X76, X22, X32, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X4,X22,X32)),c_List_Olist_Olist__size(X4,X76,X32)))<=![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X22,X19)),hAPP(X76,X19)))<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__size__pointwise)). 4.02/4.27 fof(fact_power__diff, axiom, ![X2, X5, X11, X4]:(((hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X2)))<=c_Groups_Ozero__class_Ozero(X4)!=X11)<=class_Fields_Ofield(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__diff)). 4.02/4.27 fof(fact_abs__triangle__ineq3, axiom, ![X12, X11, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)))),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X12))))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__triangle__ineq3)). 4.02/4.27 fof(fact_fold1__strict__below__iff, axiom, ![X9, X3, X4]:((((?[X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X19),X9))&hBOOL(hAPP(hAPP(c_member(X4),X19),X3)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X3)),X9)))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__strict__below__iff)). 4.02/4.27 fof(fact_fold1__below__iff, axiom, ![X9, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X3)),X9))<=>?[X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X19),X9))&hBOOL(hAPP(hAPP(c_member(X4),X19),X3))))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__below__iff)). 4.02/4.27 fof(fact_folding__one__idem_Osubset__idem, axiom, ![X6, X3, X87, X22, X4]:(c_Finite__Set_Ofolding__one__idem(X4,X22,X87)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X3))=>hAPP(X87,X3)=hAPP(hAPP(X22,hAPP(X87,X6)),hAPP(X87,X3)))<=X6!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Osubset__idem)). 4.02/4.27 fof(fact_divide__left__mono__neg, axiom, ![X10, X12, X11, X4]:(class_Fields_Olinordered__field__inverse__zero(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X10),X11)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X10),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),c_Groups_Ozero__class_Ozero(X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__left__mono__neg)). 4.02/4.27 fof(fact_folding__image__simple_Oinsert, axiom, ![X9, X3, X87, X76, X16, X22, X7, X4]:(((~(hBOOL(hAPP(hAPP(c_member(X7),X9),X3)))=>hAPP(hAPP(X22,hAPP(X76,X9)),hAPP(X87,X3))=hAPP(X87,hAPP(hAPP(c_Set_Oinsert(X7),X9),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3)))<=c_Finite__Set_Ofolding__image__simple(X4,X7,X22,X16,X76,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Oinsert)). 4.02/4.27 fof(fact_power__Suc__less, axiom, ![X5, X11, X4]:(class_Rings_Olinordered__semidom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Oone__class_Oone(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__Suc__less)). 4.02/4.27 fof(fact_Ints__odd__less__0, axiom, ![X26, X4]:(class_Rings_Olinordered__idom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),X26)),X26)),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),c_Groups_Ozero__class_Ozero(X4))))<=hBOOL(hAPP(hAPP(c_member(X4),X26),c_Int_Oring__1__class_OInts(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__odd__less__0)). 4.02/4.27 fof(fact_transfer__nat__int__set__relations_I4_J, axiom, ![X6, X3]:(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)),X3)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X6)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__relations_I4_J)). 4.02/4.27 fof(fact_Image__singleton__iff, axiom, ![X26, X18, X7, X25, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X4),X26),X25)),X18))<=>hBOOL(hAPP(hAPP(c_member(X4),X25),hAPP(c_Relation_OImage(X7,X4,X18),hAPP(hAPP(c_Set_Oinsert(X7),X26),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__singleton__iff)). 4.02/4.27 fof(fact_INT__iff, axiom, ![X6, X3, X7, X25, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X25),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=>![X19]:(hBOOL(hAPP(hAPP(c_member(X7),X19),X3))=>hBOOL(hAPP(hAPP(c_member(X4),X25),hAPP(X6,X19))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__iff)). 4.02/4.27 fof(fact_map__of__eq__Some__iff, axiom, ![X17, X9, X145, X7, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X9),X17)),hAPP(c_List_Oset(tc_prod(X4,X7)),X145)))<=>hAPP(hAPP(c_Map_Omap__of(X4,X7),X145),X9)=hAPP(c_Option_Ooption_OSome(X7),X17))<=hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(tc_prod(X4,X7),X4),c_Product__Type_Ofst(X4,X7)),X145)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__eq__Some__iff)). 4.02/4.27 fof(fact_setprod__insert, axiom, ![X22, X26, X3, X4, X7]:(((~(hBOOL(hAPP(hAPP(c_member(X4),X26),X3)))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(X22,X26)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),hAPP(hAPP(c_Set_Oinsert(X4),X26),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Groups_Ocomm__monoid__mult(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__insert)). 4.02/4.27 fof(fact_add__number__of__left, axiom, ![X29, X53, X1, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X53))),X29)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X53)),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__number__of__left)). 4.02/4.27 fof(fact_zmult__zless__mono2__lemma, axiom, ![X107, X135, X46]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X107))=>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),X107)),X46)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X107)),X135))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X46),X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__zless__mono2__lemma)). 4.02/4.27 fof(fact_finite__UN__I, axiom, ![X6, X7, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(![X27]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(X6,X27)))<=hBOOL(hAPP(hAPP(c_member(X4),X27),X3)))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X3),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UN__I)). 4.02/4.27 fof(fact_finite__UN, axiom, ![X6, X7, X3, X4]:((![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(X6,X19))))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X3),X6))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UN)). 4.02/4.27 fof(fact_finite__SigmaI, axiom, ![X6, X7, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),X6)))<=![X27]:(hBOOL(hAPP(hAPP(c_member(X4),X27),X3))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(X6,X27)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__SigmaI)). 4.02/4.27 fof(fact_map__of__zip__map, axiom, ![X22, X7, X32, X9, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))=>hAPP(hAPP(c_Map_Omap__of(X4,X7),hAPP(hAPP(c_List_Ozip(X4,X7),X32),hAPP(hAPP(c_List_Omap(X4,X7),X22),X32))),X9)=hAPP(c_Option_Ooption_OSome(X7),hAPP(X22,X9)))&(hAPP(hAPP(c_Map_Omap__of(X4,X7),hAPP(hAPP(c_List_Ozip(X4,X7),X32),hAPP(hAPP(c_List_Omap(X4,X7),X22),X32))),X9)=c_Option_Ooption_ONone(X7)<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__zip__map)). 4.02/4.27 fof(fact_transfer__int__nat__set__relations_I4_J, axiom, ![X6, X3]:(c_Nat__Transfer_Onat__set(X3)=>((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),X3)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X6)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X3),X6)))<=c_Nat__Transfer_Onat__set(X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__relations_I4_J)). 4.02/4.27 fof(fact_wf__iff__no__infinite__down__chain, axiom, ![X18, X4]:(~(?[X160]:![X42]:hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(X160,hAPP(c_Nat_OSuc,X42))),hAPP(X160,X42))),X18)))<=>c_Wellfounded_Owf(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__iff__no__infinite__down__chain)). 4.02/4.27 fof(fact_diff__single__insert, axiom, ![X6, X9, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))),X6))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),X6)))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__single__insert)). 4.02/4.27 fof(fact_setsum__insert, axiom, ![X22, X26, X87, X4, X7]:(((~(hBOOL(hAPP(hAPP(c_member(X4),X26),X87)))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),hAPP(hAPP(c_Set_Oinsert(X4),X26),X87))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),hAPP(X22,X26)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X87)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X87)))<=class_Groups_Ocomm__monoid__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__insert)). 4.02/4.27 fof(fact_posDivAlg__div__mod, axiom, ![X47, X107]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X107))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X47))=>hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X107),X47)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X107,X47))=c_Divides_OposDivAlg(X107,X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_posDivAlg__div__mod)). 4.02/4.27 fof(fact_negDivAlg__div__mod, axiom, ![X47, X107]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X107),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>(c_Divides_OnegDivAlg(X107,X47)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X107),X47)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X107,X47))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg__div__mod)). 4.02/4.27 fof(fact_Inf__fin_Ounion__idem, axiom, ![X6, X3, X4]:((((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>(c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),c_Big__Operators_Olattice__class_OInf__fin(X4,X3)),c_Big__Operators_Olattice__class_OInf__fin(X4,X6))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X6))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Ounion__idem)). 4.02/4.27 fof(fact_mem__Sigma__iff, axiom, ![X6, X3, X25, X26, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X26),X25)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),X6)))<=>(hBOOL(hAPP(hAPP(c_member(X4),X26),X3))&hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(X6,X26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mem__Sigma__iff)). 4.02/4.27 fof(fact_Inter__subset, axiom, ![X6, X3, X4]:((X3!=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X3)),X6)))<=![X241]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X241),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X241),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__subset)). 4.02/4.27 fof(fact_rev__nth, axiom, ![X45, X4, X5]:(hAPP(hAPP(c_List_Onth(X4),X45),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),hAPP(c_Nat_OSuc,X5)))=hAPP(hAPP(c_List_Onth(X4),hAPP(c_List_Orev(X4),X45)),X5)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__nth)). 4.02/4.27 fof(fact_times__divide__times__eq, axiom, ![X53, X29, X43, X13, X4]:(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X13),X29)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X43),X53))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X29),X53))<=class_Fields_Ofield__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_times__divide__times__eq)). 4.02/4.27 fof(fact_single__Diff__lessThan, axiom, ![X28, X4]:(hAPP(hAPP(c_Set_Oinsert(X4),X28),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X28),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X28))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__Diff__lessThan)). 4.02/4.27 fof(fact_fun__left__comm_Ofold__graph__insertE, axiom, ![X64, X3, X9, X16, X22, X7, X4]:(((~(![X34]:(~(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X7,X22,X16,X3),X34)))<=hAPP(hAPP(X22,X9),X34)=X64))<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3))))<=hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X7,X22,X16,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3)),X64)))<=c_Finite__Set_Ofun__left__comm(X4,X7,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__graph__insertE)). 4.02/4.27 fof(fact_list__all2__update__cong2, axiom, ![X37, X17, X9, X31, X32, X56, X7, X4]:((hBOOL(hAPP(hAPP(X56,X9),X17))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31)))=>c_List_Olist__all2(X4,X7,X56,hAPP(hAPP(c_List_Olist__update(X4,X32),X37),X9),hAPP(hAPP(c_List_Olist__update(X7,X31),X37),X17))))<=c_List_Olist__all2(X4,X7,X56,X32,X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__update__cong2)). 4.02/4.27 fof(fact_list__all2__update__cong, axiom, ![X17, X9, X31, X56, X7, X32, X4, X37]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))=>(c_List_Olist__all2(X4,X7,X56,X32,X31)=>(hBOOL(hAPP(hAPP(X56,X9),X17))=>c_List_Olist__all2(X4,X7,X56,hAPP(hAPP(c_List_Olist__update(X4,X32),X37),X9),hAPP(hAPP(c_List_Olist__update(X7,X31),X37),X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__update__cong)). 4.02/4.27 fof(fact_ivl__disj__un_I17_J, axiom, ![X115, X21, X60, X4]:(class_Orderings_Olinorder(X4)=>((hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X60),X21)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X21),X115))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X60),X115)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X21),X115)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X60),X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I17_J)). 4.02/4.27 fof(fact_div__pos__neg, axiom, ![X12, X11]:((hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__pos__neg)). 4.02/4.27 fof(fact_Max_Ohom__commute, axiom, ![X176, X48, X4]:((((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X176=>c_Big__Operators_Olinorder__class_OMax(X4,hAPP(c_Set_Oimage(X4,X4,X48),X176))=hAPP(X48,c_Big__Operators_Olinorder__class_OMax(X4,X176)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X176)))<=![X19, X34]:hAPP(X48,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X19),X34))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(X48,X19)),hAPP(X48,X34)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Ohom__commute)). 4.02/4.27 fof(fact_Inf__fin_Ohom__commute, axiom, ![X176, X48, X4]:(class_Lattices_Olattice(X4)=>(![X19, X34]:hAPP(X48,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X19),X34))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(X48,X19)),hAPP(X48,X34))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X176))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X176=>c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(c_Set_Oimage(X4,X4,X48),X176))=hAPP(X48,c_Big__Operators_Olattice__class_OInf__fin(X4,X176)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Ohom__commute)). 4.02/4.27 fof(fact_Min_Ohom__commute, axiom, ![X176, X48, X4]:(class_Orderings_Olinorder(X4)=>(![X19, X34]:hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(X48,X19)),hAPP(X48,X34))=hAPP(X48,hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X19),X34))=>((hAPP(X48,c_Big__Operators_Olinorder__class_OMin(X4,X176))=c_Big__Operators_Olinorder__class_OMin(X4,hAPP(c_Set_Oimage(X4,X4,X48),X176))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X176)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X176))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Ohom__commute)). 4.02/4.27 fof(fact_list__update__swap, axiom, ![X236, X13, X45, X4, X237, X46]:(hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Olist__update(X4,X45),X46),X13)),X237),X236)=hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Olist__update(X4,X45),X237),X236)),X46),X13)<=X237!=X46), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__swap)). 4.02/4.27 fof(fact_div__neg__neg, axiom, ![X12, X11]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12)=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),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__neg__neg)). 4.02/4.27 fof(fact_add__divide__eq__iff, axiom, ![X43, X13, X29, X4]:(class_Fields_Ofield(X4)=>(c_Groups_Ozero__class_Ozero(X4)!=X29=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X13),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X43),X29))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X29),X13)),X43)),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__divide__eq__iff)). 4.02/4.27 fof(fact_diff__divide__eq__iff, axiom, ![X43, X13, X29, X4]:(class_Fields_Ofield(X4)=>(X29!=c_Groups_Ozero__class_Ozero(X4)=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X29),X13)),X43)),X29)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X13),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X43),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__divide__eq__iff)). 4.02/4.27 fof(fact_divide__diff__eq__iff, axiom, ![X43, X13, X29, X4]:((hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X29),X43))),X29)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X29)),X43)<=c_Groups_Ozero__class_Ozero(X4)!=X29)<=class_Fields_Ofield(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__diff__eq__iff)). 4.02/4.27 fof(fact_Sup__fin_Ohom__commute, axiom, ![X176, X48, X4]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X176))=>(X176!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hAPP(X48,c_Big__Operators_Olattice__class_OSup__fin(X4,X176))=c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(c_Set_Oimage(X4,X4,X48),X176))))<=![X19, X34]:hAPP(X48,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X19),X34))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(X48,X19)),hAPP(X48,X34)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Ohom__commute)). 4.02/4.27 fof(fact_divide__add__eq__iff, axiom, ![X43, X13, X29, X4]:((c_Groups_Ozero__class_Ozero(X4)!=X29=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X29)),X43)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X29),X43))),X29))<=class_Fields_Ofield(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__add__eq__iff)). 4.02/4.27 fof(fact_Sup__fin_Ounion__idem, axiom, ![X6, X3, X4]:((((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X6=>c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),c_Big__Operators_Olattice__class_OSup__fin(X4,X3)),c_Big__Operators_Olattice__class_OSup__fin(X4,X6))))<=X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Ounion__idem)). 4.02/4.27 fof(fact_add__frac__num, axiom, ![X29, X13, X43, X4]:((X43!=c_Groups_Ozero__class_Ozero(X4)=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X29),X43))),X43)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43)),X29))<=class_Fields_Ofield__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__frac__num)). 4.02/4.27 fof(fact_div__mult__self1, axiom, ![X10, X11, X12, X4]:((hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12))),X12)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X11),X12))<=c_Groups_Ozero__class_Ozero(X4)!=X12)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self1)). 4.02/4.27 fof(fact_add__num__frac, axiom, ![X13, X29, X43, X4]:(class_Fields_Ofield__inverse__zero(X4)=>(X43!=c_Groups_Ozero__class_Ozero(X4)=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X29),X43))),X43)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X29),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__num__frac)). 4.02/4.27 fof(fact_set__drop__subset__set__drop, axiom, ![X32, X4, X21, X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Odrop(X4),X21),X32))),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Odrop(X4),X20),X32))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),X21))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__drop__subset__set__drop)). 4.02/4.27 fof(fact_div__mult__self2, axiom, ![X10, X11, X12, X4]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X11),X12))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10))),X12)<=X12!=c_Groups_Ozero__class_Ozero(X4))<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self2)). 4.02/4.27 fof(fact_Int__atLeastLessThan, axiom, ![X102, X24, X25, X26, X4]:(class_Orderings_Olinorder(X4)=>hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X26),X24)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X25),X102))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X26),X25)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X24),X102))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastLessThan)). 4.02/4.27 fof(fact_Min__Un, axiom, ![X6, X3, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>(hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olinorder__class_OMin(X4,X3)),c_Big__Operators_Olinorder__class_OMin(X4,X6))=c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X6))<=X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__Un)). 4.02/4.27 fof(fact_set__take__subset__set__take, axiom, ![X32, X4, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Otake(X4),X21),X32))),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Otake(X4),X20),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__take__subset__set__take)). 4.02/4.27 fof(fact_SUP__le__iff, axiom, ![X115, X54, X3, X7, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X4),X3),X54)),X115))<=>![X19]:(hBOOL(hAPP(hAPP(c_member(X7),X19),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(X54,X19)),X115))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__le__iff)). 4.02/4.27 fof(fact_le__INF__iff, axiom, ![X54, X3, X7, X115, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X115),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,X4),X3),X54)))<=>![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X115),hAPP(X54,X19)))<=hBOOL(hAPP(hAPP(c_member(X7),X19),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__INF__iff)). 4.02/4.27 fof(fact_setprod__pos, axiom, ![X22, X3, X4, X7]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),X3)))<=![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(X22,X19)))))<=class_Rings_Olinordered__semidom(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__pos)). 4.02/4.27 fof(fact_refl__on__def, axiom, ![X18, X3, X4]:((![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X19)),X18)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X3)))))<=>c_Relation_Orefl__on(X4,X3,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__def)). 4.02/4.27 fof(fact_finite__equiv__class, axiom, ![X156, X18, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X3))))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X156))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X156),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X3),X18)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__equiv__class)). 4.02/4.27 fof(fact_equiv__type, axiom, ![X18, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X3))))<=c_Equiv__Relations_Oequiv(X4,X3,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__type)). 4.02/4.27 fof(fact_Max__Un, axiom, ![X6, X3, X4]:(((X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>((hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olinorder__class_OMax(X4,X3)),c_Big__Operators_Olinorder__class_OMax(X4,X6))=c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))<=X6!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__Un)). 4.02/4.27 fof(fact_setprod__nonneg, axiom, ![X22, X3, X4, X7]:(class_Rings_Olinordered__semidom(X7)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),X3)))<=![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(X22,X19)))<=hBOOL(hAPP(hAPP(c_member(X4),X19),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__nonneg)). 4.02/4.27 fof(fact_add__number__of__diff1, axiom, ![X10, X53, X1, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X53)),X10))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X53))),X10)<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__number__of__diff1)). 4.02/4.27 fof(fact_mult__number__of__left, axiom, ![X29, X53, X1, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X53))),X29)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X53)),X29))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__number__of__left)). 4.02/4.27 fof(fact_mod__pos__neg, axiom, ![X12, X11]:((hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12))))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__neg)). 4.02/4.27 fof(fact_in__rtrancl__UnI, axiom, ![X86, X39, X9, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X9),c_Transitive__Closure_Ortrancl(X4,X86)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X9),c_Transitive__Closure_Ortrancl(X4,X39))))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X9),c_Transitive__Closure_Ortrancl(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X39),X86))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__rtrancl__UnI)). 4.02/4.27 fof(fact_mod__neg__neg, axiom, ![X12, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)=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),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__neg__neg)). 4.02/4.27 fof(fact_gt__half__sum, axiom, ![X12, X11, X4]:(class_Fields_Olinordered__field(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Oone__class_Oone(X4)))),X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_gt__half__sum)). 4.02/4.27 fof(fact_less__half__sum, axiom, ![X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Oone__class_Oone(X4)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12)))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__half__sum)). 4.02/4.27 fof(fact_card__inj__on__le, axiom, ![X6, X3, X22, X7, X4]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X6))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X3)),hAPP(c_Finite__Set_Ocard(X7),X6))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X7,X22),X3)),X6)))<=c_Fun_Oinj__on(X4,X7,X22,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__inj__on__le)). 4.02/4.27 fof(fact_power__minus, axiom, ![X5, X11, X4]:(class_Rings_Oring__1(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))),X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__minus)). 4.02/4.27 fof(fact_fold__graph_OinsertI, axiom, ![X17, X16, X22, X7, X3, X9, X4]:((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X7,X22,X16,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3)),hAPP(hAPP(X22,X9),X17)))<=hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X7,X22,X16,X3),X17)))<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph_OinsertI)). 4.02/4.27 fof(fact_setsum__right__distrib, axiom, ![X3, X22, X7, X18, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),hAPP(hAPP(c_COMBB(X4,X4,X7),hAPP(c_Groups_Otimes__class_Otimes(X4),X18)),X22)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X18),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),X22),X3))<=class_Rings_Osemiring__0(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__right__distrib)). 4.02/4.27 fof(fact_fun__left__comm__idem_Ofold__set, axiom, ![X32, X17, X22, X7, X4]:(c_Finite__Set_Ofun__left__comm__idem(X4,X7,X22)=>hAPP(c_List_Ofoldl(X7,X4,hAPP(c_COMBC(X4,X7,X7),X22),X17),X32)=hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),X17),hAPP(c_List_Oset(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofold__set)). 4.02/4.27 fof(fact_dom__minus, axiom, ![X3, X7, X4, X9, X22]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),c_Map_Odom(X7,X4,X22)),hAPP(hAPP(c_Set_Oinsert(X7),X9),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),c_Map_Odom(X7,X4,X22)),X3)<=hAPP(X22,X9)=c_Option_Ooption_ONone(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__minus)). 4.02/4.27 fof(fact_map__of__zip__is__None, axiom, ![X9, X31, X7, X32, X4]:((hAPP(hAPP(c_Map_Omap__of(X4,X7),hAPP(hAPP(c_List_Ozip(X4,X7),X32),X31)),X9)=c_Option_Ooption_ONone(X7)<=>~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__zip__is__None)). 4.02/4.27 fof(fact_folding__one_Oeq__fold_H, axiom, ![X9, X3, X87, X22, X4]:(c_Finite__Set_Ofolding__one(X4,X22,X87)=>((hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,X22),X9),X3)=hAPP(X87,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oeq__fold_H)). 4.02/4.27 fof(fact_map__upd__Some__unfold, axiom, ![X17, X9, X25, X26, X21, X4, X7]:(((X9!=X26&hAPP(X21,X9)=hAPP(c_Option_Ooption_OSome(X4),X17))|(X26=X9&X17=X25))<=>hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X4)),X21),X26),hAPP(c_Option_Ooption_OSome(X4),X25)),X9)=hAPP(c_Option_Ooption_OSome(X4),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upd__Some__unfold)). 4.02/4.27 fof(fact_listrel1__subset__listrel, axiom, ![X214, X18, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),X214))=>(c_Relation_Orefl__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),X214)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool)),c_List_Olistrel1(X4,X18)),c_List_Olistrel(X4,X214))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__subset__listrel)). 4.02/4.27 fof(fact_set__remove1__eq, axiom, ![X9, X32, X4]:(hAPP(c_List_Oset(X4),c_List_Oremove1(X4,X9,X32))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X32)),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=hBOOL(hAPP(c_List_Odistinct(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__remove1__eq)). 4.02/4.27 fof(fact_power__strict__mono, axiom, ![X5, X12, X11, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X5)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__strict__mono)). 4.02/4.27 fof(fact_power__strict__decreasing, axiom, ![X11, X88, X5, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),X88))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Oone__class_Oone(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X88)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5))))))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__strict__decreasing)). 4.02/4.27 fof(fact_power__decreasing, axiom, ![X11, X88, X5, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X88))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),c_Groups_Oone__class_Oone(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X88)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__decreasing)). 4.02/4.27 fof(fact_set__update__subsetI, axiom, ![X37, X9, X3, X32, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist__update(X4,X32),X37),X9))),X3))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X32)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__update__subsetI)). 4.02/4.27 fof(fact_map__le__upd, axiom, ![X25, X26, X76, X22, X7, X4]:(c_Map_Omap__le(X4,X7,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X22),X26),X25),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X76),X26),X25))<=c_Map_Omap__le(X4,X7,X22,X76)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__le__upd)). 4.02/4.27 fof(fact_refl__on__comp__subset, axiom, ![X18, X3, X4]:(c_Relation_Orefl__on(X4,X3,X18)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(c_Relation_Oconverse(X4,X4),X18)),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__comp__subset)). 4.02/4.27 fof(fact_inj__on__Inter, axiom, ![X22, X7, X4, X86]:((![X195]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X195),X86))=>c_Fun_Oinj__on(X4,X7,X22,X195))=>c_Fun_Oinj__on(X4,X7,X22,c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X86)))<=X86!=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__Inter)). 4.02/4.27 fof(fact_converseI, axiom, ![X18, X25, X26, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X4),X25),X26)),hAPP(c_Relation_Oconverse(X4,X7),X18)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X26),X25)),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converseI)). 4.02/4.27 fof(fact_map__of__is__SomeD, axiom, ![X17, X9, X145, X4, X7]:(hAPP(c_Option_Ooption_OSome(X4),X17)=hAPP(hAPP(c_Map_Omap__of(X7,X4),X145),X9)=>hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X4),X9),X17)),hAPP(c_List_Oset(tc_prod(X7,X4)),X145)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__is__SomeD)). 4.02/4.27 fof(fact_sorted__equals__nth__mono, axiom, ![X32, X4]:((c_List_Olinorder__class_Osorted(X4,X32)<=>![X139]:(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_List_Onth(X4),X32),X42)),hAPP(hAPP(c_List_Onth(X4),X32),X139)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X139)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X139),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__equals__nth__mono)). 4.02/4.27 fof(fact_all__set__conv__all__nth, axiom, ![X56, X32, X4]:(![X42]:(hBOOL(hAPP(X56,hAPP(hAPP(c_List_Onth(X4),X32),X42)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))))<=>![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32)))=>hBOOL(hAPP(X56,X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__set__conv__all__nth)). 4.02/4.27 fof(fact_abs__eq__mult, axiom, ![X12, X11, X4]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),c_Groups_Ozero__class_Ozero(X4))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),c_Groups_Ozero__class_Ozero(X4)))))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),hAPP(c_Groups_Oabs__class_Oabs(X4),X12))=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)))<=class_Rings_Oordered__ring__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__eq__mult)). 4.02/4.27 fof(fact_rtrancl__power, axiom, ![X39, X51, X4]:(?[X104]:hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X51),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X104),X39)))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X51),c_Transitive__Closure_Ortrancl(X4,X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__power)). 4.02/4.27 fof(fact_card__Diff__subset, axiom, ![X3, X6, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X3))=>hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X3)),hAPP(c_Finite__Set_Ocard(X4),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Diff__subset)). 4.02/4.27 fof(fact_sort__foldl__insort, axiom, ![X32, X4]:(c_List_Olinorder__class_Osort__key(X4,X4,c_COMBI(X4),X32)=hAPP(c_List_Ofoldl(tc_List_Olist(X4),X4,hAPP(c_COMBC(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4))),c_List_Olist_ONil(X4)),X32)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sort__foldl__insort)). 4.02/4.27 fof(fact_Diff__insert__absorb, axiom, ![X3, X9, X4]:(X3=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3)),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__insert__absorb)). 4.02/4.27 fof(fact_fold__sup__insert, axiom, ![X26, X25, X3, X4]:(class_Lattices_Osemilattice__sup(X4)=>(hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4)),X25),hAPP(hAPP(c_Set_Oinsert(X4),X26),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X26),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4)),X25),X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__sup__insert)). 4.02/4.27 fof(fact_min__max_Ofold__inf__insert, axiom, ![X26, X25, X3, X4]:((hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X26),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omin(X4)),X25),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omin(X4)),X25),hAPP(hAPP(c_Set_Oinsert(X4),X26),X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofold__inf__insert)). 4.02/4.27 fof(fact_nonzero__power__divide, axiom, ![X5, X11, X12, X4]:((hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X12)),X5)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X5))<=c_Groups_Ozero__class_Ozero(X4)!=X12)<=class_Fields_Ofield(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__power__divide)). 4.02/4.27 fof(fact_min__max_Ofold__inf__le__inf, axiom, ![X25, X26, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_member(X4),X26),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omin(X4)),X25),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X26),X25)))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofold__inf__le__inf)). 4.02/4.27 fof(fact_fold__inf__insert, axiom, ![X26, X25, X3, X4]:(class_Lattices_Osemilattice__inf(X4)=>(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X26),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X25),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X25),hAPP(hAPP(c_Set_Oinsert(X4),X26),X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__inf__insert)). 4.02/4.27 fof(fact_min__max_Ofold__sup__insert, axiom, ![X26, X25, X3, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X26),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omax(X4)),X25),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omax(X4)),X25),hAPP(hAPP(c_Set_Oinsert(X4),X26),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofold__sup__insert)). 4.02/4.27 fof(fact_quotientE, axiom, ![X18, X3, X156, X4]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X156),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X3),X18)))=>~(![X19]:(~(hBOOL(hAPP(hAPP(c_member(X4),X19),X3)))<=X156=hAPP(c_Relation_OImage(X4,X4,X18),hAPP(hAPP(c_Set_Oinsert(X4),X19),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_quotientE)). 4.02/4.27 fof(fact_fold__inf__le__inf, axiom, ![X25, X26, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_member(X4),X26),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X25),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X26),X25)))))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__inf__le__inf)). 4.02/4.27 fof(fact_min__max_Osup__le__fold__sup, axiom, ![X25, X26, X3, X4]:(class_Orderings_Olinorder(X4)=>((hBOOL(hAPP(hAPP(c_member(X4),X26),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X26),X25)),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omax(X4)),X25),X3))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__le__fold__sup)). 4.02/4.27 fof(fact_sup__le__fold__sup, axiom, ![X25, X26, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_member(X4),X26),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X26),X25)),hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4)),X25),X3)))))<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__le__fold__sup)). 4.02/4.27 fof(fact_divide__less__eq, axiom, ![X26, X24, X25, X4]:(class_Fields_Olinordered__field__inverse__zero(X4)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X24))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24))))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X24)))=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),c_Groups_Ozero__class_Ozero(X4))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X26)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24)),X25))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),c_Groups_Ozero__class_Ozero(X4)))))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X25),X24)),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__less__eq)). 4.02/4.27 fof(fact_inj__on__strict__subset, axiom, ![X3, X6, X22, X7, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X7,X22),X3)),hAPP(c_Set_Oimage(X4,X7,X22),X6)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=c_Fun_Oinj__on(X4,X7,X22,X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__strict__subset)). 4.02/4.27 fof(fact_divide__le__eq, axiom, ![X26, X24, X25, X4]:(class_Fields_Olinordered__field__inverse__zero(X4)=>(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24)),X25))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),c_Groups_Ozero__class_Ozero(X4))))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),c_Groups_Ozero__class_Ozero(X4))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X26))))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X24))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X24))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24)))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X25),X24)),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__le__eq)). 4.02/4.27 fof(fact_less__divide__eq, axiom, ![X24, X25, X26, X4]:((((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),c_Groups_Ozero__class_Ozero(X4))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),c_Groups_Ozero__class_Ozero(X4)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),c_Groups_Ozero__class_Ozero(X4))))))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X24))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24)),X25))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X24))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X25),X24))))<=class_Fields_Olinordered__field__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__divide__eq)). 4.02/4.27 fof(fact_le__divide__eq, axiom, ![X24, X25, X26, X4]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X24))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24)),X25)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),c_Groups_Ozero__class_Ozero(X4))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),c_Groups_Ozero__class_Ozero(X4)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),c_Groups_Ozero__class_Ozero(X4))))))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X24)))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X25),X24))))<=class_Fields_Olinordered__field__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__divide__eq)). 4.02/4.27 fof(fact_abs__triangle__ineq2, axiom, ![X12, X11, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),hAPP(c_Groups_Oabs__class_Oabs(X4),X12))),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X12))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__triangle__ineq2)). 4.02/4.27 fof(fact_abs__triangle__ineq2__sym, axiom, ![X12, X11, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),hAPP(c_Groups_Oabs__class_Oabs(X4),X12))),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__triangle__ineq2__sym)). 4.02/4.27 fof(fact_abs__triangle__ineq4, axiom, ![X12, X11, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X12))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),hAPP(c_Groups_Oabs__class_Oabs(X4),X12))))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__triangle__ineq4)). 4.02/4.27 fof(fact_Image__iff, axiom, ![X3, X18, X7, X25, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X25),hAPP(c_Relation_OImage(X7,X4,X18),X3)))<=>?[X19]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X4),X19),X25)),X18))&hBOOL(hAPP(hAPP(c_member(X7),X19),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__iff)). 4.02/4.27 fof(fact_abs__triangle__ineq, axiom, ![X12, X11, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),hAPP(c_Groups_Oabs__class_Oabs(X4),X12))))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__triangle__ineq)). 4.02/4.27 fof(fact_mlex__less, axiom, ![X39, X4, X17, X9, X22]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),c_Wellfounded_Omlex__prod(X4,X22,X39)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X22,X9)),hAPP(X22,X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mlex__less)). 4.02/4.27 fof(fact_ImageE, axiom, ![X3, X18, X7, X25, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X25),hAPP(c_Relation_OImage(X7,X4,X18),X3)))=>~(![X19]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X4),X19),X25)),X18))=>~(hBOOL(hAPP(hAPP(c_member(X7),X19),X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ImageE)). 4.02/4.27 fof(fact_fold__graph_H_Ointros_I2_J, axiom, ![X17, X16, X22, X7, X3, X9, X4]:((c_Nitpick_Ofold__graph_H(X4,X7,X22,X16,X3,hAPP(hAPP(X22,X9),X17))<=c_Nitpick_Ofold__graph_H(X4,X7,X22,X16,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X17))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph_H_Ointros_I2_J)). 4.02/4.27 fof(fact_folding_Ocommute__comp, axiom, ![X9, X17, X87, X22, X7, X4]:(hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X22,X9)),hAPP(X22,X17))=hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X22,X17)),hAPP(X22,X9))<=c_Finite__Set_Ofolding(X4,X7,X22,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Ocommute__comp)). 4.02/4.27 fof(fact_list__all2__all__nthI, axiom, ![X56, X25, X7, X26, X4]:((![X104]:(hBOOL(hAPP(hAPP(X56,hAPP(hAPP(c_List_Onth(X4),X26),X104)),hAPP(hAPP(c_List_Onth(X7),X25),X104)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X104),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X26))))=>c_List_Olist__all2(X4,X7,X56,X26,X25))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X26)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__all__nthI)). 4.02/4.27 fof(fact_list__all2__conv__all__nth, axiom, ![X31, X32, X56, X7, X4]:(c_List_Olist__all2(X4,X7,X56,X32,X31)<=>(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))=>hBOOL(hAPP(hAPP(X56,hAPP(hAPP(c_List_Onth(X4),X32),X42)),hAPP(hAPP(c_List_Onth(X7),X31),X42))))&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__conv__all__nth)). 4.02/4.27 fof(fact_insert__Diff__if, axiom, ![X3, X6, X9, X4]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3)),X6)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)<=hBOOL(hAPP(hAPP(c_member(X4),X9),X6)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3)),X6)=hAPP(hAPP(c_Set_Oinsert(X4),X9),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6))<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__Diff__if)). 4.02/4.27 fof(fact_nth__drop_H, axiom, ![X45, X4, X46]:(hAPP(hAPP(c_List_Olist_OCons(X4),hAPP(hAPP(c_List_Onth(X4),X45),X46)),hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_OSuc,X46)),X45))=hAPP(hAPP(c_List_Odrop(X4),X46),X45)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__drop_H)). 4.02/4.27 fof(fact_the__inv__into__into, axiom, ![X6, X9, X3, X22, X7, X4]:(((hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Fun_Othe__inv__into(X4,X7,X3,X22),X9)),X6))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=hBOOL(hAPP(hAPP(c_member(X7),X9),hAPP(c_Set_Oimage(X4,X7,X22),X3))))<=c_Fun_Oinj__on(X4,X7,X22,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__into__into)). 4.02/4.27 fof(fact_wf__union__compatible, axiom, ![X86, X39, X4]:(c_Wellfounded_Owf(X4,X39)=>(c_Wellfounded_Owf(X4,X86)=>(c_Wellfounded_Owf(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X39),X86))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X39),X86)),X39))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__union__compatible)). 4.02/4.27 fof(fact_inj__fun, axiom, ![X49, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>c_Fun_Oinj__on(X4,tc_fun(X49,X7),hAPP(hAPP(c_COMBB(X7,tc_fun(X49,X7),X4),c_COMBK(X7,X49)),X22),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__fun)). 4.02/4.27 fof(fact_INF2__iff, axiom, ![X24, X25, X6, X3, X49, X7, X4]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_fun(X49,tc_HOL_Obool))),X3),X6),X25),X24))<=>![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(hAPP(hAPP(X6,X19),X25),X24)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF2__iff)). 4.02/4.27 fof(fact_map__fun__upd, axiom, ![X64, X22, X7, X32, X17, X4]:(hAPP(hAPP(c_List_Omap(X4,X7),X22),X32)=hAPP(hAPP(c_List_Omap(X4,X7),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X7),X22),X17),X64)),X32)<=~(hBOOL(hAPP(hAPP(c_member(X4),X17),hAPP(c_List_Oset(X4),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__fun__upd)). 4.02/4.27 fof(fact_fold1__eq__fold, axiom, ![X26, X3, X4]:(class_Groups_Oab__semigroup__mult(X4)=>((~(hBOOL(hAPP(hAPP(c_member(X4),X26),X3)))=>hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Groups_Otimes__class_Otimes(X4)),X26),X3)=hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),hAPP(hAPP(c_Set_Oinsert(X4),X26),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__eq__fold)). 4.02/4.27 fof(fact_zip__rev, axiom, ![X59, X7, X45, X4]:(hAPP(c_List_Orev(tc_prod(X4,X7)),hAPP(hAPP(c_List_Ozip(X4,X7),X45),X59))=hAPP(hAPP(c_List_Ozip(X4,X7),hAPP(c_List_Orev(X4),X45)),hAPP(c_List_Orev(X7),X59))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__rev)). 4.02/4.27 fof(fact_take__Cons_H, axiom, ![X45, X13, X4, X5]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X5=>c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Otake(X4),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)))&(hAPP(hAPP(c_List_Olist_OCons(X4),X13),hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X45))=hAPP(hAPP(c_List_Otake(X4),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Cons_H)). 4.02/4.27 fof(fact_rev__ImageI, axiom, ![X18, X25, X7, X3, X26, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X26),X3))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X26),X25)),X18))=>hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(c_Relation_OImage(X4,X7,X18),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__ImageI)). 4.02/4.27 fof(fact_double__diff, axiom, ![X8, X6, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X8))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X8),X3))=X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__diff)). 4.02/4.27 fof(fact_fun__left__comm_Ofun__comp__comm, axiom, ![X17, X9, X22, X7, X4]:(c_Finite__Set_Ofun__left__comm(X4,X7,X22)=>hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X22,X9)),hAPP(X22,X17))=hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X22,X17)),hAPP(X22,X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofun__comp__comm)). 4.02/4.27 fof(fact_refl__on__Int, axiom, ![X40, X6, X18, X3, X4]:((c_Relation_Orefl__on(X4,X6,X40)=>c_Relation_Orefl__on(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),X40)))<=c_Relation_Orefl__on(X4,X3,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__Int)). 4.02/4.27 fof(fact_refl__on__Un, axiom, ![X40, X6, X18, X3, X4]:(c_Relation_Orefl__on(X4,X3,X18)=>(c_Relation_Orefl__on(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),X40))<=c_Relation_Orefl__on(X4,X6,X40))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__Un)). 4.02/4.27 fof(fact_Int__insert__left, axiom, ![X6, X8, X26, X4]:((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X26),X6)),X8)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X6),X8)<=~(hBOOL(hAPP(hAPP(c_member(X4),X26),X8))))&(hAPP(hAPP(c_Set_Oinsert(X4),X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X6),X8))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X26),X6)),X8)<=hBOOL(hAPP(hAPP(c_member(X4),X26),X8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__insert__left)). 4.02/4.27 fof(fact_map__of__zip__enum__is__Some, axiom, ![X13, X59, X7, X4]:((?[X34]:hAPP(hAPP(c_Map_Omap__of(X4,X7),hAPP(hAPP(c_List_Ozip(X4,X7),c_Enum_Oenum__class_Oenum(X4)),X59)),X13)=hAPP(c_Option_Ooption_OSome(X7),X34)<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X59)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_Enum_Oenum__class_Oenum(X4)))<=class_Enum_Oenum(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__zip__enum__is__Some)). 4.02/4.27 fof(fact_SigmaE, axiom, ![X6, X3, X24, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),X24),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),X6)))=>~(![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>![X34]:(hAPP(hAPP(c_Product__Type_OPair(X4,X7),X19),X34)!=X24<=hBOOL(hAPP(hAPP(c_member(X7),X34),hAPP(X6,X19))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SigmaE)). 4.02/4.27 fof(fact_single__valued__def, axiom, ![X18, X7, X4]:(![X19, X34]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X19),X34)),X18))=>![X36]:(X34=X36<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X19),X36)),X18))))<=>c_Relation_Osingle__valued(X4,X7,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__def)). 4.02/4.27 fof(fact_ivl__disj__un_I15_J, axiom, ![X115, X21, X60, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X60),X21))=>(c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X60,X115)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X60,X21)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X21),X115))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X21),X115))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I15_J)). 4.02/4.27 fof(fact_ivl__disj__un_I21_J, axiom, ![X115, X21, X60, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X60),X21))=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X60),X21)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X21,X115))=c_SetInterval_Oord__class_OatLeastAtMost(X4,X60,X115)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X21),X115))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I21_J)). 4.02/4.27 fof(fact_folding__idem_Oidem__left__comp, axiom, ![X76, X9, X49, X87, X22, X7, X4]:(c_Finite__Set_Ofolding__idem(X4,X7,X22,X87)=>hAPP(c_Fun_Ocomp(X7,X7,X49,hAPP(X22,X9)),hAPP(c_Fun_Ocomp(X7,X7,X49,hAPP(X22,X9)),X76))=hAPP(c_Fun_Ocomp(X7,X7,X49,hAPP(X22,X9)),X76)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Oidem__left__comp)). 4.02/4.27 fof(fact_min__number__of, axiom, ![X1, X106, X7]:(((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X106)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1))))=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X106)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1))=hAPP(c_Int_Onumber__class_Onumber__of(X7),X1))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X106)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1)))=>hAPP(c_Int_Onumber__class_Onumber__of(X7),X106)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X106)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1))))<=(class_Orderings_Oord(X7)&class_Int_Onumber(X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__number__of)). 4.02/4.27 fof(fact_max__number__of, axiom, ![X1, X106, X7]:(((hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X106)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1))=hAPP(c_Int_Onumber__class_Onumber__of(X7),X106)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X106)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X106)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1)))=>hAPP(c_Int_Onumber__class_Onumber__of(X7),X1)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X7),hAPP(c_Int_Onumber__class_Onumber__of(X7),X106)),hAPP(c_Int_Onumber__class_Onumber__of(X7),X1))))<=(class_Orderings_Oord(X7)&class_Int_Onumber(X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__number__of)). 4.02/4.27 fof(fact_zdiv__mono2, axiom, ![X12, X110, X11]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X110))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X110)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X110),X12))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono2)). 4.02/4.27 fof(fact_insort__is__Cons, axiom, ![X26, X22, X32, X4, X7]:(class_Orderings_Olinorder(X7)=>(hAPP(hAPP(c_List_Olist_OCons(X4),X26),X32)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X7,X22),X26),X32)<=![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(X22,X26)),hAPP(X22,X19)))<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__is__Cons)). 4.02/4.27 fof(fact_wf__eq__minimal, axiom, ![X18, X4]:(![X100]:(?[X19]:(![X34]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X34),X19)),X18))=>~(hBOOL(hAPP(hAPP(c_member(X4),X34),X100))))&hBOOL(hAPP(hAPP(c_member(X4),X19),X100)))<=?[X19]:hBOOL(hAPP(hAPP(c_member(X4),X19),X100)))<=>c_Wellfounded_Owf(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__eq__minimal)). 4.02/4.27 fof(fact_setsum__constant, axiom, ![X3, X17, X7, X4]:(class_Rings_Osemiring__1(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Finite__Set_Ocard(X7),X3))),X17)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),hAPP(c_COMBK(X4,X7),X17)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__constant)). 4.02/4.27 fof(fact_zdiv__mono2__neg, axiom, ![X12, X110, X11]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X110),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X110)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X110)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono2__neg)). 4.02/4.27 fof(fact_finite__cartesian__product, axiom, ![X6, X7, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),X6))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__cartesian__product)). 4.02/4.27 fof(fact_SUP2__I, axiom, ![X49, X7, X24, X25, X6, X3, X26, X4]:((hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_fun(X49,tc_HOL_Obool))),X3),X6),X25),X24))<=hBOOL(hAPP(hAPP(hAPP(X6,X26),X25),X24)))<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP2__I)). 4.02/4.27 fof(fact_folding__idem_Oinsert__idem, axiom, ![X9, X3, X87, X22, X7, X4]:((hAPP(X87,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X87,X3)),hAPP(X22,X9))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=c_Finite__Set_Ofolding__idem(X4,X7,X22,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Oinsert__idem)). 4.02/4.27 fof(fact_setsum__eq__1__iff, axiom, ![X22, X3, X4]:((hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X22),X3)=c_Groups_Oone__class_Oone(tc_Nat_Onat)<=>?[X19]:((hBOOL(hAPP(hAPP(c_member(X4),X19),X3))&![X114]:(hBOOL(hAPP(hAPP(c_member(X4),X114),X3))=>(X114!=X19=>hAPP(X22,X114)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(X22,X19)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__eq__1__iff)). 4.02/4.27 fof(fact_div__add__self1, axiom, ![X11, X12, X4]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X11),X12)),c_Groups_Oone__class_Oone(X4))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11)),X12)<=c_Groups_Ozero__class_Ozero(X4)!=X12)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__add__self1)). 4.02/4.27 fof(fact_list__ball__nth, axiom, ![X56, X32, X4, X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))=>(hBOOL(hAPP(X56,hAPP(hAPP(c_List_Onth(X4),X32),X20)))<=![X19]:(hBOOL(hAPP(X56,X19))<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ball__nth)). 4.02/4.27 fof(fact_minus__number__of__mult, axiom, ![X29, X53, X4]:(class_Int_Onumber__ring(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X53))),X29)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X53))),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__number__of__mult)). 4.02/4.27 fof(fact_setsum__nonneg__0, axiom, ![X37, X22, X40, X4, X7]:(((![X42]:(hBOOL(hAPP(hAPP(c_member(X4),X42),X40))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(X22,X42))))=>((hBOOL(hAPP(hAPP(c_member(X4),X37),X40))=>c_Groups_Ozero__class_Ozero(X7)=hAPP(X22,X37))<=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X40)=c_Groups_Ozero__class_Ozero(X7)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X40)))<=class_Groups_Oordered__ab__group__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__nonneg__0)). 4.02/4.27 fof(fact_ran__map__upd, axiom, ![X25, X7, X4, X26, X21]:(hAPP(hAPP(c_Set_Oinsert(X4),X25),c_Map_Oran(X7,X4,X21))=c_Map_Oran(X7,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X4)),X21),X26),hAPP(c_Option_Ooption_OSome(X4),X25)))<=c_Option_Ooption_ONone(X4)=hAPP(X21,X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ran__map__upd)). 4.02/4.27 fof(fact_div__add__self2, axiom, ![X11, X12, X4]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X11),X12)),c_Groups_Oone__class_Oone(X4))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),X12)<=X12!=c_Groups_Ozero__class_Ozero(X4))<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__add__self2)). 4.02/4.27 fof(fact_INF__less__iff, axiom, ![X26, X22, X3, X7, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,X4),X3),X22)),X26))<=>?[X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(X22,X19)),X26))&hBOOL(hAPP(hAPP(c_member(X7),X19),X3))))<=(class_Complete__Lattice_Ocomplete__lattice(X4)&class_Orderings_Olinorder(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__less__iff)). 4.02/4.27 fof(fact_less__SUP__iff, axiom, ![X22, X3, X7, X26, X4]:((class_Orderings_Olinorder(X4)&class_Complete__Lattice_Ocomplete__lattice(X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X4),X3),X22)))<=>?[X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),hAPP(X22,X19)))&hBOOL(hAPP(hAPP(c_member(X7),X19),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__SUP__iff)). 4.02/4.27 fof(fact_Compl__anti__mono, axiom, ![X6, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X6)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X3)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__anti__mono)). 4.02/4.27 fof(fact_map__eq__conv, axiom, ![X76, X32, X22, X4, X7]:(hAPP(hAPP(c_List_Omap(X7,X4),X22),X32)=hAPP(hAPP(c_List_Omap(X7,X4),X76),X32)<=>![X19]:(hAPP(X76,X19)=hAPP(X22,X19)<=hBOOL(hAPP(hAPP(c_member(X7),X19),hAPP(c_List_Oset(X7),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__eq__conv)). 4.02/4.27 fof(fact_power__less__power__Suc, axiom, ![X5, X11, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__less__power__Suc)). 4.02/4.27 fof(fact_Un__least, axiom, ![X6, X8, X3, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X8))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)),X8)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__least)). 4.02/4.27 fof(fact_Int__greatest, axiom, ![X6, X3, X8, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X8),X6))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X8),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__greatest)). 4.02/4.27 fof(fact_setprod__pos__nat__iff, axiom, ![X22, X86, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,tc_Nat_Onat),X22),X86)))<=>![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X86))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X22,X19)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X86))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__pos__nat__iff)). 4.02/4.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, axiom, ![X2, X11, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),c_Groups_Oone__class_Oone(X4))),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X2)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J)). 4.02/4.27 fof(fact_all__n__lists__def, axiom, ![X20, X56, X4]:(class_Enum_Oenum(X4)=>(c_Enum_Oall__n__lists(X4,X56,X20)<=>![X19]:(hBOOL(hAPP(X56,X19))<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X19),hAPP(c_List_Oset(tc_List_Olist(X4)),c_Enum_On__lists(X4,X20,c_Enum_Oenum__class_Oenum(X4)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__n__lists__def)). 4.02/4.27 fof(fact_weak__map__of__SomeI, axiom, ![X60, X9, X28, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X28),X9)),hAPP(c_List_Oset(tc_prod(X4,X7)),X60)))=>?[X19]:hAPP(c_Option_Ooption_OSome(X7),X19)=hAPP(hAPP(c_Map_Omap__of(X4,X7),X60),X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_weak__map__of__SomeI)). 4.02/4.27 fof(fact_UN__iff, axiom, ![X6, X3, X7, X25, X4]:(?[X19]:(hBOOL(hAPP(hAPP(c_member(X7),X19),X3))&hBOOL(hAPP(hAPP(c_member(X4),X25),hAPP(X6,X19))))<=>hBOOL(hAPP(hAPP(c_member(X4),X25),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__iff)). 4.02/4.27 fof(fact_nth__drop, axiom, ![X45, X4, X46, X5]:(hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Odrop(X4),X5),X45)),X46)=hAPP(hAPP(c_List_Onth(X4),X45),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X46))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X46)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__drop)). 4.02/4.27 fof(fact_RangeE, axiom, ![X18, X7, X25, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X25),hAPP(c_Relation_ORange(X7,X4),X18)))=>~(![X19]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X4),X19),X25)),X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_RangeE)). 4.02/4.27 fof(fact_Range__iff, axiom, ![X18, X7, X26, X4]:(?[X34]:hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X4),X34),X26)),X18))<=>hBOOL(hAPP(hAPP(c_member(X4),X26),hAPP(c_Relation_ORange(X7,X4),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__iff)). 4.02/4.27 fof(fact_DomainE, axiom, ![X18, X7, X26, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X26),hAPP(c_Relation_ODomain(X4,X7),X18)))=>~(![X34]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X26),X34)),X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DomainE)). 4.02/4.27 fof(fact_Domain__iff, axiom, ![X18, X7, X26, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X26),hAPP(c_Relation_ODomain(X4,X7),X18)))<=>?[X34]:hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X26),X34)),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__iff)). 4.02/4.27 fof(fact_takeWhile__append2, axiom, ![X31, X56, X32, X4]:(![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32)))=>hBOOL(hAPP(X56,X19)))=>c_List_OtakeWhile(X4,X56,hAPP(hAPP(c_List_Oappend(X4),X32),X31))=hAPP(hAPP(c_List_Oappend(X4),X32),c_List_OtakeWhile(X4,X56,X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__append2)). 4.02/4.27 fof(fact_append__in__lists__conv, axiom, ![X3, X31, X32, X4]:((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X32),c_List_Olists(X4,X3)))&hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X31),c_List_Olists(X4,X3))))<=>hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),hAPP(hAPP(c_List_Oappend(X4),X32),X31)),c_List_Olists(X4,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__in__lists__conv)). 4.02/4.27 fof(fact_fold1__insert, axiom, ![X9, X3, X4]:(class_Groups_Oab__semigroup__mult(X4)=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3=>((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X9),hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),X3))=hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__insert)). 4.02/4.27 fof(fact_acc_Osimps, axiom, ![X18, X26, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X26),c_Wellfounded_Oacc(X4,X18)))<=>![X19]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X26)),X18))=>hBOOL(hAPP(hAPP(c_member(X4),X19),c_Wellfounded_Oacc(X4,X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acc_Osimps)). 4.02/4.27 fof(fact_diff__divide__distrib, axiom, ![X10, X12, X11, X4]:(class_Rings_Odivision__ring(X4)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X10))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X12)),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__divide__distrib)). 4.02/4.27 fof(fact_sup__inf__distrib2, axiom, ![X13, X29, X43, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X43),X13)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X29),X13))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X43),X29)),X13)<=class_Lattices_Odistrib__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__inf__distrib2)). 4.02/4.27 fof(fact_inf__sup__distrib2, axiom, ![X13, X29, X43, X4]:(class_Lattices_Odistrib__lattice(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X43),X13)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X29),X13))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X43),X29)),X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__distrib2)). 4.02/4.27 fof(fact_add__divide__distrib, axiom, ![X10, X12, X11, X4]:(class_Rings_Odivision__ring(X4)=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__divide__distrib)). 4.02/4.27 fof(fact_not__acc__down, axiom, ![X39, X9, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X9),c_Wellfounded_Oacc(X4,X39))))=>~(![X36]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X36),X9)),X39))=>hBOOL(hAPP(hAPP(c_member(X4),X36),c_Wellfounded_Oacc(X4,X39)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__acc__down)). 4.02/4.27 fof(fact_ivl__disj__un_I18_J, axiom, ![X115, X21, X60, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X60),X21))=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X60,X21)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X21,X115))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X60),X115)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X21),X115))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I18_J)). 4.02/4.27 fof(fact_ivl__diff, axiom, ![X21, X20, X37, X4]:(class_Orderings_Olinorder(X4)=>(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X37),X21)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X37),X20))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X20),X21)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__diff)). 4.02/4.27 fof(fact_insert__fold1SetE, axiom, ![X9, X156, X26, X22, X4]:(hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,X22,hAPP(hAPP(c_Set_Oinsert(X4),X26),X156)),X9))=>~(![X27, X195]:((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X4,X22,X27,X195),X9))=>hBOOL(hAPP(hAPP(c_member(X4),X27),X195)))<=hAPP(hAPP(c_Set_Oinsert(X4),X27),X195)=hAPP(hAPP(c_Set_Oinsert(X4),X26),X156)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__fold1SetE)). 4.02/4.27 fof(fact_acc_OaccI, axiom, ![X18, X9, X4]:(![X34]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X34),X9)),X18))=>hBOOL(hAPP(hAPP(c_member(X4),X34),c_Wellfounded_Oacc(X4,X18))))=>hBOOL(hAPP(hAPP(c_member(X4),X9),c_Wellfounded_Oacc(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acc_OaccI)). 4.02/4.27 fof(fact_comm__semiring__class_Odistrib, axiom, ![X10, X12, X11, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10))<=class_Rings_Ocomm__semiring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__class_Odistrib)). 4.02/4.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, axiom, ![X10, X12, X11, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J)). 4.02/4.27 fof(fact_min__add__distrib__left, axiom, ![X29, X43, X13, X4]:(class_Groups_Oordered__ab__semigroup__add__imp__le(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),X43)),X29)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X13),X29)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X43),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__add__distrib__left)). 4.02/4.27 fof(fact_map__upds__list__update2__drop, axiom, ![X17, X21, X31, X7, X37, X32, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31)))=>c_Map_Omap__upds(X4,X7,X21,X32,hAPP(hAPP(c_List_Olist__update(X7,X31),X37),X17))=c_Map_Omap__upds(X4,X7,X21,X32,X31))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__list__update2__drop)). 4.02/4.27 fof(fact_image__mono, axiom, ![X22, X7, X6, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X7,X22),X3)),hAPP(c_Set_Oimage(X4,X7,X22),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__mono)). 4.02/4.27 fof(fact_max__add__distrib__left, axiom, ![X29, X43, X13, X4]:(class_Groups_Oordered__ab__semigroup__add__imp__le(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),X43)),X29)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X13),X29)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X43),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__add__distrib__left)). 4.02/4.27 fof(fact_sup__inf__distrib1, axiom, ![X29, X43, X13, X4]:(class_Lattices_Odistrib__lattice(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X29))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X43),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__inf__distrib1)). 4.02/4.27 fof(fact_inf__sup__distrib1, axiom, ![X29, X43, X13, X4]:(class_Lattices_Odistrib__lattice(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X43),X29))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__distrib1)). 4.02/4.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, axiom, ![X29, X43, X13, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X43),X29))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X13),X43)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X13),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J)). 4.02/4.27 fof(fact_acc__downwards, axiom, ![X25, X18, X26, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X25),c_Wellfounded_Oacc(X4,X18)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X25),X26)),c_Transitive__Closure_Ortrancl(X4,X18))))<=hBOOL(hAPP(hAPP(c_member(X4),X26),c_Wellfounded_Oacc(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acc__downwards)). 4.02/4.27 fof(fact_Union__mono, axiom, ![X6, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X3),X6))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X3)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__mono)). 4.02/4.27 fof(fact_Inter__anti__mono, axiom, ![X3, X6, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X3)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X6)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X6),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__anti__mono)). 4.02/4.27 fof(fact_power__add, axiom, ![X5, X2, X11, X4]:(class_Groups_Omonoid__mult(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__add)). 4.02/4.27 fof(fact_of__int__setprod, axiom, ![X3, X22, X7, X4]:((class_Rings_Oring__1(X4)&class_Groups_Ocomm__monoid__mult(X4))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X4),hAPP(hAPP(c_COMBB(tc_Int_Oint,X4,X7),c_Int_Oring__1__class_Oof__int(X4)),X22)),X3)=hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,tc_Int_Oint),X22),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__setprod)). 4.02/4.27 fof(fact_of__nat__setprod, axiom, ![X3, X22, X7, X4]:((class_Rings_Osemiring__1(X4)&class_Groups_Ocomm__monoid__mult(X4))=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,X7),c_Nat_Osemiring__1__class_Oof__nat(X4)),X22)),X3)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,tc_Nat_Onat),X22),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__setprod)). 4.02/4.27 fof(fact_finite__quotient, axiom, ![X18, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X3),X18)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__quotient)). 4.02/4.27 fof(fact_sorted__append, axiom, ![X31, X32, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Oappend(X4),X32),X31))<=>((c_List_Olinorder__class_Osorted(X4,X32)&c_List_Olinorder__class_Osorted(X4,X31))&![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32)))=>![X114]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X19),X114))<=hBOOL(hAPP(hAPP(c_member(X4),X114),hAPP(c_List_Oset(X4),X31)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__append)). 4.02/4.27 fof(fact_Int__atLeastAtMost, axiom, ![X102, X24, X25, X26, X4]:(c_SetInterval_Oord__class_OatLeastAtMost(X4,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X26),X24),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X25),X102))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X26,X25)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X24,X102))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastAtMost)). 4.02/4.27 fof(fact_Int__greaterThanAtMost, axiom, ![X102, X24, X25, X26, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X26,X25)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X24,X102))=c_SetInterval_Oord__class_OgreaterThanAtMost(X4,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X26),X24),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X25),X102))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__greaterThanAtMost)). 4.02/4.27 fof(fact_Int__greaterThanLessThan, axiom, ![X102, X24, X25, X26, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X26,X25)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X24,X102))=c_SetInterval_Oord__class_OgreaterThanLessThan(X4,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X26),X24),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X25),X102))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__greaterThanLessThan)). 4.02/4.27 fof(fact_folding__one_Oinsert, axiom, ![X9, X3, X87, X22, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3=>hAPP(hAPP(X22,X9),hAPP(X87,X3))=hAPP(X87,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3)))<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))))<=c_Finite__Set_Ofolding__one(X4,X22,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oinsert)). 4.02/4.27 fof(fact_abs__add__abs, axiom, ![X12, X11, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),hAPP(c_Groups_Oabs__class_Oabs(X4),X12))=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__add__abs)). 4.02/4.27 fof(fact_log_Osimps, axiom, ![X46, X12]:((~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X46),X12))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X12),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))=>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(X12,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X46),X12)))=c_Random_Olog(X12,X46))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X46),X12))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X12),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))=>c_Random_Olog(X12,X46)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_log_Osimps)). 4.02/4.27 fof(fact_listsum__abs, axiom, ![X32, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(c_List_Omonoid__add__class_Olistsum(X4),X32))),hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X4,X4),c_Groups_Oabs__class_Oabs(X4)),X32))))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__abs)). 4.02/4.27 fof(fact_diff__add__assoc2, axiom, ![X46, X135, X107]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X135),X46)),X107)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X135),X107)),X46)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__add__assoc2)). 4.02/4.27 fof(fact_folding__image__simple__idem_Oinsert__idem, axiom, ![X9, X3, X87, X76, X16, X22, X7, X4]:((hAPP(X87,hAPP(hAPP(c_Set_Oinsert(X7),X9),X3))=hAPP(hAPP(X22,hAPP(X76,X9)),hAPP(X87,X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3)))<=c_Finite__Set_Ofolding__image__simple__idem(X4,X7,X22,X16,X76,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple__idem_Oinsert__idem)). 4.02/4.27 fof(fact_fold1__set, axiom, ![X32, X4]:((hAPP(c_List_Ofoldl(X4,X4,c_Groups_Otimes__class_Otimes(X4),hAPP(c_List_Ohd(X4),X32)),hAPP(c_List_Otl(X4),X32))=hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),hAPP(c_List_Oset(X4),X32))<=X32!=c_List_Olist_ONil(X4))<=class_Lattices_Oab__semigroup__idem__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__set)). 4.02/4.27 fof(fact_Diff__subset__conv, axiom, ![X8, X6, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X6),X8)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)),X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__subset__conv)). 4.02/4.27 fof(fact_listsum__triv, axiom, ![X32, X18, X7, X4]:(class_Rings_Osemiring__1(X4)=>hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X7,X4),hAPP(c_COMBK(X4,X7),X18)),X32))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X32))),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__triv)). 4.02/4.27 fof(fact_div__geq, axiom, ![X2, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5))=>(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X5)=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),X5)),X5))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__geq)). 4.02/4.27 fof(fact_setsum__abs__ge__zero, axiom, ![X3, X22, X7, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),hAPP(hAPP(c_COMBB(X4,X4,X7),c_Groups_Oabs__class_Oabs(X4)),X22)),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__abs__ge__zero)). 4.02/4.27 fof(fact_divmod__int__def, axiom, ![X12, X11]:((((((c_Divides_Odivmod__int(X11,X12)=hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12)))<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X11)&(X11=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(X11,X12)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))))&(c_Divides_Odivmod__int(X11,X12)=c_Divides_OposDivAlg(X11,X12)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11)))=>((c_Divides_Odivmod__int(X11,X12)=hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12)))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))=>c_Divides_Odivmod__int(X11,X12)=c_Divides_OnegDivAlg(X11,X12))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__def)). 4.02/4.27 fof(fact_subset__card__intvl__is__intvl, axiom, ![X28, X3]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X28),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X3)))))=>X3=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X28),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__card__intvl__is__intvl)). 4.02/4.27 fof(fact_folding__idem_Osubset__comp__idem, axiom, ![X6, X3, X87, X22, X7, X4]:(c_Finite__Set_Ofolding__idem(X4,X7,X22,X87)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X87,X3)),hAPP(X87,X6))=hAPP(X87,X3)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Osubset__comp__idem)). 4.02/4.27 fof(fact_of__nat__setsum, axiom, ![X3, X22, X7, X4]:(class_Rings_Osemiring__1(X4)=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X22),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4,X7),c_Nat_Osemiring__1__class_Oof__nat(X4)),X22)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__setsum)). 4.02/4.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, axiom, ![X11, X2, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),c_Groups_Oone__class_Oone(X4))),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J)). 4.02/4.27 fof(fact_INF__subset, axiom, ![X22, X6, X3, X4, X7]:(class_Complete__Lattice_Ocomplete__lattice(X7)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7),X6),X22)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7),X3),X22))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__subset)). 4.02/4.27 fof(fact_SUP__subset, axiom, ![X22, X6, X3, X4, X7]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X7),X3),X22)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X7),X6),X22)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=class_Complete__Lattice_Ocomplete__lattice(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__subset)). 4.02/4.27 fof(fact_listrel1__mono, axiom, ![X40, X18, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool)),c_List_Olistrel1(X4,X18)),c_List_Olistrel1(X4,X40)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),X40))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__mono)). 4.02/4.27 fof(fact_listrel__mono, axiom, ![X40, X18, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),X40))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool)),c_List_Olistrel(X4,X18)),c_List_Olistrel(X4,X40)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__mono)). 4.02/4.27 fof(fact_divide__strict__right__mono, axiom, ![X10, X12, X11, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X10))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12)))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__strict__right__mono)). 4.02/4.27 fof(fact_mult__strict__right__mono, axiom, ![X10, X12, X11, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12)))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__strict__right__mono)). 4.02/4.27 fof(fact_mult__less__cancel__right__disj, axiom, ![X25, X24, X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X25),X24)))<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X25),X26)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X24))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X25)))))<=class_Rings_Olinordered__ring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel__right__disj)). 4.02/4.27 fof(fact_inj__on__fun__updI, axiom, ![X9, X17, X3, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,X3)=>(~(hBOOL(hAPP(hAPP(c_member(X7),X17),hAPP(c_Set_Oimage(X4,X7,X22),X3))))=>c_Fun_Oinj__on(X4,X7,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X7),X22),X9),X17),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__fun__updI)). 4.02/4.27 fof(fact_length__transpose__sorted, axiom, ![X32, X4]:(c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),X32)))=>((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X4)),X32),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),c_List_Otranspose(X4,X32))<=X32!=c_List_Olist_ONil(tc_List_Olist(X4)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),c_List_Otranspose(X4,X32))<=c_List_Olist_ONil(tc_List_Olist(X4))=X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__transpose__sorted)). 4.02/4.27 fof(fact_ivl__disj__un_I20_J, axiom, ![X115, X21, X60, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X60),X21))=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X60,X21)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X21,X115))=c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X60,X115)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X21),X115))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I20_J)). 4.02/4.27 fof(fact_ivl__disj__un_I19_J, axiom, ![X115, X21, X60, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X60),X21))=>(c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X60,X115)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X60,X21)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X21,X115))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X21),X115))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I19_J)). 4.02/4.27 fof(fact_comm__mult__strict__left__mono, axiom, ![X10, X12, X11, X4]:(class_Rings_Olinordered__comm__semiring__strict(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__mult__strict__left__mono)). 4.02/4.27 fof(fact_mult__less__cancel__left__pos, axiom, ![X25, X26, X24, X4]:(class_Rings_Olinordered__ring__strict(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X24),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X24),X25)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X25)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X24)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel__left__pos)). 4.02/4.27 fof(fact_mult__strict__left__mono, axiom, ![X10, X12, X11, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12)))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__strict__left__mono)). 4.02/4.27 fof(fact_mult__right__mono, axiom, ![X10, X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))))<=class_Rings_Oordered__semiring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__right__mono)). 4.02/4.27 fof(fact_ivl__disj__un_I16_J, axiom, ![X115, X21, X60, X4]:(((c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X60,X115)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X60,X21)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X21,X115))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X21),X115)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X60),X21)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I16_J)). 4.02/4.27 fof(fact_ivl__disj__un_I22_J, axiom, ![X115, X21, X60, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X60),X21))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X21),X115))=>c_SetInterval_Oord__class_OatLeastAtMost(X4,X60,X115)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X60,X21)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X21,X115))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I22_J)). 4.02/4.27 fof(fact_min__max_OInf__fin_Oinsert__idem, axiom, ![X9, X3, X4]:(class_Orderings_Olinorder(X4)=>((c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X9),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X3))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oinsert__idem)). 4.02/4.27 fof(fact_min__max_OSup__fin_Oinsert__idem, axiom, ![X9, X3, X4]:(((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3=>c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X9),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oinsert__idem)). 4.02/4.27 fof(fact_distinct__set__sublists, axiom, ![X32, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X32))=>hBOOL(hAPP(c_List_Odistinct(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool)),c_List_Oset(X4)),c_Enum_Osublists(X4,X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__set__sublists)). 4.02/4.27 fof(fact_mult__le__cancel__left__pos, axiom, ![X25, X26, X24, X4]:(class_Rings_Olinordered__ring__strict(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X24),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X24),X25)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),X25)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X24)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__cancel__left__pos)). 4.02/4.27 fof(fact_comm__mult__left__mono, axiom, ![X10, X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))))<=class_Rings_Oordered__comm__semiring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__mult__left__mono)). 4.02/4.27 fof(fact_mult__left__mono, axiom, ![X10, X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))))<=class_Rings_Oordered__semiring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__mono)). 4.02/4.27 fof(fact_divide__strict__right__mono__neg, axiom, ![X10, X11, X12, X4]:(class_Fields_Olinordered__field(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X10),c_Groups_Ozero__class_Ozero(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__strict__right__mono__neg)). 4.02/4.27 fof(fact_card_Oeq__fold__g, axiom, ![X3, X4]:(hAPP(c_Finite__Set_Ocard(X4),X3)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X4),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card_Oeq__fold__g)). 4.02/4.27 fof(fact_div__mult__mult2, axiom, ![X12, X11, X10, X4]:(class_Divides_Osemiring__div(X4)=>(hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X11),X12)<=c_Groups_Ozero__class_Ozero(X4)!=X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__mult2)). 4.02/4.27 fof(fact_of__int__setsum, axiom, ![X3, X22, X7, X4]:(class_Rings_Oring__1(X4)=>hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Int_Oint),X22),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),hAPP(hAPP(c_COMBB(tc_Int_Oint,X4,X7),c_Int_Oring__1__class_Oof__int(X4)),X22)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__setsum)). 4.02/4.27 fof(fact_map__of__zip__inject, axiom, ![X30, X32, X7, X31, X4]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X31)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X32)=>(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X30)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X32)=>(hBOOL(hAPP(c_List_Odistinct(X7),X32))=>(X30=X31<=hAPP(c_Map_Omap__of(X7,X4),hAPP(hAPP(c_List_Ozip(X7,X4),X32),X31))=hAPP(c_Map_Omap__of(X7,X4),hAPP(hAPP(c_List_Ozip(X7,X4),X32),X30)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__zip__inject)). 4.02/4.27 fof(fact_folding__image_Oreindex, axiom, ![X76, X48, X3, X87, X16, X22, X7, X4]:(c_Finite__Set_Ofolding__image(X4,X7,X22,X16,X87)=>((hAPP(hAPP(X87,hAPP(c_Fun_Ocomp(X7,X4,X7,X76),X48)),X3)=hAPP(hAPP(X87,X76),hAPP(c_Set_Oimage(X7,X7,X48),X3))<=c_Fun_Oinj__on(X7,X7,X48,X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image_Oreindex)). 4.02/4.27 fof(fact_mult__strict__left__mono__neg, axiom, ![X10, X11, X12, X4]:(class_Rings_Olinordered__ring__strict(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X10),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__strict__left__mono__neg)). 4.02/4.27 fof(fact_mult__right__mono__neg, axiom, ![X10, X11, X12, X4]:(class_Rings_Oordered__ring(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__right__mono__neg)). 4.02/4.27 fof(fact_mult__le__cancel__left__neg, axiom, ![X25, X26, X24, X4]:(class_Rings_Olinordered__ring__strict(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),c_Groups_Ozero__class_Ozero(X4)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),X26))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X24),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X24),X25)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__cancel__left__neg)). 4.02/4.27 fof(fact_mult__left__mono__neg, axiom, ![X10, X11, X12, X4]:(class_Rings_Oordered__ring(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__mono__neg)). 4.02/4.27 fof(fact_fun__left__comm_Ofold__fun__comm, axiom, ![X16, X9, X3, X22, X7, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(hAPP(X22,X9),hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),X16),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),hAPP(hAPP(X22,X9),X16)),X3))<=c_Finite__Set_Ofun__left__comm(X4,X7,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__fun__comm)). 4.02/4.27 fof(fact_ex__n__lists__def, axiom, ![X20, X56, X4]:((?[X19]:(hBOOL(hAPP(X56,X19))&hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X19),hAPP(c_List_Oset(tc_List_Olist(X4)),c_Enum_On__lists(X4,X20,c_Enum_Oenum__class_Oenum(X4))))))<=>c_Enum_Oex__n__lists(X4,X56,X20))<=class_Enum_Oenum(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__n__lists__def)). 4.02/4.27 fof(fact_mult__divide__mult__cancel__left, axiom, ![X12, X11, X10, X4]:((c_Groups_Ozero__class_Ozero(X4)!=X10=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X12)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)))<=class_Fields_Ofield__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__divide__mult__cancel__left)). 4.02/4.27 fof(fact_min__max_Osup__inf__distrib2, axiom, ![X13, X29, X43, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X43),X13)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X29),X13))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X43),X29)),X13)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__inf__distrib2)). 4.02/4.27 fof(fact_min__max_Oinf__sup__distrib2, axiom, ![X13, X29, X43, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X43),X13)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X29),X13))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X43),X29)),X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__sup__distrib2)). 4.02/4.27 fof(fact_min__max_OInf__le__Sup, axiom, ![X3, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X3)),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X3)))<=X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__le__Sup)). 4.02/4.27 fof(fact_Max_Osubset__idem, axiom, ![X6, X3, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((c_Big__Operators_Olinorder__class_OMax(X4,X3)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),c_Big__Operators_Olinorder__class_OMax(X4,X6)),c_Big__Operators_Olinorder__class_OMax(X4,X3))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X3)))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Osubset__idem)). 4.02/4.27 fof(fact_Inf__fin_Osubset__idem, axiom, ![X6, X3, X4]:((((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),c_Big__Operators_Olattice__class_OInf__fin(X4,X6)),c_Big__Operators_Olattice__class_OInf__fin(X4,X3))=c_Big__Operators_Olattice__class_OInf__fin(X4,X3)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X3)))<=X6!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Osubset__idem)). 4.02/4.27 fof(fact_Min_Osubset__idem, axiom, ![X6, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(X6!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>(c_Big__Operators_Olinorder__class_OMin(X4,X3)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),c_Big__Operators_Olinorder__class_OMin(X4,X6)),c_Big__Operators_Olinorder__class_OMin(X4,X3))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X3)))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Osubset__idem)). 4.02/4.27 fof(fact_mult__divide__mult__cancel__right, axiom, ![X12, X11, X10, X4]:((c_Groups_Ozero__class_Ozero(X4)!=X10=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X12)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)))<=class_Fields_Ofield__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__divide__mult__cancel__right)). 4.02/4.27 fof(fact_max__diff__distrib__left, axiom, ![X29, X43, X13, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X13),X29)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X43),X29))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),X43)),X29)<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__diff__distrib__left)). 4.02/4.27 fof(fact_power__divide, axiom, ![X5, X12, X11, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X12)),X5)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X5))<=class_Fields_Ofield__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__divide)). 4.02/4.27 fof(fact_power__mult__distrib, axiom, ![X5, X12, X11, X4]:(class_Groups_Ocomm__monoid__mult(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__mult__distrib)). 4.02/4.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, axiom, ![X14, X43, X13, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X13),X43)),X14)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),X14)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X43),X14))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J)). 4.02/4.27 fof(fact_Sup__fin_Osubset__idem, axiom, ![X6, X3, X4]:((((c_Big__Operators_Olattice__class_OSup__fin(X4,X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),c_Big__Operators_Olattice__class_OSup__fin(X4,X6)),c_Big__Operators_Olattice__class_OSup__fin(X4,X3))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X3)))<=X6!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Osubset__idem)). 4.02/4.27 fof(fact_div__mult__mult1, axiom, ![X12, X11, X10, X4]:((X10!=c_Groups_Ozero__class_Ozero(X4)=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X11),X12))<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__mult1)). 4.02/4.27 fof(fact_min__diff__distrib__left, axiom, ![X29, X43, X13, X4]:(class_Groups_Oordered__ab__group__add(X4)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),X43)),X29)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X13),X29)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X43),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__diff__distrib__left)). 4.02/4.27 fof(fact_min__max_Oinf__sup__distrib1, axiom, ![X29, X43, X13, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X43),X29))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),X43)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),X29))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__sup__distrib1)). 4.02/4.27 fof(fact_min__max_Osup__inf__distrib1, axiom, ![X29, X43, X13, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X43),X29))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),X43)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),X29))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__inf__distrib1)). 4.02/4.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, axiom, ![X14, X15, X13, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15),X14))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),X15)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),X14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J)). 4.02/4.27 fof(fact_acc__downward, axiom, ![X26, X18, X25, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X25),c_Wellfounded_Oacc(X4,X18)))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X25)),X18))=>hBOOL(hAPP(hAPP(c_member(X4),X26),c_Wellfounded_Oacc(X4,X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acc__downward)). 4.02/4.27 fof(fact_setsum__negf, axiom, ![X3, X22, X7, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),hAPP(hAPP(c_COMBB(X4,X4,X7),c_Groups_Ouminus__class_Ouminus(X4)),X22)),X3)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),X22),X3))<=class_Groups_Oab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__negf)). 4.02/4.27 fof(fact_Not__Domain__rtrancl, axiom, ![X17, X39, X9, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_Relation_ODomain(X4,X4),X39))))=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),c_Transitive__Closure_Ortrancl(X4,X39)))<=>X17=X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Not__Domain__rtrancl)). 4.02/4.27 fof(fact_in__set__conv__decomp__last, axiom, ![X32, X9, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))<=>?[X146, X258]:(hAPP(hAPP(c_List_Oappend(X4),X146),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X258))=X32&~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X258)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__conv__decomp__last)). 4.02/4.27 fof(fact_in__set__conv__decomp__first, axiom, ![X32, X9, X4]:(?[X146]:(?[X258]:X32=hAPP(hAPP(c_List_Oappend(X4),X146),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X258))&~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X146)))))<=>hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__conv__decomp__first)). 4.02/4.27 fof(fact_fold1__insert__idem, axiom, ![X9, X3, X4]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X9),hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),X3))=hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3)))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3)<=class_Lattices_Oab__semigroup__idem__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__insert__idem)). 4.02/4.27 fof(fact_sum__squares__ge__zero, axiom, ![X43, X13, X4]:(class_Rings_Olinordered__ring(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X13),X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X43),X43))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sum__squares__ge__zero)). 4.02/4.27 fof(fact_Domain__mono, axiom, ![X40, X18, X7, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X4,X7),X18)),hAPP(c_Relation_ODomain(X4,X7),X40)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X18),X40))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__mono)). 4.02/4.27 fof(fact_ivl__disj__un_I14_J, axiom, ![X115, X60, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X60),X115))=>hAPP(c_SetInterval_Oord__class_OatLeast(X4),X60)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X60),X115)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X115)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I14_J)). 4.02/4.27 fof(fact_ivl__disj__un_I8_J, axiom, ![X115, X60, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X60),X115))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X60)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X60),X115))=hAPP(c_SetInterval_Oord__class_OlessThan(X4),X115))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I8_J)). 4.02/4.27 fof(fact_take__Suc, axiom, ![X5, X4, X45]:(hAPP(hAPP(c_List_Olist_OCons(X4),hAPP(c_List_Ohd(X4),X45)),hAPP(hAPP(c_List_Otake(X4),X5),hAPP(c_List_Otl(X4),X45)))=hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_OSuc,X5)),X45)<=X45!=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Suc)). 4.02/4.27 fof(fact_q__neg__lemma, axiom, ![X212, X213, X110]:(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),X110),X213)),X212)),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)),X212))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X213),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)),X110))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_q__neg__lemma)). 4.02/4.27 fof(fact_subset__image__iff, axiom, ![X3, X22, X7, X6, X4]:(?[X312]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X312),X3))&X6=hAPP(c_Set_Oimage(X7,X4,X22),X312))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),hAPP(c_Set_Oimage(X7,X4,X22),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__image__iff)). 4.02/4.27 fof(fact_folding__image__simple__idem_Osubset__idem, axiom, ![X6, X3, X87, X76, X16, X22, X7, X4]:(c_Finite__Set_Ofolding__image__simple__idem(X4,X7,X22,X16,X76,X87)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3))=>(hAPP(X87,X3)=hAPP(hAPP(X22,hAPP(X87,X6)),hAPP(X87,X3))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X6),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple__idem_Osubset__idem)). 4.02/4.27 fof(fact_nth__Cons_H, axiom, ![X45, X13, X4, X5]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X5=>hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)),X5)=X13)&(hAPP(hAPP(c_List_Onth(X4),X45),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)),X5)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__Cons_H)). 4.02/4.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, axiom, ![X89, X90, X91, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X91),X89)),X90)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X91),X90)),X89)<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J)). 4.02/4.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, axiom, ![X10, X12, X11, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)),X12)<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J)). 4.02/4.27 fof(fact_list__ex1__iff, axiom, ![X32, X56, X4]:(c_List_Olist__ex1(X4,X56,X32)<=>?[X19]:((hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32)))&![X34]:(X34=X19<=(hBOOL(hAPP(X56,X34))&hBOOL(hAPP(hAPP(c_member(X4),X34),hAPP(c_List_Oset(X4),X32))))))&hBOOL(hAPP(X56,X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex1__iff)). 4.02/4.27 fof(fact_listsum__distinct__conv__setsum__set, axiom, ![X22, X32, X4, X7]:((hBOOL(hAPP(c_List_Odistinct(X4),X32))=>hAPP(c_List_Omonoid__add__class_Olistsum(X7),hAPP(hAPP(c_List_Omap(X4,X7),X22),X32))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),hAPP(c_List_Oset(X4),X32)))<=class_Groups_Ocomm__monoid__add(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__distinct__conv__setsum__set)). 4.02/4.27 fof(fact_diff__Suc__diff__eq2, axiom, ![X2, X135, X107]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),X135))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X135)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X107),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X135),X107))),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__Suc__diff__eq2)). 4.02/4.27 fof(fact_diff__Suc__diff__eq1, axiom, ![X2, X135, X107]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X107)),hAPP(c_Nat_OSuc,X135))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X135),X107)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__Suc__diff__eq1)). 4.02/4.27 fof(fact_mult__right__le__one__le, axiom, ![X43, X13, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X43))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X43),c_Groups_Oone__class_Oone(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X13),X43)),X13))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X13)))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__right__le__one__le)). 4.02/4.27 fof(fact_nat__mod__eq__lemma, axiom, ![X43, X5, X13]:((?[X103]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X103))=X13<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X43),X13)))<=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X43,X5)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X13,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mod__eq__lemma)). 4.02/4.27 fof(fact_finite__empty__induct, axiom, ![X56, X3, X4]:((hBOOL(hAPP(X56,X3))=>(![X27, X195]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X195))=>((hBOOL(hAPP(X56,X195))=>hBOOL(hAPP(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X195),hAPP(hAPP(c_Set_Oinsert(X4),X27),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))))<=hBOOL(hAPP(hAPP(c_member(X4),X27),X195))))=>hBOOL(hAPP(X56,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__empty__induct)). 4.02/4.27 fof(fact_mult__left__le__one__le, axiom, ![X43, X13, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X13))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X43),c_Groups_Oone__class_Oone(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X43),X13)),X13)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X43))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__le__one__le)). 4.02/4.27 fof(fact_refl__onI, axiom, ![X3, X18, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X3))))=>(![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X19)),X18)))=>c_Relation_Orefl__on(X4,X3,X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__onI)). 4.02/4.27 fof(fact_Ball__set__replicate, axiom, ![X56, X26, X20, X4]:(![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),c_List_Oreplicate(X4,X20,X26))))=>hBOOL(hAPP(X56,X19)))<=>(hBOOL(hAPP(X56,X26))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ball__set__replicate)). 4.02/4.27 fof(fact_add__strict__mono, axiom, ![X44, X10, X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X44)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X10),X44))))<=class_Groups_Oordered__cancel__ab__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__strict__mono)). 4.02/4.27 fof(fact_add__le__less__mono, axiom, ![X44, X10, X12, X11, X4]:(class_Groups_Oordered__cancel__ab__semigroup__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X44)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X10),X44))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__le__less__mono)). 4.02/4.27 fof(fact_add__less__le__mono, axiom, ![X44, X10, X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),X44))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X44)))))<=class_Groups_Oordered__cancel__ab__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__le__mono)). 4.02/4.27 fof(fact_abs__setprod, axiom, ![X3, X22, X7, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X4),hAPP(hAPP(c_COMBB(X4,X4,X7),c_Groups_Oabs__class_Oabs(X4)),X22)),X3)=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X4),X22),X3))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__setprod)). 4.02/4.27 fof(fact_inf__mono, axiom, ![X44, X12, X10, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X10))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X44))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X11),X12)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X10),X44)))))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__mono)). 4.02/4.27 fof(fact_sup__mono, axiom, ![X44, X12, X10, X11, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X44))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X11),X12)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X10),X44))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X10)))<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__mono)). 4.02/4.27 fof(fact_add__mono, axiom, ![X44, X10, X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X44)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),X44))))<=class_Groups_Oordered__ab__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__mono)). 4.02/4.27 fof(fact_power__mono, axiom, ![X5, X12, X11, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X5)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__mono)). 4.02/4.27 fof(fact_divide__right__mono, axiom, ![X10, X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X10)))))<=class_Fields_Olinordered__field__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__right__mono)). 4.02/4.27 fof(fact_power__strict__increasing__iff, axiom, ![X17, X9, X25, X4]:(class_Rings_Olinordered__semidom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X25),X9)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X25),X17)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X17)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__strict__increasing__iff)). 4.02/4.27 fof(fact_power__increasing, axiom, ![X11, X88, X5, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X88))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Oone__class_Oone(X4)),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X88)))))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__increasing)). 4.02/4.27 fof(fact_Int__insert__right__if0, axiom, ![X6, X3, X26, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X26),X3)))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),X6))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__insert__right__if0)). 4.02/4.27 fof(fact_simp__from__to, axiom, ![X37, X38]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X38),X37))=>c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X37,X38))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X38),X37)))=>c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X37,X38)=hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X37),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X37),c_Groups_Oone__class_Oone(tc_Int_Oint)),X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_simp__from__to)). 4.02/4.27 fof(fact_power__increasing__iff, axiom, ![X17, X9, X25, X4]:(class_Rings_Olinordered__semidom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9),X17))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X25),X9)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X25),X17))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__increasing__iff)). 4.02/4.27 fof(fact_divide__right__mono__neg, axiom, ![X10, X12, X11, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X10),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X10))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12)))<=class_Fields_Olinordered__field__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__right__mono__neg)). 4.02/4.27 fof(fact_small__lazy_H_Osimps, axiom, ![X46, X44]:((c_Lazy__Sequence_Oempty(tc_Int_Oint)=c_Lazy__Sequence_Osmall__lazy_H(X44,X46)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X44),X46)))&(c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X46),c_Lazy__Sequence_Osmall__lazy_H(X44,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X46),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Lazy__Sequence_Osmall__lazy_H(X44,X46)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X44),X46))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__lazy_H_Osimps)). 4.02/4.27 fof(fact_finite__subset__induct, axiom, ![X56, X3, X87, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X87))=>((hBOOL(hAPP(X56,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>(![X27, X210]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X210))=>(((hBOOL(hAPP(X56,X210))=>hBOOL(hAPP(X56,hAPP(hAPP(c_Set_Oinsert(X4),X27),X210))))<=~(hBOOL(hAPP(hAPP(c_member(X4),X27),X210))))<=hBOOL(hAPP(hAPP(c_member(X4),X27),X3))))=>hBOOL(hAPP(X56,X87))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X87),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__subset__induct)). 4.02/4.27 fof(fact_divmod__int__rel__div__mod, axiom, ![X11, X12]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X12=>hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X12),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__div__mod)). 4.02/4.27 fof(fact_distinct__append, axiom, ![X31, X32, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Oappend(X4),X32),X31)))<=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),X32)),hAPP(c_List_Oset(X4),X31))&hBOOL(hAPP(c_List_Odistinct(X4),X31)))&hBOOL(hAPP(c_List_Odistinct(X4),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__append)). 4.02/4.27 fof(fact_of__nat__diff, axiom, ![X2, X5, X4]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X5))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X2)))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__diff)). 4.02/4.27 fof(fact_all__nth__imp__all__set, axiom, ![X9, X56, X32, X4]:(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))=>hBOOL(hAPP(X56,hAPP(hAPP(c_List_Onth(X4),X32),X42))))=>(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))=>hBOOL(hAPP(X56,X9)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__nth__imp__all__set)). 4.02/4.27 fof(fact_select, axiom, ![X40, X4, X32]:(hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Product__Type_Ofst(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X4,X32),X40))),hAPP(c_List_Oset(X4),X32)))<=X32!=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select)). 4.02/4.27 fof(fact_nat__mult__div__cancel1, axiom, ![X5, X2, X107]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X107))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X5))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__div__cancel1)). 4.02/4.27 fof(fact_list__all2__nthD2, axiom, ![X51, X31, X32, X56, X7, X4]:(c_List_Olist__all2(X4,X7,X56,X32,X31)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31)))=>hBOOL(hAPP(hAPP(X56,hAPP(hAPP(c_List_Onth(X4),X32),X51)),hAPP(hAPP(c_List_Onth(X7),X31),X51))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__nthD2)). 4.02/4.27 fof(fact_foldl__assoc, axiom, ![X30, X17, X9, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X9),hAPP(c_List_Ofoldl(X4,X4,c_Groups_Oplus__class_Oplus(X4),X17),X30))=hAPP(c_List_Ofoldl(X4,X4,c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X9),X17)),X30)<=class_Groups_Osemigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__assoc)). 4.02/4.27 fof(fact_folding__idem_Oin__comp__idem, axiom, ![X9, X3, X87, X22, X7, X4]:(c_Finite__Set_Ofolding__idem(X4,X7,X22,X87)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_member(X4),X9),X3))=>hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X87,X3)),hAPP(X22,X9))=hAPP(X87,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Oin__comp__idem)). 4.02/4.27 fof(fact_Bex__set__replicate, axiom, ![X56, X26, X20, X4]:((hBOOL(hAPP(X56,X26))&c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X20)<=>?[X19]:(hBOOL(hAPP(X56,X19))&hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),c_List_Oreplicate(X4,X20,X26)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Bex__set__replicate)). 4.02/4.27 fof(fact_mult__eq__if, axiom, ![X5, X2]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),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))),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5))&(X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__eq__if)). 4.02/4.27 fof(fact_drop__Cons_H, axiom, ![X45, X13, X4, X5]:((hAPP(hAPP(c_List_Odrop(X4),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45))=hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)<=X5=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X5=>hAPP(hAPP(c_List_Odrop(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X45)=hAPP(hAPP(c_List_Odrop(X4),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Cons_H)). 4.02/4.27 fof(fact_Cons__in__lists__iff, axiom, ![X3, X32, X9, X4]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)),c_List_Olists(X4,X3)))<=>(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X32),c_List_Olists(X4,X3)))&hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__in__lists__iff)). 4.02/4.27 fof(fact_q__pos__lemma, axiom, ![X212, X213, X110]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X110))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X213)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X212),X110)))<=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),X110),X213)),X212)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_q__pos__lemma)). 4.02/4.27 fof(fact_rotate1__hd__tl, axiom, ![X4, X45]:(hAPP(hAPP(c_List_Oappend(X4),hAPP(c_List_Otl(X4),X45)),hAPP(hAPP(c_List_Olist_OCons(X4),hAPP(c_List_Ohd(X4),X45)),c_List_Olist_ONil(X4)))=hAPP(c_List_Orotate1(X4),X45)<=c_List_Olist_ONil(X4)!=X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate1__hd__tl)). 4.02/4.27 fof(fact_atLeastatMost__subset__iff, axiom, ![X102, X24, X25, X26, X4]:(class_Orderings_Oorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X26,X25)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X24,X102)))<=>(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),X25)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),X102))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X24),X26)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastatMost__subset__iff)). 4.02/4.27 fof(fact_Max__mono, axiom, ![X176, X54, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X54),X176))=>((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X176))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Big__Operators_Olinorder__class_OMax(X4,X54)),c_Big__Operators_Olinorder__class_OMax(X4,X176))))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X54))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__mono)). 4.02/4.27 fof(fact_Min__antimono, axiom, ![X176, X54, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X54),X176))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X54=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X176))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Big__Operators_Olinorder__class_OMin(X4,X176)),c_Big__Operators_Olinorder__class_OMin(X4,X54))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__antimono)). 4.02/4.27 fof(fact_listsum__setsum__nth, axiom, ![X32, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(c_List_Omonoid__add__class_Olistsum(X4),X32)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4),hAPP(c_List_Onth(X4),X32)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__setsum__nth)). 4.02/4.27 fof(fact_mult__less__cancel__left__disj, axiom, ![X25, X26, X24, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X24),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X24),X25)))<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X24))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X25)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X25),X26))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),c_Groups_Ozero__class_Ozero(X4))))))<=class_Rings_Olinordered__ring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel__left__disj)). 4.02/4.27 fof(fact_crossproduct__eq, axiom, ![X16, X9, X17, X23, X4]:(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)=>((X17=X16|X23=X9)<=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X23),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X9),X17))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X23),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X9),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_crossproduct__eq)). 4.02/4.27 fof(fact_refl__onD, axiom, ![X26, X18, X3, X4]:(c_Relation_Orefl__on(X4,X3,X18)=>(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X26)),X18))<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__onD)). 4.02/4.27 fof(fact_INFI__apply, axiom, ![X9, X22, X3, X49, X7, X4]:(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X49,X4)),X3),X22),X9)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,X4),X3),hAPP(hAPP(c_COMBC(X7,X49,X4),X22),X9))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INFI__apply)). 4.02/4.27 fof(fact_SUPR__apply, axiom, ![X9, X22, X3, X49, X7, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X49,X4)),X3),X22),X9)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,X4),X3),hAPP(hAPP(c_COMBC(X7,X49,X4),X22),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUPR__apply)). 4.02/4.27 fof(fact_all__nat__less__eq, axiom, ![X56, X20]:(![X50]:(hBOOL(hAPP(X56,X50))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X20)))<=>![X19]:(hBOOL(hAPP(X56,X19))<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X19),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__nat__less__eq)). 4.02/4.27 fof(fact_le__div__geq, axiom, ![X2, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5))=>(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),X5)),X5))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X5)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__div__geq)). 4.02/4.27 fof(fact_INT__lower, axiom, ![X6, X7, X3, X26, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X3),X6)),hAPP(X6,X26)))<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__lower)). 4.02/4.27 fof(fact_UN__upper, axiom, ![X6, X7, X3, X26, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X26),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(X6,X26)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__upper)). 4.02/4.27 fof(fact_irrefl__def, axiom, ![X18, X4]:(c_Relation_Oirrefl(X4,X18)<=>![X19]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X19)),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_irrefl__def)). 4.02/4.27 fof(fact_Cons__eq__append__conv, axiom, ![X30, X31, X32, X9, X4]:(hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)=hAPP(hAPP(c_List_Oappend(X4),X31),X30)<=>(?[X33]:(X32=hAPP(hAPP(c_List_Oappend(X4),X33),X30)&X31=hAPP(hAPP(c_List_Olist_OCons(X4),X9),X33))|(hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)=X30&X31=c_List_Olist_ONil(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cons__eq__append__conv)). 4.02/4.27 fof(fact_append__eq__Cons__conv, axiom, ![X32, X9, X30, X31, X4]:(((X30=hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)&X31=c_List_Olist_ONil(X4))|?[X33]:(hAPP(hAPP(c_List_Oappend(X4),X33),X30)=X32&hAPP(hAPP(c_List_Olist_OCons(X4),X9),X33)=X31))<=>hAPP(hAPP(c_List_Oappend(X4),X31),X30)=hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__eq__Cons__conv)). 4.02/4.27 fof(fact_insert__mono, axiom, ![X26, X61, X8, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X8),X61))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X26),X8)),hAPP(hAPP(c_Set_Oinsert(X4),X26),X61)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__mono)). 4.02/4.27 fof(fact_min__max_Oinf__mono, axiom, ![X44, X12, X10, X11, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X11),X12)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X10),X44)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X44)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X10)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__mono)). 4.02/4.27 fof(fact_min__max_Osup__mono, axiom, ![X44, X12, X10, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X10))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X11),X12)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X10),X44)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X44))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__mono)). 4.02/4.27 fof(fact_all__nat__less, axiom, ![X56, X20]:(![X50]:(hBOOL(hAPP(X56,X50))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X50),X20)))<=>![X19]:(hBOOL(hAPP(X56,X19))<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X19),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__nat__less)). 4.02/4.27 fof(fact_finite__Union, axiom, ![X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X3)))<=![X283]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X283))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X283),X3))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,tc_HOL_Obool)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Union)). 4.02/4.27 fof(fact_power__gt1__lemma, axiom, ![X5, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)))))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__gt1__lemma)). 4.02/4.27 fof(fact_self__quotient__aux2, axiom, ![X14, X101, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14),c_Groups_Oone__class_Oone(tc_Int_Oint))))<=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X101),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X14))=X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_self__quotient__aux2)). 4.02/4.27 fof(fact_wf__map__pair__image, axiom, ![X22, X7, X18, X4]:((c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>c_Wellfounded_Owf(X7,hAPP(c_Set_Oimage(tc_prod(X4,X4),tc_prod(X7,X7),c_Product__Type_Omap__pair(X4,X7,X4,X7,X22,X22)),X18)))<=c_Wellfounded_Owf(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__map__pair__image)). 4.02/4.27 fof(fact_fun__left__comm_Ofold__set__remdups, axiom, ![X32, X17, X22, X7, X4]:(hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),X17),hAPP(c_List_Oset(X4),X32))=hAPP(c_List_Ofoldl(X7,X4,hAPP(c_COMBC(X4,X7,X7),X22),X17),c_List_Oremdups(X4,X32))<=c_Finite__Set_Ofun__left__comm(X4,X7,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__set__remdups)). 4.02/4.27 fof(fact_insert__Diff1, axiom, ![X3, X6, X9, X4]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3)),X6)<=hBOOL(hAPP(hAPP(c_member(X4),X9),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__Diff1)). 4.02/4.27 fof(fact_subset__singletonD, axiom, ![X9, X3, X4]:((X3=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))|hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=X3)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__singletonD)). 4.02/4.27 fof(fact_mod__diff__eq, axiom, ![X10, X12, X11, X4]:(c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X12),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),c_Divides_Odiv__class_Omod(X4,X11,X10)),c_Divides_Odiv__class_Omod(X4,X12,X10)),X10)<=class_Divides_Oring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__diff__eq)). 4.02/4.27 fof(fact_enum__ex__option__def, axiom, ![X56, X4]:(class_Enum_Oenum(X4)=>(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X4)),X56))<=>(hBOOL(hAPP(X56,c_Option_Ooption_ONone(X4)))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X4),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X4),tc_HOL_Obool,X4),X56),c_Option_Ooption_OSome(X4))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__ex__option__def)). 4.02/4.27 fof(fact_takeWhile__append1, axiom, ![X31, X56, X32, X9, X4]:((c_List_OtakeWhile(X4,X56,X32)=c_List_OtakeWhile(X4,X56,hAPP(hAPP(c_List_Oappend(X4),X32),X31))<=~(hBOOL(hAPP(X56,X9))))<=hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__append1)). 4.02/4.27 fof(fact_finite__Diff__insert, axiom, ![X6, X26, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),X6))))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Diff__insert)). 4.02/4.27 fof(fact_in__set__butlast__appendI, axiom, ![X31, X32, X9, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),c_List_Obutlast(X4,hAPP(hAPP(c_List_Oappend(X4),X32),X31)))))<=(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),c_List_Obutlast(X4,X31))))|hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),c_List_Obutlast(X4,X32)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__butlast__appendI)). 4.02/4.27 fof(fact_inj__comp, axiom, ![X76, X49, X22, X7, X4]:((c_Fun_Oinj__on(X49,X7,hAPP(c_Fun_Ocomp(X4,X7,X49,X22),X76),c_Orderings_Otop__class_Otop(tc_fun(X49,tc_HOL_Obool)))<=c_Fun_Oinj__on(X49,X4,X76,c_Orderings_Otop__class_Otop(tc_fun(X49,tc_HOL_Obool))))<=c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__comp)). 4.02/4.27 fof(fact_abs__number__of, axiom, ![X13, X4]:((class_Rings_Olinordered__idom(X4)&class_Int_Onumber__ring(X4))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X13)),c_Groups_Ozero__class_Ozero(X4)))=>hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X13))=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X13)))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X13)),c_Groups_Ozero__class_Ozero(X4))))=>hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X13))=hAPP(c_Int_Onumber__class_Onumber__of(X4),X13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__number__of)). 4.02/4.27 fof(fact_psubset__imp__ex__mem, axiom, ![X6, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X3),X6))=>?[X78]:hBOOL(hAPP(hAPP(c_member(X4),X78),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X6),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubset__imp__ex__mem)). 4.02/4.27 fof(fact_Pow__mono, axiom, ![X6, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X4),X3)),hAPP(c_Set_OPow(X4),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__mono)). 4.02/4.27 fof(fact_power__eq__imp__eq__base, axiom, ![X12, X5, X11, X4]:(class_Rings_Olinordered__semidom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5))=>X11=X12)))<=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X5)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__eq__imp__eq__base)). 4.02/4.27 fof(fact_power__Suc__less__one, axiom, ![X5, X11, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(c_Nat_OSuc,X5))),c_Groups_Oone__class_Oone(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Oone__class_Oone(X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__Suc__less__one)). 4.02/4.27 fof(fact_list__size__estimation, axiom, ![X22, X17, X32, X9, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(X22,X9)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),c_List_Olist_Olist__size(X4,X22,X32))))<=hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__size__estimation)). 4.02/4.27 fof(fact_list__size__estimation_H, axiom, ![X22, X17, X32, X9, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),hAPP(X22,X9)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),c_List_Olist_Olist__size(X4,X22,X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__size__estimation_H)). 4.02/4.27 fof(fact_power__one__over, axiom, ![X5, X11, X4]:(class_Fields_Ofield__inverse__zero(X4)=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),c_Groups_Oone__class_Oone(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),c_Groups_Oone__class_Oone(X4)),X11)),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__one__over)). 4.02/4.27 fof(fact_Sup__binary, axiom, ![X25, X26, X4]:(c_Complete__Lattice_OSup__class_OSup(X4,hAPP(hAPP(c_Set_Oinsert(X4),X26),hAPP(hAPP(c_Set_Oinsert(X4),X25),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X26),X25)<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__binary)). 4.02/4.27 fof(fact_folding__one__idem_Oinsert__idem, axiom, ![X9, X3, X87, X22, X4]:(c_Finite__Set_Ofolding__one__idem(X4,X22,X87)=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3=>hAPP(X87,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=hAPP(hAPP(X22,X9),hAPP(X87,X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Oinsert__idem)). 4.02/4.27 fof(fact_finite__INT, axiom, ![X3, X7, X41, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X41),X3)))<=?[X19]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(X3,X19)))&hBOOL(hAPP(hAPP(c_member(X4),X19),X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__INT)). 4.02/4.27 fof(fact_Inf__binary, axiom, ![X25, X26, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>c_Complete__Lattice_OInf__class_OInf(X4,hAPP(hAPP(c_Set_Oinsert(X4),X26),hAPP(hAPP(c_Set_Oinsert(X4),X25),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X26),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__binary)). 4.02/4.27 fof(fact_set__zip__leftD, axiom, ![X31, X32, X17, X9, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X9),X17)),hAPP(c_List_Oset(tc_prod(X4,X7)),hAPP(hAPP(c_List_Ozip(X4,X7),X32),X31))))=>hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__zip__leftD)). 4.02/4.27 fof(fact_set__zip__rightD, axiom, ![X31, X32, X17, X9, X7, X4]:(hBOOL(hAPP(hAPP(c_member(X7),X17),hAPP(c_List_Oset(X7),X31)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X9),X17)),hAPP(c_List_Oset(tc_prod(X4,X7)),hAPP(hAPP(c_List_Ozip(X4,X7),X32),X31))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__zip__rightD)). 4.02/4.27 fof(fact_rtrancl__subset__rtrancl, axiom, ![X40, X18, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X18)),c_Transitive__Closure_Ortrancl(X4,X40)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),c_Transitive__Closure_Ortrancl(X4,X40)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__subset__rtrancl)). 4.02/4.27 fof(fact_remove1__append, axiom, ![X31, X32, X9, X4]:((hAPP(hAPP(c_List_Oappend(X4),X32),c_List_Oremove1(X4,X9,X31))=c_List_Oremove1(X4,X9,hAPP(hAPP(c_List_Oappend(X4),X32),X31))<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))))&(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))=>c_List_Oremove1(X4,X9,hAPP(hAPP(c_List_Oappend(X4),X32),X31))=hAPP(hAPP(c_List_Oappend(X4),c_List_Oremove1(X4,X9,X32)),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__append)). 4.02/4.27 fof(fact_nth__map, axiom, ![X22, X7, X32, X4, X20]:(hAPP(hAPP(c_List_Onth(X7),hAPP(hAPP(c_List_Omap(X4,X7),X22),X32)),X20)=hAPP(X22,hAPP(hAPP(c_List_Onth(X4),X32),X20))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__map)). 4.02/4.27 fof(fact_setprod__pos__nat, axiom, ![X22, X86, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,tc_Nat_Onat),X22),X86)))<=![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X22,X19)))<=hBOOL(hAPP(hAPP(c_member(X4),X19),X86))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X86))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__pos__nat)). 4.02/4.27 fof(fact_sorted_OCons, axiom, ![X9, X32, X4]:(class_Orderings_Olinorder(X4)=>(![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X19))<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32))))=>(c_List_Olinorder__class_Osorted(X4,X32)=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted_OCons)). 4.02/4.27 fof(fact_sorted__Cons, axiom, ![X32, X9, X4]:((c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32))<=>(![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X19))<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32))))&c_List_Olinorder__class_Osorted(X4,X32)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__Cons)). 4.02/4.27 fof(fact_sorted_Oequations_I2_J, axiom, ![X70, X67, X4]:(((![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X67),X19))<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X70))))&c_List_Olinorder__class_Osorted(X4,X70))<=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X67),X70)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted_Oequations_I2_J)). 4.02/4.27 fof(fact_atMost__Int__atLeast, axiom, ![X20, X4]:(class_Orderings_Oorder(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X20)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X20))=hAPP(hAPP(c_Set_Oinsert(X4),X20),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atMost__Int__atLeast)). 4.02/4.27 fof(fact_distinct__insort, axiom, ![X32, X9, X22, X4, X7]:((hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X7,X22),X9),X32)))<=>(~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32))))&hBOOL(hAPP(c_List_Odistinct(X4),X32))))<=class_Orderings_Olinorder(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__insort)). 4.02/4.27 fof(fact_mod__mult__eq, axiom, ![X10, X12, X11, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Divides_Odiv__class_Omod(X4,X11,X10)),c_Divides_Odiv__class_Omod(X4,X12,X10)),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__eq)). 4.02/4.27 fof(fact_mod__add__eq, axiom, ![X10, X12, X11, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Divides_Odiv__class_Omod(X4,X11,X10)),c_Divides_Odiv__class_Omod(X4,X12,X10)),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__eq)). 4.02/4.27 fof(fact_image__uminus__atLeastLessThan, axiom, ![X17, X9, X4]:(class_Groups_Oordered__ab__group__add(X4)=>c_SetInterval_Oord__class_OgreaterThanAtMost(X4,hAPP(c_Groups_Ouminus__class_Ouminus(X4),X17),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X9))=hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X9),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__atLeastLessThan)). 4.02/4.27 fof(fact_zmult__zless__mono2, axiom, ![X107, X135, X46]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X107))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X107),X46)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X107),X135))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X46),X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__zless__mono2)). 4.02/4.27 fof(fact_mult__less__cancel2, axiom, ![X20, X28, X21]:((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),X21),X20)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X28)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel2)). 4.02/4.27 fof(fact_card__Plus__conv__if, axiom, ![X6, X7, X3, X4]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(tc_sum(X4,X7)),c_Sum__Type_OPlus(X4,X7,X3,X6))<=~((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))&hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X6)))))&(hAPP(c_Finite__Set_Ocard(tc_sum(X4,X7)),c_Sum__Type_OPlus(X4,X7,X3,X6))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X3)),hAPP(c_Finite__Set_Ocard(X7),X6))<=(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))&hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__Plus__conv__if)). 4.02/4.27 fof(fact_ivl__disj__un_I11_J, axiom, ![X115, X60, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X60),X115))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X60,X115)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X115))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X60))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I11_J)). 4.02/4.27 fof(fact_mult__less__cancel1, axiom, ![X20, X21, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X20)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel1)). 4.02/4.27 fof(fact_zdiv__mono1, axiom, ![X12, X111, X11]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X111),X12))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11),X111))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono1)). 4.02/4.27 fof(fact_ivl__disj__un_I13_J, axiom, ![X115, X60, X4]:(class_Orderings_Olinorder(X4)=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X60,X115)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X115))=hAPP(c_SetInterval_Oord__class_OatLeast(X4),X60)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X60),X115)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I13_J)). 4.02/4.27 fof(fact_ivl__disj__un_I12_J, axiom, ![X115, X60, X4]:((hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X60)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X60,X115)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X115))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X60),X115)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I12_J)). 4.02/4.27 fof(fact_Int__atLeastAtMostL2, axiom, ![X24, X25, X26, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X26,X25)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X24))=c_SetInterval_Oord__class_OatLeastAtMost(X4,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X26),X24),X25)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastAtMostL2)). 4.02/4.27 fof(fact_Int__atLeastAtMostL1, axiom, ![X102, X25, X26, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X26,X25)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X102))=c_SetInterval_Oord__class_OatLeastAtMost(X4,X26,hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X25),X102))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastAtMostL1)). 4.02/4.27 fof(fact_div__le__mono2, axiom, ![X107, X5, X2]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X5))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X107),X5)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X107),X2))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__le__mono2)). 4.02/4.27 fof(fact_zdiv__mono1__neg, axiom, ![X12, X111, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11),X111))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X111),X12)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__mono1__neg)). 4.02/4.27 fof(fact_ivl__disj__un_I7_J, axiom, ![X115, X60, X4]:(class_Orderings_Olinorder(X4)=>(hAPP(c_SetInterval_Oord__class_OlessThan(X4),X115)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X60)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X60,X115))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X60),X115)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I7_J)). 4.02/4.27 fof(fact_ivl__disj__un_I10_J, axiom, ![X115, X60, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X60),X115))=>hAPP(c_SetInterval_Oord__class_OatMost(X4),X115)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X60)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X60,X115)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I10_J)). 4.02/4.27 fof(fact_ivl__disj__un_I9_J, axiom, ![X115, X60, X4]:(class_Orderings_Olinorder(X4)=>(hAPP(c_SetInterval_Oord__class_OatMost(X4),X115)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X60)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X60,X115))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X60),X115)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__un_I9_J)). 4.02/4.27 fof(fact_minus__apply, axiom, ![X9, X6, X3, X7, X4]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(X3,X9)),hAPP(X6,X9))=hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,X4)),X3),X6),X9)<=class_Groups_Ominus(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__apply)). 4.02/4.27 fof(fact_inf__apply, axiom, ![X9, X76, X22, X7, X4]:(class_Lattices_Olattice(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(X22,X9)),hAPP(X76,X9))=hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,X4)),X22),X76),X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__apply)). 4.02/4.27 fof(fact_sup__apply, axiom, ![X9, X76, X22, X7, X4]:(class_Lattices_Olattice(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(X22,X9)),hAPP(X76,X9))=hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,X4)),X22),X76),X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__apply)). 4.02/4.27 fof(fact_Int__atLeastAtMostR1, axiom, ![X102, X24, X25, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X25)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X24,X102))=c_SetInterval_Oord__class_OatLeastAtMost(X4,X24,hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X25),X102))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastAtMostR1)). 4.02/4.27 fof(fact_Int__atLeastAtMostR2, axiom, ![X102, X24, X26, X4]:(c_SetInterval_Oord__class_OatLeastAtMost(X4,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X26),X24),X102)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X26)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X24,X102))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__atLeastAtMostR2)). 4.02/4.27 fof(fact_filter_Osimps_I2_J, axiom, ![X32, X4, X9, X56]:((hAPP(c_List_Ofilter(X4,X56),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32))=hAPP(c_List_Ofilter(X4,X56),X32)<=~(hBOOL(hAPP(X56,X9))))&(hAPP(hAPP(c_List_Olist_OCons(X4),X9),hAPP(c_List_Ofilter(X4,X56),X32))=hAPP(c_List_Ofilter(X4,X56),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32))<=hBOOL(hAPP(X56,X9)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter_Osimps_I2_J)). 4.02/4.27 fof(fact_self__quotient__aux1, axiom, ![X14, X101, X11]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X101),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X14))=X11=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X14))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_self__quotient__aux1)). 4.02/4.27 fof(fact_folding__image__simple__idem_Oin__idem, axiom, ![X9, X3, X87, X76, X16, X22, X7, X4]:(((hBOOL(hAPP(hAPP(c_member(X7),X9),X3))=>hAPP(X87,X3)=hAPP(hAPP(X22,hAPP(X76,X9)),hAPP(X87,X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3)))<=c_Finite__Set_Ofolding__image__simple__idem(X4,X7,X22,X16,X76,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple__idem_Oin__idem)). 4.02/4.27 fof(fact_zdiff__int__split, axiom, ![X17, X9, X56]:(((hBOOL(hAPP(X56,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X17)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17),X9))=>hBOOL(hAPP(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X9)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17))))))<=>hBOOL(hAPP(X56,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9),X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__int__split)). 4.02/4.27 fof(fact_wfI__pf, axiom, ![X39, X4]:(c_Wellfounded_Owf(X4,X39)<=![X195]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X195),hAPP(c_Relation_OImage(X4,X4,X39),X195)))=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X195)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfI__pf)). 4.02/4.27 fof(fact_list__all2__map1, axiom, ![X108, X109, X22, X49, X56, X7, X4]:(c_List_Olist__all2(X49,X7,hAPP(hAPP(c_COMBB(X4,tc_fun(X7,tc_HOL_Obool),X49),X56),X22),X109,X108)<=>c_List_Olist__all2(X4,X7,X56,hAPP(hAPP(c_List_Omap(X49,X4),X22),X109),X108)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__map1)). 4.02/4.27 fof(fact_inj__image__subset__iff, axiom, ![X6, X3, X22, X7, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X7,X22),X3)),hAPP(c_Set_Oimage(X4,X7,X22),X6))))<=c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__image__subset__iff)). 4.02/4.27 fof(fact_enum__option__def, axiom, ![X4]:(c_Enum_Oenum__class_Oenum(tc_Option_Ooption(X4))=hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(X4)),c_Option_Ooption_ONone(X4)),hAPP(hAPP(c_List_Omap(X4,tc_Option_Ooption(X4)),c_Option_Ooption_OSome(X4)),c_Enum_Oenum__class_Oenum(X4)))<=class_Enum_Oenum(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__option__def)). 4.02/4.27 fof(fact_Suc__mult__less__cancel1, axiom, ![X20, X21, X28]:(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,X28)),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X28)),X20)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__mult__less__cancel1)). 4.02/4.27 fof(fact_ex__nat__less__eq, axiom, ![X56, X20]:(?[X50]:(hBOOL(hAPP(X56,X50))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X20)))<=>?[X19]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X19),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)))&hBOOL(hAPP(X56,X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__nat__less__eq)). 4.02/4.27 fof(fact_UnionI, axiom, ![X3, X8, X156, X4]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X156),X8))=>(hBOOL(hAPP(hAPP(c_member(X4),X3),X156))=>hBOOL(hAPP(hAPP(c_member(X4),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X8))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UnionI)). 4.02/4.27 fof(fact_mod__mult__mult2, axiom, ![X12, X10, X11, X4]:(c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Divides_Odiv__class_Omod(X4,X11,X12)),X10)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__mult2)). 4.02/4.27 fof(fact_mod__mult__mult1, axiom, ![X12, X11, X10, X4]:(class_Divides_Osemiring__div(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),c_Divides_Odiv__class_Omod(X4,X11,X12))=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__mult1)). 4.02/4.27 fof(fact_ex__nat__less, axiom, ![X56, X20]:(?[X50]:(hBOOL(hAPP(X56,X50))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X50),X20)))<=>?[X19]:(hBOOL(hAPP(X56,X19))&hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X19),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__nat__less)). 4.02/4.27 fof(fact_zdiv__zmult2__eq, axiom, ![X12, X11, X10]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12)),X10)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zmult2__eq)). 4.02/4.27 fof(fact_rtrancl__listrel1__eq__len, axiom, ![X18, X17, X9, X4]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X17)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X9)<=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)),X9),X17)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__listrel1__eq__len)). 4.02/4.27 fof(fact_select__weigth__select, axiom, ![X4, X32]:(c_Random_Oselect__weight(X4,hAPP(hAPP(c_List_Omap(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,X4)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X4),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X32))=c_Random_Oselect(X4,X32)<=X32!=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__weigth__select)). 4.02/4.27 fof(fact_divide__neg__pos, axiom, ![X43, X13, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),c_Groups_Ozero__class_Ozero(X4)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43)),c_Groups_Ozero__class_Ozero(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X43))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__neg__pos)). 4.02/4.27 fof(fact_divide__pos__neg, axiom, ![X43, X13, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43)),c_Groups_Ozero__class_Ozero(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X43),c_Groups_Ozero__class_Ozero(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X13)))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__pos__neg)). 4.02/4.27 fof(fact_mult__pos__neg, axiom, ![X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)),c_Groups_Ozero__class_Ozero(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),c_Groups_Ozero__class_Ozero(X4)))))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__pos__neg)). 4.02/4.27 fof(fact_list__eq__iff__nth__eq, axiom, ![X4, X31, X32]:(X31=X32<=>(![X42]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))=>hAPP(hAPP(c_List_Onth(X4),X31),X42)=hAPP(hAPP(c_List_Onth(X4),X32),X42))&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__eq__iff__nth__eq)). 4.02/4.27 fof(fact_min__max_Oinf_Oleft__commute, axiom, ![X10, X11, X12, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X11),X10))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X11),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X12),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf_Oleft__commute)). 4.02/4.27 fof(fact_mult__pos__neg2, axiom, ![X12, X11, X4]:(class_Rings_Olinordered__semiring__strict(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)),c_Groups_Ozero__class_Ozero(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),c_Groups_Ozero__class_Ozero(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__pos__neg2)). 4.02/4.27 fof(fact_divide__nonneg__neg, axiom, ![X43, X13, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X43),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43)),c_Groups_Ozero__class_Ozero(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X13)))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__nonneg__neg)). 4.02/4.27 fof(fact_divide__nonpos__pos, axiom, ![X43, X13, X4]:(class_Fields_Olinordered__field(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43)),c_Groups_Ozero__class_Ozero(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X43)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__nonpos__pos)). 4.02/4.27 fof(fact_mult__le__0__iff, axiom, ![X25, X26, X4]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X26))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),c_Groups_Ozero__class_Ozero(X4))))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X25))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X25)),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__ring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__0__iff)). 4.02/4.27 fof(fact_INF2__D, axiom, ![X26, X24, X25, X6, X3, X49, X7, X4]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_fun(X49,tc_HOL_Obool))),X3),X6),X25),X24))=>(hBOOL(hAPP(hAPP(hAPP(X6,X26),X25),X24))<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF2__D)). 4.02/4.27 fof(fact_split__mult__neg__le, axiom, ![X12, X11, X4]:(class_Rings_Oordered__cancel__semiring(X4)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),c_Groups_Ozero__class_Ozero(X4)))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__mult__neg__le)). 4.02/4.27 fof(fact_Inf__fin_Oeq__fold__idem_H, axiom, ![X26, X3, X4]:(class_Lattices_Olattice(X4)=>(hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X26),X3)=c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X26),X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oeq__fold__idem_H)). 4.02/4.27 fof(fact_Sup__fin_Oeq__fold__idem_H, axiom, ![X26, X3, X4]:((hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4)),X26),X3)=c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X26),X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oeq__fold__idem_H)). 4.02/4.27 fof(fact_inf__Inf__fold__inf, axiom, ![X6, X3, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X6),c_Complete__Lattice_OInf__class_OInf(X4,X3))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X6),X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__Inf__fold__inf)). 4.02/4.27 fof(fact_inf__left__commute, axiom, ![X29, X43, X13, X4]:(class_Lattices_Osemilattice__inf(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X43),X29))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X43),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__left__commute)). 4.02/4.27 fof(fact_add__neg__neg, axiom, ![X12, X11, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),c_Groups_Ozero__class_Ozero(X4))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Ozero__class_Ozero(X4))))<=class_Groups_Oordered__comm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__neg__neg)). 4.02/4.27 fof(fact_add__nonpos__neg, axiom, ![X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),c_Groups_Ozero__class_Ozero(X4)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),c_Groups_Ozero__class_Ozero(X4)))))<=class_Groups_Oordered__comm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__nonpos__neg)). 4.02/4.27 fof(fact_converseD, axiom, ![X18, X25, X26, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X4),X25),X26)),X18))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X26),X25)),hAPP(c_Relation_Oconverse(X7,X4),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converseD)). 4.02/4.27 fof(fact_wf__Un, axiom, ![X40, X18, X4]:(((c_Wellfounded_Owf(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),X40))<=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X4,X4),X18)),hAPP(c_Relation_ORange(X4,X4),X40))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=c_Wellfounded_Owf(X4,X40))<=c_Wellfounded_Owf(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__Un)). 4.02/4.27 fof(fact_inf__sup__aci_I3_J, axiom, ![X29, X43, X13, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X43),X29))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X43),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X29))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I3_J)). 4.02/4.27 fof(fact_add__neg__nonpos, axiom, ![X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Ozero__class_Ozero(X4)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),c_Groups_Ozero__class_Ozero(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),c_Groups_Ozero__class_Ozero(X4)))))<=class_Groups_Oordered__comm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__neg__nonpos)). 4.02/4.27 fof(fact_add__nonpos__nonpos, axiom, ![X12, X11, X4]:(class_Groups_Oordered__comm__monoid__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),c_Groups_Ozero__class_Ozero(X4)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),c_Groups_Ozero__class_Ozero(X4)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),c_Groups_Ozero__class_Ozero(X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__nonpos__nonpos)). 4.02/4.27 fof(fact_divide__pos__pos, axiom, ![X43, X13, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X13))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X43))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__pos__pos)). 4.02/4.27 fof(fact_mult__pos__pos, axiom, ![X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12))))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__pos__pos)). 4.02/4.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, axiom, ![X2, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Oone__class_Oone(X4))),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X2),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J)). 4.02/4.27 fof(fact_folding__one__idem_Oeq__fold__idem_H, axiom, ![X26, X3, X87, X22, X4]:(c_Finite__Set_Ofolding__one__idem(X4,X22,X87)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(X87,hAPP(hAPP(c_Set_Oinsert(X4),X26),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,X22),X26),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Oeq__fold__idem_H)). 4.02/4.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, axiom, ![X244, X89, X91, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X89),X244))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X89),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X91),X244))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J)). 4.02/4.27 fof(fact_add__pos__pos, axiom, ![X12, X11, X4]:(class_Groups_Oordered__comm__monoid__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__pos__pos)). 4.02/4.27 fof(fact_less__1__mult, axiom, ![X5, X2, X4]:(class_Rings_Olinordered__semidom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X5))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X5))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__1__mult)). 4.02/4.27 fof(fact_in__rel__def, axiom, ![X17, X9, X39, X7, X4]:(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X7,X39),X9),X17))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X9),X17)),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__rel__def)). 4.02/4.27 fof(fact_power__inject__base, axiom, ![X12, X5, X11, X4]:(class_Rings_Olinordered__semidom(X4)=>(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Nat_OSuc,X5))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(c_Nat_OSuc,X5))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>X12=X11)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__inject__base)). 4.02/4.27 fof(fact_divide__nonneg__pos, axiom, ![X43, X13, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X13))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X43))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__nonneg__pos)). 4.02/4.27 fof(fact_mult__nonneg__nonneg, axiom, ![X12, X11, X4]:(class_Rings_Oordered__cancel__semiring(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__nonneg__nonneg)). 4.02/4.27 fof(fact_zero__le__mult__iff, axiom, ![X25, X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X25)))<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X25))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X26)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),c_Groups_Ozero__class_Ozero(X4))))))<=class_Rings_Olinordered__ring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__mult__iff)). 4.02/4.27 fof(fact_split__mult__pos__le, axiom, ![X12, X11, X4]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),c_Groups_Ozero__class_Ozero(X4))))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12))))<=class_Rings_Oordered__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__mult__pos__le)). 4.02/4.27 fof(fact_SUP2__iff, axiom, ![X24, X25, X6, X3, X49, X7, X4]:(?[X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))&hBOOL(hAPP(hAPP(hAPP(X6,X19),X25),X24)))<=>hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_fun(X49,tc_HOL_Obool))),X3),X6),X25),X24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP2__iff)). 4.02/4.27 fof(fact_mod__div__decomp, axiom, ![X12, X11, X4]:(X11=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X11),X12)),X12)),c_Divides_Odiv__class_Omod(X4,X11,X12))<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__div__decomp)). 4.02/4.27 fof(fact_one__less__power, axiom, ![X5, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5))))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__less__power)). 4.02/4.27 fof(fact_divide__neg__neg, axiom, ![X43, X13, X4]:(class_Fields_Olinordered__field(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),c_Groups_Ozero__class_Ozero(X4)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X43),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__neg__neg)). 4.02/4.27 fof(fact_mult__neg__neg, axiom, ![X12, X11, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__ring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__neg__neg)). 4.02/4.27 fof(fact_semiring__div__class_Omod__div__equality_H, axiom, ![X12, X11, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Divides_Odiv__class_Omod(X4,X11,X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X11),X12)),X12))=X11<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_semiring__div__class_Omod__div__equality_H)). 4.02/4.27 fof(fact_mod__div__equality2, axiom, ![X11, X12, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X11),X12))),c_Divides_Odiv__class_Omod(X4,X11,X12))=X11<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__div__equality2)). 4.02/4.27 fof(fact_divide__nonpos__neg, axiom, ![X43, X13, X4]:(class_Fields_Olinordered__field(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X43),c_Groups_Ozero__class_Ozero(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__nonpos__neg)). 4.02/4.27 fof(fact_rtrancl__mono, axiom, ![X40, X18, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),X40))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X18)),c_Transitive__Closure_Ortrancl(X4,X40)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__mono)). 4.02/4.27 fof(fact_power__le__imp__le__base, axiom, ![X12, X5, X11, X4]:(class_Rings_Olinordered__semidom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(c_Nat_OSuc,X5))),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),hAPP(c_Nat_OSuc,X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__le__imp__le__base)). 4.02/4.27 fof(fact_min__max_Osup__left__commute, axiom, ![X29, X43, X13, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X43),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),X29))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X43),X29))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__left__commute)). 4.02/4.27 fof(fact_ivl__disj__int_I11_J, axiom, ![X115, X21, X60, X4]:(class_Orderings_Oorder(X4)=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X60),X21)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X21),X115))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I11_J)). 4.02/4.27 fof(fact_neg__divide__less__eq, axiom, ![X26, X25, X24, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24)),X25))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X25),X24)),X26)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),c_Groups_Ozero__class_Ozero(X4))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__divide__less__eq)). 4.02/4.27 fof(fact_neg__divide__le__eq, axiom, ![X26, X25, X24, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24)),X25))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X25),X24)),X26)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),c_Groups_Ozero__class_Ozero(X4))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__divide__le__eq)). 4.02/4.27 fof(fact_foldl__absorb0, axiom, ![X30, X9, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X9),hAPP(c_List_Ofoldl(X4,X4,c_Groups_Oplus__class_Oplus(X4),c_Groups_Ozero__class_Ozero(X4)),X30))=hAPP(c_List_Ofoldl(X4,X4,c_Groups_Oplus__class_Oplus(X4),X9),X30)<=class_Groups_Omonoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__absorb0)). 4.02/4.27 fof(fact_less__fun__def, axiom, ![X76, X22, X4, X7]:(class_Orderings_Oord(X7)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X7)),X22),X76))&~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X7)),X76),X22))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,X7)),X22),X76)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__fun__def)). 4.02/4.27 fof(fact_zmod__zminus2__eq__if, axiom, ![X12, X11]:((c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)),X12)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12)))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12))<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zminus2__eq__if)). 4.02/4.27 fof(fact_sup__left__commute, axiom, ![X29, X43, X13, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X43),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X29))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X43),X29))<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__left__commute)). 4.02/4.27 fof(fact_mult__imp__less__div__pos, axiom, ![X13, X29, X43, X4]:(class_Fields_Olinordered__field(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X43))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X29),X43)),X13))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X29),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__imp__less__div__pos)). 4.02/4.27 fof(fact_mult__imp__le__div__pos, axiom, ![X13, X29, X43, X4]:(class_Fields_Olinordered__field(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X29),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X29),X43)),X13)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__imp__le__div__pos)). 4.02/4.27 fof(fact_mult__imp__div__pos__less, axiom, ![X29, X13, X43, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X43))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43)),X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X29),X43)))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__imp__div__pos__less)). 4.02/4.27 fof(fact_mult__imp__div__pos__le, axiom, ![X29, X13, X43, X4]:(class_Fields_Olinordered__field(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43)),X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X29),X43))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__imp__div__pos__le)). 4.02/4.27 fof(fact_list__all2__Cons, axiom, ![X31, X17, X32, X9, X56, X7, X4]:(c_List_Olist__all2(X4,X7,X56,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32),hAPP(hAPP(c_List_Olist_OCons(X7),X17),X31))<=>(hBOOL(hAPP(hAPP(X56,X9),X17))&c_List_Olist__all2(X4,X7,X56,X32,X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__Cons)). 4.02/4.27 fof(fact_comm__monoid__big_OF__eq, axiom, ![X76, X3, X87, X16, X22, X7, X4]:(c_Big__Operators_Ocomm__monoid__big(X4,X7,X22,X16,X87)=>((hAPP(hAPP(X87,X76),X3)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X7,X22),X76),X16),X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3)))&(X16=hAPP(hAPP(X87,X76),X3)<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__monoid__big_OF__eq)). 4.02/4.27 fof(fact_folding__image_Oeq__fold, axiom, ![X76, X3, X87, X16, X22, X7, X4]:((hAPP(hAPP(X87,X76),X3)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X7,X22),X76),X16),X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3)))<=c_Finite__Set_Ofolding__image(X4,X7,X22,X16,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image_Oeq__fold)). 4.02/4.27 fof(fact_inf__sup__aci_I7_J, axiom, ![X29, X43, X13, X4]:(class_Lattices_Olattice(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X43),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X29))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X43),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I7_J)). 4.02/4.27 fof(fact_neg__less__divide__eq, axiom, ![X25, X26, X24, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X25),X24)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),c_Groups_Ozero__class_Ozero(X4))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__less__divide__eq)). 4.02/4.27 fof(fact_neg__le__divide__eq, axiom, ![X25, X26, X24, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),c_Groups_Ozero__class_Ozero(X4)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X25),X24)))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__le__divide__eq)). 4.02/4.27 fof(fact_zadd__zless__mono, axiom, ![X29, X157, X53, X275]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X157),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X275),X157)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),X29))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X275),X53))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__zless__mono)). 4.02/4.27 fof(fact_diff__less__mono, axiom, ![X10, X12, X11]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11),X10)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12),X10))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__less__mono)). 4.02/4.27 fof(fact_diff__less__mono2, axiom, ![X47, X5, X2]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X47),X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X47),X2)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X47)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__less__mono2)). 4.02/4.27 fof(fact_add__less__mono, axiom, ![X47, X107, X135, X46]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X107)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X135),X47)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),X47)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__mono)). 4.02/4.27 fof(fact_mult__le__mono, axiom, ![X47, X107, X135, X46]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),X47))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X46),X107)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X135),X47))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__mono)). 4.02/4.27 fof(fact_add__le__mono, axiom, ![X47, X107, X135, X46]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),X47))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X107)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X135),X47))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__le__mono)). 4.02/4.27 fof(fact_single__valuedD, axiom, ![X16, X17, X9, X18, X7, X4]:(c_Relation_Osingle__valued(X4,X7,X18)=>((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X9),X16)),X18))=>X17=X16)<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X9),X17)),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valuedD)). 4.02/4.27 fof(fact_fold1Set_Ointros, axiom, ![X9, X3, X26, X22, X4]:(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X4,X22,X26,X3),X9))=>(~(hBOOL(hAPP(hAPP(c_member(X4),X26),X3)))=>hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,X22,hAPP(hAPP(c_Set_Oinsert(X4),X26),X3)),X9)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1Set_Ointros)). 4.02/4.27 fof(fact_sorted__insort__key, axiom, ![X32, X9, X22, X7, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X7,X4),X22),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7,X4,X22),X9),X32)))<=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X7,X4),X22),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__insort__key)). 4.02/4.27 fof(fact_Powp__mono, axiom, ![X6, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X4,X3)),c_Predicate_OPowp(X4,X6)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Powp__mono)). 4.02/4.27 fof(fact_psubset__trans, axiom, ![X8, X6, X3, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X6),X8))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X3),X8)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubset__trans)). 4.02/4.27 fof(fact_subset__psubset__trans, axiom, ![X8, X6, X3, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X3),X8))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X6),X8)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__psubset__trans)). 4.02/4.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, axiom, ![X44, X10, X11, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X44))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X44))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J)). 4.02/4.27 fof(fact_zdiff__int, axiom, ![X2, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X2))=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5))=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),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__int)). 4.02/4.27 fof(fact_psubset__subset__trans, axiom, ![X8, X6, X3, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X8))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X3),X8)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubset__subset__trans)). 4.02/4.27 fof(fact_subset__trans, axiom, ![X8, X6, X3, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X8))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X8)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__trans)). 4.02/4.27 fof(fact_pred__nat__trancl__eq__le, axiom, ![X20, X21]:(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),X21),X20)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__nat__trancl__eq__le)). 4.02/4.27 fof(fact_DiffI, axiom, ![X6, X3, X24, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X24),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=~(hBOOL(hAPP(hAPP(c_member(X4),X24),X6))))<=hBOOL(hAPP(hAPP(c_member(X4),X24),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DiffI)). 4.02/4.27 fof(fact_butlast__take, axiom, ![X45, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))=>c_List_Obutlast(X4,hAPP(hAPP(c_List_Otake(X4),X5),X45))=hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast__take)). 4.02/4.27 fof(fact_mod__minus__cong, axiom, ![X111, X12, X11, X4]:(class_Divides_Oring__div(X4)=>(c_Divides_Odiv__class_Omod(X4,X111,X12)=c_Divides_Odiv__class_Omod(X4,X11,X12)=>c_Divides_Odiv__class_Omod(X4,hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11),X12)=c_Divides_Odiv__class_Omod(X4,hAPP(c_Groups_Ouminus__class_Ouminus(X4),X111),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__minus__cong)). 4.02/4.27 fof(fact_list__all2__appendI, axiom, ![X102, X24, X25, X26, X56, X7, X4]:(c_List_Olist__all2(X4,X7,X56,X26,X25)=>(c_List_Olist__all2(X4,X7,X56,X24,X102)=>c_List_Olist__all2(X4,X7,X56,hAPP(hAPP(c_List_Oappend(X4),X26),X24),hAPP(hAPP(c_List_Oappend(X7),X25),X102)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__appendI)). 4.02/4.27 fof(fact_mult__le__cancel1, axiom, ![X20, X21, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X20)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__cancel1)). 4.02/4.27 fof(fact_mult__le__cancel2, axiom, ![X20, X28, X21]:((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__eq(tc_Nat_Onat),X21),X20)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X28)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__cancel2)). 4.02/4.27 fof(fact_elem__le__sum, axiom, ![X144, X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),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)),X144)))<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X20),hAPP(c_List_Oset(tc_Nat_Onat),X144)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_elem__le__sum)). 4.02/4.27 fof(fact_upto_Osimps, axiom, ![X135, X46]:((c_List_Olist_ONil(tc_Int_Oint)=c_List_Oupto(X46,X135)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X46),X135))))&(c_List_Oupto(X46,X135)=hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X46),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X46),c_Groups_Oone__class_Oone(tc_Int_Oint)),X135))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X46),X135)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upto_Osimps)). 4.02/4.27 fof(fact_INF1__iff, axiom, ![X25, X6, X3, X7, X4]:(![X19]:(hBOOL(hAPP(hAPP(X6,X19),X25))<=hBOOL(hAPP(hAPP(c_member(X4),X19),X3)))<=>hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X3),X6),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF1__iff)). 4.02/4.27 fof(fact_atLeastLessThan__subset__iff, axiom, ![X102, X24, X25, X26, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X26),X25)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X24),X102)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),X26))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),X102))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X24),X26)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__subset__iff)). 4.02/4.27 fof(fact_insert__subset, axiom, ![X6, X3, X9, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))&hBOOL(hAPP(hAPP(c_member(X4),X9),X6)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3)),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__subset)). 4.02/4.27 fof(fact_mono__Field, axiom, ![X40, X18, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OField(X4),X18)),hAPP(c_Relation_OField(X4),X40)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),X40))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mono__Field)). 4.02/4.27 fof(fact_hd__drop__conv__nth, axiom, ![X5, X4, X45]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))=>hAPP(c_List_Ohd(X4),hAPP(hAPP(c_List_Odrop(X4),X5),X45))=hAPP(hAPP(c_List_Onth(X4),X45),X5))<=X45!=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__drop__conv__nth)). 4.02/4.27 fof(fact_transfer__int__nat__set__relations_I5_J, axiom, ![X6, X3]:(((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),X3)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X6)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X3),X6)))<=c_Nat__Transfer_Onat__set(X6))<=c_Nat__Transfer_Onat__set(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__relations_I5_J)). 4.02/4.27 fof(fact_insort__insert__insort, axiom, ![X32, X9, X4]:((~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32))))=>c_List_Olinorder__class_Oinsort__insert__key(X4,X4,c_COMBI(X4),X9,X32)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X9),X32))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__insert__insort)). 4.02/4.27 fof(fact_diff__diff__right, axiom, ![X46, X135, X107]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),X135))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X107)),X135)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X46),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X135),X107))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__diff__right)). 4.02/4.27 fof(fact_diff__add__assoc, axiom, ![X46, X135, X107]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),X135))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X135),X107))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X135)),X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__add__assoc)). 4.02/4.27 fof(fact_divide__less__0__iff, axiom, ![X25, X26, X4]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X25),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X26)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X25))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),X25)),c_Groups_Ozero__class_Ozero(X4))))<=class_Fields_Olinordered__field__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__less__0__iff)). 4.02/4.27 fof(fact_divide__le__0__iff, axiom, ![X25, X26, X4]:(class_Fields_Olinordered__field__inverse__zero(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),X25)),c_Groups_Ozero__class_Ozero(X4)))<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X25))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),c_Groups_Ozero__class_Ozero(X4))))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X26))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),c_Groups_Ozero__class_Ozero(X4))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__le__0__iff)). 4.02/4.27 fof(fact_Ints__diff, axiom, ![X25, X26, X4]:(((hBOOL(hAPP(hAPP(c_member(X4),X25),c_Int_Oring__1__class_OInts(X4)))=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X26),X25)),c_Int_Oring__1__class_OInts(X4))))<=hBOOL(hAPP(hAPP(c_member(X4),X26),c_Int_Oring__1__class_OInts(X4))))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__diff)). 4.02/4.27 fof(fact_Nats__mult, axiom, ![X25, X26, X4]:(class_Rings_Osemiring__1(X4)=>((hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X25)),c_Nat_Osemiring__1__class_ONats(X4)))<=hBOOL(hAPP(hAPP(c_member(X4),X25),c_Nat_Osemiring__1__class_ONats(X4))))<=hBOOL(hAPP(hAPP(c_member(X4),X26),c_Nat_Osemiring__1__class_ONats(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nats__mult)). 4.02/4.27 fof(fact_Ints__mult, axiom, ![X25, X26, X4]:(((hBOOL(hAPP(hAPP(c_member(X4),X25),c_Int_Oring__1__class_OInts(X4)))=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X25)),c_Int_Oring__1__class_OInts(X4))))<=hBOOL(hAPP(hAPP(c_member(X4),X26),c_Int_Oring__1__class_OInts(X4))))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__mult)). 4.02/4.27 fof(fact_lists_Osimps, axiom, ![X3, X26, X4]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X26),c_List_Olists(X4,X3)))<=>(?[X27, X233]:((X26=hAPP(hAPP(c_List_Olist_OCons(X4),X27),X233)&hBOOL(hAPP(hAPP(c_member(X4),X27),X3)))&hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X233),c_List_Olists(X4,X3))))|c_List_Olist_ONil(X4)=X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists_Osimps)). 4.02/4.27 fof(fact_setsum__reindex__id, axiom, ![X6, X22, X4, X7]:(class_Groups_Ocomm__monoid__add(X7)=>(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X7),c_Fun_Oid(X7)),hAPP(c_Set_Oimage(X4,X7,X22),X6))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X7),X22),X6)<=c_Fun_Oinj__on(X4,X7,X22,X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__reindex__id)). 4.02/4.27 fof(fact_setprod__reindex__id, axiom, ![X6, X22, X4, X7]:((c_Fun_Oinj__on(X4,X7,X22,X6)=>hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X7),c_Fun_Oid(X7)),hAPP(c_Set_Oimage(X4,X7,X22),X6)))<=class_Groups_Ocomm__monoid__mult(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__reindex__id)). 4.02/4.27 fof(fact_Nats__add, axiom, ![X25, X26, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X26),c_Nat_Osemiring__1__class_ONats(X4)))=>(hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X26),X25)),c_Nat_Osemiring__1__class_ONats(X4)))<=hBOOL(hAPP(hAPP(c_member(X4),X25),c_Nat_Osemiring__1__class_ONats(X4)))))<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nats__add)). 4.02/4.27 fof(fact_Ints__add, axiom, ![X25, X26, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X26),c_Int_Oring__1__class_OInts(X4)))=>(hBOOL(hAPP(hAPP(c_member(X4),X25),c_Int_Oring__1__class_OInts(X4)))=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X26),X25)),c_Int_Oring__1__class_OInts(X4)))))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__add)). 4.02/4.27 fof(fact_map__upds__apply__nontin, axiom, ![X31, X22, X7, X32, X9, X4]:(hAPP(c_Map_Omap__upds(X4,X7,X22,X32,X31),X9)=hAPP(X22,X9)<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__apply__nontin)). 4.02/4.27 fof(fact_disjoint__eq__subset__Compl, axiom, ![X6, X3, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_disjoint__eq__subset__Compl)). 4.02/4.27 fof(fact_sorted__many, axiom, ![X175, X43, X13, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X43))=>(c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X43),X175))=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X13),hAPP(hAPP(c_List_Olist_OCons(X4),X43),X175)))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__many)). 4.02/4.27 fof(fact_transfer__nat__int__set__relations_I5_J, axiom, ![X6, X3]:(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)),X3)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X6)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__relations_I5_J)). 4.02/4.27 fof(fact_zero__less__divide__iff, axiom, ![X25, X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),X25)))<=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X25),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),c_Groups_Ozero__class_Ozero(X4))))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X25))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X26)))))<=class_Fields_Olinordered__field__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__divide__iff)). 4.02/4.27 fof(fact_zero__le__divide__iff, axiom, ![X25, X26, X4]:(class_Fields_Olinordered__field__inverse__zero(X4)=>(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X25))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X26)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),c_Groups_Ozero__class_Ozero(X4)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),c_Groups_Ozero__class_Ozero(X4)))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),X25))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__divide__iff)). 4.02/4.27 fof(fact_last__conv__nth, axiom, ![X4, X45]:(c_List_Olist_ONil(X4)!=X45=>hAPP(hAPP(c_List_Onth(X4),X45),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_List_Olast(X4,X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__conv__nth)). 4.02/4.27 fof(fact_image__constant__conv, axiom, ![X24, X7, X4, X3]:((hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))=hAPP(c_Set_Oimage(X4,X7,hAPP(c_COMBK(X7,X4),X24)),X3)<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3)&(hAPP(c_Set_Oimage(X4,X7,hAPP(c_COMBK(X7,X4),X24)),X3)=c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__constant__conv)). 4.02/4.27 fof(fact_INT__constant, axiom, ![X24, X7, X4, X3]:((hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X3),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),X24))=X24<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3)&(c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X3),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),X24))<=X3=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__constant)). 4.02/4.27 fof(fact_DomainI, axiom, ![X18, X25, X26, X7, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X26),hAPP(c_Relation_ODomain(X4,X7),X18)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X26),X25)),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DomainI)). 4.02/4.27 fof(fact_nat__diff__split, axiom, ![X25, X26, X56]:(hBOOL(hAPP(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26),X25)))<=>(![X132]:(hBOOL(hAPP(X56,X132))<=X26=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X132))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),X25))=>hBOOL(hAPP(X56,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__diff__split)). 4.02/4.27 fof(fact_drop__Cons__number__of, axiom, ![X45, X13, X4, X1]:((hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45))=hAPP(hAPP(c_List_Odrop(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X45)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))&(hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)=hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Cons__number__of)). 4.02/4.27 fof(fact_nat__diff__split__asm, axiom, ![X25, X26, X56]:(~((?[X132]:(X26=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X132)&~(hBOOL(hAPP(X56,X132))))|(~(hBOOL(hAPP(X56,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),X25)))))<=>hBOOL(hAPP(X56,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__diff__split__asm)). 4.02/4.27 fof(fact_nonzero__abs__divide, axiom, ![X11, X12, X4]:((c_Groups_Ozero__class_Ozero(X4)!=X12=>hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X12))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),hAPP(c_Groups_Oabs__class_Oabs(X4),X12)))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__abs__divide)). 4.02/4.27 fof(fact_InterI, axiom, ![X3, X8, X4]:(![X241]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X241),X8))=>hBOOL(hAPP(hAPP(c_member(X4),X3),X241)))=>hBOOL(hAPP(hAPP(c_member(X4),X3),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_InterI)). 4.02/4.27 fof(fact_finite__Plus__UNIV__iff, axiom, ![X7, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))&hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X4,X7)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X4,X7),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Plus__UNIV__iff)). 4.02/4.27 fof(fact_atLeastAtMostSuc__conv, axiom, ![X20, X21]:(hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X21,X20))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X21,hAPP(c_Nat_OSuc,X20))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),hAPP(c_Nat_OSuc,X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastAtMostSuc__conv)). 4.02/4.27 fof(fact_card__image__le, axiom, ![X22, X7, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7),hAPP(c_Set_Oimage(X4,X7,X22),X3))),hAPP(c_Finite__Set_Ocard(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__image__le)). 4.02/4.27 fof(fact_finite__Prod__UNIV, axiom, ![X7, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X7)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X4,X7),tc_HOL_Obool))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Prod__UNIV)). 4.02/4.27 fof(fact_ivl__disj__int_I9_J, axiom, ![X115, X21, X60, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X60,X21)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X21),X115))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I9_J)). 4.02/4.27 fof(fact_ivl__disj__int_I15_J, axiom, ![X115, X21, X60, X4]:(class_Orderings_Oorder(X4)=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X60),X21)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X21,X115))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I15_J)). 4.02/4.27 fof(fact_minus__Min__eq__Max, axiom, ![X86, X4]:(class_Groups_Olinordered__ab__group__add(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X86))=>(c_Big__Operators_Olinorder__class_OMax(X4,hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),X86))=hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Big__Operators_Olinorder__class_OMin(X4,X86))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X86))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__Min__eq__Max)). 4.02/4.27 fof(fact_add__less__cancel__right, axiom, ![X25, X24, X26, X4]:(class_Groups_Oordered__ab__semigroup__add__imp__le(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X25))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X26),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X25),X24))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__cancel__right)). 4.02/4.27 fof(fact_minus__Max__eq__Min, axiom, ![X86, X4]:(class_Groups_Olinordered__ab__group__add(X4)=>((hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Big__Operators_Olinorder__class_OMax(X4,X86))=c_Big__Operators_Olinorder__class_OMin(X4,hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),X86))<=X86!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X86)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__Max__eq__Min)). 4.02/4.27 fof(fact_insert__image, axiom, ![X22, X7, X3, X9, X4]:(hAPP(c_Set_Oimage(X4,X7,X22),X3)=hAPP(hAPP(c_Set_Oinsert(X7),hAPP(X22,X9)),hAPP(c_Set_Oimage(X4,X7,X22),X3))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__image)). 4.02/4.27 fof(fact_image__constant, axiom, ![X24, X7, X3, X9, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X9),X3))=>hAPP(hAPP(c_Set_Oinsert(X7),X24),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))=hAPP(c_Set_Oimage(X4,X7,hAPP(c_COMBK(X7,X4),X24)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__constant)). 4.02/4.27 fof(fact_fold1__eq__fold__idem, axiom, ![X26, X3, X4]:(class_Lattices_Oab__semigroup__idem__mult(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Groups_Otimes__class_Otimes(X4)),X26),X3)=hAPP(c_Finite__Set_Ofold1(X4,c_Groups_Otimes__class_Otimes(X4)),hAPP(hAPP(c_Set_Oinsert(X4),X26),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__eq__fold__idem)). 4.02/4.27 fof(fact_Times__eq__cancel2, axiom, ![X6, X3, X7, X8, X9, X4]:((X6=X3<=>hAPP(hAPP(c_Product__Type_OSigma(X7,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X7),X8))=hAPP(hAPP(c_Product__Type_OSigma(X7,X4),X6),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X7),X8)))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X8))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Times__eq__cancel2)). 4.02/4.27 fof(fact_ran__restrictD, axiom, ![X3, X21, X7, X17, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X17),c_Map_Oran(X7,X4,c_Map_Orestrict__map(X7,X4,X21,X3))))=>?[X19]:(hAPP(c_Option_Ooption_OSome(X4),X17)=hAPP(X21,X19)&hBOOL(hAPP(hAPP(c_member(X7),X19),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ran__restrictD)). 4.02/4.27 fof(fact_Max__insert, axiom, ![X9, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X9),c_Big__Operators_Olinorder__class_OMax(X4,X3))=c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__insert)). 4.02/4.27 fof(fact_add__strict__right__mono, axiom, ![X10, X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10))))<=class_Groups_Oordered__cancel__ab__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__strict__right__mono)). 4.02/4.27 fof(fact_add__less__cancel__left, axiom, ![X25, X26, X24, X4]:(class_Groups_Oordered__ab__semigroup__add__imp__le(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X25))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X24),X26)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X24),X25))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__cancel__left)). 4.02/4.27 fof(fact_add__strict__left__mono, axiom, ![X10, X12, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X12))))<=class_Groups_Oordered__cancel__ab__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__strict__left__mono)). 4.02/4.27 fof(fact_add__le__cancel__right, axiom, ![X25, X24, X26, X4]:(class_Groups_Oordered__ab__semigroup__add__imp__le(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X26),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X25),X24)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__le__cancel__right)). 4.02/4.27 fof(fact_Sup__fin_Oinsert__idem, axiom, ![X9, X3, X4]:(class_Lattices_Olattice(X4)=>((hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X9),c_Big__Operators_Olattice__class_OSup__fin(X4,X3))=c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oinsert__idem)). 4.02/4.27 fof(fact_add__right__mono, axiom, ![X10, X12, X11, X4]:(class_Groups_Oordered__ab__semigroup__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__right__mono)). 4.02/4.27 fof(fact_add__le__cancel__left, axiom, ![X25, X26, X24, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),X25))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X24),X26)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X24),X25))))<=class_Groups_Oordered__ab__semigroup__add__imp__le(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__le__cancel__left)). 4.02/4.27 fof(fact_add__left__mono, axiom, ![X10, X12, X11, X4]:(class_Groups_Oordered__ab__semigroup__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X12))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__left__mono)). 4.02/4.27 fof(fact_power__Suc2, axiom, ![X5, X11, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(c_Nat_OSuc,X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)),X11)<=class_Groups_Omonoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__Suc2)). 4.02/4.27 fof(fact_in__lists__conv__set, axiom, ![X3, X32, X4]:(![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32))))<=>hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X32),c_List_Olists(X4,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__lists__conv__set)). 4.02/4.27 fof(fact_Min__insert, axiom, ![X9, X3, X4]:(class_Orderings_Olinorder(X4)=>((c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X9),c_Big__Operators_Olinorder__class_OMin(X4,X3))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__insert)). 4.02/4.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, axiom, ![X14, X13, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),hAPP(c_Nat_OSuc,X14))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),X14)),X13)<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J)). 4.02/4.27 fof(fact_remdups_Osimps_I2_J, axiom, ![X32, X9, X4]:((hAPP(hAPP(c_List_Olist_OCons(X4),X9),c_List_Oremdups(X4,X32))=c_List_Oremdups(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32))<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))))&(c_List_Oremdups(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32))=c_List_Oremdups(X4,X32)<=hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups_Osimps_I2_J)). 4.02/4.27 fof(fact_setprod__constant, axiom, ![X17, X3, X4, X7]:(class_Groups_Ocomm__monoid__mult(X7)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(hAPP(c_Power_Opower__class_Opower(X7),X17),hAPP(c_Finite__Set_Ocard(X4),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),hAPP(c_COMBK(X7,X4),X17)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__constant)). 4.02/4.27 fof(fact_distinct__conv__nth, axiom, ![X32, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X32))<=>![X42]:(![X139]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X139),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))=>(X42!=X139=>hAPP(hAPP(c_List_Onth(X4),X32),X42)!=hAPP(hAPP(c_List_Onth(X4),X32),X139)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__conv__nth)). 4.02/4.27 fof(fact_ivl__disj__int_I8_J, axiom, ![X115, X60, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X60),X115)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X115))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I8_J)). 4.02/4.27 fof(fact_Inf__fin_Oinsert__idem, axiom, ![X9, X3, X4]:(class_Lattices_Olattice(X4)=>((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3=>c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X9),c_Big__Operators_Olattice__class_OInf__fin(X4,X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oinsert__idem)). 4.02/4.27 fof(fact_set__update__memI, axiom, ![X9, X32, X4, X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))=>hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist__update(X4,X32),X20),X9))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__update__memI)). 4.02/4.27 fof(fact_minus__max__eq__min, axiom, ![X43, X13, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X13)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X43))=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),X43))<=class_Groups_Olinordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__max__eq__min)). 4.02/4.27 fof(fact_compl__sup, axiom, ![X43, X13, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X13)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X43))=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43))<=class_Lattices_Oboolean__algebra(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__sup)). 4.02/4.27 fof(fact_ivl__disj__int_I2_J, axiom, ![X115, X60, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X60)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X60),X115))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I2_J)). 4.02/4.27 fof(fact_listrel1__eq__len, axiom, ![X18, X31, X32, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)),c_List_Olistrel1(X4,X18)))=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__eq__len)). 4.02/4.27 fof(fact_minus__min__eq__max, axiom, ![X43, X13, X4]:(class_Groups_Olinordered__ab__group__add(X4)=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X13)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X43))=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),X43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__min__eq__max)). 4.02/4.27 fof(fact_compl__inf, axiom, ![X43, X13, X4]:(class_Lattices_Oboolean__algebra(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X13)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X43))=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__inf)). 4.02/4.27 fof(fact_less__diff__iff, axiom, ![X20, X21, X28]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21),X28)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X28))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X20)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X21))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__diff__iff)). 4.02/4.27 fof(fact_le__diff__iff, axiom, ![X20, X21, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X21))=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21),X28)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X28))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__diff__iff)). 4.02/4.27 fof(fact_range, axiom, ![X159, X107]:(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(X107),X159))),X107))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X107))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_range)). 4.02/4.27 fof(fact_card__psubset, axiom, ![X3, X6, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X3)),hAPP(c_Finite__Set_Ocard(X4),X6)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__psubset)). 4.02/4.27 fof(fact_minus__add__distrib, axiom, ![X12, X11, X4]:(hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12))<=class_Groups_Oab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__add__distrib)). 4.02/4.27 fof(fact_pos__divide__less__eq, axiom, ![X26, X25, X24, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X24))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X25),X24)),X26))))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__divide__less__eq)). 4.02/4.27 fof(fact_pos__divide__le__eq, axiom, ![X26, X25, X24, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X25),X24)),X26)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X24)))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__divide__le__eq)). 4.02/4.27 fof(fact_pos__less__divide__eq, axiom, ![X25, X26, X24, X4]:(class_Fields_Olinordered__field(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X24))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24)),X25))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X25),X24)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__less__divide__eq)). 4.02/4.27 fof(fact_map__add__dom__app__simps_I3_J, axiom, ![X206, X205, X7, X21, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X21),c_Map_Odom(X4,X7,X205))))=>hAPP(c_Map_Omap__add(X4,X7,X206,X205),X21)=hAPP(X206,X21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__dom__app__simps_I3_J)). 4.02/4.27 fof(fact_minus__add, axiom, ![X12, X11, X4]:(hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11))<=class_Groups_Ogroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__add)). 4.02/4.27 fof(fact_map__add__dom__app__simps_I2_J, axiom, ![X205, X206, X7, X21, X4]:(hAPP(X205,X21)=hAPP(c_Map_Omap__add(X4,X7,X206,X205),X21)<=~(hBOOL(hAPP(hAPP(c_member(X4),X21),c_Map_Odom(X4,X7,X206))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__dom__app__simps_I2_J)). 4.02/4.27 fof(fact_pos__le__divide__eq, axiom, ![X25, X26, X24, X4]:(class_Fields_Olinordered__field(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X24))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X24)),X25))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X25),X24)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__le__divide__eq)). 4.02/4.27 fof(fact_listrelp_Oequations_I2_J, axiom, ![X66, X67, X69, X70, X18, X4]:((hBOOL(hAPP(hAPP(X18,X70),X67))&c_List_Olistrelp(X4,X18,X69,X66))<=>c_List_Olistrelp(X4,X18,hAPP(hAPP(c_List_Olist_OCons(X4),X70),X69),hAPP(hAPP(c_List_Olist_OCons(X4),X67),X66))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrelp_Oequations_I2_J)). 4.02/4.27 fof(fact_inj__map, axiom, ![X22, X7, X4]:(c_Fun_Oinj__on(tc_List_Olist(X4),tc_List_Olist(X7),hAPP(c_List_Omap(X4,X7),X22),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)))<=>c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__map)). 4.02/4.27 fof(fact_length__remove1, axiom, ![X32, X9, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Oremove1(X4,X9,X32)))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Oremove1(X4,X9,X32))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__remove1)). 4.02/4.27 fof(fact_setsum__SucD, axiom, ![X20, X3, X22, X4]:(?[X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X22,X19)))&hBOOL(hAPP(hAPP(c_member(X4),X19),X3)))<=hAPP(c_Nat_OSuc,X20)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X22),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__SucD)). 4.02/4.27 fof(fact_times__divide__eq__right, axiom, ![X10, X12, X11, X4]:(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)),X10)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X12),X10))<=class_Rings_Odivision__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_times__divide__eq__right)). 4.02/4.27 fof(fact_abs__mult__pos, axiom, ![X43, X13, X4]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X43)),X13)=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X43),X13))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X13)))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__mult__pos)). 4.02/4.27 fof(fact_fun__left__comm_Ofold__graph__fold, axiom, ![X16, X3, X22, X7, X4]:(c_Finite__Set_Ofun__left__comm(X4,X7,X22)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X7,X22,X16,X3),hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),X16),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__graph__fold)). 4.02/4.27 fof(fact_UNION__empty__conv_I2_J, axiom, ![X6, X3, X4, X7]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),X6)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=>![X19]:(hBOOL(hAPP(hAPP(c_member(X7),X19),X3))=>hAPP(X6,X19)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNION__empty__conv_I2_J)). 4.02/4.27 fof(fact_inf__sup__aci_I2_J, axiom, ![X29, X43, X13, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43)),X29)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X43),X29))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I2_J)). 4.02/4.27 fof(fact_power__commutes, axiom, ![X5, X11, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)),X11)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5))<=class_Groups_Omonoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__commutes)). 4.02/4.27 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J, axiom, ![X10, X12, X11, X4]:(class_Groups_Oab__semigroup__mult(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)),X10)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ab__semigroup__mult__class_Omult__ac_I1_J)). 4.02/4.27 fof(fact_UNION__empty__conv_I1_J, axiom, ![X6, X3, X7, X4]:(![X19]:(hAPP(X6,X19)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=hBOOL(hAPP(hAPP(c_member(X7),X19),X3)))<=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),X6)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNION__empty__conv_I1_J)). 4.02/4.27 fof(fact_semiring__1__class_Oof__nat__code, axiom, ![X20, X4]:(class_Rings_Osemiring__1(X4)=>c_Nat_Osemiring__1__class_Oof__nat__aux(X4,hAPP(hAPP(c_COMBC(X4,X4,X4),c_Groups_Oplus__class_Oplus(X4)),c_Groups_Oone__class_Oone(X4)),X20,c_Groups_Ozero__class_Ozero(X4))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_semiring__1__class_Oof__nat__code)). 4.02/4.27 fof(fact_doubleton__eq__iff, axiom, ![X102, X24, X25, X26, X4]:(hAPP(hAPP(c_Set_Oinsert(X4),X26),hAPP(hAPP(c_Set_Oinsert(X4),X25),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=hAPP(hAPP(c_Set_Oinsert(X4),X24),hAPP(hAPP(c_Set_Oinsert(X4),X102),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=>((X26=X102&X24=X25)|(X25=X102&X24=X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_doubleton__eq__iff)). 4.02/4.27 fof(fact_INTER__UNIV__conv_I2_J, axiom, ![X6, X3, X4, X7]:(![X19]:(hAPP(X6,X19)=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))<=hBOOL(hAPP(hAPP(c_member(X7),X19),X3)))<=>c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INTER__UNIV__conv_I2_J)). 4.02/4.27 fof(fact_zmod__zminus1__eq__if, axiom, ![X12, X11]:((c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11),X12)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12))<=c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)!=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),X11),X12)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<=c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zminus1__eq__if)). 4.02/4.27 fof(fact_sup__assoc, axiom, ![X29, X43, X13, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43)),X29)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X43),X29))<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__assoc)). 4.02/4.27 fof(fact_inf__sup__aci_I6_J, axiom, ![X29, X43, X13, X4]:(class_Lattices_Olattice(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43)),X29)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X43),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I6_J)). 4.02/4.27 fof(fact_inf__assoc, axiom, ![X29, X43, X13, X4]:(class_Lattices_Osemilattice__inf(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X43),X29))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43)),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__assoc)). 4.02/4.27 fof(fact_INTER__UNIV__conv_I1_J, axiom, ![X6, X3, X7, X4]:(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X3),X6)<=>![X19]:(hBOOL(hAPP(hAPP(c_member(X7),X19),X3))=>c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(X6,X19))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INTER__UNIV__conv_I1_J)). 4.02/4.27 fof(fact_lists__mono, axiom, ![X6, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),c_List_Olists(X4,X3)),c_List_Olists(X4,X6)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__mono)). 4.02/4.27 fof(fact_listsp__mono, axiom, ![X6, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),c_List_Olistsp(X4,X3)),c_List_Olistsp(X4,X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp__mono)). 4.02/4.27 fof(fact_takeWhile__tail, axiom, ![X60, X32, X4, X9, X56]:(c_List_OtakeWhile(X4,X56,X32)=c_List_OtakeWhile(X4,X56,hAPP(hAPP(c_List_Oappend(X4),X32),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X60)))<=~(hBOOL(hAPP(X56,X9)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__tail)). 4.02/4.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, axiom, ![X89, X90, X91, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X90),X89))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X91),X90)),X89)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J)). 4.02/4.27 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, ![X10, X12, X11, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),X10)<=class_Groups_Oab__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ab__semigroup__add__class_Oadd__ac_I1_J)). 4.02/4.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, axiom, ![X10, X12, X11, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X10))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J)). 4.02/4.27 fof(fact_filter__insort__triv, axiom, ![X32, X22, X4, X9, X56, X7]:(class_Orderings_Olinorder(X7)=>(~(hBOOL(hAPP(X56,X9)))=>hAPP(c_List_Ofilter(X4,X56),X32)=hAPP(c_List_Ofilter(X4,X56),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X7,X22),X9),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__insort__triv)). 4.02/4.27 fof(fact_frac__eq__eq, axiom, ![X23, X9, X16, X17, X4]:(class_Fields_Ofield(X4)=>(((hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X9),X17)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X23),X16)<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X23),X17)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X9),X16))<=c_Groups_Ozero__class_Ozero(X4)!=X16)<=c_Groups_Ozero__class_Ozero(X4)!=X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_frac__eq__eq)). 4.02/4.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, axiom, ![X14, X15, X13, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X14))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),X15)),X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J)). 4.02/4.27 fof(fact_power__mult, axiom, ![X5, X2, X11, X4]:(class_Groups_Omonoid__mult(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X2)),X5)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__mult)). 4.02/4.28 fof(fact_abs__div__pos, axiom, ![X13, X43, X4]:(class_Fields_Olinordered__field__inverse__zero(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X43))=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X13)),X43)=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__div__pos)). 4.02/4.28 fof(fact_InterD, axiom, ![X156, X8, X3, X4]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X156),X8))=>hBOOL(hAPP(hAPP(c_member(X4),X3),X156)))<=hBOOL(hAPP(hAPP(c_member(X4),X3),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_InterD)). 4.02/4.28 fof(fact_min__max_OInf__fin_Oin__idem, axiom, ![X9, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_member(X4),X9),X3))=>c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X3)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X9),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X3))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oin__idem)). 4.02/4.28 fof(fact_min__max_OSup__fin_Oin__idem, axiom, ![X9, X3, X4]:(((c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X3)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X9),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X3))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oin__idem)). 4.02/4.28 fof(fact_folding__image__simple_Oeq__fold__g, axiom, ![X3, X87, X76, X16, X22, X7, X4]:(c_Finite__Set_Ofolding__image__simple(X4,X7,X22,X16,X76,X87)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3))=>hAPP(X87,X3)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X7,X22),X76),X16),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Oeq__fold__g)). 4.02/4.28 fof(fact_add__eq__if, axiom, ![X5, X2]:((X5=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X5)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2)&(X2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X5)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__eq__if)). 4.02/4.28 fof(fact_in__set__remove1, axiom, ![X32, X4, X25, X26]:((hBOOL(hAPP(hAPP(c_member(X4),X26),hAPP(c_List_Oset(X4),c_List_Oremove1(X4,X25,X32))))<=>hBOOL(hAPP(hAPP(c_member(X4),X26),hAPP(c_List_Oset(X4),X32))))<=X26!=X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__remove1)). 4.02/4.28 fof(fact_SUP1__iff, axiom, ![X25, X6, X3, X7, X4]:(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),X3),X6),X25))<=>?[X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))&hBOOL(hAPP(hAPP(X6,X19),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP1__iff)). 4.02/4.28 fof(fact_union__fold__insert, axiom, ![X6, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)=hAPP(hAPP(c_Finite__Set_Ofold(X4,tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4)),X6),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_union__fold__insert)). 4.02/4.28 fof(fact_ivl__disj__int_I5_J, axiom, ![X115, X60, X4]:(class_Orderings_Oorder(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X60,X115)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X115))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I5_J)). 4.02/4.28 fof(fact_number__of__diff, axiom, ![X53, X1, X4]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X53))=hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X53))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__diff)). 4.02/4.28 fof(fact_inf2I, axiom, ![X7, X4, X6, X17, X9, X3]:((hBOOL(hAPP(hAPP(X6,X9),X17))=>hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),X3),X6),X9),X17)))<=hBOOL(hAPP(hAPP(X3,X9),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf2I)). 4.02/4.28 fof(fact_subset__insert, axiom, ![X6, X3, X9, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X9),X6)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__insert)). 4.02/4.28 fof(fact_ivl__disj__int_I6_J, axiom, ![X115, X60, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X60,X115)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X115))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I6_J)). 4.02/4.28 fof(fact_Inf__less__iff, axiom, ![X26, X86, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Complete__Lattice_OInf__class_OInf(X4,X86)),X26))<=>?[X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X19),X26))&hBOOL(hAPP(hAPP(c_member(X4),X19),X86))))<=(class_Complete__Lattice_Ocomplete__lattice(X4)&class_Orderings_Olinorder(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__less__iff)). 4.02/4.28 fof(fact_less__Sup__iff, axiom, ![X86, X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),c_Complete__Lattice_OSup__class_OSup(X4,X86)))<=>?[X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X19))&hBOOL(hAPP(hAPP(c_member(X4),X19),X86))))<=(class_Orderings_Olinorder(X4)&class_Complete__Lattice_Ocomplete__lattice(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Sup__iff)). 4.02/4.28 fof(fact_insort__remove1, axiom, ![X32, X26, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_member(X4),X26),hAPP(c_List_Oset(X4),X32)))=>(c_List_Olinorder__class_Osorted(X4,X32)=>hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X26),c_List_Oremove1(X4,X26,X32))=X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__remove1)). 4.02/4.28 fof(fact_ivl__disj__int_I7_J, axiom, ![X115, X60, X4]:(class_Orderings_Oorder(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X60,X115)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X115))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I7_J)). 4.02/4.28 fof(fact_fun__left__comm_Ofun__left__comm, axiom, ![X16, X17, X9, X22, X7, X4]:(hAPP(hAPP(X22,X9),hAPP(hAPP(X22,X17),X16))=hAPP(hAPP(X22,X17),hAPP(hAPP(X22,X9),X16))<=c_Finite__Set_Ofun__left__comm(X4,X7,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofun__left__comm)). 4.02/4.28 fof(fact_ivl__disj__int_I4_J, axiom, ![X115, X60, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X60)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X60,X115))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I4_J)). 4.02/4.28 fof(fact_Max__eqI, axiom, ![X9, X3, X4]:(class_Orderings_Olinorder(X4)=>(((c_Big__Operators_Olinorder__class_OMax(X4,X3)=X9<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))<=![X34]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X34),X9))<=hBOOL(hAPP(hAPP(c_member(X4),X34),X3))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__eqI)). 4.02/4.28 fof(fact_ivl__disj__int_I3_J, axiom, ![X115, X60, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X60)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X60,X115))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I3_J)). 4.02/4.28 fof(fact_of__nat__mult, axiom, ![X5, X2, X4]:(class_Rings_Osemiring__1(X4)=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__mult)). 4.02/4.28 fof(fact_card__insert__if, axiom, ![X9, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))=>hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X4),X3))=hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3)))&(hBOOL(hAPP(hAPP(c_member(X4),X9),X3))=>hAPP(c_Finite__Set_Ocard(X4),X3)=hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__insert__if)). 4.02/4.28 fof(fact_ivl__disj__int_I1_J, axiom, ![X115, X60, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X60)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X60,X115))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I1_J)). 4.02/4.28 fof(fact_Min__eqI, axiom, ![X9, X3, X4]:((((X9=c_Big__Operators_Olinorder__class_OMin(X4,X3)<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))<=![X34]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X34))<=hBOOL(hAPP(hAPP(c_member(X4),X34),X3))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__eqI)). 4.02/4.28 fof(fact_mod__diff__left__eq, axiom, ![X10, X12, X11, X4]:(class_Divides_Oring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X12),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),c_Divides_Odiv__class_Omod(X4,X11,X10)),X12),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__diff__left__eq)). 4.02/4.28 fof(fact_of__nat__add, axiom, ![X5, X2, X4]:(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X5))<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__add)). 4.02/4.28 fof(fact_IntI, axiom, ![X6, X3, X24, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X24),X3))=>(hBOOL(hAPP(hAPP(c_member(X4),X24),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=hBOOL(hAPP(hAPP(c_member(X4),X24),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_IntI)). 4.02/4.28 fof(fact_zmod__simps_I4_J, axiom, ![X12, X10, X11, X4]:(c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Divides_Odiv__class_Omod(X4,X11,X10)),X12),X10)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__simps_I4_J)). 4.02/4.28 fof(fact_mod__add__left__eq, axiom, ![X10, X12, X11, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Divides_Odiv__class_Omod(X4,X11,X10)),X12),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__left__eq)). 4.02/4.28 fof(fact_number__of__mult, axiom, ![X53, X1, X4]:(class_Int_Onumber__ring(X4)=>hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X53))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X53))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__mult)). 4.02/4.28 fof(fact_mod__mult__right__eq, axiom, ![X10, X12, X11, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),c_Divides_Odiv__class_Omod(X4,X12,X10)),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__right__eq)). 4.02/4.28 fof(fact_abs__power__minus, axiom, ![X5, X11, X4]:(hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5))=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)),X5))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__power__minus)). 4.02/4.28 fof(fact_lessThan__strict__subset__iff, axiom, ![X20, X21, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X21),X20))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X21)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X20))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__strict__subset__iff)). 4.02/4.28 fof(fact_greaterThan__subset__iff, axiom, ![X17, X9, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X9)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X17)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X17),X9)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThan__subset__iff)). 4.02/4.28 fof(fact_mod__add__right__eq, axiom, ![X10, X12, X11, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),c_Divides_Odiv__class_Omod(X4,X12,X10)),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__right__eq)). 4.02/4.28 fof(fact_mod__diff__right__eq, axiom, ![X10, X12, X11, X4]:(class_Divides_Oring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X12),X10)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),c_Divides_Odiv__class_Omod(X4,X12,X10)),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__diff__right__eq)). 4.02/4.28 fof(fact_unique__quotient, axiom, ![X212, X213, X101, X14, X12, X11]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X12),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X14),X101)))=>((X14=X213<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X12)<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X12),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X213),X212))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_unique__quotient)). 4.02/4.28 fof(fact_abs__divide, axiom, ![X12, X11, X4]:(class_Fields_Olinordered__field__inverse__zero(X4)=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),hAPP(c_Groups_Oabs__class_Oabs(X4),X12))=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__divide)). 4.02/4.28 fof(fact_lessThan__subset__iff, axiom, ![X17, X9, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X17))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X9)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__subset__iff)). 4.02/4.28 fof(fact_atMost__subset__iff, axiom, ![X17, X9, X4]:(class_Orderings_Oorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X17))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X9)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atMost__subset__iff)). 4.02/4.28 fof(fact_atLeast__subset__iff, axiom, ![X17, X9, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X9)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X17)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X17),X9)))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast__subset__iff)). 4.02/4.28 fof(fact_listsum__append, axiom, ![X59, X45, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_List_Omonoid__add__class_Olistsum(X4),X45)),hAPP(c_List_Omonoid__add__class_Olistsum(X4),X59))=hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Oappend(X4),X45),X59))<=class_Groups_Omonoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__append)). 4.02/4.28 fof(fact_unique__remainder, axiom, ![X212, X213, X101, X14, X12, X11]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X12),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X14),X101)))=>((X12!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>X101=X212)<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X12),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X213),X212))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_unique__remainder)). 4.02/4.28 fof(fact_div__pos__pos, axiom, ![X12, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12)=hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X11,X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__pos__pos)). 4.02/4.28 fof(fact_div__neg__pos, axiom, ![X12, X11]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12)=hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X11,X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__neg__pos)). 4.02/4.28 fof(fact_abs__mult, axiom, ![X12, X11, X4]:(class_Rings_Olinordered__idom(X4)=>hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),hAPP(c_Groups_Oabs__class_Oabs(X4),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__mult)). 4.02/4.28 fof(fact_number__of__add, axiom, ![X53, X1, X4]:(hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X53))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X53))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__add)). 4.02/4.28 fof(fact_of__int__add, axiom, ![X29, X53, X4]:(class_Rings_Oring__1(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X53)),hAPP(c_Int_Oring__1__class_Oof__int(X4),X29))=hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__add)). 4.02/4.28 fof(fact_acc__subset, axiom, ![X98, X99, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Wellfounded_Oacc(X4,X98)),c_Wellfounded_Oacc(X4,X99)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X99),X98))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acc__subset)). 4.02/4.28 fof(fact_accp__subset, axiom, ![X98, X99, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X99),X98))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Wellfounded_Oaccp(X4,X98)),c_Wellfounded_Oaccp(X4,X99)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_accp__subset)). 4.02/4.28 fof(fact_ivl__disj__int_I14_J, axiom, ![X115, X21, X60, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X60,X21)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X21,X115))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I14_J)). 4.02/4.28 fof(fact_ivl__disj__int_I10_J, axiom, ![X115, X21, X60, X4]:(class_Orderings_Oorder(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X60,X21)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X21,X115))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I10_J)). 4.02/4.28 fof(fact_of__int__diff, axiom, ![X29, X53, X4]:(hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X53),X29))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X53)),hAPP(c_Int_Oring__1__class_Oof__int(X4),X29))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__diff)). 4.02/4.28 fof(fact_minus1__divide, axiom, ![X13, X4]:((class_Fields_Ofield__inverse__zero(X4)&class_Int_Onumber__ring(X4))=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),c_Groups_Oone__class_Oone(X4)),X13))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin)),X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus1__divide)). 4.02/4.28 fof(fact_of__int__mult, axiom, ![X29, X53, X4]:(hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),X29))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X53)),hAPP(c_Int_Oring__1__class_Oof__int(X4),X29))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__mult)). 4.02/4.28 fof(fact_ivl__disj__int_I16_J, axiom, ![X115, X21, X60, X4]:(class_Orderings_Oorder(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X60,X21)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X21,X115))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I16_J)). 4.02/4.28 fof(fact_ivl__disj__int_I12_J, axiom, ![X115, X21, X60, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X60,X21)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X21,X115))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I12_J)). 4.02/4.28 fof(fact_ivl__disj__int_I13_J, axiom, ![X115, X21, X60, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X60,X21)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X21,X115))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ivl__disj__int_I13_J)). 4.02/4.28 fof(fact_Inf__le__Sup, axiom, ![X3, X4]:(class_Lattices_Olattice(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Big__Operators_Olattice__class_OInf__fin(X4,X3)),c_Big__Operators_Olattice__class_OSup__fin(X4,X3)))<=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__le__Sup)). 4.02/4.28 fof(fact_setprod__zero, axiom, ![X22, X3, X4, X7]:(class_Rings_Ocomm__semiring__1(X7)=>((c_Groups_Ozero__class_Ozero(X7)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),X3)<=?[X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))&c_Groups_Ozero__class_Ozero(X7)=hAPP(X22,X19)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__zero)). 4.02/4.28 fof(fact_mult__right__less__imp__less, axiom, ![X12, X10, X11, X4]:(class_Rings_Olinordered__semiring(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__right__less__imp__less)). 4.02/4.28 fof(fact_mult__less__imp__less__right, axiom, ![X12, X10, X11, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10))))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__imp__less__right)). 4.02/4.28 fof(fact_mult__left__less__imp__less, axiom, ![X12, X11, X10, X4]:(class_Rings_Olinordered__semiring(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__less__imp__less)). 4.02/4.28 fof(fact_in__set__conv__nth, axiom, ![X32, X9, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))<=>?[X42]:(X9=hAPP(hAPP(c_List_Onth(X4),X32),X42)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__conv__nth)). 4.02/4.28 fof(fact_pos__imp__zdiv__neg__iff, axiom, ![X26, X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26),X25)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__imp__zdiv__neg__iff)). 4.02/4.28 fof(fact_neg__imp__zdiv__neg__iff, axiom, ![X26, X25]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),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),X26),X25)),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)),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__imp__zdiv__neg__iff)). 4.02/4.28 fof(fact_mult__less__imp__less__left, axiom, ![X12, X11, X10, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__imp__less__left)). 4.02/4.28 fof(fact_mult__right__le__imp__le, axiom, ![X12, X10, X11, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10))))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__right__le__imp__le)). 4.02/4.28 fof(fact_div__nonneg__neg__le0, axiom, ![X12, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),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),X11),X12)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__nonneg__neg__le0)). 4.02/4.28 fof(fact_div__nonpos__pos__le0, axiom, ![X12, X11]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__nonpos__pos__le0)). 4.02/4.28 fof(fact_nat__0__less__mult__iff, axiom, ![X20, X21]:(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),X21),X20)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__0__less__mult__iff)). 4.02/4.28 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, axiom, ![X43, X13]:((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),X13),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(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J)). 4.02/4.28 fof(fact_mult__left__le__imp__le, axiom, ![X12, X11, X10, X4]:(class_Rings_Olinordered__semiring__strict(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X12))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__le__imp__le)). 4.02/4.28 fof(fact_mult__less__cancel__left__neg, axiom, ![X25, X26, X24, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),c_Groups_Ozero__class_Ozero(X4)))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X24),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X24),X25)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X25),X26))))<=class_Rings_Olinordered__ring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__less__cancel__left__neg)). 4.02/4.28 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, axiom, ![X43, X13]:((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),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(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J)). 4.02/4.28 fof(fact_pos__imp__zdiv__nonneg__iff, axiom, ![X26, X25]:((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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26),X25))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__imp__zdiv__nonneg__iff)). 4.02/4.28 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J, axiom, ![X43, X13]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X43))=>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),X13),X43))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Otransfer__nat__int__function__closures_I1_J)). 4.02/4.28 fof(fact_neg__imp__zdiv__nonneg__iff, axiom, ![X26, X25]:((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),X26),X25)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__imp__zdiv__nonneg__iff)). 4.02/4.28 fof(fact_enum__all__option__def, axiom, ![X56, X4]:(class_Enum_Oenum(X4)=>((hBOOL(hAPP(X56,c_Option_Ooption_ONone(X4)))&hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X4),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X4),tc_HOL_Obool,X4),X56),c_Option_Ooption_OSome(X4)))))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X4)),X56)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__all__option__def)). 4.02/4.28 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H, axiom, ![X26, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Set_Oinsert(X4),X26),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omin(X4)),X26),X3))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Oeq__fold__idem_H)). 4.02/4.28 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H, axiom, ![X26, X3, X4]:((hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omax(X4)),X26),X3)=c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Set_Oinsert(X4),X26),X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Oeq__fold__idem_H)). 4.02/4.28 fof(fact_mod__mult__self2, axiom, ![X10, X12, X11, X4]:(c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X10)),X12)=c_Divides_Odiv__class_Omod(X4,X11,X12)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self2)). 4.02/4.28 fof(fact_add__strict__increasing2, axiom, ![X10, X12, X11, X4]:(class_Groups_Oordered__comm__monoid__add(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__strict__increasing2)). 4.02/4.28 fof(fact_add__strict__increasing, axiom, ![X10, X12, X11, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))<=class_Groups_Oordered__comm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__strict__increasing)). 4.02/4.28 fof(fact_pos__add__strict, axiom, ![X10, X12, X11, X4]:(class_Rings_Olinordered__semidom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X10))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__add__strict)). 4.02/4.28 fof(fact_mod__mult__self1, axiom, ![X12, X10, X11, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X10),X12)),X12)=c_Divides_Odiv__class_Omod(X4,X11,X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self1)). 4.02/4.28 fof(fact_list__all2__dropI, axiom, ![X20, X108, X109, X56, X7, X4]:(c_List_Olist__all2(X4,X7,X56,hAPP(hAPP(c_List_Odrop(X4),X20),X109),hAPP(hAPP(c_List_Odrop(X7),X20),X108))<=c_List_Olist__all2(X4,X7,X56,X109,X108)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__dropI)). 4.02/4.28 fof(fact_list__all2__takeI, axiom, ![X20, X31, X32, X56, X7, X4]:(c_List_Olist__all2(X4,X7,X56,hAPP(hAPP(c_List_Otake(X4),X20),X32),hAPP(hAPP(c_List_Otake(X7),X20),X31))<=c_List_Olist__all2(X4,X7,X56,X32,X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__takeI)). 4.02/4.28 fof(fact_add__increasing, axiom, ![X10, X12, X11, X4]:(class_Groups_Oordered__comm__monoid__add(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X10)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__increasing)). 4.02/4.28 fof(fact_add__increasing2, axiom, ![X11, X12, X10, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X10))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)))))<=class_Groups_Oordered__comm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__increasing2)). 4.02/4.28 fof(fact_listsp__infI, axiom, ![X6, X60, X3, X4]:(hBOOL(hAPP(c_List_Olistsp(X4,X3),X60))=>(hBOOL(hAPP(c_List_Olistsp(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)),X60))<=hBOOL(hAPP(c_List_Olistsp(X4,X6),X60)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp__infI)). 4.02/4.28 fof(fact_finite__UNIV__card__ge__0, axiom, ![X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UNIV__card__ge__0)). 4.02/4.28 fof(fact_power__less__imp__less__exp, axiom, ![X5, X2, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X5))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)))))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__less__imp__less__exp)). 4.02/4.28 fof(fact_min__max_Oinf__assoc, axiom, ![X29, X43, X13, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X43),X29))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),X43)),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__assoc)). 4.02/4.28 fof(fact_power__le__imp__le__exp, axiom, ![X5, X2, X11, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X5)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X11)))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__le__imp__le__exp)). 4.02/4.28 fof(fact_takeWhile__nth, axiom, ![X32, X56, X4, X38]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X38),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X56,X32))))=>hAPP(hAPP(c_List_Onth(X4),X32),X38)=hAPP(hAPP(c_List_Onth(X4),c_List_OtakeWhile(X4,X56,X32)),X38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__nth)). 4.02/4.28 fof(fact_min__max_Osup__assoc, axiom, ![X29, X43, X13, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X43),X29))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),X43)),X29)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__assoc)). 4.02/4.28 fof(fact_card__insert__le, axiom, ![X9, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X3)),hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__insert__le)). 4.02/4.28 fof(fact_setsum__eq__0__iff, axiom, ![X22, X87, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X87))=>(![X19]:(hAPP(X22,X19)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<=hBOOL(hAPP(hAPP(c_member(X4),X19),X87)))<=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X22),X87))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__eq__0__iff)). 4.02/4.28 fof(fact_setprod__eq__1__iff, axiom, ![X22, X87, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X87))=>(![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X87))=>c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(X22,X19))<=>c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,tc_Nat_Onat),X22),X87))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__eq__1__iff)). 4.02/4.28 fof(fact_fun__upds__append__drop, axiom, ![X30, X21, X31, X7, X32, X4]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31)=>c_Map_Omap__upds(X4,X7,X21,X32,X31)=c_Map_Omap__upds(X4,X7,X21,hAPP(hAPP(c_List_Oappend(X4),X32),X30),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upds__append__drop)). 4.02/4.28 fof(fact_fun__upds__append2__drop, axiom, ![X30, X21, X31, X7, X32, X4]:(c_Map_Omap__upds(X4,X7,X21,X32,X31)=c_Map_Omap__upds(X4,X7,X21,X32,hAPP(hAPP(c_List_Oappend(X7),X31),X30))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upds__append2__drop)). 4.02/4.28 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J, axiom, ![X43, X13]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))=>(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,X13,X43)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Otransfer__nat__int__function__closures_I2_J)). 4.02/4.28 fof(conj_1, hypothesis, c_Com_OWT__bodies, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_1)). 4.02/4.28 fof(fact_sort__key__simps_I2_J, axiom, ![X32, X9, X22, X4, X7]:(class_Orderings_Olinorder(X7)=>hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X7,X22),X9),c_List_Olinorder__class_Osort__key(X4,X7,X22,X32))=c_List_Olinorder__class_Osort__key(X4,X7,X22,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sort__key__simps_I2_J)). 4.02/4.28 fof(fact_sublist__singleton, axiom, ![X9, X4, X3]:((~(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))=>c_List_Osublist(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X9),c_List_Olist_ONil(X4)),X3)=c_List_Olist_ONil(X4))&(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))=>hAPP(hAPP(c_List_Olist_OCons(X4),X9),c_List_Olist_ONil(X4))=c_List_Osublist(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X9),c_List_Olist_ONil(X4)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__singleton)). 4.02/4.28 fof(fact_INF__leI, axiom, ![X54, X3, X37, X4, X7]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7),X3),X54)),hAPP(X54,X37)))<=hBOOL(hAPP(hAPP(c_member(X4),X37),X3)))<=class_Complete__Lattice_Ocomplete__lattice(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__leI)). 4.02/4.28 fof(fact_nth__mem, axiom, ![X32, X4, X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_List_Onth(X4),X32),X20)),hAPP(c_List_Oset(X4),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__mem)). 4.02/4.28 fof(fact_elem__le__listsum__nat, axiom, ![X309, X107]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X309)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X309),X107)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X309)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_elem__le__listsum__nat)). 4.02/4.28 fof(fact_Inter__lower, axiom, ![X3, X6, X4]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X6),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X3)),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__lower)). 4.02/4.28 fof(fact_Union__upper, axiom, ![X3, X6, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X3)))<=hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X6),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__upper)). 4.02/4.28 fof(fact_le__SUPI, axiom, ![X54, X3, X37, X4, X7]:(class_Complete__Lattice_Ocomplete__lattice(X7)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(X54,X37)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X7),X3),X54)))<=hBOOL(hAPP(hAPP(c_member(X4),X37),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__SUPI)). 4.02/4.28 fof(fact_power__gt1, axiom, ![X5, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(c_Nat_OSuc,X5))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X11)))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__gt1)). 4.02/4.28 fof(fact_finite__cartesian__productD1, axiom, ![X6, X3, X7, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))<=c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))!=X6)<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__cartesian__productD1)). 4.02/4.28 fof(fact_finite__cartesian__productD2, axiom, ![X6, X3, X7, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),X6))))=>(X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__cartesian__productD2)). 4.02/4.28 fof(fact_Id__onE, axiom, ![X3, X24, X4]:(~(![X19]:(X24!=hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X19)<=hBOOL(hAPP(hAPP(c_member(X4),X19),X3))))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X24),c_Relation_OId__on(X4,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__onE)). 4.02/4.28 fof(fact_pos__imp__zdiv__pos__iff, axiom, ![X37, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X28))=>(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),X37),X28)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X28),X37)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__imp__zdiv__pos__iff)). 4.02/4.28 fof(fact_power__less__imp__less__base, axiom, ![X12, X5, X11, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),X5))))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__less__imp__less__base)). 4.02/4.28 fof(fact_finite__map__freshness, axiom, ![X22, X7, X4]:((~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))=>?[X19]:c_Option_Ooption_ONone(X7)=hAPP(X22,X19))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Map_Odom(X4,X7,X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__map__freshness)). 4.02/4.28 fof(fact_inj__on__diff__nat, axiom, ![X28, X176]:(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)),X28),X176)<=![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X19))<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X19),X176)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__diff__nat)). 4.02/4.28 fof(fact_length__insort, axiom, ![X32, X9, X22, X4, X7]:(class_Orderings_Olinorder(X7)=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X7,X22),X9),X32))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__insort)). 4.02/4.28 fof(fact_lists__accI, axiom, ![X18, X32, X4]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X32),c_Wellfounded_Oacc(tc_List_Olist(X4),c_List_Olistrel1(X4,X18))))=>hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X32),c_List_Olists(X4,c_Wellfounded_Oacc(X4,X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__accI)). 4.02/4.28 fof(fact_less__add__eq__less, axiom, ![X5, X2, X47, X107]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X107),X47))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X5))<=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X47)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X107),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__add__eq__less)). 4.02/4.28 fof(fact_folding_Oeq__fold, axiom, ![X40, X3, X87, X22, X7, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),X40),X3)=hAPP(hAPP(X87,X3),X40))<=c_Finite__Set_Ofolding(X4,X7,X22,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Oeq__fold)). 4.02/4.28 fof(fact_finite__compl, axiom, ![X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X3))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__compl)). 4.02/4.28 fof(fact_add__gr__0, axiom, ![X20, X21]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)))<=>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),X21),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__gr__0)). 4.02/4.28 fof(fact_psubset__card__mono, axiom, ![X3, X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X3)),hAPP(c_Finite__Set_Ocard(X4),X6)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubset__card__mono)). 4.02/4.28 fof(fact_card__mono, axiom, ![X3, X6, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X3)),hAPP(c_Finite__Set_Ocard(X4),X6))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__mono)). 4.02/4.28 fof(fact_o__eq__dest, axiom, ![X64, X102, X24, X126, X25, X26, X4, X7, X49]:(hAPP(X24,hAPP(X102,X64))=hAPP(X26,hAPP(X25,X64))<=hAPP(c_Fun_Ocomp(X49,X7,X4,X26),X25)=hAPP(c_Fun_Ocomp(X126,X7,X4,X24),X102)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_o__eq__dest)). 4.02/4.28 fof(fact_le__sup__iff, axiom, ![X16, X17, X9, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X9),X17)),X16))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X17),X16))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X16))))<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__sup__iff)). 4.02/4.28 fof(fact_listsum__0, axiom, ![X32, X7, X4]:(c_Groups_Ozero__class_Ozero(X4)=hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Omap(X7,X4),hAPP(c_COMBK(X4,X7),c_Groups_Ozero__class_Ozero(X4))),X32))<=class_Groups_Omonoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__0)). 4.02/4.28 fof(fact_f__the__inv__into__f, axiom, ![X17, X3, X22, X7, X4]:((hBOOL(hAPP(hAPP(c_member(X7),X17),hAPP(c_Set_Oimage(X4,X7,X22),X3)))=>hAPP(X22,hAPP(c_Fun_Othe__inv__into(X4,X7,X3,X22),X17))=X17)<=c_Fun_Oinj__on(X4,X7,X22,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_f__the__inv__into__f)). 4.02/4.28 fof(fact_inf__greatest, axiom, ![X29, X43, X13, X4]:(class_Lattices_Osemilattice__inf(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X43),X29))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__greatest)). 4.02/4.28 fof(fact_less__number__of, axiom, ![X17, X9, X4]:((class_Rings_Olinordered__idom(X4)&class_Int_Onumber__ring(X4))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X9)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X17)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__number__of)). 4.02/4.28 fof(fact_sorted__insort__insert__key, axiom, ![X9, X32, X22, X7, X4]:((c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X7,X4),X22),X32))=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X7,X4),X22),c_List_Olinorder__class_Oinsort__insert__key(X7,X4,X22,X9,X32))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__insort__insert__key)). 4.02/4.28 fof(fact_image__iff, axiom, ![X3, X22, X7, X16, X4]:(?[X19]:(hBOOL(hAPP(hAPP(c_member(X7),X19),X3))&hAPP(X22,X19)=X16)<=>hBOOL(hAPP(hAPP(c_member(X4),X16),hAPP(c_Set_Oimage(X7,X4,X22),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__iff)). 4.02/4.28 fof(fact_le__number__of, axiom, ![X17, X9, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9),X17))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X9)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X17))))<=(class_Int_Onumber__ring(X4)&class_Rings_Olinordered__idom(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__number__of)). 4.02/4.28 fof(fact_min__max_Ofold1__belowI, axiom, ![X26, X3, X4]:(class_Orderings_Olinorder(X4)=>((hBOOL(hAPP(hAPP(c_member(X4),X26),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X3)),X26)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofold1__belowI)). 4.02/4.28 fof(fact_fold1__belowI, axiom, ![X26, X3, X4]:(class_Lattices_Osemilattice__inf(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Finite__Set_Ofold1(X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X3)),X26))<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__belowI)). 4.02/4.28 fof(fact_length__pos__if__in__set, axiom, ![X32, X9, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__pos__if__in__set)). 4.02/4.28 fof(fact_Compl__subset__Compl__iff, axiom, ![X6, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X3))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__subset__Compl__iff)). 4.02/4.28 fof(fact_insert__ident, axiom, ![X6, X3, X9, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))=>((hAPP(hAPP(c_Set_Oinsert(X4),X9),X3)=hAPP(hAPP(c_Set_Oinsert(X4),X9),X6)<=>X6=X3)<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__ident)). 4.02/4.28 fof(fact_le__add__diff, axiom, ![X2, X5, X107]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X2)),X107)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X107),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__add__diff)). 4.02/4.28 fof(fact_folding__one__idem_Oin__idem, axiom, ![X9, X3, X87, X22, X4]:(c_Finite__Set_Ofolding__one__idem(X4,X22,X87)=>((hAPP(X87,X3)=hAPP(hAPP(X22,X9),hAPP(X87,X3))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Oin__idem)). 4.02/4.28 fof(fact_zadd__strict__right__mono, axiom, ![X107, X135, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X46),X135))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X46),X107)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X135),X107)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__strict__right__mono)). 4.02/4.28 fof(fact_add__less__mono1, axiom, ![X107, X135, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X135))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X107)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X135),X107)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__mono1)). 4.02/4.28 fof(fact_nat__add__left__cancel__less, axiom, ![X20, X21, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X20)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__left__cancel__less)). 4.02/4.28 fof(fact_zadd__left__mono, axiom, ![X107, X135, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),X46)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X107),X135)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X46),X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__left__mono)). 4.02/4.28 fof(fact_SigmaD2, axiom, ![X6, X3, X25, X26, X7, X4]:(hBOOL(hAPP(hAPP(c_member(X7),X25),hAPP(X6,X26)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X26),X25)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SigmaD2)). 4.02/4.28 fof(fact_distinct__map, axiom, ![X32, X22, X7, X4]:((hBOOL(hAPP(c_List_Odistinct(X7),X32))&c_Fun_Oinj__on(X7,X4,X22,hAPP(c_List_Oset(X7),X32)))<=>hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__map)). 4.02/4.28 fof(fact_setprod__zero__iff, axiom, ![X22, X3, X4, X7]:(((c_Groups_Ozero__class_Ozero(X7)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X7),X22),X3)<=>?[X19]:(c_Groups_Ozero__class_Ozero(X7)=hAPP(X22,X19)&hBOOL(hAPP(hAPP(c_member(X4),X19),X3))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=(class_Rings_Ono__zero__divisors(X7)&class_Rings_Ocomm__semiring__1(X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__zero__iff)). 4.02/4.28 fof(fact_diff__le__mono, axiom, ![X47, X5, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X47)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),X47)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__le__mono)). 4.02/4.28 fof(fact_diff__le__mono2, axiom, ![X47, X5, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X47),X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X47),X2)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__le__mono2)). 4.02/4.28 fof(fact_transpose__empty, axiom, ![X32, X4]:(c_List_Olist_ONil(tc_List_Olist(X4))=c_List_Otranspose(X4,X32)<=>![X19]:(c_List_Olist_ONil(X4)=X19<=hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X19),hAPP(c_List_Oset(tc_List_Olist(X4)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__empty)). 4.02/4.28 fof(fact_map__le__implies__dom__le, axiom, ![X76, X22, X7, X4]:(c_Map_Omap__le(X4,X7,X22,X76)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X7,X22)),c_Map_Odom(X4,X7,X76)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__le__implies__dom__le)). 4.02/4.28 fof(fact_set__insort, axiom, ![X32, X9, X22, X4, X7]:(hAPP(hAPP(c_Set_Oinsert(X4),X9),hAPP(c_List_Oset(X4),X32))=hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X7,X22),X9),X32))<=class_Orderings_Olinorder(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__insort)). 4.02/4.28 fof(fact_mult__le__mono2, axiom, ![X107, X135, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X46)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X135)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__le__mono2)). 4.02/4.28 fof(fact_add__le__mono1, axiom, ![X107, X135, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),X135))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X107)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X135),X107)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__le__mono1)). 4.02/4.28 fof(fact_nat__add__left__cancel__le, axiom, ![X20, X21, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X20)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__left__cancel__le)). 4.02/4.28 fof(fact_List_Oinsert__def, axiom, ![X32, X9, X4]:((c_List_Oinsert(X4,X9,X32)=hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))))&(X32=c_List_Oinsert(X4,X9,X32)<=hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Oinsert__def)). 4.02/4.28 fof(fact_wf__asym, axiom, ![X9, X26, X18, X4]:(c_Wellfounded_Owf(X4,X18)=>(~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X26)),X18)))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X9)),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__asym)). 4.02/4.28 fof(fact_div__le__mono, axiom, ![X107, X5, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X5))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X107)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X5),X107)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__le__mono)). 4.02/4.28 fof(fact_refl__onD1, axiom, ![X17, X9, X18, X3, X4]:(c_Relation_Orefl__on(X4,X3,X18)=>(hBOOL(hAPP(hAPP(c_member(X4),X9),X3))<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__onD1)). 4.02/4.28 fof(fact_refl__onD2, axiom, ![X17, X9, X18, X3, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),X18))=>hBOOL(hAPP(hAPP(c_member(X4),X17),X3)))<=c_Relation_Orefl__on(X4,X3,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__onD2)). 4.02/4.28 fof(fact_abs__less__iff, axiom, ![X25, X26, X4]:(class_Rings_Olinordered__idom(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X25))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26)),X25)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X26)),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__less__iff)). 4.02/4.28 fof(fact_abs__le__iff, axiom, ![X25, X26, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),X25))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26)),X25)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X26)),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__le__iff)). 4.02/4.28 fof(fact_map__le__def, axiom, ![X307, X308, X7, X4]:(![X19]:(hAPP(X307,X19)=hAPP(X308,X19)<=hBOOL(hAPP(hAPP(c_member(X4),X19),c_Map_Odom(X4,X7,X308))))<=>c_Map_Omap__le(X4,X7,X308,X307)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__le__def)). 4.02/4.28 fof(fact_map__add__Some__iff, axiom, ![X9, X28, X20, X21, X4, X7]:(((c_Option_Ooption_ONone(X4)=hAPP(X20,X28)&hAPP(c_Option_Ooption_OSome(X4),X9)=hAPP(X21,X28))|hAPP(c_Option_Ooption_OSome(X4),X9)=hAPP(X20,X28))<=>hAPP(c_Option_Ooption_OSome(X4),X9)=hAPP(c_Map_Omap__add(X7,X4,X21,X20),X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__Some__iff)). 4.02/4.28 fof(fact_eq__divide__eq__number__of, axiom, ![X24, X25, X23, X4]:((hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X25),X24)=hAPP(c_Int_Onumber__class_Onumber__of(X4),X23)<=>((c_Groups_Ozero__class_Ozero(X4)!=X24=>X25=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X23)),X24))&(X24=c_Groups_Ozero__class_Ozero(X4)=>hAPP(c_Int_Onumber__class_Onumber__of(X4),X23)=c_Groups_Ozero__class_Ozero(X4))))<=(class_Fields_Ofield__inverse__zero(X4)&class_Int_Onumber(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__divide__eq__number__of)). 4.02/4.28 fof(fact_Nitpick_Orefl_H__def, axiom, ![X18, X4]:(c_Nitpick_Orefl_H(X4,X18)<=>![X19]:hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X19),X19)),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Orefl_H__def)). 4.02/4.28 fof(fact_the__inv__into__onto, axiom, ![X3, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,X3)=>X3=hAPP(c_Set_Oimage(X7,X4,c_Fun_Othe__inv__into(X4,X7,X3,X22)),hAPP(c_Set_Oimage(X4,X7,X22),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__into__onto)). 4.02/4.28 fof(fact_image__uminus__greaterThanAtMost, axiom, ![X17, X9, X4]:(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,hAPP(c_Groups_Ouminus__class_Ouminus(X4),X17)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X9))=hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X9,X17))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__greaterThanAtMost)). 4.02/4.28 fof(fact_Sup__le__iff, axiom, ![X25, X3, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Complete__Lattice_OSup__class_OSup(X4,X3)),X25))<=>![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X19),X25))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__le__iff)). 4.02/4.28 fof(fact_le__Inf__iff, axiom, ![X3, X25, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),c_Complete__Lattice_OInf__class_OInf(X4,X3)))<=>![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),X19))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__Inf__iff)). 4.02/4.28 fof(fact_less__than__iff, axiom, ![X17, X9]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X17))<=>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),X9),X17)),c_Wellfounded_Oless__than))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__than__iff)). 4.02/4.28 fof(fact_mod__induct__0, axiom, ![X37, X56, X51]:(![X42]:((hBOOL(hAPP(X56,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X42),X51)))<=hBOOL(hAPP(X56,X42)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),X51)))=>(hBOOL(hAPP(X56,X37))=>(hBOOL(hAPP(X56,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37),X51))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__induct__0)). 4.02/4.28 fof(fact_pred__comp_Oequations, axiom, ![X69, X70, X40, X18, X49, X7, X4]:(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X4,X7,X49,X18,X40),X70),X69))<=>?[X78]:(hBOOL(hAPP(hAPP(X40,X78),X69))&hBOOL(hAPP(hAPP(X18,X70),X78)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__comp_Oequations)). 4.02/4.28 fof(fact_lexn__length, axiom, ![X20, X18, X31, X32, X4]:((X20=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)&hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X31)=X20)<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),X31)),hAPP(c_List_Olexn(X4,X18),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexn__length)). 4.02/4.28 fof(fact_divmod__int__rel__0, axiom, ![X12]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12),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)!=X12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__0)). 4.02/4.28 fof(fact_nat__power__less__imp__less, axiom, ![X5, X2, X46]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X46),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X46),X5)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X5)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__power__less__imp__less)). 4.02/4.28 fof(fact_sorted__filter, axiom, ![X56, X32, X22, X7, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X7,X4),X22),hAPP(c_List_Ofilter(X7,X56),X32)))<=c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X7,X4),X22),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__filter)). 4.02/4.28 fof(fact_mod__pos__pos, axiom, ![X12, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))=>hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X11,X12))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__pos)). 4.02/4.28 fof(fact_mod__neg__pos, axiom, ![X12, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>(hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X11,X12))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__neg__pos)). 4.02/4.28 fof(fact_list__all__length, axiom, ![X32, X56, X4]:(c_List_Olist__all(X4,X56,X32)<=>![X104]:(hBOOL(hAPP(X56,hAPP(hAPP(c_List_Onth(X4),X32),X104)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X104),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__length)). 4.02/4.28 fof(fact_start__le__sum, axiom, ![X144, X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X144)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_start__le__sum)). 4.02/4.28 fof(fact_subset__insertI2, axiom, ![X25, X6, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X25),X6)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__insertI2)). 4.02/4.28 fof(fact_filter__empty__conv, axiom, ![X32, X56, X4]:(hAPP(c_List_Ofilter(X4,X56),X32)=c_List_Olist_ONil(X4)<=>![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32)))=>~(hBOOL(hAPP(X56,X19))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__empty__conv)). 4.02/4.28 fof(fact_nth__list__update__eq, axiom, ![X13, X45, X4, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))=>X13=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist__update(X4,X45),X46),X13)),X46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__list__update__eq)). 4.02/4.28 fof(fact_map__upd__triv, axiom, ![X7, X9, X4, X28, X123]:(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X4)),X123),X28),hAPP(c_Option_Ooption_OSome(X4),X9))=X123<=hAPP(X123,X28)=hAPP(c_Option_Ooption_OSome(X4),X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upd__triv)). 4.02/4.28 fof(fact_max__less__iff__conj, axiom, ![X16, X17, X9, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X9),X17)),X16))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X9),X16))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X17),X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__less__iff__conj)). 4.02/4.28 fof(fact_sorted__nth__monoI, axiom, ![X45, X4]:((![X42, X139]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X139),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_List_Onth(X4),X45),X42)),hAPP(hAPP(c_List_Onth(X4),X45),X139))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X42),X139)))=>c_List_Olinorder__class_Osorted(X4,X45))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__nth__monoI)). 4.02/4.28 fof(fact_UnionE, axiom, ![X8, X3, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X8)))=>~(![X241]:(~(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X241),X8)))<=hBOOL(hAPP(hAPP(c_member(X4),X3),X241))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UnionE)). 4.02/4.28 fof(fact_min__max_Ole__sup__iff, axiom, ![X16, X17, X9, X4]:(class_Orderings_Olinorder(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X17),X16))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X16)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X9),X17)),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__sup__iff)). 4.02/4.28 fof(fact_min__less__iff__conj, axiom, ![X17, X9, X16, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X16),X9))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X16),X17)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X16),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X9),X17))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__less__iff__conj)). 4.02/4.28 fof(fact_take__Cons__number__of, axiom, ![X45, X13, X4, X1]:((hAPP(hAPP(c_List_Otake(X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45))=c_List_Olist_ONil(X4)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>hAPP(hAPP(c_List_Otake(X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45))=hAPP(hAPP(c_List_Olist_OCons(X4),X13),hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Cons__number__of)). 4.02/4.28 fof(fact_min__max_Ole__infI, axiom, ![X12, X11, X13, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X11),X12))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X11)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__infI)). 4.02/4.28 fof(fact_int__div__less__self, axiom, ![X107, X13]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X107))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X13),X107)),X13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__div__less__self)). 4.02/4.28 fof(fact_diff__less, axiom, ![X2, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5))=>(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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5)),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__less)). 4.02/4.28 fof(fact_abs__minus__commute, axiom, ![X12, X11, X4]:(hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X11))=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X12))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__minus__commute)). 4.02/4.28 fof(fact_div__less__dividend, axiom, ![X2, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5))=>(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),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X5)),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__less__dividend)). 4.02/4.28 fof(fact_zero__less__mult__pos2, axiom, ![X11, X12, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11))))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__mult__pos2)). 4.02/4.28 fof(fact_zero__less__mult__pos, axiom, ![X12, X11, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X12))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12))))<=class_Rings_Olinordered__semiring__strict(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__mult__pos)). 4.02/4.28 fof(fact_of__int__power, axiom, ![X5, X29, X4]:(hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X29),X5))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X29)),X5)<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__power)). 4.02/4.28 fof(fact_finite__Inter, axiom, ![X54, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X54)))<=?[X19]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X19))&hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X19),X54)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Inter)). 4.02/4.28 fof(fact_of__nat__power, axiom, ![X5, X2, X4]:(class_Rings_Osemiring__1(X4)=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X5))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X2)),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__power)). 4.02/4.28 fof(fact_comp__inj__on__iff, axiom, ![X274, X49, X3, X22, X7, X4]:((c_Fun_Oinj__on(X4,X49,hAPP(c_Fun_Ocomp(X7,X49,X4,X274),X22),X3)<=>c_Fun_Oinj__on(X7,X49,X274,hAPP(c_Set_Oimage(X4,X7,X22),X3)))<=c_Fun_Oinj__on(X4,X7,X22,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comp__inj__on__iff)). 4.02/4.28 fof(fact_Sup__set__fold, axiom, ![X32, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>hAPP(c_List_Ofoldl(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4),c_Orderings_Obot__class_Obot(X4)),X32)=c_Complete__Lattice_OSup__class_OSup(X4,hAPP(c_List_Oset(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__set__fold)). 4.02/4.28 fof(fact_double__add__less__zero__iff__single__add__less__zero, axiom, ![X26, X4]:(class_Groups_Olinordered__ab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X26),X26)),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__add__less__zero__iff__single__add__less__zero)). 4.02/4.28 fof(fact_even__less__0__iff, axiom, ![X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X26),X26)),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_even__less__0__iff)). 4.02/4.28 fof(fact_double__add__le__zero__iff__single__add__le__zero, axiom, ![X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X26),X26)),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),c_Groups_Ozero__class_Ozero(X4))))<=class_Groups_Olinordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__add__le__zero__iff__single__add__le__zero)). 4.02/4.28 fof(fact_distinct__listsum__conv__Setsum, axiom, ![X32, X4]:((hBOOL(hAPP(c_List_Odistinct(X4),X32))=>hAPP(c_List_Omonoid__add__class_Olistsum(X4),X32)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X4),c_COMBI(X4)),hAPP(c_List_Oset(X4),X32)))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__listsum__conv__Setsum)). 4.02/4.28 fof(fact_zero__less__power, axiom, ![X5, X11, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__power)). 4.02/4.28 fof(fact_zero__less__double__add__iff__zero__less__single__add, axiom, ![X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X26),X26)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X26)))<=class_Groups_Olinordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__double__add__iff__zero__less__single__add)). 4.02/4.28 fof(fact_zero__le__power, axiom, ![X5, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__power)). 4.02/4.28 fof(fact_zero__le__double__add__iff__zero__le__single__add, axiom, ![X26, X4]:(class_Groups_Olinordered__ab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X26))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X26),X26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__double__add__iff__zero__le__single__add)). 4.02/4.28 fof(fact_le__fun__def, axiom, ![X76, X22, X4, X7]:((![X19]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(X22,X19)),hAPP(X76,X19)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X7)),X22),X76)))<=class_Orderings_Oord(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__fun__def)). 4.02/4.28 fof(fact_congruentD, axiom, ![X16, X17, X22, X18, X7, X4]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X17),X16)),X18))=>hAPP(X22,X17)=hAPP(X22,X16))<=c_Equiv__Relations_Ocongruent(X4,X7,X18,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_congruentD)). 4.02/4.28 fof(fact_one__le__power, axiom, ![X5, X11, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Oone__class_Oone(X4)),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Oone__class_Oone(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_one__le__power)). 4.02/4.28 fof(fact_in__listsp__conv__set, axiom, ![X32, X3, X4]:(![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32)))=>hBOOL(hAPP(X3,X19)))<=>hBOOL(hAPP(c_List_Olistsp(X4,X3),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__listsp__conv__set)). 4.02/4.28 fof(fact_wf__same__fst, axiom, ![X4, X39, X7, X56]:(c_Wellfounded_Owf(tc_prod(X4,X7),c_Recdef_Osame__fst(X4,X7,X56,X39))<=![X19]:(hBOOL(hAPP(X56,X19))=>c_Wellfounded_Owf(X7,hAPP(X39,X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__same__fst)). 4.02/4.28 fof(fact_list__ex__length, axiom, ![X32, X56, X4]:(c_List_Olist__ex(X4,X56,X32)<=>?[X104]:(hBOOL(hAPP(X56,hAPP(hAPP(c_List_Onth(X4),X32),X104)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X104),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__length)). 4.02/4.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, axiom, ![X14, X13, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),hAPP(c_Nat_OSuc,X14))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X13),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),X14))<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J)). 4.02/4.28 fof(fact_card__gt__0__iff, axiom, ![X3, 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(X4),X3)))<=>(X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))&hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__gt__0__iff)). 4.02/4.28 fof(fact_distinct_Osimps_I2_J, axiom, ![X32, X9, X4]:((~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32))))&hBOOL(hAPP(c_List_Odistinct(X4),X32)))<=>hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct_Osimps_I2_J)). 4.02/4.28 fof(fact_partition__P, axiom, ![X141, X142, X32, X56, X4]:(hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X142),X141)=c_List_Opartition(X4,X56,X32)=>(![X19]:(~(hBOOL(hAPP(X56,X19)))<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X141))))&![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X142)))=>hBOOL(hAPP(X56,X19))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition__P)). 4.02/4.28 fof(fact_evaln__elim__cases_I6_J, axiom, ![X187, X5, X159, X209]:(~(![X104]:(~(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X209)),X159,X104,X187))<=hAPP(c_Nat_OSuc,X104)=X5))<=c_Natural_Oevaln(c_Com_Ocom_OBODY(X209),X159,X5,X187)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evaln__elim__cases_I6_J)). 4.02/4.28 fof(fact_power__Suc, axiom, ![X5, X11, X4]:(class_Power_Opower(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),hAPP(c_Nat_OSuc,X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__Suc)). 4.02/4.28 fof(fact_UnE, axiom, ![X6, X3, X24, X4]:((~(hBOOL(hAPP(hAPP(c_member(X4),X24),X3)))=>hBOOL(hAPP(hAPP(c_member(X4),X24),X6)))<=hBOOL(hAPP(hAPP(c_member(X4),X24),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UnE)). 4.02/4.28 fof(fact_field__le__mult__one__interval, axiom, ![X43, X13, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X43))<=![X36]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Oone__class_Oone(X4)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X36),X13)),X43)))))<=class_Fields_Olinordered__field__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_field__le__mult__one__interval)). 4.02/4.28 fof(fact_image__uminus__greaterThanLessThan, axiom, ![X17, X9, X4]:(c_SetInterval_Oord__class_OgreaterThanLessThan(X4,hAPP(c_Groups_Ouminus__class_Ouminus(X4),X17),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X9))=hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X9,X17))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__greaterThanLessThan)). 4.02/4.28 fof(fact_image__uminus__atLeastAtMost, axiom, ![X17, X9, X4]:(hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X9,X17))=c_SetInterval_Oord__class_OatLeastAtMost(X4,hAPP(c_Groups_Ouminus__class_Ouminus(X4),X17),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X9))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__atLeastAtMost)). 4.02/4.28 fof(fact_field__le__epsilon, axiom, ![X43, X13, X4]:((![X310]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X43),X310)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X310)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X43)))<=class_Fields_Olinordered__field(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_field__le__epsilon)). 4.02/4.28 fof(fact_Image__closed__trancl, axiom, ![X156, X18, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X18),X156)),X156))=>X156=hAPP(c_Relation_OImage(X4,X4,c_Transitive__Closure_Ortrancl(X4,X18)),X156)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__closed__trancl)). 4.02/4.28 fof(fact_inj__image__mem__iff, axiom, ![X3, X26, X22, X7, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X26),X3))<=>hBOOL(hAPP(hAPP(c_member(X7),hAPP(X22,X26)),hAPP(c_Set_Oimage(X4,X7,X22),X3))))<=c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__image__mem__iff)). 4.02/4.28 fof(fact_nonzero__minus__divide__divide, axiom, ![X11, X12, X4]:(class_Rings_Odivision__ring(X4)=>(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X12)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12))<=X12!=c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__minus__divide__divide)). 4.02/4.28 fof(fact_Min_Oeq__fold__idem_H, axiom, ![X26, X3, X4]:((hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omin(X4)),X26),X3)=c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X26),X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Oeq__fold__idem_H)). 4.02/4.28 fof(fact_Max_Oeq__fold__idem_H, axiom, ![X26, X3, X4]:(class_Orderings_Olinorder(X4)=>(hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Orderings_Oord__class_Omax(X4)),X26),X3)=c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Set_Oinsert(X4),X26),X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Oeq__fold__idem_H)). 4.02/4.28 fof(fact_sup__Sup__fold__sup, axiom, ![X6, X3, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4)),X6),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X6),c_Complete__Lattice_OSup__class_OSup(X4,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__Sup__fold__sup)). 4.02/4.28 fof(fact_zdiv__eq__0__iff, axiom, ![X28, X37]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X28)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<=>(X28=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X37),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),X37)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),X28))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__eq__0__iff)). 4.02/4.28 fof(fact_filter__id__conv, axiom, ![X32, X56, X4]:(![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32)))=>hBOOL(hAPP(X56,X19)))<=>hAPP(c_List_Ofilter(X4,X56),X32)=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__id__conv)). 4.02/4.28 fof(fact_min__max_Oinf__Sup__absorb, axiom, ![X26, X3, X4]:(class_Orderings_Olinorder(X4)=>((hBOOL(hAPP(hAPP(c_member(X4),X26),X3))=>hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X26),c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X3))=X26)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__Sup__absorb)). 4.02/4.28 fof(fact_min__max_Osup__Inf__absorb, axiom, ![X26, X3, X4]:(((hBOOL(hAPP(hAPP(c_member(X4),X26),X3))=>X26=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X26),c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__Inf__absorb)). 4.02/4.28 fof(fact_minus__less__iff, axiom, ![X25, X26, X4]:(class_Groups_Oordered__ab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X25)),X26))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26)),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__less__iff)). 4.02/4.28 fof(fact_minus__le__iff, axiom, ![X25, X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26)),X25))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X25)),X26)))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__le__iff)). 4.02/4.28 fof(fact_less__minus__iff, axiom, ![X25, X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X25))))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__minus__iff)). 4.02/4.28 fof(fact_le__minus__iff, axiom, ![X25, X26, X4]:(class_Groups_Oordered__ab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X25))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__minus__iff)). 4.02/4.28 fof(fact_the__inv__f__f, axiom, ![X9, X22, X7, X4]:(hAPP(c_Fun_Othe__inv__into(X4,X7,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),X22),hAPP(X22,X9))=X9<=c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__f__f)). 4.02/4.28 fof(fact_mod__pos__neg__trivial, axiom, ![X12, X11]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11),X12)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11),X12)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__neg__trivial)). 4.02/4.28 fof(fact_nth__take, axiom, ![X45, X4, X5, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X5))=>hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Otake(X4),X5),X45)),X46)=hAPP(hAPP(c_List_Onth(X4),X45),X46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__take)). 4.02/4.28 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J, axiom, ![X43, X13]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X13,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(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J)). 4.02/4.28 fof(fact_nth__Cons__number__of, axiom, ![X45, X13, X4, X1]:((X13=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))<=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(hAPP(c_List_Onth(X4),X45),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),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__Cons__number__of)). 4.02/4.28 fof(fact_ord_OatLeastLessThan__iff, axiom, ![X115, X60, X194, X201, X37, X4]:((hBOOL(hAPP(hAPP(X194,X37),X115))&hBOOL(hAPP(hAPP(X201,X60),X37)))<=>hBOOL(hAPP(hAPP(c_member(X4),X37),c_SetInterval_Oord_OatLeastLessThan(X4,X201,X194,X60,X115)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OatLeastLessThan__iff)). 4.02/4.28 fof(fact_ord_OgreaterThanAtMost__iff, axiom, ![X115, X60, X194, X201, X37, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X37),c_SetInterval_Oord_OgreaterThanAtMost(X4,X201,X194,X60,X115)))<=>(hBOOL(hAPP(hAPP(X194,X60),X37))&hBOOL(hAPP(hAPP(X201,X37),X115)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OgreaterThanAtMost__iff)). 4.02/4.28 fof(fact_take__butlast, axiom, ![X45, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))=>hAPP(hAPP(c_List_Otake(X4),X5),c_List_Obutlast(X4,X45))=hAPP(hAPP(c_List_Otake(X4),X5),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__butlast)). 4.02/4.28 fof(fact_sup2CI, axiom, ![X7, X4, X3, X17, X9, X6]:(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),X3),X6),X9),X17))<=(hBOOL(hAPP(hAPP(X3,X9),X17))<=~(hBOOL(hAPP(hAPP(X6,X9),X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup2CI)). 4.02/4.28 fof(fact_insort__insert__key__triv, axiom, ![X32, X7, X9, X22, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Oinsort__insert__key(X7,X4,X22,X9,X32)=X32<=hBOOL(hAPP(hAPP(c_member(X4),hAPP(X22,X9)),hAPP(c_Set_Oimage(X7,X4,X22),hAPP(c_List_Oset(X7),X32)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__insert__key__triv)). 4.02/4.28 fof(fact_nth__list__update__neq, axiom, ![X13, X45, X4, X135, X46]:(hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist__update(X4,X45),X46),X13)),X135)=hAPP(hAPP(c_List_Onth(X4),X45),X135)<=X46!=X135), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__list__update__neq)). 4.02/4.28 fof(fact_minus__mult__minus, axiom, ![X12, X11, X4]:(class_Rings_Oring(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__mult__minus)). 4.02/4.28 fof(fact_sup2I2, axiom, ![X3, X7, X4, X17, X9, X6]:(hBOOL(hAPP(hAPP(X6,X9),X17))=>hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),X3),X6),X9),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup2I2)). 4.02/4.28 fof(fact_set__insort__insert, axiom, ![X32, X9, X4]:(class_Orderings_Olinorder(X4)=>hAPP(c_List_Oset(X4),c_List_Olinorder__class_Oinsort__insert__key(X4,X4,c_COMBI(X4),X9,X32))=hAPP(hAPP(c_Set_Oinsert(X4),X9),hAPP(c_List_Oset(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__insort__insert)). 4.02/4.28 fof(fact_minus__divide__divide, axiom, ![X12, X11, X4]:(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X12)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12))<=class_Fields_Ofield__inverse__zero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__divide__divide)). 4.02/4.28 fof(fact_Suc__times__mod__eq, axiom, ![X2, X107]:(c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X2)),X107)=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)),X107))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__times__mod__eq)). 4.02/4.28 fof(fact_Max__in, axiom, ![X3, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=>hBOOL(hAPP(hAPP(c_member(X4),c_Big__Operators_Olinorder__class_OMax(X4,X3)),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__in)). 4.02/4.28 fof(fact_abs__mult__self, axiom, ![X11, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X11)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),hAPP(c_Groups_Oabs__class_Oabs(X4),X11))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__mult__self)). 4.02/4.28 fof(fact_Min__in, axiom, ![X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_member(X4),c_Big__Operators_Olinorder__class_OMin(X4,X3)),X3))<=X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__in)). 4.02/4.28 fof(fact_mod__geq, axiom, ![X5, X2]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X5)))=>c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__geq)). 4.02/4.28 fof(fact_le__imp__0__less, axiom, ![X29]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X29))=>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)),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__imp__0__less)). 4.02/4.28 fof(fact_zero__less__two, axiom, ![X4]:(class_Rings_Olinordered__semidom(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Oone__class_Oone(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__two)). 4.02/4.28 fof(fact_SigmaD1, axiom, ![X6, X3, X25, X26, X7, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X26),X25)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),X6)))=>hBOOL(hAPP(hAPP(c_member(X4),X26),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SigmaD1)). 4.02/4.28 fof(fact_tl__append2, axiom, ![X59, X4, X45]:(hAPP(hAPP(c_List_Oappend(X4),hAPP(c_List_Otl(X4),X45)),X59)=hAPP(c_List_Otl(X4),hAPP(hAPP(c_List_Oappend(X4),X45),X59))<=c_List_Olist_ONil(X4)!=X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl__append2)). 4.02/4.28 fof(fact_INF1__E, axiom, ![X26, X25, X6, X3, X7, X4]:((~(hBOOL(hAPP(hAPP(c_member(X4),X26),X3)))<=~(hBOOL(hAPP(hAPP(X6,X26),X25))))<=hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X7,tc_HOL_Obool)),X3),X6),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF1__E)). 4.02/4.28 fof(fact_takeWhile__eq__all__conv, axiom, ![X32, X56, X4]:(![X19]:(hBOOL(hAPP(X56,X19))<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32))))<=>c_List_OtakeWhile(X4,X56,X32)=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__eq__all__conv)). 4.02/4.28 fof(fact_nonzero__minus__divide__right, axiom, ![X11, X12, X4]:((X12!=c_Groups_Ozero__class_Ozero(X4)=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X12))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12)))<=class_Rings_Odivision__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__minus__divide__right)). 4.02/4.28 fof(fact_less__iff__diff__less__0, axiom, ![X25, X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X26),X25)),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X25)))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__iff__diff__less__0)). 4.02/4.28 fof(fact_le__iff__diff__le__0, axiom, ![X25, X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X26),X25)),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),X25)))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__iff__diff__le__0)). 4.02/4.28 fof(fact_neg__less__iff__less, axiom, ![X26, X25, X4]:(class_Groups_Oordered__ab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X25)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__less__iff__less)). 4.02/4.28 fof(fact_map__add__SomeD, axiom, ![X9, X28, X20, X21, X4, X7]:(((c_Option_Ooption_ONone(X4)=hAPP(X20,X28)&hAPP(c_Option_Ooption_OSome(X4),X9)=hAPP(X21,X28))|hAPP(X20,X28)=hAPP(c_Option_Ooption_OSome(X4),X9))<=hAPP(c_Map_Omap__add(X7,X4,X21,X20),X28)=hAPP(c_Option_Ooption_OSome(X4),X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__SomeD)). 4.02/4.28 fof(fact_compl__le__compl__iff, axiom, ![X17, X9, X4]:(class_Lattices_Oboolean__algebra(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X17),X9))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X9)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__le__compl__iff)). 4.02/4.28 fof(fact_neg__le__iff__le, axiom, ![X26, X25, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),X25))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X25)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26))))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__le__iff__le)). 4.02/4.28 fof(fact_minus__divide__left, axiom, ![X12, X11, X4]:(class_Rings_Odivision__ring(X4)=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X12))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__divide__left)). 4.02/4.28 fof(fact_Ball__set__list__all, axiom, ![X56, X32, X4]:(![X19]:(hBOOL(hAPP(X56,X19))<=hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32))))<=>c_List_Olist__all(X4,X56,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ball__set__list__all)). 4.02/4.28 fof(fact_minus__mult__left, axiom, ![X12, X11, X4]:(hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)),X12)<=class_Rings_Oring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__mult__left)). 4.02/4.28 fof(fact_minus__mult__commute, axiom, ![X12, X11, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)),X12)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12))<=class_Rings_Oring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__mult__commute)). 4.02/4.28 fof(fact_Ints__power, axiom, ![X20, X26, X4]:(class_Rings_Oring__1(X4)=>(hBOOL(hAPP(hAPP(c_member(X4),X26),c_Int_Oring__1__class_OInts(X4)))=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X26),X20)),c_Int_Oring__1__class_OInts(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__power)). 4.02/4.28 fof(fact_min__less__iff__disj, axiom, ![X16, X17, X9, X4]:(class_Orderings_Olinorder(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X9),X16))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X17),X16)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X9),X17)),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__less__iff__disj)). 4.02/4.28 fof(fact_list__all__iff, axiom, ![X32, X56, X4]:(c_List_Olist__all(X4,X56,X32)<=>![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32)))=>hBOOL(hAPP(X56,X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__iff)). 4.02/4.28 fof(fact_tl__replicate, axiom, ![X13, X4, X5]:(c_List_Oreplicate(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X13)=hAPP(c_List_Otl(X4),c_List_Oreplicate(X4,X5,X13))<=X5!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl__replicate)). 4.02/4.28 fof(fact_list__all__iff__raw, axiom, ![X32, X56, X4]:(c_List_Olist__all(X4,X56,X32)<=>![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32)))=>hBOOL(hAPP(X56,X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__iff__raw)). 4.02/4.28 fof(fact_min__le__iff__disj, axiom, ![X16, X17, X9, X4]:(class_Orderings_Olinorder(X4)=>((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X16))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X17),X16)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X9),X17)),X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__le__iff__disj)). 4.02/4.28 fof(fact_less__max__iff__disj, axiom, ![X17, X9, X16, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X16),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X9),X17)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X16),X9))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X16),X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__max__iff__disj)). 4.02/4.28 fof(fact_le__max__iff__disj, axiom, ![X17, X9, X16, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X16),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X9),X17)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X16),X9))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X16),X17))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__max__iff__disj)). 4.02/4.28 fof(fact_z3div__def, axiom, ![X107, X47]:((hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X107),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X47)))=c_SMT_Oz3div(X107,X47)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X47))))&(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X107),X47)=c_SMT_Oz3div(X107,X47)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_z3div__def)). 4.02/4.28 fof(fact_lists__accD, axiom, ![X18, X32, X4]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X32),c_List_Olists(X4,c_Wellfounded_Oacc(X4,X18))))=>hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X32),c_Wellfounded_Oacc(tc_List_Olist(X4),c_List_Olistrel1(X4,X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__accD)). 4.02/4.28 fof(fact_min__max_OSup__fin_Osingleton, axiom, ![X9, X4]:(class_Orderings_Olinorder(X4)=>c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=X9), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_Osingleton)). 4.02/4.28 fof(fact_minus__divide__right, axiom, ![X12, X11, X4]:(class_Fields_Ofield__inverse__zero(X4)=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X12))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__divide__right)). 4.02/4.28 fof(fact_min__max_OInf__fin_Osingleton, axiom, ![X9, X4]:(X9=c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_Osingleton)). 4.02/4.28 fof(fact_sgn__times, axiom, ![X12, X11, X4]:(c_Groups_Osgn__class_Osgn(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Osgn__class_Osgn(X4,X11)),c_Groups_Osgn__class_Osgn(X4,X12))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__times)). 4.02/4.28 fof(fact_sorted__map__remove1, axiom, ![X9, X32, X22, X7, X4]:((c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X7,X4),X22),X32))=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X7,X4),X22),c_List_Oremove1(X7,X9,X32))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__map__remove1)). 4.02/4.28 fof(fact_minus__mult__right, axiom, ![X12, X11, X4]:(class_Rings_Oring(X4)=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__mult__right)). 4.02/4.28 fof(fact_nonneg1__imp__zdiv__pos__iff, axiom, ![X25, 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)),X25))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25),X26)))<=>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),X26),X25))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonneg1__imp__zdiv__pos__iff)). 4.02/4.28 fof(fact_takeWhile_Osimps_I2_J, axiom, ![X32, X4, X9, X56]:((hBOOL(hAPP(X56,X9))=>c_List_OtakeWhile(X4,X56,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32))=hAPP(hAPP(c_List_Olist_OCons(X4),X9),c_List_OtakeWhile(X4,X56,X32)))&(c_List_OtakeWhile(X4,X56,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32))=c_List_Olist_ONil(X4)<=~(hBOOL(hAPP(X56,X9))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile_Osimps_I2_J)). 4.02/4.28 fof(fact_zero__le__power__abs, axiom, ![X5, X11, X4]:(class_Rings_Olinordered__idom(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__power__abs)). 4.02/4.28 fof(fact_inf__left__idem, axiom, ![X43, X13, X4]:(class_Lattices_Osemilattice__inf(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__left__idem)). 4.02/4.28 fof(fact_map__upd__eqD1, axiom, ![X17, X20, X9, X26, X21, X7, X4]:(X17=X9<=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X20),X26),hAPP(c_Option_Ooption_OSome(X7),X17))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X21),X26),hAPP(c_Option_Ooption_OSome(X7),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upd__eqD1)). 4.02/4.28 fof(fact_list__all2__append, axiom, ![X284, X285, X56, X31, X7, X32, X4]:((c_List_Olist__all2(X4,X7,X56,hAPP(hAPP(c_List_Oappend(X4),X32),X285),hAPP(hAPP(c_List_Oappend(X7),X31),X284))<=>(c_List_Olist__all2(X4,X7,X56,X285,X284)&c_List_Olist__all2(X4,X7,X56,X32,X31)))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__append)). 4.02/4.28 fof(fact_mult__left__idem, axiom, ![X12, X11, X4]:(class_Lattices_Oab__semigroup__idem__mult(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__idem)). 4.02/4.28 fof(fact_inf__sup__aci_I8_J, axiom, ![X43, X13, X4]:(class_Lattices_Olattice(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I8_J)). 4.02/4.28 fof(fact_inf__sup__aci_I4_J, axiom, ![X43, X13, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I4_J)). 4.02/4.28 fof(fact_map__add__le__mapI, axiom, ![X76, X48, X22, X7, X4]:(c_Map_Omap__le(X4,X7,X22,X48)=>((c_Map_Omap__le(X4,X7,c_Map_Omap__add(X4,X7,X22,X76),X48)<=c_Map_Omap__le(X4,X7,X22,c_Map_Omap__add(X4,X7,X22,X76)))<=c_Map_Omap__le(X4,X7,X76,X48))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__le__mapI)). 4.02/4.28 fof(fact_inj__on__Int, axiom, ![X6, X3, X22, X7, X4]:((c_Fun_Oinj__on(X4,X7,X22,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6))<=c_Fun_Oinj__on(X4,X7,X22,X6))<=c_Fun_Oinj__on(X4,X7,X22,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__Int)). 4.02/4.28 fof(fact_finite__UNIV__inj__surj, axiom, ![X22, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))=>(c_Fun_Oinj__on(X4,X4,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>hAPP(c_Set_Oimage(X4,X4,X22),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UNIV__inj__surj)). 4.02/4.28 fof(fact_finite__UNIV__surj__inj, axiom, ![X22, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))=>(c_Fun_Oinj__on(X4,X4,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))<=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_Oimage(X4,X4,X22),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UNIV__surj__inj)). 4.02/4.28 fof(fact_sup__left__idem, axiom, ![X43, X13, X4]:(class_Lattices_Osemilattice__sup(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__left__idem)). 4.02/4.28 fof(fact_finite__induct, axiom, ![X56, X87, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X87))=>(hBOOL(hAPP(X56,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=>(hBOOL(hAPP(X56,X87))<=![X19, X210]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X210))=>(~(hBOOL(hAPP(hAPP(c_member(X4),X19),X210)))=>(hBOOL(hAPP(X56,hAPP(hAPP(c_Set_Oinsert(X4),X19),X210)))<=hBOOL(hAPP(X56,X210)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__induct)). 4.02/4.28 fof(fact_abs__power__minus__one, axiom, ![X5, X4]:((class_Rings_Olinordered__idom(X4)&class_Int_Onumber__ring(X4))=>c_Groups_Oone__class_Oone(X4)=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin)),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__power__minus__one)). 4.02/4.28 fof(fact_order__less__trans, axiom, ![X29, X43, X13, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),X43))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X43),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),X29))))<=class_Orderings_Opreorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__trans)). 4.02/4.28 fof(fact_Abs__Integ__induct, axiom, ![X9, X56]:(hBOOL(hAPP(X56,X9))<=![X34]:(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X34),c_Int_OInteg))=>hBOOL(hAPP(X56,hAPP(c_Int_OAbs__Integ,X34))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Abs__Integ__induct)). 4.02/4.28 fof(fact_insert__dom, axiom, ![X7, X17, X4, X9, X22]:(c_Map_Odom(X7,X4,X22)=hAPP(hAPP(c_Set_Oinsert(X7),X9),c_Map_Odom(X7,X4,X22))<=hAPP(c_Option_Ooption_OSome(X4),X17)=hAPP(X22,X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__dom)). 4.02/4.28 fof(fact_image__uminus__greaterThan, axiom, ![X9, X4]:(class_Groups_Oordered__ab__group__add(X4)=>hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X9))=hAPP(c_SetInterval_Oord__class_OlessThan(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__greaterThan)). 4.02/4.28 fof(fact_image__uminus__lessThan, axiom, ![X9, X4]:(hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X9))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X9))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__lessThan)). 4.02/4.28 fof(fact_order__le__less__trans, axiom, ![X29, X43, X13, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X43),X29))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X43)))<=class_Orderings_Opreorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__le__less__trans)). 4.02/4.28 fof(fact_order__less__le__trans, axiom, ![X29, X43, X13, X4]:(class_Orderings_Opreorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),X43))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X43),X29))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__le__trans)). 4.02/4.28 fof(fact_xt1_I10_J, axiom, ![X29, X13, X43, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X29),X13))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X29),X43)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X43),X13)))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I10_J)). 4.02/4.28 fof(fact_xt1_I8_J, axiom, ![X29, X13, X43, X4]:(class_Orderings_Oorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X43),X13))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X29),X13))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X29),X43))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I8_J)). 4.02/4.28 fof(fact_image__uminus__atMost, axiom, ![X9, X4]:(hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X9))=hAPP(c_SetInterval_Oord__class_OatLeast(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X9))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__atMost)). 4.02/4.28 fof(fact_image__uminus__atLeast, axiom, ![X9, X4]:(hAPP(c_SetInterval_Oord__class_OatMost(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X9))=hAPP(c_Set_Oimage(X4,X4,c_Groups_Ouminus__class_Ouminus(X4)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X9))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__uminus__atLeast)). 4.02/4.28 fof(fact_INF__const, axiom, ![X54, X4, X3, X7]:(class_Complete__Lattice_Ocomplete__lattice(X7)=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=X3=>hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7),X3),hAPP(c_COMBK(X7,X4),X54))=X54)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INF__const)). 4.02/4.28 fof(fact_xt1_I7_J, axiom, ![X29, X13, X43, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X43),X13))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X29),X43))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X29),X13))))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I7_J)). 4.02/4.28 fof(fact_order__trans, axiom, ![X29, X43, X13, X4]:(class_Orderings_Opreorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X43))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X29))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X43),X29))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__trans)). 4.02/4.28 fof(fact_xt1_I6_J, axiom, ![X29, X13, X43, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X29),X13))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X29),X43)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X43),X13)))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I6_J)). 4.02/4.28 fof(fact_congruent2__implies__congruent, axiom, ![X26, X22, X83, X49, X7, X84, X3, X4]:(c_Equiv__Relations_Oequiv(X4,X3,X84)=>((c_Equiv__Relations_Ocongruent(X7,X49,X83,hAPP(X22,X26))<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3)))<=c_Equiv__Relations_Ocongruent2(X4,X7,X49,X84,X83,X22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_congruent2__implies__congruent)). 4.02/4.28 fof(fact_endo__inj__surj, axiom, ![X22, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X4,X22),X3)),X3))=>(X3=hAPP(c_Set_Oimage(X4,X4,X22),X3)<=c_Fun_Oinj__on(X4,X4,X22,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_endo__inj__surj)). 4.02/4.28 fof(fact_rtrancl__subset, axiom, ![X86, X39, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X39),X86))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X86),c_Transitive__Closure_Ortrancl(X4,X39)))=>c_Transitive__Closure_Ortrancl(X4,X39)=c_Transitive__Closure_Ortrancl(X4,X86))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__subset)). 4.02/4.28 fof(fact_inj__on__map__add__dom, axiom, ![X196, X21, X7, X4]:(c_Fun_Oinj__on(X4,tc_Option_Ooption(X7),X196,c_Map_Odom(X4,X7,X196))<=>c_Fun_Oinj__on(X4,tc_Option_Ooption(X7),c_Map_Omap__add(X4,X7,X21,X196),c_Map_Odom(X4,X7,X196))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__map__add__dom)). 4.02/4.28 fof(fact_SUP__const, axiom, ![X54, X4, X3, X7]:(class_Complete__Lattice_Ocomplete__lattice(X7)=>(X54=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X7),X3),hAPP(c_COMBK(X7,X4),X54))<=X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SUP__const)). 4.02/4.28 fof(fact_Suc__mult__le__cancel1, axiom, ![X20, X21, X28]:(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,X28)),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X28)),X20)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__mult__le__cancel1)). 4.02/4.28 fof(fact_add__minus__cancel, axiom, ![X12, X11, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)),X12))=X12<=class_Groups_Ogroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__minus__cancel)). 4.02/4.28 fof(fact_minus__add__cancel, axiom, ![X12, X11, X4]:(X12=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12))<=class_Groups_Ogroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__add__cancel)). 4.02/4.28 fof(fact_sup2E, axiom, ![X17, X9, X6, X3, X7, X4]:((hBOOL(hAPP(hAPP(X6,X9),X17))<=~(hBOOL(hAPP(hAPP(X3,X9),X17))))<=hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),X3),X6),X9),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup2E)). 4.02/4.28 fof(fact_Min_Oin__idem, axiom, ![X9, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X9),c_Big__Operators_Olinorder__class_OMin(X4,X3))=c_Big__Operators_Olinorder__class_OMin(X4,X3)<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Oin__idem)). 4.02/4.28 fof(fact_Max_Oin__idem, axiom, ![X9, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X9),c_Big__Operators_Olinorder__class_OMax(X4,X3))=c_Big__Operators_Olinorder__class_OMax(X4,X3)<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Oin__idem)). 4.02/4.28 fof(fact_psubsetD, axiom, ![X24, X6, X3, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X24),X3))=>hBOOL(hAPP(hAPP(c_member(X4),X24),X6)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_psubsetD)). 4.02/4.28 fof(fact_Inf__fin_Oin__idem, axiom, ![X9, X3, X4]:(class_Lattices_Olattice(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_member(X4),X9),X3))=>c_Big__Operators_Olattice__class_OInf__fin(X4,X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X9),c_Big__Operators_Olattice__class_OInf__fin(X4,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oin__idem)). 4.02/4.28 fof(fact_Sup__fin_Oin__idem, axiom, ![X9, X3, X4]:(((c_Big__Operators_Olattice__class_OSup__fin(X4,X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X9),c_Big__Operators_Olattice__class_OSup__fin(X4,X3))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oin__idem)). 4.02/4.28 fof(fact_le__mod__geq, axiom, ![X2, X5]:(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5),X5)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__mod__geq)). 4.02/4.28 fof(fact_imageI, axiom, ![X22, X7, X3, X9, X4]:(hBOOL(hAPP(hAPP(c_member(X7),hAPP(X22,X9)),hAPP(c_Set_Oimage(X4,X7,X22),X3)))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_imageI)). 4.02/4.28 fof(fact_UnCI, axiom, ![X3, X6, X24, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X24),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=(hBOOL(hAPP(hAPP(c_member(X4),X24),X3))<=~(hBOOL(hAPP(hAPP(c_member(X4),X24),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UnCI)). 4.02/4.28 fof(fact_map__le__upds, axiom, ![X108, X109, X76, X22, X7, X4]:(c_Map_Omap__le(X4,X7,c_Map_Omap__upds(X4,X7,X22,X109,X108),c_Map_Omap__upds(X4,X7,X76,X109,X108))<=c_Map_Omap__le(X4,X7,X22,X76)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__le__upds)). 4.02/4.28 fof(fact_map__add__comm, axiom, ![X162, X163, X7, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X7,X163)),c_Map_Odom(X4,X7,X162))=>c_Map_Omap__add(X4,X7,X162,X163)=c_Map_Omap__add(X4,X7,X163,X162)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__comm)). 4.02/4.28 fof(fact_sgn__if, axiom, ![X13, X4]:(((c_Groups_Ozero__class_Ozero(X4)=X13=>c_Groups_Ozero__class_Ozero(X4)=c_Groups_Osgn__class_Osgn(X4,X13))&(c_Groups_Ozero__class_Ozero(X4)!=X13=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X13)))=>c_Groups_Osgn__class_Osgn(X4,X13)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4)))&(c_Groups_Oone__class_Oone(X4)=c_Groups_Osgn__class_Osgn(X4,X13)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X13))))))<=class_Groups_Osgn__if(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__if)). 4.02/4.28 fof(fact_div__mult__self1__is__id, axiom, ![X11, X12, X4]:(class_Divides_Osemiring__div(X4)=>(X11=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)),X12)<=c_Groups_Ozero__class_Ozero(X4)!=X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self1__is__id)). 4.02/4.28 fof(fact_div__mult__self2__is__id, axiom, ![X11, X12, X4]:(class_Divides_Osemiring__div(X4)=>(X12!=c_Groups_Ozero__class_Ozero(X4)=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)),X12)=X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self2__is__id)). 4.02/4.28 fof(fact_nth__length__takeWhile, axiom, ![X32, X56, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X56,X32))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))=>~(hBOOL(hAPP(X56,hAPP(hAPP(c_List_Onth(X4),X32),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X56,X32))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__length__takeWhile)). 4.02/4.28 fof(fact_linorder__neqE__linordered__idom, axiom, ![X43, X13, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X43),X13))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),X43))))<=X13!=X43)<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__neqE__linordered__idom)). 4.02/4.28 fof(fact_add__less__imp__less__left, axiom, ![X12, X11, X10, X4]:(class_Groups_Oordered__ab__semigroup__add__imp__le(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X12))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__less__imp__less__left)). 4.02/4.28 fof(fact_equivp__def, axiom, ![X39, X4]:(![X19, X34]:(hAPP(X39,X19)=hAPP(X39,X34)<=>hBOOL(hAPP(hAPP(X39,X19),X34)))<=>c_Equiv__Relations_Oequivp(X4,X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivp__def)). 4.02/4.28 fof(fact_linorder__antisym__conv3, axiom, ![X9, X17, X4]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X17),X9)))=>(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X9),X17)))<=>X17=X9))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__antisym__conv3)). 4.02/4.28 fof(fact_folding__idem_Oidem__comp, axiom, ![X9, X87, X22, X7, X4]:(hAPP(X22,X9)=hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X22,X9)),hAPP(X22,X9))<=c_Finite__Set_Ofolding__idem(X4,X7,X22,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__idem_Oidem__comp)). 4.02/4.28 fof(fact_of__int__less__iff, axiom, ![X16, X23, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23),X16))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X23)),hAPP(c_Int_Oring__1__class_Oof__int(X4),X16))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__less__iff)). 4.02/4.28 fof(fact_of__nat__less__iff, axiom, ![X20, X21, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X21)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X20))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__less__iff)). 4.02/4.28 fof(fact_of__int__le__iff, axiom, ![X16, X23, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X23)),hAPP(c_Int_Oring__1__class_Oof__int(X4),X16)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23),X16)))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__le__iff)). 4.02/4.28 fof(fact_mod__minus__eq, axiom, ![X12, X11, X4]:(c_Divides_Odiv__class_Omod(X4,hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Divides_Odiv__class_Omod(X4,X11,X12)),X12)=c_Divides_Odiv__class_Omod(X4,hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11),X12)<=class_Divides_Oring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__minus__eq)). 4.02/4.28 fof(fact_wf__no__infinite__down__chainE, axiom, ![X22, X18, X4]:(c_Wellfounded_Owf(X4,X18)=>~(![X137]:hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(X22,hAPP(c_Nat_OSuc,X137))),hAPP(X22,X137))),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__no__infinite__down__chainE)). 4.02/4.28 fof(fact_of__nat__le__iff, axiom, ![X20, X21, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X21)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X20)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20)))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__le__iff)). 4.02/4.28 fof(fact_power__abs, axiom, ![X5, X11, X4]:(hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5))=hAPP(hAPP(c_Power_Opower__class_Opower(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),X5)<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__abs)). 4.02/4.28 fof(fact_listsum__simps_I2_J, axiom, ![X45, X13, X4]:(hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X13),hAPP(c_List_Omonoid__add__class_Olistsum(X4),X45))<=class_Groups_Omonoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__simps_I2_J)). 4.02/4.28 fof(fact_diff__eq__diff__less, axiom, ![X102, X24, X25, X26, X4]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X26),X25)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X24),X102)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X25))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),X102))))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__eq__diff__less)). 4.02/4.28 fof(fact_Compl__iff, axiom, ![X3, X24, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X24),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X3)))<=>~(hBOOL(hAPP(hAPP(c_member(X4),X24),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__iff)). 4.02/4.28 fof(fact_diff__eq__diff__less__eq, axiom, ![X102, X24, X25, X26, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),X25))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X24),X102)))<=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X24),X102)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X26),X25))<=class_Groups_Oordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__eq__diff__less__eq)). 4.02/4.28 fof(fact_compl__unique, axiom, ![X43, X13, X4]:(class_Lattices_Oboolean__algebra(X4)=>(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43)=c_Orderings_Obot__class_Obot(X4)=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43)=c_Orderings_Otop__class_Otop(X4)=>X43=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__unique)). 4.02/4.28 fof(fact_hd__map, axiom, ![X22, X7, X4, X32]:(c_List_Olist_ONil(X4)!=X32=>hAPP(X22,hAPP(c_List_Ohd(X4),X32))=hAPP(c_List_Ohd(X7),hAPP(hAPP(c_List_Omap(X4,X7),X22),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__map)). 4.02/4.28 fof(fact_finite__UnI, axiom, ![X253, X87, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X87))=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X87),X253)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X253)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__UnI)). 4.02/4.28 fof(fact_ord_OatLeastAtMost__iff, axiom, ![X115, X60, X201, X37, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X37),c_SetInterval_Oord_OatLeastAtMost(X4,X201,X60,X115)))<=>(hBOOL(hAPP(hAPP(X201,X37),X115))&hBOOL(hAPP(hAPP(X201,X60),X37)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OatLeastAtMost__iff)). 4.02/4.28 fof(fact_ord_OgreaterThanLessThan__iff, axiom, ![X115, X60, X194, X37, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X37),c_SetInterval_Oord_OgreaterThanLessThan(X4,X194,X60,X115)))<=>(hBOOL(hAPP(hAPP(X194,X60),X37))&hBOOL(hAPP(hAPP(X194,X37),X115)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OgreaterThanLessThan__iff)). 4.02/4.28 fof(fact_of__nat__aux_Osimps_I2_J, axiom, ![X37, X20, X306, X4]:(class_Rings_Osemiring__1(X4)=>c_Nat_Osemiring__1__class_Oof__nat__aux(X4,X306,hAPP(c_Nat_OSuc,X20),X37)=c_Nat_Osemiring__1__class_Oof__nat__aux(X4,X306,X20,hAPP(X306,X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__aux_Osimps_I2_J)). 4.02/4.28 fof(fact_map__eq__imp__length__eq, axiom, ![X31, X76, X49, X32, X22, X4, X7]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X49)),X31)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X32)<=hAPP(hAPP(c_List_Omap(X7,X4),X22),X32)=hAPP(hAPP(c_List_Omap(X49,X4),X76),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__eq__imp__length__eq)). 4.02/4.28 fof(fact_evaln_Oequations_I8_J, axiom, ![X68, X66, X67, X69, X70]:(c_Natural_Oevaln(c_Com_Ocom_OWhile(X70,X69),X67,X66,X68)<=>((X67=X68&~(hBOOL(hAPP(X70,X67))))|(?[X136]:(c_Natural_Oevaln(c_Com_Ocom_OWhile(X70,X69),X136,X66,X68)&c_Natural_Oevaln(X69,X67,X66,X136))&hBOOL(hAPP(X70,X67))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evaln_Oequations_I8_J)). 4.02/4.28 fof(fact_PowI, axiom, ![X6, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))=>hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(c_Set_OPow(X4),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_PowI)). 4.02/4.28 fof(fact_nat__zero__less__power__iff, axiom, ![X20, X9]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9))|X20=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X9),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__zero__less__power__iff)). 4.02/4.28 fof(fact_set__replicate__conv__if, axiom, ![X9, X4, X20]:((hAPP(c_List_Oset(X4),c_List_Oreplicate(X4,X20,X9))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X20)&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X20=>hAPP(c_List_Oset(X4),c_List_Oreplicate(X4,X20,X9))=hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__replicate__conv__if)). 4.02/4.28 fof(fact_less__trans__Suc, axiom, ![X107, X135, X46]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X46)),X107))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X135),X107)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__trans__Suc)). 4.02/4.28 fof(fact_list__ex__iff, axiom, ![X32, X56, X4]:(?[X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),hAPP(c_List_Oset(X4),X32)))&hBOOL(hAPP(X56,X19)))<=>c_List_Olist__ex(X4,X56,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__iff)). 4.02/4.28 fof(fact_append__in__listsp__conv, axiom, ![X31, X32, X3, X4]:(hBOOL(hAPP(c_List_Olistsp(X4,X3),hAPP(hAPP(c_List_Oappend(X4),X32),X31)))<=>(hBOOL(hAPP(c_List_Olistsp(X4,X3),X31))&hBOOL(hAPP(c_List_Olistsp(X4,X3),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__in__listsp__conv)). 4.02/4.28 fof(fact_equiv__comp__eq, axiom, ![X18, X3, X4]:(X18=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(c_Relation_Oconverse(X4,X4),X18)),X18)<=c_Equiv__Relations_Oequiv(X4,X3,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__comp__eq)). 4.02/4.28 fof(fact_Sup__fold__sup, axiom, ![X3, X4]:((c_Complete__Lattice_OSup__class_OSup(X4,X3)=hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4)),c_Orderings_Obot__class_Obot(X4)),X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fold__sup)). 4.02/4.28 fof(fact_Inf__fold__inf, axiom, ![X3, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>(c_Complete__Lattice_OInf__class_OInf(X4,X3)=hAPP(hAPP(c_Finite__Set_Ofold(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),c_Orderings_Otop__class_Otop(X4)),X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fold__inf)). 4.02/4.28 fof(fact_neg__less__0__iff__less, axiom, ![X26, X4]:(class_Groups_Oordered__ab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26)),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__less__0__iff__less)). 4.02/4.28 fof(fact_neg__le__0__iff__le, axiom, ![X26, X4]:(class_Groups_Oordered__ab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26)),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__le__0__iff__le)). 4.02/4.28 fof(fact_neg__0__less__iff__less, axiom, ![X26, X4]:(class_Groups_Oordered__ab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__0__less__iff__less)). 4.02/4.28 fof(fact_folding__one_Osingleton, axiom, ![X9, X87, X22, X4]:(c_Finite__Set_Ofolding__one(X4,X22,X87)=>X9=hAPP(X87,hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Osingleton)). 4.02/4.28 fof(fact_type__definition_OAbs__inject, axiom, ![X17, X9, X3, X170, X171, X7, X4]:((((hAPP(X170,X9)=hAPP(X170,X17)<=>X17=X9)<=hBOOL(hAPP(hAPP(c_member(X7),X17),X3)))<=hBOOL(hAPP(hAPP(c_member(X7),X9),X3)))<=c_Typedef_Otype__definition(X4,X7,X171,X170,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_OAbs__inject)). 4.02/4.28 fof(fact_neg__0__le__iff__le, axiom, ![X26, X4]:(class_Groups_Oordered__ab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__0__le__iff__le)). 4.02/4.28 fof(fact_of__nat__0__less__iff, axiom, ![X20, X4]:(class_Rings_Olinordered__semidom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X20)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__0__less__iff)). 4.02/4.28 fof(fact_rev__predicate2D, axiom, ![X112, X7, X4, X17, X9, X56]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),X56),X112))=>hBOOL(hAPP(hAPP(X112,X9),X17)))<=hBOOL(hAPP(hAPP(X56,X9),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__predicate2D)). 4.02/4.28 fof(fact_inj__on__the__inv__into, axiom, ![X3, X22, X7, X4]:(c_Fun_Oinj__on(X7,X4,c_Fun_Othe__inv__into(X4,X7,X3,X22),hAPP(c_Set_Oimage(X4,X7,X22),X3))<=c_Fun_Oinj__on(X4,X7,X22,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__the__inv__into)). 4.02/4.28 fof(fact_distinct__product, axiom, ![X59, X7, X45, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X45))=>(hBOOL(hAPP(c_List_Odistinct(tc_prod(X4,X7)),c_Enum_Oproduct(X4,X7,X45,X59)))<=hBOOL(hAPP(c_List_Odistinct(X7),X59)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__product)). 4.02/4.28 fof(fact_min__max_Oinf__left__idem, axiom, ![X43, X13, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),X43)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),X43))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__left__idem)). 4.02/4.28 fof(fact_min__max_Osup_Oleft__idem, axiom, ![X12, X11, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X11),X12)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X11),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X11),X12))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup_Oleft__idem)). 4.02/4.28 fof(fact_diff__Suc__less, axiom, ![X46, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),hAPP(c_Nat_OSuc,X46))),X5))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__Suc__less)). 4.02/4.28 fof(fact_finite__Plus__iff, axiom, ![X6, X3, X7, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X6))&hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X4,X7)),c_Sum__Type_OPlus(X4,X7,X3,X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Plus__iff)). 4.02/4.28 fof(fact_r__into__rtrancl, axiom, ![X18, X51, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X51),X18))=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X51),c_Transitive__Closure_Ortrancl(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_r__into__rtrancl)). 4.02/4.28 fof(fact_butlast__append, axiom, ![X45, X4, X59]:((c_List_Olist_ONil(X4)=X59=>c_List_Obutlast(X4,X45)=c_List_Obutlast(X4,hAPP(hAPP(c_List_Oappend(X4),X45),X59)))&(c_List_Olist_ONil(X4)!=X59=>hAPP(hAPP(c_List_Oappend(X4),X45),c_List_Obutlast(X4,X59))=c_List_Obutlast(X4,hAPP(hAPP(c_List_Oappend(X4),X45),X59)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast__append)). 4.02/4.28 fof(fact_inj__on__imageI, axiom, ![X3, X22, X76, X49, X7, X4]:(c_Fun_Oinj__on(X49,X7,X76,hAPP(c_Set_Oimage(X4,X49,X22),X3))<=c_Fun_Oinj__on(X4,X7,hAPP(c_Fun_Ocomp(X49,X7,X4,X76),X22),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__imageI)). 4.02/4.28 fof(fact_add__diff__inverse, axiom, ![X5, X2]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X5)))=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5))=X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__diff__inverse)). 4.02/4.28 fof(fact_atLeastAtMost__singleton, axiom, ![X26, X4]:(hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=c_SetInterval_Oord__class_OatLeastAtMost(X4,X26,X26)<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastAtMost__singleton)). 4.02/4.28 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, axiom, ![X5, X13]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))=>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),X13),X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J)). 4.02/4.28 fof(fact_less__diff__conv, axiom, ![X28, X38, X37]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),X28)),X38))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X38),X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__diff__conv)). 4.02/4.28 fof(fact_le__diff__conv, axiom, ![X37, X28, X38]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X38),X28)),X37))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X38),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__diff__conv)). 4.02/4.28 fof(fact_fun__left__comm__idem_Ofun__comp__idem, axiom, ![X9, X22, X7, X4]:(c_Finite__Set_Ofun__left__comm__idem(X4,X7,X22)=>hAPP(c_Fun_Ocomp(X7,X7,X7,hAPP(X22,X9)),hAPP(X22,X9))=hAPP(X22,X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofun__comp__idem)). 4.02/4.28 fof(fact_distinct__zipI1, axiom, ![X59, X7, X45, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X45))=>hBOOL(hAPP(c_List_Odistinct(tc_prod(X4,X7)),hAPP(hAPP(c_List_Ozip(X4,X7),X45),X59)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__zipI1)). 4.02/4.28 fof(fact_distinct__zipI2, axiom, ![X45, X7, X59, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X59))=>hBOOL(hAPP(c_List_Odistinct(tc_prod(X7,X4)),hAPP(hAPP(c_List_Ozip(X7,X4),X45),X59)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__zipI2)). 4.02/4.28 fof(fact_append1__eq__conv, axiom, ![X17, X31, X9, X32, X4]:((X32=X31&X17=X9)<=>hAPP(hAPP(c_List_Oappend(X4),X31),hAPP(hAPP(c_List_Olist_OCons(X4),X17),c_List_Olist_ONil(X4)))=hAPP(hAPP(c_List_Oappend(X4),X32),hAPP(hAPP(c_List_Olist_OCons(X4),X9),c_List_Olist_ONil(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append1__eq__conv)). 4.02/4.28 fof(fact_setprod__1, axiom, ![X3, X7, X4]:(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X4),hAPP(c_COMBK(X4,X7),c_Groups_Oone__class_Oone(X4))),X3)=c_Groups_Oone__class_Oone(X4)<=class_Groups_Ocomm__monoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__1)). 4.02/4.28 fof(fact_setsum__0, axiom, ![X3, X7, X4]:(class_Groups_Ocomm__monoid__add(X4)=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),hAPP(c_COMBK(X4,X7),c_Groups_Ozero__class_Ozero(X4))),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum__0)). 4.02/4.28 fof(fact_divmod__int__rel__div, axiom, ![X101, X14, X12, X11]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X12),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X14),X101)))=>(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12)=X14<=c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__div)). 4.02/4.28 fof(fact_of__nat__Suc, axiom, ![X2, X4]:(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),hAPP(c_Nat_OSuc,X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X2))<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__Suc)). 4.02/4.28 fof(fact_less__infI1, axiom, ![X12, X13, X11, X4]:(class_Lattices_Osemilattice__inf(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X13))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X11),X12)),X13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__infI1)). 4.02/4.28 fof(fact_less__infI2, axiom, ![X11, X13, X12, X4]:(class_Lattices_Osemilattice__inf(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X11),X12)),X13))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__infI2)). 4.02/4.28 fof(fact_posDivAlg__correct, axiom, ![X12, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))=>hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X12),c_Divides_OposDivAlg(X11,X12))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_posDivAlg__correct)). 4.02/4.28 fof(fact_negDivAlg__correct, axiom, ![X12, X11]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))=>hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X12),c_Divides_OnegDivAlg(X11,X12))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negDivAlg__correct)). 4.02/4.28 fof(fact_finite__option__UNIV, axiom, ![X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X4)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X4),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__option__UNIV)). 4.02/4.28 fof(fact_le__infI1, axiom, ![X12, X13, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X13))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X11),X12)),X13)))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__infI1)). 4.02/4.28 fof(fact_le__infI2, axiom, ![X11, X13, X12, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X11),X12)),X13))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X13)))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__infI2)). 4.02/4.28 fof(fact_less__supI1, axiom, ![X12, X11, X13, X4]:(class_Lattices_Osemilattice__sup(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X11),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__supI1)). 4.02/4.28 fof(fact_less__supI2, axiom, ![X11, X12, X13, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X11),X12))))<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__supI2)). 4.02/4.28 fof(fact_rel__pow__0__E, axiom, ![X39, X17, X9, X4]:(X17=X9<=hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__0__E)). 4.02/4.28 fof(fact_le__supI1, axiom, ![X12, X11, X13, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X11),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X11)))<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__supI1)). 4.02/4.28 fof(fact_le__supI2, axiom, ![X11, X12, X13, X4]:(class_Lattices_Osemilattice__sup(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X11),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__supI2)). 4.02/4.28 fof(fact_less__Suc__eq__0__disj, axiom, ![X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_OSuc,X20)))<=>(?[X139]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X139),X20))&hAPP(c_Nat_OSuc,X139)=X21)|X21=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Suc__eq__0__disj)). 4.02/4.28 fof(fact_comm__monoid__big_Oinfinite, axiom, ![X76, X3, X87, X16, X22, X7, X4]:((X16=hAPP(hAPP(X87,X76),X3)<=~(hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3))))<=c_Big__Operators_Ocomm__monoid__big(X4,X7,X22,X16,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__monoid__big_Oinfinite)). 4.02/4.28 fof(fact_Suc__diff__le, axiom, ![X2, X5]:(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X5)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__diff__le)). 4.02/4.28 fof(fact_Ints__minus, axiom, ![X26, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X26),c_Int_Oring__1__class_OInts(X4)))=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26)),c_Int_Oring__1__class_OInts(X4))))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__minus)). 4.02/4.28 fof(fact_of__int__less__0__iff, axiom, ![X16, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X16)),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__less__0__iff)). 4.02/4.28 fof(fact_last__drop, axiom, ![X45, X4, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)))=>c_List_Olast(X4,hAPP(hAPP(c_List_Odrop(X4),X5),X45))=c_List_Olast(X4,X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__drop)). 4.02/4.28 fof(fact_of__int__le__0__iff, axiom, ![X16, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X16)),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__le__0__iff)). 4.02/4.28 fof(fact_of__int__0__less__iff, axiom, ![X16, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Oring__1__class_Oof__int(X4),X16))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__0__less__iff)). 4.02/4.28 fof(fact_of__int__0__le__iff, axiom, ![X16, X4]:(class_Rings_Olinordered__idom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Oring__1__class_Oof__int(X4),X16))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__0__le__iff)). 4.02/4.28 fof(fact_inj__on__contraD, axiom, ![X17, X9, X3, X22, X7, X4]:((((hBOOL(hAPP(hAPP(c_member(X4),X17),X3))=>hAPP(X22,X17)!=hAPP(X22,X9))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))<=X17!=X9)<=c_Fun_Oinj__on(X4,X7,X22,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__contraD)). 4.02/4.28 fof(fact_mod__Suc, axiom, ![X5, X2]:((hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5))=X5=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X5))&(hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5))!=X5=>hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__Suc)). 4.02/4.28 fof(fact_listrel__Nil1, axiom, ![X18, X32, X4]:(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_ONil(X4)),X32)),c_List_Olistrel(X4,X18)))=>c_List_Olist_ONil(X4)=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Nil1)). 4.02/4.28 fof(fact_in__set__dropD, axiom, ![X32, X20, X9, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Odrop(X4),X20),X32))))=>hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__dropD)). 4.02/4.28 fof(fact_listrel__Nil2, axiom, ![X18, X32, X4]:(X32=c_List_Olist_ONil(X4)<=hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),c_List_Olist_ONil(X4))),c_List_Olistrel(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__Nil2)). 4.02/4.28 fof(fact_filter__sort, axiom, ![X32, X22, X56, X4, X7]:(class_Orderings_Olinorder(X7)=>c_List_Olinorder__class_Osort__key(X4,X7,X22,hAPP(c_List_Ofilter(X4,X56),X32))=hAPP(c_List_Ofilter(X4,X56),c_List_Olinorder__class_Osort__key(X4,X7,X22,X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__sort)). 4.02/4.28 fof(fact_in__set__takeD, axiom, ![X32, X20, X9, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Otake(X4),X20),X32))))=>hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__takeD)). 4.02/4.28 fof(fact_domD, axiom, ![X21, X7, X26, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X26),c_Map_Odom(X4,X7,X21)))=>?[X78]:hAPP(c_Option_Ooption_OSome(X7),X78)=hAPP(X21,X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_domD)). 4.02/4.28 fof(fact_neg__mod__sign, axiom, ![X11, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__mod__sign)). 4.02/4.28 fof(fact_inf__Sup__absorb, axiom, ![X26, X3, X4]:(class_Lattices_Olattice(X4)=>((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X26),c_Big__Operators_Olattice__class_OSup__fin(X4,X3))=X26<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__Sup__absorb)). 4.02/4.28 fof(fact_sup__Inf__absorb, axiom, ![X26, X3, X4]:(class_Lattices_Olattice(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(X26=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X26),c_Big__Operators_Olattice__class_OInf__fin(X4,X3))<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__Inf__absorb)). 4.02/4.28 fof(fact_pos__mod__sign, axiom, ![X11, X12]:(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,X11,X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__mod__sign)). 4.02/4.28 fof(fact_transfer__int__nat__quantifiers_I1_J, axiom, ![X56]:(![X19]:(hBOOL(hAPP(X56,X19))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19)))<=>![X19]:hBOOL(hAPP(X56,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__quantifiers_I1_J)). 4.02/4.28 fof(fact_inj__on__def, axiom, ![X3, X22, X7, X4]:(![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X3))=>![X114]:(hBOOL(hAPP(hAPP(c_member(X4),X114),X3))=>(X19=X114<=hAPP(X22,X19)=hAPP(X22,X114))))<=>c_Fun_Oinj__on(X4,X7,X22,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__def)). 4.02/4.28 fof(fact_Min__le, axiom, ![X9, X3, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_member(X4),X9),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Big__Operators_Olinorder__class_OMin(X4,X3)),X9))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min__le)). 4.02/4.28 fof(fact_Max__ge, axiom, ![X9, X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>(hBOOL(hAPP(hAPP(c_member(X4),X9),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),c_Big__Operators_Olinorder__class_OMax(X4,X3)))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max__ge)). 4.02/4.28 fof(fact_domI, axiom, ![X7, X25, X4, X26, X21]:(hBOOL(hAPP(hAPP(c_member(X7),X26),c_Map_Odom(X7,X4,X21)))<=hAPP(c_Option_Ooption_OSome(X4),X25)=hAPP(X21,X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_domI)). 4.02/4.28 fof(fact_ranI, axiom, ![X7, X25, X4, X26, X21]:(hBOOL(hAPP(hAPP(c_member(X4),X25),c_Map_Oran(X7,X4,X21)))<=hAPP(X21,X26)=hAPP(c_Option_Ooption_OSome(X4),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ranI)). 4.02/4.28 fof(fact_insort__key_Osimps_I1_J, axiom, ![X9, X22, X4, X7]:(hAPP(hAPP(c_List_Olist_OCons(X4),X9),c_List_Olist_ONil(X4))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X7,X22),X9),c_List_Olist_ONil(X4))<=class_Orderings_Olinorder(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__key_Osimps_I1_J)). 4.02/4.28 fof(fact_fun__left__comm_Ofun__left__comm__apply, axiom, ![X76, X49, X22, X7, X4]:(c_Finite__Set_Ofun__left__comm(X4,X7,X22)=>c_Finite__Set_Ofun__left__comm(X49,X7,hAPP(hAPP(c_COMBB(X4,tc_fun(X7,X7),X49),X22),X76))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofun__left__comm__apply)). 4.02/4.28 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J, axiom, ![X13, X4]:(hAPP(c_Groups_Ouminus__class_Ouminus(X4),X13)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))),X13)<=class_Rings_Ocomm__ring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J)). 4.02/4.28 fof(fact_sgn__less, axiom, ![X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Osgn__class_Osgn(X4,X26)),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__less)). 4.02/4.28 fof(fact_sgn__greater, axiom, ![X26, X4]:(class_Rings_Olinordered__idom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X26))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),c_Groups_Osgn__class_Osgn(X4,X26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__greater)). 4.02/4.28 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply, axiom, ![X76, X49, X22, X7, X4]:(c_Finite__Set_Ofun__left__comm__idem(X49,X7,hAPP(hAPP(c_COMBB(X4,tc_fun(X7,X7),X49),X22),X76))<=c_Finite__Set_Ofun__left__comm__idem(X4,X7,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofun__left__comm__idem__apply)). 4.02/4.28 fof(fact_finite__converse, axiom, ![X18, X7, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X7,X4)),X18))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X7)),hAPP(c_Relation_Oconverse(X7,X4),X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__converse)). 4.02/4.28 fof(fact_exists1__code, axiom, ![X56, X4]:((?[X19]:(![X34]:(hBOOL(hAPP(X56,X34))=>X34=X19)&hBOOL(hAPP(X56,X19)))<=>c_List_Olist__ex1(X4,X56,c_Enum_Oenum__class_Oenum(X4)))<=class_Enum_Oenum(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_exists1__code)). 4.02/4.28 fof(fact_override__on__def, axiom, ![X76, X22, X7, X3, X26, X4]:((hAPP(X76,X26)=hAPP(c_Fun_Ooverride__on(X4,X7,X22,X76,X3),X26)<=hBOOL(hAPP(hAPP(c_member(X4),X26),X3)))&(hAPP(X22,X26)=hAPP(c_Fun_Ooverride__on(X4,X7,X22,X76,X3),X26)<=~(hBOOL(hAPP(hAPP(c_member(X4),X26),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_override__on__def)). 4.02/4.28 fof(fact_transfer__nat__int__set__relations_I2_J, axiom, ![X3, X9]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X9)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X3)))<=>hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X9),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__relations_I2_J)). 4.02/4.28 fof(fact_notin__set__remove1, axiom, ![X17, X32, X9, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),c_List_Oremove1(X4,X17,X32)))))<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_notin__set__remove1)). 4.02/4.28 fof(fact_in__set__sublistD, axiom, ![X41, X32, X9, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),c_List_Osublist(X4,X32,X41))))=>hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__sublistD)). 4.02/4.28 fof(fact_set__takeWhileD, axiom, ![X32, X56, X9, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))&hBOOL(hAPP(X56,X9)))<=hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),c_List_OtakeWhile(X4,X56,X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__takeWhileD)). 4.02/4.28 fof(fact_evaln_Oequations_I7_J, axiom, ![X66, X67, X69, X70]:((hBOOL(hAPP(X70,X67))=>?[X136]:(c_Natural_Oevaln(X69,X67,X66,X136)&c_Natural_Oevaln(c_Com_Ocom_OWhile(X70,X69),X136,X66,X67)))<=>c_Natural_Oevaln(c_Com_Ocom_OWhile(X70,X69),X67,X66,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evaln_Oequations_I7_J)). 4.02/4.28 fof(fact_last__map, axiom, ![X22, X7, X4, X32]:(hAPP(X22,c_List_Olast(X4,X32))=c_List_Olast(X7,hAPP(hAPP(c_List_Omap(X4,X7),X22),X32))<=c_List_Olist_ONil(X4)!=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__map)). 4.02/4.28 fof(fact_less__le__not__le, axiom, ![X17, X9, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X9),X17))<=>(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X17),X9)))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X17))))<=class_Orderings_Opreorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__le__not__le)). 4.02/4.28 fof(fact_remove1__idem, axiom, ![X32, X9, X4]:(~(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32))))=>c_List_Oremove1(X4,X9,X32)=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__idem)). 4.02/4.28 fof(fact_inj__on__diff, axiom, ![X6, X3, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,X3)=>c_Fun_Oinj__on(X4,X7,X22,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__diff)). 4.02/4.28 fof(fact_hd__in__set, axiom, ![X4, X32]:(X32!=c_List_Olist_ONil(X4)=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_List_Ohd(X4),X32)),hAPP(c_List_Oset(X4),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__in__set)). 4.02/4.28 fof(fact_add1__zle__eq, axiom, ![X16, X23]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23),c_Groups_Oone__class_Oone(tc_Int_Oint))),X16))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add1__zle__eq)). 4.02/4.28 fof(fact_less__bin__lemma, axiom, ![X60, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X28),X60))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X28),X60)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__bin__lemma)). 4.02/4.28 fof(fact_sgn__neg, axiom, ![X11, X4]:(class_Rings_Olinordered__idom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Ozero__class_Ozero(X4)))=>c_Groups_Osgn__class_Osgn(X4,X11)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__neg)). 4.02/4.28 fof(fact_Id__on__iff, axiom, ![X3, X17, X9, X4]:((X9=X17&hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))<=>hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),c_Relation_OId__on(X4,X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__iff)). 4.02/4.28 fof(fact_zless__int, axiom, ![X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__int)). 4.02/4.28 fof(fact_card__seteq, axiom, ![X3, X6, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))=>(X3=X6<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X6)),hAPP(c_Finite__Set_Ocard(X4),X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__seteq)). 4.02/4.28 fof(fact_map__add__dom__app__simps_I1_J, axiom, ![X206, X205, X7, X21, X4]:(hAPP(X205,X21)=hAPP(c_Map_Omap__add(X4,X7,X206,X205),X21)<=hBOOL(hAPP(hAPP(c_member(X4),X21),c_Map_Odom(X4,X7,X205)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__dom__app__simps_I1_J)). 4.02/4.28 fof(fact_zle__int, axiom, ![X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__int)). 4.02/4.28 fof(fact_zero__less__diff, axiom, ![X21, X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__diff)). 4.02/4.28 fof(fact_zle__add1__eq__le, axiom, ![X16, X23]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16),c_Groups_Oone__class_Oone(tc_Int_Oint))))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X23),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__add1__eq__le)). 4.02/4.28 fof(fact_abs__minus__le__zero, axiom, ![X11, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11))),c_Groups_Ozero__class_Ozero(X4)))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__minus__le__zero)). 4.02/4.28 fof(fact_minus__diff__eq, axiom, ![X12, X11, X4]:(class_Groups_Oab__group__add(X4)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X12),X11)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__diff__eq)). 4.02/4.28 fof(fact_transfer__int__nat__quantifiers_I2_J, axiom, ![X56]:(?[X19]:hBOOL(hAPP(X56,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19)))<=>?[X19]:(hBOOL(hAPP(X56,X19))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__quantifiers_I2_J)). 4.02/4.28 fof(fact_atLeastLessThan__empty__iff2, axiom, ![X25, X26, X4]:((hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X26),X25)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X25))))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__empty__iff2)). 4.02/4.28 fof(fact_div__mult__self1__is__m, axiom, ![X2, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5))=>X2=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X2)),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self1__is__m)). 4.02/4.28 fof(fact_div__mult__self__is__m, axiom, ![X2, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5))=>X2=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult__self__is__m)). 4.02/4.28 fof(fact_sgn__1__neg, axiom, ![X26, X4]:(class_Rings_Olinordered__idom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),c_Groups_Ozero__class_Ozero(X4)))<=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))=c_Groups_Osgn__class_Osgn(X4,X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__1__neg)). 4.02/4.28 fof(fact_list__all2__rev, axiom, ![X31, X32, X56, X7, X4]:(c_List_Olist__all2(X4,X7,X56,hAPP(c_List_Orev(X4),X32),hAPP(c_List_Orev(X7),X31))<=>c_List_Olist__all2(X4,X7,X56,X32,X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__rev)). 4.02/4.28 fof(fact_min__max_Oless__infI1, axiom, ![X12, X13, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X13))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X11),X12)),X13)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oless__infI1)). 4.02/4.28 fof(fact_wf__Int1, axiom, ![X214, X18, X4]:(c_Wellfounded_Owf(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),X214))<=c_Wellfounded_Owf(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__Int1)). 4.02/4.28 fof(fact_wf__Int2, axiom, ![X214, X18, X4]:(c_Wellfounded_Owf(X4,X18)=>c_Wellfounded_Owf(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X214),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__Int2)). 4.02/4.28 fof(fact_the__inv__into__f__f, axiom, ![X9, X3, X22, X7, X4]:((X9=hAPP(c_Fun_Othe__inv__into(X4,X7,X3,X22),hAPP(X22,X9))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))<=c_Fun_Oinj__on(X4,X7,X22,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__inv__into__f__f)). 4.02/4.28 fof(fact_min__max_Oless__infI2, axiom, ![X11, X13, X12, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X11),X12)),X13))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oless__infI2)). 4.02/4.28 fof(fact_min__max_Ole__infI1, axiom, ![X12, X13, X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X11),X12)),X13))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X13)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__infI1)). 4.02/4.28 fof(fact_remove1__insort, axiom, ![X32, X9, X4]:(class_Orderings_Olinorder(X4)=>c_List_Oremove1(X4,X9,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X9),X32))=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__insort)). 4.02/4.28 fof(fact_Sup__insert, axiom, ![X3, X26, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>c_Complete__Lattice_OSup__class_OSup(X4,hAPP(hAPP(c_Set_Oinsert(X4),X26),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X26),c_Complete__Lattice_OSup__class_OSup(X4,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__insert)). 4.02/4.28 fof(fact_min__max_Oless__supI1, axiom, ![X12, X11, X13, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X11),X12))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oless__supI1)). 4.02/4.28 fof(fact_Inf__insert, axiom, ![X3, X26, X4]:(c_Complete__Lattice_OInf__class_OInf(X4,hAPP(hAPP(c_Set_Oinsert(X4),X26),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X26),c_Complete__Lattice_OInf__class_OInf(X4,X3))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__insert)). 4.02/4.28 fof(fact_eq__diff__iff, axiom, ![X20, X21, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X21))=>((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21),X28)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20),X28)<=>X21=X20)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__diff__iff)). 4.02/4.28 fof(fact_min__max_Oless__supI2, axiom, ![X11, X12, X13, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X11),X12))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oless__supI2)). 4.02/4.28 fof(fact_min__max_Ole__supI1, axiom, ![X12, X11, X13, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X11),X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__supI1)). 4.02/4.28 fof(fact_option__map__eq__Some, axiom, ![X17, X35, X22, X4, X7]:(?[X36]:(hAPP(c_Option_Ooption_OSome(X7),X36)=X35&X17=hAPP(X22,X36))<=>hAPP(c_Option_Ooption_OSome(X4),X17)=hAPP(hAPP(c_Option_Omap(X7,X4),X22),X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option__map__eq__Some)). 4.02/4.28 fof(fact_type__definition_ORep__range, axiom, ![X3, X170, X171, X7, X4]:(c_Typedef_Otype__definition(X4,X7,X171,X170,X3)=>X3=hAPP(c_Set_Oimage(X4,X7,X171),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_ORep__range)). 4.02/4.28 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J, axiom, ![X43, X13, X4]:(class_Rings_Ocomm__ring__1(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X13),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X43))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X13),X43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J)). 4.02/4.28 fof(fact_min__max_Ole__supI2, axiom, ![X11, X12, X13, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X12))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X11),X12))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__supI2)). 4.02/4.28 fof(fact_listsum__eq__0__nat__iff__nat, axiom, ![X144]:(![X19]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X19),hAPP(c_List_Oset(tc_Nat_Onat),X144)))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X19)<=>hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X144)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__eq__0__nat__iff__nat)). 4.02/4.28 fof(fact_single__valued__rel__pow, axiom, ![X20, X39, X4]:(c_Relation_Osingle__valued(X4,X4,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X20),X39))<=c_Relation_Osingle__valued(X4,X4,X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__rel__pow)). 4.02/4.28 fof(fact_diff__def, axiom, ![X12, X11, X4]:(class_Groups_Ogroup__add(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__def)). 4.02/4.28 fof(fact_listsp_Oequations_I2_J, axiom, ![X67, X70, X3, X4]:(hBOOL(hAPP(c_List_Olistsp(X4,X3),hAPP(hAPP(c_List_Olist_OCons(X4),X70),X67)))<=>(hBOOL(hAPP(c_List_Olistsp(X4,X3),X67))&hBOOL(hAPP(X3,X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp_Oequations_I2_J)). 4.02/4.28 fof(fact_negD, axiom, ![X13]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>?[X104]:X13=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X104)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negD)). 4.02/4.28 fof(fact_evaln_OWhileTrue, axiom, ![X192, X148, X20, X24, X193, X25]:(hBOOL(hAPP(X25,X193))=>(c_Natural_Oevaln(X24,X193,X20,X148)=>(c_Natural_Oevaln(c_Com_Ocom_OWhile(X25,X24),X148,X20,X192)=>c_Natural_Oevaln(c_Com_Ocom_OWhile(X25,X24),X193,X20,X192)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evaln_OWhileTrue)). 4.02/4.28 fof(fact_ab__diff__minus, axiom, ![X12, X11, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X12)<=class_Groups_Oab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ab__diff__minus)). 4.02/4.28 fof(fact_inj__mapD, axiom, ![X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))<=c_Fun_Oinj__on(tc_List_Olist(X4),tc_List_Olist(X7),hAPP(c_List_Omap(X4,X7),X22),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__mapD)). 4.02/4.28 fof(fact_diff__eq, axiom, ![X43, X13, X4]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X13),X43)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X43))<=class_Lattices_Oboolean__algebra(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__eq)). 4.02/4.28 fof(fact_fun__left__comm__idem_Ofun__left__idem, axiom, ![X16, X9, X22, X7, X4]:(hAPP(hAPP(X22,X9),hAPP(hAPP(X22,X9),X16))=hAPP(hAPP(X22,X9),X16)<=c_Finite__Set_Ofun__left__comm__idem(X4,X7,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem_Ofun__left__idem)). 4.02/4.28 fof(fact_neg__less__nonneg, axiom, ![X26, X4]:(class_Groups_Olinordered__ab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26)),X26))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__less__nonneg)). 4.02/4.28 fof(fact_minus__le__self__iff, axiom, ![X26, X4]:(class_Groups_Olinordered__ab__group__add(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26)),X26))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__le__self__iff)). 4.02/4.28 fof(fact_sorted__sort__key, axiom, ![X32, X22, X7, X4]:(class_Orderings_Olinorder(X4)=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X7,X4),X22),c_List_Olinorder__class_Osort__key(X7,X4,X22,X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__sort__key)). 4.02/4.28 fof(fact_Inf__set__fold, axiom, ![X32, X4]:(hAPP(c_List_Ofoldl(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4),c_Orderings_Otop__class_Otop(X4)),X32)=c_Complete__Lattice_OInf__class_OInf(X4,hAPP(c_List_Oset(X4),X32))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__set__fold)). 4.02/4.28 fof(fact_not__sum__squares__lt__zero, axiom, ![X43, X13, X4]:(class_Rings_Olinordered__ring(X4)=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X13),X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X43),X43))),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__sum__squares__lt__zero)). 4.02/4.28 fof(fact_diff__minus__eq__add, axiom, ![X12, X11, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12))<=class_Groups_Ogroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__minus__eq__add)). 4.02/4.28 fof(fact_less__minus__self__iff, axiom, ![X26, X4]:(class_Rings_Olinordered__idom(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__minus__self__iff)). 4.02/4.28 fof(fact_le__minus__self__iff, axiom, ![X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),c_Groups_Ozero__class_Ozero(X4)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26))))<=class_Groups_Olinordered__ab__group__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__minus__self__iff)). 4.02/4.28 fof(fact_Powp__def, axiom, ![X6, X3, X4]:(hBOOL(hAPP(c_Predicate_OPowp(X4,X3),X6))<=>![X19]:(hBOOL(hAPP(hAPP(c_member(X4),X19),X6))=>hBOOL(hAPP(X3,X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Powp__def)). 4.02/4.28 fof(fact_zle__trans, axiom, ![X107, X135, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X46),X135))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X46),X107))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X135),X107)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__trans)). 4.02/4.28 fof(fact_le__trans, axiom, ![X107, X135, X46]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),X107))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X135),X107)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__trans)). 4.02/4.28 fof(fact_last__in__set, axiom, ![X4, X109]:(hBOOL(hAPP(hAPP(c_member(X4),c_List_Olast(X4,X109)),hAPP(c_List_Oset(X4),X109)))<=X109!=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__in__set)). 4.02/4.28 fof(fact_abs__if, axiom, ![X11, X4]:(class_Groups_Oabs__if(X4)=>((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Ozero__class_Ozero(X4))))=>hAPP(c_Groups_Oabs__class_Oabs(X4),X11)=X11)&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Ozero__class_Ozero(X4)))=>hAPP(c_Groups_Oabs__class_Oabs(X4),X11)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__if)). 4.02/4.28 fof(fact_linorder__linear, axiom, ![X43, X13, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X43),X13))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__linear)). 4.02/4.28 fof(fact_setsum_Oempty, axiom, ![X76, X7, X4]:(class_Groups_Ocomm__monoid__add(X4)=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,X4),X76),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setsum_Oempty)). 4.02/4.28 fof(fact_power__inject__exp, axiom, ![X20, X21, X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),X26))=>(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X26),X20)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X26),X21)<=>X20=X21))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__inject__exp)). 4.02/4.28 fof(fact_card__eq__UNIV__imp__eq__UNIV, axiom, ![X3, X4]:((c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=X3<=hAPP(c_Finite__Set_Ocard(X4),X3)=hAPP(c_Finite__Set_Ocard(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__eq__UNIV__imp__eq__UNIV)). 4.02/4.28 fof(fact_length__greater__0__conv, axiom, ![X32, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))<=>c_List_Olist_ONil(X4)!=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__greater__0__conv)). 4.02/4.28 fof(fact_card__image, axiom, ![X3, X22, X7, X4]:(hAPP(c_Finite__Set_Ocard(X4),X3)=hAPP(c_Finite__Set_Ocard(X7),hAPP(c_Set_Oimage(X4,X7,X22),X3))<=c_Fun_Oinj__on(X4,X7,X22,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__image)). 4.02/4.28 fof(fact_zless__linear, axiom, ![X43, X13]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X43),X13))|X43=X13|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13),X43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zless__linear)). 4.02/4.28 fof(fact_linorder__neqE__nat, axiom, ![X43, X13]:(X13!=X43=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),X13))<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),X43))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__neqE__nat)). 4.02/4.28 fof(fact_list__update__same__conv, axiom, ![X9, X32, X4, X37]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)))=>(X32=hAPP(hAPP(c_List_Olist__update(X4,X32),X37),X9)<=>X9=hAPP(hAPP(c_List_Onth(X4),X32),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__same__conv)). 4.02/4.28 fof(fact_diff__diff__cancel, axiom, ![X5, X46]:(X46=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),X46))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__diff__cancel)). 4.02/4.28 fof(fact_le__add__diff__inverse, axiom, ![X2, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X2))=>X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__add__diff__inverse)). 4.02/4.28 fof(fact_single__valued__rel__comp, axiom, ![X40, X49, X18, X7, X4]:((c_Relation_Osingle__valued(X7,X49,X40)=>c_Relation_Osingle__valued(X4,X49,hAPP(hAPP(c_Relation_Orel__comp(X4,X7,X49),X18),X40)))<=c_Relation_Osingle__valued(X4,X7,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__rel__comp)). 4.02/4.28 fof(fact_Max_Osingleton, axiom, ![X9, X4]:(c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=X9<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_Osingleton)). 4.02/4.28 fof(fact_Min_Osingleton, axiom, ![X9, X4]:(X9=c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Osingleton)). 4.02/4.28 fof(fact_Inf__fin_Osingleton, axiom, ![X9, X4]:(class_Lattices_Olattice(X4)=>X9=c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Osingleton)). 4.02/4.28 fof(fact_split__paired__All, axiom, ![X7, X4, X56]:(![X77]:hBOOL(hAPP(X56,X77))<=>![X27, X78]:hBOOL(hAPP(X56,hAPP(hAPP(c_Product__Type_OPair(X4,X7),X27),X78)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__paired__All)). 4.02/4.28 fof(fact_Sup__singleton, axiom, ![X26, X4]:(X26=c_Complete__Lattice_OSup__class_OSup(X4,hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__singleton)). 4.02/4.28 fof(fact_nat__mult__eq__cancel1, axiom, ![X20, X21, X28]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28))=>(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X20)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X21)<=>X21=X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__eq__cancel1)). 4.02/4.28 fof(fact_Inf__singleton, axiom, ![X26, X4]:(X26=c_Complete__Lattice_OInf__class_OInf(X4,hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__singleton)). 4.02/4.28 fof(fact_in__set__butlastD, axiom, ![X32, X9, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))<=hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),c_List_Obutlast(X4,X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__butlastD)). 4.02/4.28 fof(fact_abs__ge__minus__self, axiom, ![X11, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__ge__minus__self)). 4.02/4.28 fof(fact_Sup__fin_Osingleton, axiom, ![X9, X4]:(X9=c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Osingleton)). 4.02/4.28 fof(fact_minus__shift__def, axiom, ![X101, X47, X107]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X107),X47)))=>c_Random_Ominus__shift(X101,X107,X47)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X107),X47))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X101),X107)),X47)=c_Random_Ominus__shift(X101,X107,X47)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X107),X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__shift__def)). 4.02/4.28 fof(fact_small__lazy__prod__def, axiom, ![X44, X7, X4]:(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X4,X7),X44)=c_Lazy__Sequence_Oproduct(X4,X7,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X4,X44),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X7,X44))<=(class_Lazy__Sequence_Osmall__lazy(X4)&class_Lazy__Sequence_Osmall__lazy(X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__lazy__prod__def)). 4.02/4.28 fof(fact_sorted__distinct__set__unique, axiom, ![X31, X32, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Osorted(X4,X32)=>((((hAPP(c_List_Oset(X4),X31)=hAPP(c_List_Oset(X4),X32)=>X31=X32)<=hBOOL(hAPP(c_List_Odistinct(X4),X31)))<=c_List_Olinorder__class_Osorted(X4,X31))<=hBOOL(hAPP(c_List_Odistinct(X4),X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__distinct__set__unique)). 4.02/4.28 fof(fact_zero__le__square, axiom, ![X11, X4]:(class_Rings_Olinordered__ring(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__square)). 4.02/4.28 fof(fact_less__add__one, axiom, ![X11, X4]:(class_Rings_Olinordered__semidom(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),c_Groups_Oone__class_Oone(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__add__one)). 4.02/4.28 fof(fact_length__sort, axiom, ![X32, X22, X4, X7]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Olinorder__class_Osort__key(X4,X7,X22,X32))<=class_Orderings_Olinorder(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__sort)). 4.02/4.28 fof(fact_list__all2__rev1, axiom, ![X31, X32, X56, X7, X4]:(c_List_Olist__all2(X4,X7,X56,hAPP(c_List_Orev(X4),X32),X31)<=>c_List_Olist__all2(X4,X7,X56,X32,hAPP(c_List_Orev(X7),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__rev1)). 4.02/4.28 fof(fact_finite__Diff, axiom, ![X6, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Diff)). 4.02/4.28 fof(fact_finite__Int, axiom, ![X253, X87, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X253))|hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X87)))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X87),X253)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Int)). 4.02/4.28 fof(fact_equivp__transp, axiom, ![X16, X17, X9, X39, X4]:(c_Equiv__Relations_Oequivp(X4,X39)=>((hBOOL(hAPP(hAPP(X39,X17),X16))=>hBOOL(hAPP(hAPP(X39,X9),X16)))<=hBOOL(hAPP(hAPP(X39,X9),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivp__transp)). 4.02/4.28 fof(fact_Pow__iff, axiom, ![X6, X3, X4]:(hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(c_Set_OPow(X4),X6)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__iff)). 4.02/4.28 fof(fact_div__pos__pos__trivial, axiom, ![X12, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))=>(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__pos__pos__trivial)). 4.02/4.28 fof(fact_div__neg__neg__trivial, axiom, ![X12, X11]:((hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),X11)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__neg__neg__trivial)). 4.02/4.28 fof(fact_zero__less__int__conv, axiom, ![X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20))<=>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),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__int__conv)). 4.02/4.28 fof(fact_Union__quotient, axiom, ![X18, X3, X4]:(c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X3),X18))=X3<=c_Equiv__Relations_Oequiv(X4,X3,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__quotient)). 4.02/4.28 fof(fact_pos__mod__bound, axiom, ![X11, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)),X12))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__mod__bound)). 4.02/4.28 fof(fact_mod__less__divisor, axiom, ![X2, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5)),X5))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__less__divisor)). 4.02/4.28 fof(fact_zmod__le__nonneg__dividend, axiom, ![X107, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X107)),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_zmod__le__nonneg__dividend)). 4.02/4.28 fof(fact_mod__le__divisor, axiom, ![X2, X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5)),X5))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__le__divisor)). 4.02/4.28 fof(fact_fun__Compl__def, axiom, ![X9, X3, X7, X4]:(class_Groups_Ouminus(X4)=>hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,X4)),X3),X9)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(X3,X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__Compl__def)). 4.02/4.28 fof(fact_inj__map__eq__map, axiom, ![X31, X32, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=>(hAPP(hAPP(c_List_Omap(X4,X7),X22),X32)=hAPP(hAPP(c_List_Omap(X4,X7),X22),X31)<=>X32=X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__map__eq__map)). 4.02/4.28 fof(fact_neg__mod__bound, axiom, ![X11, X12]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__mod__bound)). 4.02/4.28 fof(fact_mult__minus1, axiom, ![X29, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin)),X29)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X29)<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__minus1)). 4.02/4.28 fof(fact_evalc_Oequations_I8_J, axiom, ![X65, X67, X69, X70]:(c_Natural_Oevalc(c_Com_Ocom_OWhile(X70,X69),X67,X65)<=>((?[X136]:(c_Natural_Oevalc(c_Com_Ocom_OWhile(X70,X69),X136,X65)&c_Natural_Oevalc(X69,X67,X136))&hBOOL(hAPP(X70,X67)))|(X67=X65&~(hBOOL(hAPP(X70,X67)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evalc_Oequations_I8_J)). 4.02/4.28 fof(fact_fun__upd__other, axiom, ![X17, X22, X7, X4, X9, X16]:(X16!=X9=>hAPP(X22,X16)=hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X7),X22),X9),X17),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__other)). 4.02/4.28 fof(fact_Int__absorb2, axiom, ![X6, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)=X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__absorb2)). 4.02/4.28 fof(fact_Int__absorb1, axiom, ![X3, X6, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)=X6<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__absorb1)). 4.02/4.28 fof(fact_divmod__int__rel__mod, axiom, ![X101, X14, X12, X11]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X12=>c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)=X101)<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X12),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X14),X101)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__mod)). 4.02/4.28 fof(fact_divide__minus1, axiom, ![X13, X4]:(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X13),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin))=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X13)<=(class_Int_Onumber__ring(X4)&class_Fields_Ofield__inverse__zero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__minus1)). 4.02/4.28 fof(fact_subset__Un__eq, axiom, ![X6, X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))<=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)=X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__Un__eq)). 4.02/4.28 fof(fact_Un__absorb2, axiom, ![X3, X6, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X3))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)=X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__absorb2)). 4.02/4.28 fof(fact_fun__left__comm_Ofold__graph__determ, axiom, ![X17, X9, X3, X16, X22, X7, X4]:(((X17=X9<=hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X7,X22,X16,X3),X17)))<=hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X7,X22,X16,X3),X9)))<=c_Finite__Set_Ofun__left__comm(X4,X7,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__graph__determ)). 4.02/4.28 fof(fact_finite__surj, axiom, ![X22, X6, X7, X3, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X6),hAPP(c_Set_Oimage(X4,X7,X22),X3)))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__surj)). 4.02/4.28 fof(fact_of__int__minus, axiom, ![X29, X4]:(hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X29))=hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__minus)). 4.02/4.28 fof(fact_rev__finite__subset, axiom, ![X3, X6, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__finite__subset)). 4.02/4.28 fof(fact_sorted__insort, axiom, ![X32, X9, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Osorted(X4,X32)<=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)),X9),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__insort)). 4.02/4.28 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J, axiom, ![X3]:(hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X3)=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X3))<=c_Nat__Transfer_Onat__set(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J)). 4.02/4.28 fof(fact_arith__simps_I30_J, axiom, ![X53, X4]:(class_Int_Onumber__ring(X4)=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X53))=hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X53))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_arith__simps_I30_J)). 4.02/4.28 fof(fact_nat__set__def, axiom, ![X86]:(c_Nat__Transfer_Onat__set(X86)<=>![X19]:(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X19),X86))=>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_nat__set__def)). 4.02/4.28 fof(fact_z3mod__def, axiom, ![X107, X47]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X47)))=>c_SMT_Oz3mod(X107,X47)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X107,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X47)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X47))=>c_Divides_Odiv__class_Omod(tc_Int_Oint,X107,X47)=c_SMT_Oz3mod(X107,X47))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_z3mod__def)). 4.02/4.28 fof(fact_nth__replicate, axiom, ![X13, X4, X5, X46]:(hAPP(hAPP(c_List_Onth(X4),c_List_Oreplicate(X4,X5,X13)),X46)=X13<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__replicate)). 4.02/4.28 fof(fact_setprod__empty, axiom, ![X22, X7, X4]:(class_Groups_Ocomm__monoid__mult(X4)=>c_Groups_Oone__class_Oone(X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X4),X22),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_setprod__empty)). 4.02/4.28 fof(fact_finite__fun__UNIVD2, axiom, ![X7, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,X7)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X4,X7),tc_HOL_Obool))))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__fun__UNIVD2)). 4.02/4.28 fof(fact_Compl__greaterThan, axiom, ![X28, X4]:(class_Orderings_Olinorder(X4)=>hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X28))=hAPP(c_SetInterval_Oord__class_OatMost(X4),X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__greaterThan)). 4.02/4.28 fof(fact_less__imp__diff__less, axiom, ![X5, X107, X135]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X135),X5)),X107))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X135),X107))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__imp__diff__less)). 4.02/4.28 fof(fact_Compl__lessThan, axiom, ![X28, X4]:(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X28))=hAPP(c_SetInterval_Oord__class_OatLeast(X4),X28)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__lessThan)). 4.02/4.28 fof(fact_length__n__lists__elem, axiom, ![X32, X20, X31, X4]:(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X31),hAPP(c_List_Oset(tc_List_Olist(X4)),c_Enum_On__lists(X4,X20,X32))))=>hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X31)=X20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__n__lists__elem)). 4.02/4.28 fof(fact_Compl__atMost, axiom, ![X28, X4]:(class_Orderings_Olinorder(X4)=>hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X28)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X4),X28))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__atMost)). 4.02/4.28 fof(fact_insertCI, axiom, ![X25, X6, X26, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X26),hAPP(hAPP(c_Set_Oinsert(X4),X25),X6)))<=(X26=X25<=~(hBOOL(hAPP(hAPP(c_member(X4),X26),X6))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insertCI)). 4.02/4.28 fof(fact_Compl__atLeast, axiom, ![X28, X4]:(hAPP(c_SetInterval_Oord__class_OlessThan(X4),X28)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X28))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__atLeast)). 4.02/4.28 fof(fact_mod__add__self1, axiom, ![X11, X12, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11),X12)=c_Divides_Odiv__class_Omod(X4,X11,X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__self1)). 4.02/4.28 fof(fact_mod__add__self2, axiom, ![X12, X11, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12),X12)=c_Divides_Odiv__class_Omod(X4,X11,X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__add__self2)). 4.02/4.28 fof(fact_mult__minus1__right, axiom, ![X29, X4]:(class_Int_Onumber__ring(X4)=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),X29)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X29),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__minus1__right)). 4.02/4.28 fof(fact_termination__basic__simps_I1_J, axiom, ![X29, X43, X13]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),X43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_termination__basic__simps_I1_J)). 4.02/4.28 fof(fact_trans__less__add2, axiom, ![X2, X135, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X135)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_trans__less__add2)). 4.02/4.28 fof(fact_atLeastatMost__empty__iff, axiom, ![X25, X26, X4]:(class_Orderings_Oorder(X4)=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastAtMost(X4,X26,X25)<=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),X25))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastatMost__empty__iff)). 4.02/4.28 fof(fact_domIff, axiom, ![X21, X7, X26, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X26),c_Map_Odom(X4,X7,X21)))<=>c_Option_Ooption_ONone(X7)!=hAPP(X21,X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_domIff)). 4.02/4.28 fof(fact_termination__basic__simps_I3_J, axiom, ![X29, X43, X13]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13),X43))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_termination__basic__simps_I3_J)). 4.02/4.28 fof(fact_termination__basic__simps_I4_J, axiom, ![X43, X29, X13]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X29)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_termination__basic__simps_I4_J)). 4.02/4.28 fof(fact_inf1I, axiom, ![X4, X6, X9, X3]:((hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6),X9))<=hBOOL(hAPP(X6,X9)))<=hBOOL(hAPP(X3,X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf1I)). 4.02/4.28 fof(fact_sorted__many__eq, axiom, ![X30, X17, X9, X4]:((c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X9),hAPP(hAPP(c_List_Olist_OCons(X4),X17),X30)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X17))&c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X17),X30))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__many__eq)). 4.02/4.28 fof(fact_inf__commute, axiom, ![X43, X13, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X43),X13)<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__commute)). 4.02/4.28 fof(fact_Suc__lessI, axiom, ![X5, X2]:((hAPP(c_Nat_OSuc,X2)!=X5=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X5)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__lessI)). 4.02/4.28 fof(fact_hd__append2, axiom, ![X59, X4, X45]:(hAPP(c_List_Ohd(X4),hAPP(hAPP(c_List_Oappend(X4),X45),X59))=hAPP(c_List_Ohd(X4),X45)<=X45!=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__append2)). 4.02/4.28 fof(fact_atLeastLessThan__inj_I1_J, axiom, ![X102, X24, X25, X26, X4]:(class_Orderings_Olinorder(X4)=>(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X26),X25)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X24),X102)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X25))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),X102))=>X26=X24)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__inj_I1_J)). 4.02/4.28 fof(fact_atLeastLessThan__inj_I2_J, axiom, ![X102, X24, X25, X26, X4]:(class_Orderings_Olinorder(X4)=>(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X24),X102)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X26),X25)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X25))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X24),X102))=>X102=X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__inj_I2_J)). 4.02/4.28 fof(fact_add__diff__cancel, axiom, ![X12, X11, X4]:(class_Groups_Ogroup__add(X4)=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)),X12)=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__diff__cancel)). 4.02/4.28 fof(fact_diff__add__cancel, axiom, ![X12, X11, X4]:(class_Groups_Ogroup__add(X4)=>X11=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X12)),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__add__cancel)). 4.02/4.28 fof(fact_inf__sup__absorb, axiom, ![X43, X13, X4]:(class_Lattices_Olattice(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43))=X13), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__absorb)). 4.02/4.28 fof(fact_fun__left__comm_Ofold__equality, axiom, ![X17, X3, X16, X22, X7, X4]:((X17=hAPP(hAPP(c_Finite__Set_Ofold(X4,X7,X22),X16),X3)<=hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X7,X22,X16,X3),X17)))<=c_Finite__Set_Ofun__left__comm(X4,X7,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm_Ofold__equality)). 4.02/4.28 fof(fact_distinct__insort__insert, axiom, ![X9, X22, X32, X4, X7]:(class_Orderings_Olinorder(X7)=>(hBOOL(hAPP(c_List_Odistinct(X4),X32))=>hBOOL(hAPP(c_List_Odistinct(X4),c_List_Olinorder__class_Oinsort__insert__key(X4,X7,X22,X9,X32))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__insort__insert)). 4.02/4.28 fof(fact_restrict__out, axiom, ![X21, X7, X3, X9, X4]:(c_Option_Ooption_ONone(X7)=hAPP(c_Map_Orestrict__map(X4,X7,X21,X3),X9)<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__out)). 4.02/4.28 fof(fact_inf__sup__aci_I1_J, axiom, ![X43, X13, X4]:(class_Lattices_Olattice(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X43),X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I1_J)). 4.02/4.28 fof(fact_sup__inf__absorb, axiom, ![X43, X13, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43))=X13<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__inf__absorb)). 4.02/4.28 fof(fact_type__definition_OAbs__inverse, axiom, ![X17, X3, X170, X171, X7, X4]:((hBOOL(hAPP(hAPP(c_member(X7),X17),X3))=>X17=hAPP(X171,hAPP(X170,X17)))<=c_Typedef_Otype__definition(X4,X7,X171,X170,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_OAbs__inverse)). 4.02/4.28 fof(fact_wfE__pf, axiom, ![X3, X39, X4]:(c_Wellfounded_Owf(X4,X39)=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X3<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(c_Relation_OImage(X4,X4,X39),X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfE__pf)). 4.02/4.28 fof(fact_distinct__card, axiom, ![X32, X4]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=hAPP(c_Finite__Set_Ocard(X4),hAPP(c_List_Oset(X4),X32))<=hBOOL(hAPP(c_List_Odistinct(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__card)). 4.02/4.28 fof(fact_mult__sgn__abs, axiom, ![X13, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Osgn__class_Osgn(X4,X13)),hAPP(c_Groups_Oabs__class_Oabs(X4),X13))=X13<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__sgn__abs)). 4.02/4.28 fof(fact_accp__downward, axiom, ![X26, X25, X18, X4]:(hBOOL(hAPP(c_Wellfounded_Oaccp(X4,X18),X25))=>(hBOOL(hAPP(c_Wellfounded_Oaccp(X4,X18),X26))<=hBOOL(hAPP(hAPP(X18,X26),X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_accp__downward)). 4.02/4.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, axiom, ![X12, X11, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J)). 4.02/4.28 fof(fact_Suc__pred_H, axiom, ![X5]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5))=>X5=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__pred_H)). 4.02/4.28 fof(fact_le__supE, axiom, ![X13, X12, X11, X4]:(class_Lattices_Osemilattice__sup(X4)=>(~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X13))=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X13)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X11),X12)),X13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__supE)). 4.02/4.28 fof(fact_finite__surj__inj, axiom, ![X22, X3, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(c_Set_Oimage(X4,X4,X22),X3)))=>c_Fun_Oinj__on(X4,X4,X22,X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__surj__inj)). 4.02/4.28 fof(fact_Ints__odd__nonzero, axiom, ![X26, X4]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Oone__class_Oone(X4)),X26)),X26)!=c_Groups_Ozero__class_Ozero(X4)<=hBOOL(hAPP(hAPP(c_member(X4),X26),c_Int_Oring__1__class_OInts(X4))))<=class_Int_Oring__char__0(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__odd__nonzero)). 4.02/4.28 fof(fact_Diff__triv, axiom, ![X6, X3, X4]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)=X3<=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__triv)). 4.02/4.28 fof(fact_sorted__list__of__set__sort__remdups, axiom, ![X32, X4]:(class_Orderings_Olinorder(X4)=>c_List_Olinorder__class_Osorted__list__of__set(X4,hAPP(c_List_Oset(X4),X32))=c_List_Olinorder__class_Osort__key(X4,X4,c_COMBI(X4),c_List_Oremdups(X4,X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set__sort__remdups)). 4.02/4.28 fof(fact_sup__commute, axiom, ![X43, X13, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X43),X13)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43)<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__commute)). 4.02/4.28 fof(fact_le__infE, axiom, ![X12, X11, X13, X4]:((~((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X11))=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X12)))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X11),X12))))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__infE)). 4.02/4.28 fof(fact_lessThan__iff, axiom, ![X28, X37, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X37),hAPP(c_SetInterval_Oord__class_OlessThan(X4),X28)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X37),X28)))<=class_Orderings_Oord(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__iff)). 4.02/4.28 fof(fact_greaterThanAtMost__empty__iff2, axiom, ![X60, X28, X4]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X28),X60)))<=>c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X28,X60)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThanAtMost__empty__iff2)). 4.02/4.28 fof(fact_inf__sup__aci_I5_J, axiom, ![X43, X13, X4]:(class_Lattices_Olattice(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X43),X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__aci_I5_J)). 4.02/4.28 fof(fact_atMost__iff, axiom, ![X28, X37, X4]:(class_Orderings_Oord(X4)=>(hBOOL(hAPP(hAPP(c_member(X4),X37),hAPP(c_SetInterval_Oord__class_OatMost(X4),X28)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X37),X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atMost__iff)). 4.02/4.28 fof(fact_greaterThan__iff, axiom, ![X28, X37, X4]:(class_Orderings_Oord(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X28),X37))<=>hBOOL(hAPP(hAPP(c_member(X4),X37),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X28))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThan__iff)). 4.02/4.28 fof(fact_atLeast__iff, axiom, ![X28, X37, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X37),hAPP(c_SetInterval_Oord__class_OatLeast(X4),X28)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X28),X37)))<=class_Orderings_Oord(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast__iff)). 4.02/4.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, axiom, ![X10, X11, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X11)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)). 4.02/4.28 fof(fact_min__max_Oinf_Ocommute, axiom, ![X12, X11, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X11),X12)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X12),X11)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf_Ocommute)). 4.02/4.28 fof(fact_min__max_Osup__commute, axiom, ![X43, X13, X4]:(hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X43),X13)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),X43)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__commute)). 4.02/4.28 fof(fact_inf2D1, axiom, ![X17, X9, X6, X3, X7, X4]:(hBOOL(hAPP(hAPP(X3,X9),X17))<=hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),X3),X6),X9),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf2D1)). 4.02/4.28 fof(fact_inf2D2, axiom, ![X17, X9, X6, X3, X7, X4]:(hBOOL(hAPP(hAPP(X6,X9),X17))<=hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),X3),X6),X9),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf2D2)). 4.02/4.28 fof(fact_DiffD1, axiom, ![X6, X3, X24, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X24),X3))<=hBOOL(hAPP(hAPP(c_member(X4),X24),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DiffD1)). 4.02/4.28 fof(fact_type__definition_ORep, axiom, ![X9, X3, X170, X171, X7, X4]:(c_Typedef_Otype__definition(X4,X7,X171,X170,X3)=>hBOOL(hAPP(hAPP(c_member(X7),hAPP(X171,X9)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_ORep)). 4.02/4.28 fof(fact_IntD1, axiom, ![X6, X3, X24, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X24),X3))<=hBOOL(hAPP(hAPP(c_member(X4),X24),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_IntD1)). 4.02/4.28 fof(fact_power__0__Suc, axiom, ![X5, X4]:((class_Power_Opower(X4)&class_Rings_Osemiring__0(X4))=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Nat_OSuc,X5))=c_Groups_Ozero__class_Ozero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__0__Suc)). 4.02/4.28 fof(fact_IntD2, axiom, ![X6, X3, X24, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X24),X6))<=hBOOL(hAPP(hAPP(c_member(X4),X24),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_IntD2)). 4.02/4.28 fof(fact_abs__of__neg, axiom, ![X11, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>(hAPP(c_Groups_Oabs__class_Oabs(X4),X11)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__of__neg)). 4.02/4.28 fof(fact_abs__of__nonpos, axiom, ![X11, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),c_Groups_Ozero__class_Ozero(X4)))=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)=hAPP(c_Groups_Oabs__class_Oabs(X4),X11))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__of__nonpos)). 4.02/4.28 fof(fact_insert__iff, axiom, ![X3, X25, X26, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X26),hAPP(hAPP(c_Set_Oinsert(X4),X25),X3)))<=>(X26=X25|hBOOL(hAPP(hAPP(c_member(X4),X26),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__iff)). 4.02/4.28 fof(fact_folding__one_Oeq__fold, axiom, ![X3, X87, X22, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(c_Finite__Set_Ofold1(X4,X22),X3)=hAPP(X87,X3))<=c_Finite__Set_Ofolding__one(X4,X22,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one_Oeq__fold)). 4.02/4.28 fof(fact_semilattice__big_OF__eq, axiom, ![X3, X87, X22, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(X87,X3)=hAPP(c_Finite__Set_Ofold1(X4,X22),X3))<=c_Big__Operators_Osemilattice__big(X4,X22,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_semilattice__big_OF__eq)). 4.02/4.28 fof(fact_Inf__lower, axiom, ![X3, X9, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Complete__Lattice_OInf__class_OInf(X4,X3)),X9))<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__lower)). 4.02/4.28 fof(fact_Sup__upper, axiom, ![X3, X9, X4]:((hBOOL(hAPP(hAPP(c_member(X4),X9),X3))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),c_Complete__Lattice_OSup__class_OSup(X4,X3))))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__upper)). 4.02/4.28 fof(fact_accp_Oequations, axiom, ![X26, X18, X4]:(![X19]:(hBOOL(hAPP(c_Wellfounded_Oaccp(X4,X18),X19))<=hBOOL(hAPP(hAPP(X18,X19),X26)))<=>hBOOL(hAPP(c_Wellfounded_Oaccp(X4,X18),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_accp_Oequations)). 4.02/4.28 fof(fact_accp_Osimps, axiom, ![X26, X18, X4]:(![X19]:(hBOOL(hAPP(c_Wellfounded_Oaccp(X4,X18),X19))<=hBOOL(hAPP(hAPP(X18,X19),X26)))<=>hBOOL(hAPP(c_Wellfounded_Oaccp(X4,X18),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_accp_Osimps)). 4.02/4.28 fof(fact_list__update__beyond, axiom, ![X13, X46, X45, X4]:(hAPP(hAPP(c_List_Olist__update(X4,X45),X46),X13)=X45<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__beyond)). 4.02/4.28 fof(fact_ex__in__conv, axiom, ![X3, X4]:(?[X19]:hBOOL(hAPP(hAPP(c_member(X4),X19),X3))<=>X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ex__in__conv)). 4.02/4.28 fof(fact_finite__Diff2, axiom, ![X3, X6, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Diff2)). 4.02/4.28 fof(fact_all__not__in__conv, axiom, ![X3, X4]:(X3=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=>![X19]:~(hBOOL(hAPP(hAPP(c_member(X4),X19),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__not__in__conv)). 4.02/4.28 fof(fact_in__set__member, axiom, ![X32, X9, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))<=>c_List_Omember(X4,X32,X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__set__member)). 4.02/4.28 fof(fact_map__add__None, axiom, ![X28, X20, X21, X4, X7]:(c_Option_Ooption_ONone(X4)=hAPP(c_Map_Omap__add(X7,X4,X21,X20),X28)<=>(hAPP(X20,X28)=c_Option_Ooption_ONone(X4)&hAPP(X21,X28)=c_Option_Ooption_ONone(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__None)). 4.02/4.28 fof(fact_evalc_Oequations_I7_J, axiom, ![X67, X69, X70]:((hBOOL(hAPP(X70,X67))=>?[X136]:(c_Natural_Oevalc(X69,X67,X136)&c_Natural_Oevalc(c_Com_Ocom_OWhile(X70,X69),X136,X67)))<=>c_Natural_Oevalc(c_Com_Ocom_OWhile(X70,X69),X67,X67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evalc_Oequations_I7_J)). 4.02/4.28 fof(fact_insort__insert__triv, axiom, ![X32, X9, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_member(X4),X9),hAPP(c_List_Oset(X4),X32)))=>c_List_Olinorder__class_Oinsort__insert__key(X4,X4,c_COMBI(X4),X9,X32)=X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__insert__triv)). 4.02/4.28 fof(fact_divmod__int__rel__neg, axiom, ![X200, X12, X11]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X12),hAPP(c_Divides_OnegateSnd,X200)))<=hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12)),X200))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__rel__neg)). 4.02/4.28 fof(fact_div__eq, axiom, ![X101, X14, X5, X2]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X5)=X14<=hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X5),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X14),X101)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__eq)). 4.02/4.28 fof(fact_int__zle__neg, axiom, ![X21, X20]:((X21=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&X20=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),X20)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__zle__neg)). 4.02/4.28 fof(fact_evalc_OWhileTrue, axiom, ![X192, X148, X24, X193, X25]:(hBOOL(hAPP(X25,X193))=>(c_Natural_Oevalc(X24,X193,X148)=>(c_Natural_Oevalc(c_Com_Ocom_OWhile(X25,X24),X193,X192)<=c_Natural_Oevalc(c_Com_Ocom_OWhile(X25,X24),X148,X192)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evalc_OWhileTrue)). 4.02/4.28 fof(fact_subset__Compl__self__eq, axiom, ![X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X3)))<=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__Compl__self__eq)). 4.02/4.28 fof(fact_self__remainder, axiom, ![X101, X14, X11]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X11),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X14),X101)))=>(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X11=>c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X101)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_self__remainder)). 4.02/4.28 fof(fact_self__quotient, axiom, ![X101, X14, X11]:(hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X11),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X14),X101)))=>(X11!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>c_Groups_Oone__class_Oone(tc_Int_Oint)=X14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_self__quotient)). 4.02/4.28 fof(fact_dual__min, axiom, ![X4]:(class_Orderings_Olinorder(X4)=>c_Orderings_Oord_Omin(X4,hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X4)))=c_Orderings_Oord__class_Omax(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dual__min)). 4.02/4.28 fof(fact_linorder__antisym__conv1, axiom, ![X17, X9, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X17))<=>X17=X9)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X9),X17))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__antisym__conv1)). 4.02/4.28 fof(fact_xt1_I12_J, axiom, ![X12, X11, X4]:(class_Orderings_Oorder(X4)=>(X11!=X12=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X11))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I12_J)). 4.02/4.28 fof(fact_compl__sup__top, axiom, ![X13, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X13)),X13)=c_Orderings_Otop__class_Otop(X4)<=class_Lattices_Oboolean__algebra(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__sup__top)). 4.02/4.28 fof(fact_compl__inf__bot, axiom, ![X13, X4]:(class_Lattices_Oboolean__algebra(X4)=>c_Orderings_Obot__class_Obot(X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X13)),X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__inf__bot)). 4.02/4.28 fof(fact_dual__max, axiom, ![X4]:(class_Orderings_Olinorder(X4)=>c_Orderings_Oord__class_Omin(X4)=c_Orderings_Oord_Omax(X4,hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dual__max)). 4.02/4.28 fof(fact_ab__left__minus, axiom, ![X11, X4]:(class_Groups_Oab__group__add(X4)=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ab__left__minus)). 4.02/4.28 fof(fact_min__max_Oinf__sup__absorb, axiom, ![X43, X13, X4]:(class_Orderings_Olinorder(X4)=>X13=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),X43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__sup__absorb)). 4.02/4.28 fof(fact_min__max_Osup__inf__absorb, axiom, ![X43, X13, X4]:(class_Orderings_Olinorder(X4)=>X13=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),X43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__inf__absorb)). 4.02/4.28 fof(fact_inf__le1, axiom, ![X43, X13, X4]:(class_Lattices_Osemilattice__inf(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43)),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__le1)). 4.02/4.28 fof(fact_inf__sup__ord_I1_J, axiom, ![X43, X13, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43)),X13))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__ord_I1_J)). 4.02/4.28 fof(fact_right__minus, axiom, ![X11, X4]:(class_Groups_Ogroup__add(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11))=c_Groups_Ozero__class_Ozero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_right__minus)). 4.02/4.28 fof(fact_inj__on__Un__image__eq__iff, axiom, ![X6, X3, X22, X7, X4]:((X6=X3<=>hAPP(c_Set_Oimage(X4,X7,X22),X3)=hAPP(c_Set_Oimage(X4,X7,X22),X6))<=c_Fun_Oinj__on(X4,X7,X22,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__Un__image__eq__iff)). 4.02/4.28 fof(fact_sup__compl__top, axiom, ![X13, X4]:(class_Lattices_Oboolean__algebra(X4)=>c_Orderings_Otop__class_Otop(X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__compl__top)). 4.02/4.28 fof(fact_inf__le2, axiom, ![X43, X13, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43)),X43))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__le2)). 4.02/4.28 fof(fact_inf__sup__ord_I2_J, axiom, ![X43, X13, X4]:(class_Lattices_Olattice(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43)),X43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__ord_I2_J)). 4.02/4.28 fof(fact_sup__ge1, axiom, ![X43, X13, X4]:(class_Lattices_Osemilattice__sup(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__ge1)). 4.02/4.28 fof(fact_inf__sup__ord_I3_J, axiom, ![X43, X13, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__ord_I3_J)). 4.02/4.28 fof(fact_inf__compl__bot, axiom, ![X13, X4]:(class_Lattices_Oboolean__algebra(X4)=>c_Orderings_Obot__class_Obot(X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__compl__bot)). 4.02/4.28 fof(fact_subset__inj__on, axiom, ![X3, X6, X22, X7, X4]:(c_Fun_Oinj__on(X4,X7,X22,X6)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))=>c_Fun_Oinj__on(X4,X7,X22,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__inj__on)). 4.02/4.28 fof(fact_mod__div__trivial, axiom, ![X12, X11, X4]:(c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),c_Divides_Odiv__class_Omod(X4,X11,X12)),X12)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__div__trivial)). 4.02/4.28 fof(fact_filter__replicate, axiom, ![X20, X4, X9, X56]:((hBOOL(hAPP(X56,X9))=>hAPP(c_List_Ofilter(X4,X56),c_List_Oreplicate(X4,X20,X9))=c_List_Oreplicate(X4,X20,X9))&(~(hBOOL(hAPP(X56,X9)))=>hAPP(c_List_Ofilter(X4,X56),c_List_Oreplicate(X4,X20,X9))=c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__replicate)). 4.02/4.28 fof(fact_sup__ge2, axiom, ![X13, X43, X4]:(class_Lattices_Osemilattice__sup(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X43),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__ge2)). 4.02/4.28 fof(fact_inf__sup__ord_I4_J, axiom, ![X13, X43, X4]:(class_Lattices_Olattice(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X43),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__sup__ord_I4_J)). 4.02/4.28 fof(fact_RangeP_Oequations, axiom, ![X67, X18, X7, X4]:(hBOOL(hAPP(c_Predicate_ORangeP(X4,X7,X18),X67))<=>?[X27]:hBOOL(hAPP(hAPP(X18,X27),X67))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_RangeP_Oequations)). 4.02/4.28 fof(fact_mod__mult__self1__is__0, axiom, ![X11, X12, X4]:(class_Divides_Osemiring__div(X4)=>c_Groups_Ozero__class_Ozero(X4)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self1__is__0)). 4.02/4.28 fof(fact_mod__mult__self2__is__0, axiom, ![X12, X11, X4]:(class_Divides_Osemiring__div(X4)=>c_Groups_Ozero__class_Ozero(X4)=c_Divides_Odiv__class_Omod(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self2__is__0)). 4.02/4.28 fof(fact_inj__image__eq__iff, axiom, ![X6, X3, X22, X7, X4]:((X6=X3<=>hAPP(c_Set_Oimage(X4,X7,X22),X3)=hAPP(c_Set_Oimage(X4,X7,X22),X6))<=c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__image__eq__iff)). 4.02/4.28 fof(fact_singleton__inject, axiom, ![X25, X26, X4]:(hAPP(hAPP(c_Set_Oinsert(X4),X25),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=>X25=X26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_singleton__inject)). 4.02/4.28 fof(fact_DomainP_Oequations, axiom, ![X70, X18, X7, X4]:(?[X77]:hBOOL(hAPP(hAPP(X18,X70),X77))<=>hBOOL(hAPP(c_Predicate_ODomainP(X4,X7,X18),X70))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DomainP_Oequations)). 4.02/4.28 fof(fact_evaln_Oequations_I5_J, axiom, ![X65, X66, X67, X68, X69, X70]:(((c_Natural_Oevaln(X68,X67,X66,X65)&~(hBOOL(hAPP(X70,X67))))|(c_Natural_Oevaln(X69,X67,X66,X65)&hBOOL(hAPP(X70,X67))))<=>c_Natural_Oevaln(c_Com_Ocom_OCond(X70,X69,X68),X67,X66,X65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evaln_Oequations_I5_J)). 4.02/4.28 fof(fact_list__all__simps_I1_J, axiom, ![X32, X9, X56, X4]:(c_List_Olist__all(X4,X56,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32))<=>(hBOOL(hAPP(X56,X9))&c_List_Olist__all(X4,X56,X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__simps_I1_J)). 4.02/4.28 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J, axiom, ![X6, X3]:(c_Nat__Transfer_Onat__set(X3)=>(c_Nat__Transfer_Onat__set(X6)=>c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J)). 4.02/4.28 fof(fact_min__max_Ole__inf__iff, axiom, ![X16, X17, X9, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X17))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X16)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X17),X16))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__inf__iff)). 4.02/4.28 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J, axiom, ![X6, X3]:(c_Nat__Transfer_Onat__set(X3)=>(c_Nat__Transfer_Onat__set(X6)=>c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J)). 4.02/4.28 fof(fact_zmod__zminus1__not__zero, axiom, ![X47, X107]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X107,X47)<=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),X107),X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zminus1__not__zero)). 4.02/4.28 fof(fact_ord_OatMost__iff, axiom, ![X28, X201, X37, X4]:(hBOOL(hAPP(hAPP(X201,X37),X28))<=>hBOOL(hAPP(hAPP(c_member(X4),X37),c_SetInterval_Oord_OatMost(X4,X201,X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OatMost__iff)). 4.02/4.28 fof(fact_ord_OlessThan__iff, axiom, ![X28, X194, X37, X4]:(hBOOL(hAPP(hAPP(X194,X37),X28))<=>hBOOL(hAPP(hAPP(c_member(X4),X37),c_SetInterval_Oord_OlessThan(X4,X194,X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OlessThan__iff)). 4.02/4.28 fof(fact_ord_OatLeast__iff, axiom, ![X28, X201, X37, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X37),c_SetInterval_Oord_OatLeast(X4,X201,X28)))<=>hBOOL(hAPP(hAPP(X201,X28),X37))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OatLeast__iff)). 4.02/4.28 fof(fact_last__append, axiom, ![X45, X4, X59]:((c_List_Olast(X4,X45)=c_List_Olast(X4,hAPP(hAPP(c_List_Oappend(X4),X45),X59))<=X59=c_List_Olist_ONil(X4))&(X59!=c_List_Olist_ONil(X4)=>c_List_Olast(X4,X59)=c_List_Olast(X4,hAPP(hAPP(c_List_Oappend(X4),X45),X59)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__append)). 4.02/4.28 fof(fact_last__ConsR, axiom, ![X13, X4, X45]:(X45!=c_List_Olist_ONil(X4)=>c_List_Olast(X4,X45)=c_List_Olast(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__ConsR)). 4.02/4.28 fof(fact_ord_OgreaterThan__iff, axiom, ![X28, X194, X37, X4]:(hBOOL(hAPP(hAPP(X194,X28),X37))<=>hBOOL(hAPP(hAPP(c_member(X4),X37),c_SetInterval_Oord_OgreaterThan(X4,X194,X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ord_OgreaterThan__iff)). 4.02/4.28 fof(fact_drop__all, axiom, ![X5, X45, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),X5))=>c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Odrop(X4),X5),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__all)). 4.02/4.28 fof(fact_sgn__1__pos, axiom, ![X26, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X26))<=>c_Groups_Osgn__class_Osgn(X4,X26)=c_Groups_Oone__class_Oone(X4))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__1__pos)). 4.02/4.28 fof(fact_abs__sgn, axiom, ![X107, X4]:(hAPP(c_Groups_Oabs__class_Oabs(X4),X107)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X107),c_Groups_Osgn__class_Osgn(X4,X107))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__sgn)). 4.02/4.28 fof(fact_abs__ge__zero, axiom, ![X11, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__ge__zero)). 4.02/4.28 fof(fact_of__nat__0__le__iff, axiom, ![X5, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X5)))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__0__le__iff)). 4.02/4.28 fof(fact_finite__imageI, axiom, ![X48, X7, X87, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Set_Oimage(X4,X7,X48),X87)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X87))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__imageI)). 4.02/4.28 fof(fact_pos__zmult__eq__1__iff, axiom, ![X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21))=>((X20=c_Groups_Oone__class_Oone(tc_Int_Oint)&c_Groups_Oone__class_Oone(tc_Int_Oint)=X21)<=>c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__zmult__eq__1__iff)). 4.02/4.28 fof(fact_nth__via__drop, axiom, ![X59, X43, X45, X5, X4]:(X43=hAPP(hAPP(c_List_Onth(X4),X45),X5)<=hAPP(hAPP(c_List_Olist_OCons(X4),X43),X59)=hAPP(hAPP(c_List_Odrop(X4),X5),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__via__drop)). 4.02/4.28 fof(fact_single__valued__subset, axiom, ![X40, X18, X7, X4]:((c_Relation_Osingle__valued(X4,X7,X40)=>c_Relation_Osingle__valued(X4,X7,X18))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X18),X40))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__subset)). 4.02/4.28 fof(fact_finite__Pow__iff, axiom, ![X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_OPow(X4),X3)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Pow__iff)). 4.02/4.28 fof(fact_le__iff__add, axiom, ![X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))<=>?[X137]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X137)=X20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__iff__add)). 4.02/4.28 fof(fact_distinct__sort, axiom, ![X32, X22, X4, X7]:((hBOOL(hAPP(c_List_Odistinct(X4),c_List_Olinorder__class_Osort__key(X4,X7,X22,X32)))<=>hBOOL(hAPP(c_List_Odistinct(X4),X32)))<=class_Orderings_Olinorder(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__sort)). 4.02/4.28 fof(fact_list__all__append, axiom, ![X31, X32, X56, X4]:(c_List_Olist__all(X4,X56,hAPP(hAPP(c_List_Oappend(X4),X32),X31))<=>(c_List_Olist__all(X4,X56,X31)&c_List_Olist__all(X4,X56,X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__append)). 4.02/4.28 fof(fact_finite__nat__set__iff__bounded, axiom, ![X176]:(?[X50]:![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X50))<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X19),X176)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X176))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__nat__set__iff__bounded)). 4.02/4.28 fof(fact_finite__nat__set__iff__bounded__le, axiom, ![X176]:(?[X50]:![X19]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19),X50))<=hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X19),X176)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X176))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__nat__set__iff__bounded__le)). 4.02/4.28 fof(fact_map__le__iff__map__add__commute, axiom, ![X76, X22, X7, X4]:(c_Map_Omap__le(X4,X7,X22,c_Map_Omap__add(X4,X7,X22,X76))<=>c_Map_Omap__add(X4,X7,X22,X76)=c_Map_Omap__add(X4,X7,X76,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__le__iff__map__add__commute)). 4.02/4.28 fof(fact_Rep__Integ__induct, axiom, ![X56, X17]:(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X17),c_Int_OInteg))=>(![X19]:hBOOL(hAPP(X56,hAPP(c_Int_ORep__Integ,X19)))=>hBOOL(hAPP(X56,X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Rep__Integ__induct)). 4.02/4.28 fof(fact_evaln_Oequations_I9_J, axiom, ![X66, X69, X67, X70]:(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X70)),X67,X69,X66)<=>c_Natural_Oevaln(c_Com_Ocom_OBODY(X70),X67,hAPP(c_Nat_OSuc,X69),X66)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evaln_Oequations_I9_J)). 4.02/4.28 fof(fact_zero__less__imp__eq__int, axiom, ![X107]:(?[X104]:(X107=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X104)&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X104)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X107))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__imp__eq__int)). 4.02/4.28 fof(fact_zle__linear, axiom, ![X53, X29]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29),X53))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X53),X29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__linear)). 4.02/4.28 fof(fact_nat__le__linear, axiom, ![X5, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X5))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__le__linear)). 4.02/4.28 fof(fact_distinct__butlast, axiom, ![X4, X45]:((hBOOL(hAPP(c_List_Odistinct(X4),c_List_Obutlast(X4,X45)))<=hBOOL(hAPP(c_List_Odistinct(X4),X45)))<=c_List_Olist_ONil(X4)!=X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__butlast)). 4.02/4.28 fof(fact_finite__Domain, axiom, ![X18, X7, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Relation_ODomain(X4,X7),X18)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X7)),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Domain)). 4.02/4.28 fof(fact_finite__Range, axiom, ![X18, X7, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_Relation_ORange(X4,X7),X18)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X7)),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Range)). 4.02/4.28 fof(fact_equalityI, axiom, ![X6, X3, X4]:((X6=X3<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),X3)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equalityI)). 4.02/4.28 fof(fact_Inf__fin__Inf, axiom, ![X3, X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>((c_Complete__Lattice_OInf__class_OInf(X4,X3)=c_Big__Operators_Olattice__class_OInf__fin(X4,X3)<=X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin__Inf)). 4.02/4.28 fof(fact_Sup__fin__Sup, axiom, ![X3, X4]:(((c_Big__Operators_Olattice__class_OSup__fin(X4,X3)=c_Complete__Lattice_OSup__class_OSup(X4,X3)<=X3!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin__Sup)). 4.02/4.28 fof(fact_drop__eq__Nil, axiom, ![X32, X20, X4]:(hAPP(hAPP(c_List_Odrop(X4),X20),X32)=c_List_Olist_ONil(X4)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__eq__Nil)). 4.02/4.28 fof(fact_linorder__not__less, axiom, ![X17, X9, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X17),X9))<=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X9),X17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__not__less)). 4.02/4.28 fof(fact_atLeastLessThan__empty, axiom, ![X26, X25, X4]:((c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4,X26),X25)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X25),X26)))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThan__empty)). 4.02/4.28 fof(fact_Nitpick_Owf_H__def, axiom, ![X18, X4]:(c_Nitpick_Owf_H(X4,X18)<=>(c_Wellfounded_Oacyclic(X4,X18)&(c_Nitpick_Ounknown(tc_HOL_Obool)|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X4)),X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Owf_H__def)). 4.02/4.28 fof(fact_diff__0, axiom, ![X11, X4]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),c_Groups_Ozero__class_Ozero(X4)),X11)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)<=class_Groups_Ogroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__0)). 4.02/4.28 fof(fact_evaln_Oequations_I4_J, axiom, ![X68, X69, X67, X65, X70]:(?[X136]:(c_Natural_Oevaln(X70,X67,X69,X136)&c_Natural_Oevaln(X65,X136,X69,X68))<=>c_Natural_Oevaln(c_Com_Ocom_OSemi(X70,X65),X67,X69,X68)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evaln_Oequations_I4_J)). 4.02/4.28 fof(fact_distinct__n__lists, axiom, ![X5, X45, X4]:(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X4)),c_Enum_On__lists(X4,X5,X45)))<=hBOOL(hAPP(c_List_Odistinct(X4),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__n__lists)). 4.02/4.28 fof(fact_pigeonhole, axiom, ![X3, X22, X7, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),hAPP(c_Set_Oimage(X7,X4,X22),X3))),hAPP(c_Finite__Set_Ocard(X7),X3)))=>~(c_Fun_Oinj__on(X7,X4,X22,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pigeonhole)). 4.02/4.28 fof(fact_set__sort, axiom, ![X32, X22, X4, X7]:(hAPP(c_List_Oset(X4),X32)=hAPP(c_List_Oset(X4),c_List_Olinorder__class_Osort__key(X4,X7,X22,X32))<=class_Orderings_Olinorder(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__sort)). 4.02/4.28 fof(fact_power__0__left, axiom, ![X5, X4]:(((hAPP(hAPP(c_Power_Opower__class_Opower(X4),c_Groups_Ozero__class_Ozero(X4)),X5)=c_Groups_Oone__class_Oone(X4)<=X5=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),c_Groups_Ozero__class_Ozero(X4)),X5)<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X5))<=(class_Rings_Osemiring__0(X4)&class_Power_Opower(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__0__left)). 4.02/4.28 fof(fact_le__SucE, axiom, ![X5, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X5)))=>(X2=hAPP(c_Nat_OSuc,X5)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__SucE)). 4.02/4.28 fof(fact_restrict__map__def, axiom, ![X21, X7, X3, X9, X4]:((hAPP(c_Map_Orestrict__map(X4,X7,X21,X3),X9)=c_Option_Ooption_ONone(X7)<=~(hBOOL(hAPP(hAPP(c_member(X4),X9),X3))))&(hAPP(c_Map_Orestrict__map(X4,X7,X21,X3),X9)=hAPP(X21,X9)<=hBOOL(hAPP(hAPP(c_member(X4),X9),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__map__def)). 4.02/4.28 fof(fact_min__max_OInf__fin_OF__eq, axiom, ![X3, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),X3)=hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OInf__fin_OF__eq)). 4.02/4.28 fof(fact_min__max_OSup__fin_OF__eq, axiom, ![X3, X4]:((c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),X3)=hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omax(X4)),X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_OSup__fin_OF__eq)). 4.02/4.28 fof(fact_enum__prod__def, axiom, ![X7, X4]:(c_Enum_Oenum__class_Oenum(tc_prod(X4,X7))=c_Enum_Oproduct(X4,X7,c_Enum_Oenum__class_Oenum(X4),c_Enum_Oenum__class_Oenum(X7))<=(class_Enum_Oenum(X4)&class_Enum_Oenum(X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__prod__def)). 4.02/4.28 fof(fact_remove1__remdups, axiom, ![X13, X45, X4]:(c_List_Oremdups(X4,c_List_Oremove1(X4,X13,X45))=c_List_Oremove1(X4,X13,c_List_Oremdups(X4,X45))<=hBOOL(hAPP(c_List_Odistinct(X4),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__remdups)). 4.02/4.28 fof(fact_mult__cancel2, axiom, ![X20, X28, X21]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X28)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X28)<=>(X28=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X21=X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__cancel2)). 4.02/4.28 fof(fact_mult__cancel1, axiom, ![X20, X21, X28]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X20)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X21)<=>(X28=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X21=X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__cancel1)). 4.02/4.28 fof(fact_less__code__numeral__def, axiom, ![X21, X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X20)),hAPP(c_Code__Numeral_Onat__of,X21)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X20),X21))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__code__numeral__def)). 4.02/4.28 fof(fact_inj__of__nat, axiom, ![X4]:(class_Nat_Osemiring__char__0(X4)=>c_Fun_Oinj__on(tc_Nat_Onat,X4,c_Nat_Osemiring__1__class_Oof__nat(X4),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__of__nat)). 4.02/4.28 fof(fact_abs__minus__cancel, axiom, ![X11, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>hAPP(c_Groups_Oabs__class_Oabs(X4),X11)=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__minus__cancel)). 4.02/4.28 fof(fact_Suc__less__eq, axiom, ![X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21)),hAPP(c_Nat_OSuc,X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__less__eq)). 4.02/4.28 fof(fact_less__eq__code__numeral__def, axiom, ![X21, X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X20),X21))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X20)),hAPP(c_Code__Numeral_Onat__of,X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__eq__code__numeral__def)). 4.02/4.28 fof(fact_mod__pos__pos__trivial, axiom, ![X12, X11]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),X12))=>c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)=X11)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__pos__pos__trivial)). 4.02/4.28 fof(fact_mod__neg__neg__trivial, axiom, ![X12, X11]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>(c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)=X11<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__neg__neg__trivial)). 4.02/4.28 fof(fact_transfer__int__nat__set__relations_I3_J, axiom, ![X6, X3]:(c_Nat__Transfer_Onat__set(X3)=>(c_Nat__Transfer_Onat__set(X6)=>(hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X3)=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X6)<=>X6=X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__relations_I3_J)). 4.02/4.28 fof(fact_wf__comp__self, axiom, ![X39, X4]:(c_Wellfounded_Owf(X4,X39)<=>c_Wellfounded_Owf(X4,hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X39),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__comp__self)). 4.02/4.28 fof(fact_min__max_Oinf__le1, axiom, ![X43, X13, X4]:(class_Orderings_Olinorder(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),X43)),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__le1)). 4.02/4.28 fof(fact_subset__empty, axiom, ![X3, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__empty)). 4.02/4.28 fof(fact_evaln__nonstrict, axiom, ![X2, X179, X5, X159, X10]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X2))=>c_Natural_Oevaln(X10,X159,X2,X179))<=c_Natural_Oevaln(X10,X159,X5,X179)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evaln__nonstrict)). 4.02/4.28 fof(fact_min__max_Oinf__le2, axiom, ![X43, X13, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),X43)),X43))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__le2)). 4.02/4.28 fof(fact_le__maxI1, axiom, ![X43, X13, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),X43)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__maxI1)). 4.02/4.28 fof(fact_le__maxI2, axiom, ![X13, X43, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X43),hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),X43)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__maxI2)). 4.02/4.28 fof(fact_listsum__foldl, axiom, ![X4]:(c_List_Ofoldl(X4,X4,c_Groups_Oplus__class_Oplus(X4),c_Groups_Ozero__class_Ozero(X4))=c_List_Omonoid__add__class_Olistsum(X4)<=class_Groups_Omonoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__foldl)). 4.02/4.28 fof(fact_sup1I1, axiom, ![X6, X4, X9, X3]:(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6),X9))<=hBOOL(hAPP(X3,X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup1I1)). 4.02/4.28 fof(fact_sup1I2, axiom, ![X3, X4, X9, X6]:(hBOOL(hAPP(X6,X9))=>hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup1I2)). 4.02/4.28 fof(fact_Min_OF__eq, axiom, ![X3, X4]:((hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omin(X4)),X3)=c_Big__Operators_Olinorder__class_OMin(X4,X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_OF__eq)). 4.02/4.28 fof(fact_Max_OF__eq, axiom, ![X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>hAPP(c_Finite__Set_Ofold1(X4,c_Orderings_Oord__class_Omax(X4)),X3)=c_Big__Operators_Olinorder__class_OMax(X4,X3))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Max_OF__eq)). 4.02/4.28 fof(fact_Inf__fin_OF__eq, axiom, ![X3, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>c_Big__Operators_Olattice__class_OInf__fin(X4,X3)=hAPP(c_Finite__Set_Ofold1(X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)),X3))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_OF__eq)). 4.02/4.28 fof(fact_Sup__fin_OF__eq, axiom, ![X3, X4]:((c_Big__Operators_Olattice__class_OSup__fin(X4,X3)=hAPP(c_Finite__Set_Ofold1(X4,c_Lattices_Osemilattice__sup__class_Osup(X4)),X3)<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_OF__eq)). 4.02/4.28 fof(fact_inj__on__iff__eq__card, axiom, ![X22, X7, X3, X4]:((c_Fun_Oinj__on(X4,X7,X22,X3)<=>hAPP(c_Finite__Set_Ocard(X7),hAPP(c_Set_Oimage(X4,X7,X22),X3))=hAPP(c_Finite__Set_Ocard(X4),X3))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__iff__eq__card)). 4.02/4.28 fof(fact_Suc__mult__cancel1, axiom, ![X20, X21, X28]:(X20=X21<=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X28)),X21)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X28)),X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__mult__cancel1)). 4.02/4.28 fof(fact_Ints__of__int, axiom, ![X16, X4]:(hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X16)),c_Int_Oring__1__class_OInts(X4)))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__of__int)). 4.02/4.28 fof(fact_of__nat__in__Nats, axiom, ![X20, X4]:(hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X20)),c_Nat_Osemiring__1__class_ONats(X4)))<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__in__Nats)). 4.02/4.28 fof(fact_wf__lex__prod, axiom, ![X221, X7, X222, X4]:((c_Wellfounded_Owf(X7,X221)=>c_Wellfounded_Owf(tc_prod(X4,X7),c_Wellfounded_Olex__prod(X4,X7,X222,X221)))<=c_Wellfounded_Owf(X4,X222)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__lex__prod)). 4.02/4.28 fof(fact_Ints__of__nat, axiom, ![X20, X4]:(class_Rings_Oring__1(X4)=>hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X20)),c_Int_Oring__1__class_OInts(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__of__nat)). 4.02/4.28 fof(fact_Ints__number__of, axiom, ![X23, X4]:(hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X23)),c_Int_Oring__1__class_OInts(X4)))<=class_Int_Onumber__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__number__of)). 4.02/4.28 fof(fact_evalc_Oequations_I6_J, axiom, ![X66, X67, X69, X65, X70]:(((hBOOL(hAPP(X70,X67))&c_Natural_Oevalc(X65,X67,X66))|(c_Natural_Oevalc(X69,X67,X66)&~(hBOOL(hAPP(X70,X67)))))<=>c_Natural_Oevalc(c_Com_Ocom_OCond(X70,X65,X69),X67,X66)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evalc_Oequations_I6_J)). 4.02/4.28 fof(fact_not__less__eq, axiom, ![X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,X21)))<=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__less__eq)). 4.02/4.28 fof(fact_abs__of__pos, axiom, ![X11, X4]:((X11=hAPP(c_Groups_Oabs__class_Oabs(X4),X11)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__of__pos)). 4.02/4.28 fof(fact_abs__of__nonneg, axiom, ![X11, X4]:((X11=hAPP(c_Groups_Oabs__class_Oabs(X4),X11)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__of__nonneg)). 4.02/4.28 fof(fact_minus__unique, axiom, ![X12, X11, X4]:(class_Groups_Ogroup__add(X4)=>(X12=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X11)<=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)=c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__unique)). 4.02/4.28 fof(fact_take__all, axiom, ![X5, X45, X4]:(hAPP(hAPP(c_List_Otake(X4),X5),X45)=X45<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__all)). 4.02/4.28 fof(fact_finite__acyclic__wf__converse, axiom, ![X18, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X4)),X18))=>(c_Wellfounded_Owf(X4,hAPP(c_Relation_Oconverse(X4,X4),X18))<=c_Wellfounded_Oacyclic(X4,X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__acyclic__wf__converse)). 4.02/4.28 fof(fact_list__ex__simps_I1_J, axiom, ![X32, X9, X56, X4]:(c_List_Olist__ex(X4,X56,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32))<=>(hBOOL(hAPP(X56,X9))|c_List_Olist__ex(X4,X56,X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__simps_I1_J)). 4.02/4.28 fof(fact_inf__absorb2, axiom, ![X13, X43, X4]:((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X43)=X43<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X43),X13)))<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__absorb2)). 4.02/4.28 fof(fact_sorted__insort__insert, axiom, ![X9, X32, X4]:((c_List_Olinorder__class_Osorted(X4,X32)=>c_List_Olinorder__class_Osorted(X4,c_List_Olinorder__class_Oinsort__insert__key(X4,X4,c_COMBI(X4),X9,X32)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__insort__insert)). 4.02/4.28 fof(fact_acyclic__subset, axiom, ![X18, X40, X4]:((c_Wellfounded_Oacyclic(X4,X18)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),X40)))<=c_Wellfounded_Oacyclic(X4,X40)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclic__subset)). 4.02/4.28 fof(fact_wf__subset, axiom, ![X51, X18, X4]:((c_Wellfounded_Owf(X4,X51)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X51),X18)))<=c_Wellfounded_Owf(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__subset)). 4.02/4.28 fof(fact_le__iff__sup, axiom, ![X17, X9, X4]:(class_Lattices_Osemilattice__sup(X4)=>(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X9),X17)=X17<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__iff__sup)). 4.02/4.28 fof(fact_sup__absorb1, axiom, ![X13, X43, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X43),X13))=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X43)=X13)<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__absorb1)). 4.02/4.28 fof(fact_le__iff__inf, axiom, ![X17, X9, X4]:(class_Lattices_Osemilattice__inf(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X17))<=>X9=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X9),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__iff__inf)). 4.02/4.28 fof(fact_listsum__rev, axiom, ![X45, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(c_List_Omonoid__add__class_Olistsum(X4),hAPP(c_List_Orev(X4),X45))=hAPP(c_List_Omonoid__add__class_Olistsum(X4),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__rev)). 4.02/4.28 fof(fact_abs__idempotent, axiom, ![X11, X4]:(hAPP(c_Groups_Oabs__class_Oabs(X4),X11)=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__idempotent)). 4.02/4.28 fof(fact_wfP__subset, axiom, ![X51, X18, X4]:(c_Wellfounded_OwfP(X4,X18)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_fun(X4,tc_HOL_Obool))),X51),X18))=>c_Wellfounded_OwfP(X4,X51))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__subset)). 4.02/4.28 fof(fact_abs__of__nat, axiom, ![X5, X4]:(class_Rings_Olinordered__idom(X4)=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X5)=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__of__nat)). 4.02/4.28 fof(fact_hd__rev, axiom, ![X4, X45]:(c_List_Olist_ONil(X4)!=X45=>c_List_Olast(X4,X45)=hAPP(c_List_Ohd(X4),hAPP(c_List_Orev(X4),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__rev)). 4.02/4.28 fof(fact_of__int__of__nat__eq, axiom, ![X5, X4]:(hAPP(c_Int_Oring__1__class_Oof__int(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X5)<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__of__nat__eq)). 4.02/4.28 fof(fact_mod__eq, axiom, ![X101, X14, X5, X2]:(X101=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5)<=hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X5),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X14),X101)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__eq)). 4.02/4.28 fof(fact_list__ex__append, axiom, ![X31, X32, X56, X4]:((c_List_Olist__ex(X4,X56,X31)|c_List_Olist__ex(X4,X56,X32))<=>c_List_Olist__ex(X4,X56,hAPP(hAPP(c_List_Oappend(X4),X32),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__append)). 4.02/4.28 fof(fact_listrel__refl__on, axiom, ![X18, X3, X4]:(c_Relation_Orefl__on(tc_List_Olist(X4),c_List_Olists(X4,X3),c_List_Olistrel(X4,X18))<=c_Relation_Orefl__on(X4,X3,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__refl__on)). 4.02/4.28 fof(fact_equiv__listrel, axiom, ![X18, X3, X4]:(c_Equiv__Relations_Oequiv(tc_List_Olist(X4),c_List_Olists(X4,X3),c_List_Olistrel(X4,X18))<=c_Equiv__Relations_Oequiv(X4,X3,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__listrel)). 4.02/4.28 fof(fact_prod__eqI, axiom, ![X14, X15, X7, X4]:(hAPP(c_Product__Type_Ofst(X4,X7),X14)=hAPP(c_Product__Type_Ofst(X4,X7),X15)=>(X15=X14<=hAPP(c_Product__Type_Osnd(X4,X7),X14)=hAPP(c_Product__Type_Osnd(X4,X7),X15))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_prod__eqI)). 4.02/4.28 fof(fact_abs__zmult__eq__1, axiom, ![X5, X2]:(c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)<=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),X2),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__zmult__eq__1)). 4.02/4.28 fof(fact_list__all2__lengthD, axiom, ![X31, X32, X56, X7, X4]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)<=c_List_Olist__all2(X4,X7,X56,X32,X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__lengthD)). 4.02/4.28 fof(fact_finite__imageD, axiom, ![X3, X22, X7, X4]:((c_Fun_Oinj__on(X7,X4,X22,X3)=>hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Set_Oimage(X7,X4,X22),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__imageD)). 4.02/4.28 fof(fact_rev__predicate1D, axiom, ![X112, X4, X9, X56]:(hBOOL(hAPP(X56,X9))=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X56),X112))=>hBOOL(hAPP(X112,X9)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__predicate1D)). 4.02/4.28 fof(fact_abs__minus__one, axiom, ![X4]:((class_Int_Onumber__ring(X4)&class_Rings_Olinordered__idom(X4))=>c_Groups_Oone__class_Oone(X4)=hAPP(c_Groups_Oabs__class_Oabs(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__minus__one)). 4.02/4.28 fof(fact_transfer__int__nat__set__relations_I1_J, axiom, ![X3]:(c_Nat__Transfer_Onat__set(X3)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X3)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__set__relations_I1_J)). 4.02/4.28 fof(fact_sup1E, axiom, ![X9, X6, X3, X4]:((~(hBOOL(hAPP(X3,X9)))=>hBOOL(hAPP(X6,X9)))<=hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup1E)). 4.02/4.28 fof(fact_add__lessD1, axiom, ![X107, X135, X46]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X135)),X107))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X107))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__lessD1)). 4.02/4.28 fof(fact_sorted__single, axiom, ![X13, X4]:(class_Orderings_Olinorder(X4)=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X13),c_List_Olist_ONil(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__single)). 4.02/4.28 fof(fact_add__leD1, axiom, ![X5, X107, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X107)),X5))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__leD1)). 4.02/4.28 fof(fact_last__rev, axiom, ![X4, X45]:(X45!=c_List_Olist_ONil(X4)=>c_List_Olast(X4,hAPP(c_List_Orev(X4),X45))=hAPP(c_List_Ohd(X4),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__rev)). 4.02/4.28 fof(fact_DiffD2, axiom, ![X6, X3, X24, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X24),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)))=>~(hBOOL(hAPP(hAPP(c_member(X4),X24),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DiffD2)). 4.02/4.28 fof(fact_distinct__drop, axiom, ![X46, X45, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Odrop(X4),X46),X45)))<=hBOOL(hAPP(c_List_Odistinct(X4),X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__drop)). 4.02/4.28 fof(fact_distinct__take, axiom, ![X46, X45, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X45))=>hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Otake(X4),X46),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__take)). 4.02/4.28 fof(fact_finite_OinsertI, axiom, ![X26, X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Set_Oinsert(X4),X26),X3)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite_OinsertI)). 4.02/4.28 fof(fact_atLeastatMost__empty, axiom, ![X26, X25, X4]:(class_Orderings_Oorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X25),X26))=>c_SetInterval_Oord__class_OatLeastAtMost(X4,X26,X25)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastatMost__empty)). 4.02/4.28 fof(fact_mod__mod__trivial, axiom, ![X12, X11, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,X11,X12)=c_Divides_Odiv__class_Omod(X4,c_Divides_Odiv__class_Omod(X4,X11,X12),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mod__trivial)). 4.02/4.28 fof(fact_transfer__nat__int__set__relations_I3_J, axiom, ![X6, X3]:(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X6)=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X3)<=>X3=X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__relations_I3_J)). 4.02/4.28 fof(fact_rp__inv__image__rp, axiom, ![X22, X7, X56, X4]:(c_FunDef_Oreduction__pair(X4,X56)=>c_FunDef_Oreduction__pair(X7,hAPP(hAPP(c_FunDef_Orp__inv__image(X4,X7),X56),X22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rp__inv__image__rp)). 4.02/4.28 fof(fact_wf__inv__image, axiom, ![X22, X7, X18, X4]:(c_Wellfounded_Owf(X4,X18)=>c_Wellfounded_Owf(X7,hAPP(hAPP(c_Relation_Oinv__image(X4,X7),X18),X22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__inv__image)). 4.02/4.28 fof(fact_less__SucE, axiom, ![X5, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X5)))=>(X5=X2<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__SucE)). 4.02/4.28 fof(fact_type__definition_OAbs__image, axiom, ![X3, X170, X171, X7, X4]:(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_Oimage(X7,X4,X170),X3)<=c_Typedef_Otype__definition(X4,X7,X171,X170,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_OAbs__image)). 4.02/4.28 fof(fact_conversep_Oequations, axiom, ![X70, X67, X18, X7, X4]:(hBOOL(hAPP(hAPP(X18,X70),X67))<=>hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4,X7,X18),X67),X70))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conversep_Oequations)). 4.02/4.28 fof(fact_xt1_I5_J, axiom, ![X13, X43, X4]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X43))=>X13=X43)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X43),X13)))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I5_J)). 4.02/4.28 fof(fact_abs__ge__self, axiom, ![X11, X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__ge__self)). 4.02/4.28 fof(fact_diffs0__imp__equal, axiom, ![X5, X2]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5)=>(X5=X2<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diffs0__imp__equal)). 4.02/4.28 fof(fact_finite__Un, axiom, ![X253, X87, X4]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X87))&hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X253)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X87),X253)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Un)). 4.02/4.28 fof(fact_sorted__drop, axiom, ![X5, X45, X4]:(class_Orderings_Olinorder(X4)=>(c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Odrop(X4),X5),X45))<=c_List_Olinorder__class_Osorted(X4,X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__drop)). 4.02/4.28 fof(fact_sorted__take, axiom, ![X5, X45, X4]:((c_List_Olinorder__class_Osorted(X4,X45)=>c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Otake(X4),X5),X45)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__take)). 4.02/4.28 fof(fact_distinct__filter, axiom, ![X56, X32, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),hAPP(c_List_Ofilter(X4,X56),X32)))<=hBOOL(hAPP(c_List_Odistinct(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__filter)). 4.02/4.28 fof(fact_transfer__nat__int__set__relations_I1_J, axiom, ![X3]:(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)),X3)))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__nat__int__set__relations_I1_J)). 4.02/4.28 fof(fact_int__one__le__iff__zero__less, axiom, ![X16]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__one__le__iff__zero__less)). 4.02/4.28 fof(fact_zero__less__one, axiom, ![X4]:(class_Rings_Olinordered__semidom(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),c_Groups_Oone__class_Oone(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__one)). 4.02/4.28 fof(fact_zero__le__one, axiom, ![X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),c_Groups_Oone__class_Oone(X4)))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__one)). 4.02/4.28 fof(fact_evaln__elim__cases_I5_J, axiom, ![X123, X20, X40, X248, X149, X25]:(c_Natural_Oevaln(c_Com_Ocom_OCond(X25,X149,X248),X40,X20,X123)=>((~(c_Natural_Oevaln(X149,X40,X20,X123))<=hBOOL(hAPP(X25,X40)))=>~((~(hBOOL(hAPP(X25,X40)))=>~(c_Natural_Oevaln(X248,X40,X20,X123)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evaln__elim__cases_I5_J)). 4.02/4.28 fof(fact_singleton__iff, axiom, ![X26, X25, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X25),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))<=>X26=X25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_singleton__iff)). 4.02/4.28 fof(fact_wf__acc__iff, axiom, ![X18, X4]:(c_Wellfounded_Owf(X4,X18)<=>![X19]:hBOOL(hAPP(hAPP(c_member(X4),X19),c_Wellfounded_Oacc(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__acc__iff)). 4.02/4.28 fof(fact_min__max_Oinf__absorb1, axiom, ![X43, X13, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X43))=>X13=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),X43))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__absorb1)). 4.02/4.28 fof(fact_Un__empty, axiom, ![X6, X3, X4]:(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)<=>(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X6&c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__empty)). 4.02/4.28 fof(fact_min__max_Oinf__absorb2, axiom, ![X13, X43, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X43),X13))=>X43=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),X43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Oinf__absorb2)). 4.02/4.28 fof(fact_min__max_Ole__iff__sup, axiom, ![X17, X9, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X17))<=>X17=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X9),X17))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__iff__sup)). 4.02/4.28 fof(fact_min__max_Osup__absorb1, axiom, ![X13, X43, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X43),X13))=>X13=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X13),X43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup__absorb1)). 4.02/4.28 fof(fact_distinct__remove1, axiom, ![X13, X45, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X45))=>hBOOL(hAPP(c_List_Odistinct(X4),c_List_Oremove1(X4,X13,X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__remove1)). 4.02/4.28 fof(fact_greaterThanAtMost__empty, axiom, ![X28, X60, X4]:(class_Orderings_Oorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X60),X28))=>c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X28,X60))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThanAtMost__empty)). 4.02/4.28 fof(fact_greaterThanLessThan__empty, axiom, ![X28, X60, X4]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X60),X28))=>c_SetInterval_Oord__class_OgreaterThanLessThan(X4,X28,X60)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThanLessThan__empty)). 4.02/4.28 fof(fact_fun__left__comm__insort, axiom, ![X4]:(c_Finite__Set_Ofun__left__comm(X4,tc_List_Olist(X4),c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__insort)). 4.02/4.28 fof(fact_power__one, axiom, ![X5, X4]:(class_Groups_Omonoid__mult(X4)=>hAPP(hAPP(c_Power_Opower__class_Opower(X4),c_Groups_Oone__class_Oone(X4)),X5)=c_Groups_Oone__class_Oone(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__one)). 4.02/4.28 fof(fact_distinct__sublistI, axiom, ![X41, X32, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X32))=>hBOOL(hAPP(c_List_Odistinct(X4),c_List_Osublist(X4,X32,X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__sublistI)). 4.02/4.28 fof(fact_distinct__insert, axiom, ![X13, X45, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X45))=>hBOOL(hAPP(c_List_Odistinct(X4),c_List_Oinsert(X4,X13,X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__insert)). 4.02/4.28 fof(fact_distinct__takeWhile, axiom, ![X56, X32, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X32))=>hBOOL(hAPP(c_List_Odistinct(X4),c_List_OtakeWhile(X4,X56,X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__takeWhile)). 4.02/4.28 fof(fact_finite__Field, axiom, ![X18, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_Relation_OField(X4),X18)))<=hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X4)),X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__Field)). 4.02/4.28 fof(fact_divide__zero__left, axiom, ![X11, X4]:(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),c_Groups_Ozero__class_Ozero(X4)),X11)=c_Groups_Ozero__class_Ozero(X4)<=class_Rings_Odivision__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__zero__left)). 4.02/4.28 fof(fact_mult__zero__left, axiom, ![X11, X4]:(class_Rings_Omult__zero(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ozero__class_Ozero(X4)),X11)=c_Groups_Ozero__class_Ozero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__zero__left)). 4.02/4.28 fof(fact_equivp__symp, axiom, ![X17, X9, X39, X4]:(c_Equiv__Relations_Oequivp(X4,X39)=>(hBOOL(hAPP(hAPP(X39,X17),X9))<=hBOOL(hAPP(hAPP(X39,X9),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivp__symp)). 4.02/4.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, axiom, ![X11, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ozero__class_Ozero(X4)),X11)=c_Groups_Ozero__class_Ozero(X4)<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J)). 4.02/4.28 fof(fact_sorted__list__of__set, axiom, ![X3, X4]:(class_Orderings_Olinorder(X4)=>(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))=>((c_List_Olinorder__class_Osorted(X4,c_List_Olinorder__class_Osorted__list__of__set(X4,X3))&hBOOL(hAPP(c_List_Odistinct(X4),c_List_Olinorder__class_Osorted__list__of__set(X4,X3))))&X3=hAPP(c_List_Oset(X4),c_List_Olinorder__class_Osorted__list__of__set(X4,X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set)). 4.02/4.28 fof(fact_atLeastAtMost__singleton__iff, axiom, ![X24, X25, X26, X4]:(((X25=X24&X26=X25)<=>c_SetInterval_Oord__class_OatLeastAtMost(X4,X26,X25)=hAPP(hAPP(c_Set_Oinsert(X4),X24),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))<=class_Orderings_Oorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastAtMost__singleton__iff)). 4.02/4.28 fof(fact_sup__top__left, axiom, ![X13, X4]:(class_Lattices_Obounded__lattice__top(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),c_Orderings_Otop__class_Otop(X4)),X13)=c_Orderings_Otop__class_Otop(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__top__left)). 4.02/4.28 fof(fact_nat__less__le, axiom, ![X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))<=>(X20!=X21&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__less__le)). 4.02/4.28 fof(fact_div__0, axiom, ![X11, X4]:(class_Divides_Osemiring__div(X4)=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),c_Groups_Ozero__class_Ozero(X4)),X11)=c_Groups_Ozero__class_Ozero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__0)). 4.02/4.28 fof(fact_no__zero__divisors, axiom, ![X12, X11, X4]:(class_Rings_Ono__zero__divisors(X4)=>((c_Groups_Ozero__class_Ozero(X4)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)<=X12!=c_Groups_Ozero__class_Ozero(X4))<=c_Groups_Ozero__class_Ozero(X4)!=X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_no__zero__divisors)). 4.02/4.28 fof(fact_inf__bot__left, axiom, ![X13, X4]:(c_Orderings_Obot__class_Obot(X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),c_Orderings_Obot__class_Obot(X4)),X13)<=class_Lattices_Obounded__lattice__bot(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__bot__left)). 4.02/4.28 fof(fact_hd__conv__nth, axiom, ![X4, X45]:(c_List_Olist_ONil(X4)!=X45=>hAPP(hAPP(c_List_Onth(X4),X45),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_List_Ohd(X4),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__conv__nth)). 4.02/4.28 fof(fact_sgn__pos, axiom, ![X11, X4]:((c_Groups_Oone__class_Oone(X4)=c_Groups_Osgn__class_Osgn(X4,X11)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11)))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__pos)). 4.02/4.28 fof(fact_divmod__int__correct, axiom, ![X11, X12]:(X12!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)=>hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11,X12),c_Divides_Odivmod__int(X11,X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__int__correct)). 4.02/4.28 fof(fact_inf__bot__right, axiom, ![X13, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),c_Orderings_Obot__class_Obot(X4))=c_Orderings_Obot__class_Obot(X4)<=class_Lattices_Obounded__lattice__bot(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__bot__right)). 4.02/4.28 fof(fact_zabs__def, axiom, ![X46]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X46),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=>hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X46)=hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X46))&(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X46),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))=>hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X46)=X46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zabs__def)). 4.02/4.28 fof(fact_evalc_Oequations_I4_J, axiom, ![X65, X67, X66, X70]:(c_Natural_Oevalc(c_Com_Ocom_OSemi(X70,X66),X67,X65)<=>?[X136]:(c_Natural_Oevalc(X66,X136,X65)&c_Natural_Oevalc(X70,X67,X136))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evalc_Oequations_I4_J)). 4.02/4.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, axiom, ![X11, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),c_Groups_Ozero__class_Ozero(X4))=c_Groups_Ozero__class_Ozero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J)). 4.02/4.28 fof(fact_rotate1__length01, axiom, ![X45, X4]:(X45=hAPP(c_List_Orotate1(X4),X45)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate1__length01)). 4.02/4.28 fof(fact_RangeP_Ointros, axiom, ![X7, X4, X25, X26, X18]:(hBOOL(hAPP(c_Predicate_ORangeP(X4,X7,X18),X25))<=hBOOL(hAPP(hAPP(X18,X26),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_RangeP_Ointros)). 4.02/4.28 fof(fact_mult__is__0, axiom, ![X20, X21]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X20)<=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X21|X20=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__is__0)). 4.02/4.28 fof(fact_tsub__eq, axiom, ![X13, X43]:(c_Nat__Transfer_Otsub(X13,X43)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X13),X43)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X43),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tsub__eq)). 4.02/4.28 fof(fact_div__by__0, axiom, ![X11, X4]:(hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X11),c_Groups_Ozero__class_Ozero(X4))=c_Groups_Ozero__class_Ozero(X4)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__by__0)). 4.02/4.28 fof(fact_DomainP_Ointros, axiom, ![X7, X4, X25, X26, X18]:(hBOOL(hAPP(c_Predicate_ODomainP(X4,X7,X18),X26))<=hBOOL(hAPP(hAPP(X18,X26),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DomainP_Ointros)). 4.02/4.28 fof(fact_Rep__Integ__cases, axiom, ![X17]:(~(![X19]:hAPP(c_Int_ORep__Integ,X19)!=X17)<=hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X17),c_Int_OInteg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Rep__Integ__cases)). 4.02/4.28 fof(fact_sup__top__right, axiom, ![X13, X4]:(class_Lattices_Obounded__lattice__top(X4)=>c_Orderings_Otop__class_Otop(X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),c_Orderings_Otop__class_Otop(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__top__right)). 4.02/4.28 fof(fact_diff__is__0__eq, axiom, ![X20, X21]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21),X20)<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__is__0__eq)). 4.02/4.28 fof(fact_div__less, axiom, ![X5, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X5))=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__less)). 4.02/4.28 fof(fact_divide__zero, axiom, ![X11, X4]:(class_Rings_Odivision__ring__inverse__zero(X4)=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__zero)). 4.02/4.28 fof(fact_negative__eq__positive, axiom, ![X21, X20]:(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21)<=>(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X20&c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negative__eq__positive)). 4.02/4.28 fof(fact_hd__replicate, axiom, ![X13, X4, X5]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X5=>hAPP(c_List_Ohd(X4),c_List_Oreplicate(X4,X5,X13))=X13), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd__replicate)). 4.02/4.28 fof(fact_mult__zero__right, axiom, ![X11, X4]:(class_Rings_Omult__zero(X4)=>c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__zero__right)). 4.02/4.28 fof(fact_less__Suc__eq, axiom, ![X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_OSuc,X20)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))|X21=X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Suc__eq)). 4.02/4.28 fof(fact_wf__not__refl, axiom, ![X26, X18, X4]:(~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X26)),X18)))<=c_Wellfounded_Owf(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__not__refl)). 4.02/4.28 fof(fact_less__Suc__eq__le, axiom, ![X20, X21]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_OSuc,X20)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__Suc__eq__le)). 4.02/4.28 fof(fact_le__SucI, axiom, ![X5, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X5))=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__SucI)). 4.02/4.28 fof(fact_div__self, axiom, ![X11, X4]:((hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X11),X11)=c_Groups_Oone__class_Oone(X4)<=c_Groups_Ozero__class_Ozero(X4)!=X11)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__self)). 4.02/4.28 fof(fact_divide__self__if, axiom, ![X11, X4]:(class_Rings_Odivision__ring__inverse__zero(X4)=>((c_Groups_Ozero__class_Ozero(X4)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X11)<=X11=c_Groups_Ozero__class_Ozero(X4))&(c_Groups_Ozero__class_Ozero(X4)!=X11=>c_Groups_Oone__class_Oone(X4)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__self__if)). 4.02/4.28 fof(fact_evalc_OIfTrue, axiom, ![X149, X148, X147, X40, X25]:((c_Natural_Oevalc(X147,X40,X148)=>c_Natural_Oevalc(c_Com_Ocom_OCond(X25,X147,X149),X40,X148))<=hBOOL(hAPP(X25,X40))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evalc_OIfTrue)). 4.02/4.28 fof(fact_wf__lexn, axiom, ![X20, X18, X4]:(c_Wellfounded_Owf(X4,X18)=>c_Wellfounded_Owf(tc_List_Olist(X4),hAPP(c_List_Olexn(X4,X18),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__lexn)). 4.02/4.28 fof(fact_n__lists__Nil, axiom, ![X4, X5]:((X5!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>c_List_Olist_ONil(tc_List_Olist(X4))=c_Enum_On__lists(X4,X5,c_List_Olist_ONil(X4)))&(hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_List_Olist_ONil(tc_List_Olist(X4)))=c_Enum_On__lists(X4,X5,c_List_Olist_ONil(X4))<=X5=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_n__lists__Nil)). 4.02/4.28 fof(fact_divide__self, axiom, ![X11, X4]:((c_Groups_Ozero__class_Ozero(X4)!=X11=>c_Groups_Oone__class_Oone(X4)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),X11))<=class_Rings_Odivision__ring(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__self)). 4.02/4.28 fof(fact_finite__PlusD_I1_J, axiom, ![X6, X3, X7, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X4,X7)),c_Sum__Type_OPlus(X4,X7,X3,X6)))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__PlusD_I1_J)). 4.02/4.28 fof(fact_finite__PlusD_I2_J, axiom, ![X6, X3, X7, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X4,X7)),c_Sum__Type_OPlus(X4,X7,X3,X6)))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__PlusD_I2_J)). 4.02/4.28 fof(fact_Nats__0, axiom, ![X4]:(hBOOL(hAPP(hAPP(c_member(X4),c_Groups_Ozero__class_Ozero(X4)),c_Nat_Osemiring__1__class_ONats(X4)))<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nats__0)). 4.02/4.28 fof(fact_Ints__0, axiom, ![X4]:(class_Rings_Oring__1(X4)=>hBOOL(hAPP(hAPP(c_member(X4),c_Groups_Ozero__class_Ozero(X4)),c_Int_Oring__1__class_OInts(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__0)). 4.02/4.28 fof(fact_Nats__1, axiom, ![X4]:(hBOOL(hAPP(hAPP(c_member(X4),c_Groups_Oone__class_Oone(X4)),c_Nat_Osemiring__1__class_ONats(X4)))<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nats__1)). 4.02/4.28 fof(fact_folding__image__simple__idem_Oidem, axiom, ![X9, X87, X76, X16, X22, X7, X4]:(c_Finite__Set_Ofolding__image__simple__idem(X4,X7,X22,X16,X76,X87)=>X9=hAPP(hAPP(X22,X9),X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple__idem_Oidem)). 4.02/4.28 fof(fact_map__le__trans, axiom, ![X235, X162, X163, X7, X4]:((c_Map_Omap__le(X4,X7,X162,X235)=>c_Map_Omap__le(X4,X7,X163,X235))<=c_Map_Omap__le(X4,X7,X163,X162)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__le__trans)). 4.02/4.28 fof(fact_Ints__1, axiom, ![X4]:(hBOOL(hAPP(hAPP(c_member(X4),c_Groups_Oone__class_Oone(X4)),c_Int_Oring__1__class_OInts(X4)))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ints__1)). 4.02/4.28 fof(fact_total__on__converse, axiom, ![X18, X3, X4]:(c_Relation_Ototal__on(X4,X3,hAPP(c_Relation_Oconverse(X4,X4),X18))<=>c_Relation_Ototal__on(X4,X3,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_total__on__converse)). 4.02/4.28 fof(fact_refl__on__converse, axiom, ![X18, X3, X4]:(c_Relation_Orefl__on(X4,X3,hAPP(c_Relation_Oconverse(X4,X4),X18))<=>c_Relation_Orefl__on(X4,X3,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__converse)). 4.02/4.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, axiom, ![X13, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X4)<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J)). 4.02/4.28 fof(fact_add__right__imp__eq, axiom, ![X10, X11, X12, X4]:((X10=X12<=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X10),X11)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X11))<=class_Groups_Ocancel__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__right__imp__eq)). 4.02/4.28 fof(fact_add__imp__eq, axiom, ![X10, X12, X11, X4]:(class_Groups_Ocancel__ab__semigroup__add(X4)=>(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12)=>X12=X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__imp__eq)). 4.02/4.28 fof(fact_add__left__imp__eq, axiom, ![X10, X12, X11, X4]:((X10=X12<=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),X12))<=class_Groups_Ocancel__semigroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__left__imp__eq)). 4.02/4.28 fof(fact_power__0, axiom, ![X11, X4]:(c_Groups_Oone__class_Oone(X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<=class_Power_Opower(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__0)). 4.02/4.28 fof(fact_mult__1__left, axiom, ![X11, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oone__class_Oone(X4)),X11)=X11<=class_Groups_Omonoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__1__left)). 4.02/4.28 fof(fact_mult__1, axiom, ![X11, X4]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oone__class_Oone(X4)),X11)=X11<=class_Groups_Ocomm__monoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__1)). 4.02/4.28 fof(fact_mult__eq__self__implies__10, axiom, ![X5, X2]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)=X2=>(X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X5=c_Groups_Oone__class_Oone(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__eq__self__implies__10)). 4.02/4.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, axiom, ![X11, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oone__class_Oone(X4)),X11)=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J)). 4.02/4.28 fof(fact_sup__bot__left, axiom, ![X13, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),c_Orderings_Obot__class_Obot(X4)),X13)=X13<=class_Lattices_Obounded__lattice__bot(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__bot__left)). 4.02/4.28 fof(fact_add__0, axiom, ![X11, X4]:(class_Groups_Ocomm__monoid__add(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Ozero__class_Ozero(X4)),X11)=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__0)). 4.02/4.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, axiom, ![X11, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Ozero__class_Ozero(X4)),X11)=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J)). 4.02/4.28 fof(fact_card__distinct, axiom, ![X32, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X32))<=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)=hAPP(c_Finite__Set_Ocard(X4),hAPP(c_List_Oset(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__distinct)). 4.02/4.28 fof(fact_sorted__list__of__set__empty, axiom, ![X4]:(class_Orderings_Olinorder(X4)=>c_List_Olinorder__class_Osorted__list__of__set(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__list__of__set__empty)). 4.02/4.28 fof(fact_Sup__empty, axiom, ![X4]:(c_Complete__Lattice_OSup__class_OSup(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(X4)<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__empty)). 4.02/4.28 fof(fact_Inf__UNIV, axiom, ![X4]:(class_Complete__Lattice_Ocomplete__lattice(X4)=>c_Complete__Lattice_OInf__class_OInf(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__UNIV)). 4.02/4.28 fof(fact_inf__top__left, axiom, ![X13, X4]:(class_Lattices_Obounded__lattice__top(X4)=>X13=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),c_Orderings_Otop__class_Otop(X4)),X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__top__left)). 4.02/4.28 fof(fact_add__0__left, axiom, ![X11, X4]:(class_Groups_Omonoid__add(X4)=>X11=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Groups_Ozero__class_Ozero(X4)),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__0__left)). 4.02/4.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, axiom, ![X11, X4]:(class_Rings_Ocomm__semiring__1(X4)=>hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),c_Groups_Oone__class_Oone(X4))=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J)). 4.02/4.28 fof(fact_sup__bot__right, axiom, ![X13, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),c_Orderings_Obot__class_Obot(X4))=X13<=class_Lattices_Obounded__lattice__bot(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__bot__right)). 4.02/4.28 fof(fact_Sup__UNIV, axiom, ![X4]:(c_Orderings_Otop__class_Otop(X4)=c_Complete__Lattice_OSup__class_OSup(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__UNIV)). 4.02/4.28 fof(fact_Inf__empty, axiom, ![X4]:(c_Orderings_Otop__class_Otop(X4)=c_Complete__Lattice_OInf__class_OInf(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=class_Complete__Lattice_Ocomplete__lattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__empty)). 4.02/4.28 fof(fact_sorted__butlast, axiom, ![X45, X4]:((c_List_Olist_ONil(X4)!=X45=>(c_List_Olinorder__class_Osorted(X4,X45)=>c_List_Olinorder__class_Osorted(X4,c_List_Obutlast(X4,X45))))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__butlast)). 4.02/4.28 fof(fact_add__0__right, axiom, ![X11, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),c_Groups_Ozero__class_Ozero(X4))=X11<=class_Groups_Omonoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__0__right)). 4.02/4.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, axiom, ![X11, X4]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),c_Groups_Ozero__class_Ozero(X4))=X11<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J)). 4.02/4.28 fof(fact_div__by__1, axiom, ![X11, X4]:(class_Divides_Osemiring__div(X4)=>hAPP(hAPP(c_Divides_Odiv__class_Odiv(X4),X11),c_Groups_Oone__class_Oone(X4))=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__by__1)). 4.02/4.28 fof(fact_divide__1, axiom, ![X11, X4]:(class_Rings_Odivision__ring(X4)=>X11=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X11),c_Groups_Oone__class_Oone(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divide__1)). 4.02/4.28 fof(fact_last__replicate, axiom, ![X13, X4, X5]:(X5!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=>X13=c_List_Olast(X4,c_List_Oreplicate(X4,X5,X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_last__replicate)). 4.02/4.28 fof(fact_take__eq__Nil, axiom, ![X32, X20, X4]:((X20=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Olist_ONil(X4)=X32)<=>hAPP(hAPP(c_List_Otake(X4),X20),X32)=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__eq__Nil)). 4.02/4.28 fof(fact_top__apply, axiom, ![X9, X7, X4]:(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X7,X4)),X9)=c_Orderings_Otop__class_Otop(X4)<=class_Orderings_Otop(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_top__apply)). 4.02/4.28 fof(fact_diff__0__right, axiom, ![X11, X4]:(class_Groups_Ogroup__add(X4)=>X11=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__0__right)). 4.02/4.28 fof(fact_inf__top__right, axiom, ![X13, X4]:(class_Lattices_Obounded__lattice__top(X4)=>X13=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),c_Orderings_Otop__class_Otop(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__top__right)). 4.02/4.28 fof(fact_mult__1__right, axiom, ![X11, X4]:(X11=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),c_Groups_Oone__class_Oone(X4))<=class_Groups_Omonoid__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__1__right)). 4.02/4.28 fof(fact_mult_Ocomm__neutral, axiom, ![X11, X4]:(class_Groups_Ocomm__monoid__mult(X4)=>X11=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),c_Groups_Oone__class_Oone(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult_Ocomm__neutral)). 4.02/4.28 fof(fact_bot__apply, axiom, ![X9, X7, X4]:(c_Orderings_Obot__class_Obot(X4)=hAPP(c_Orderings_Obot__class_Obot(tc_fun(X7,X4)),X9)<=class_Orderings_Obot(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bot__apply)). 4.02/4.28 fof(fact_injD, axiom, ![X17, X9, X22, X7, X4]:((hAPP(X22,X17)=hAPP(X22,X9)=>X17=X9)<=c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_injD)). 4.02/4.28 fof(fact_add_Ocomm__neutral, axiom, ![X11, X4]:(X11=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X11),c_Groups_Ozero__class_Ozero(X4))<=class_Groups_Ocomm__monoid__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add_Ocomm__neutral)). 4.02/4.28 fof(fact_double__compl, axiom, ![X13, X4]:(class_Lattices_Oboolean__algebra(X4)=>X13=hAPP(c_Groups_Ouminus__class_Ouminus(X4),hAPP(c_Groups_Ouminus__class_Ouminus(X4),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__compl)). 4.02/4.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, axiom, ![X13, X4]:(hAPP(hAPP(c_Power_Opower__class_Opower(X4),X13),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X13<=class_Rings_Ocomm__semiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)). 4.02/4.28 fof(fact_Pair__inject, axiom, ![X110, X111, X12, X11, X7, X4]:(~((X11=X111=>X110!=X12))<=hAPP(hAPP(c_Product__Type_OPair(X4,X7),X111),X110)=hAPP(hAPP(c_Product__Type_OPair(X4,X7),X11),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pair__inject)). 4.02/4.28 fof(fact_power__one__right, axiom, ![X11, X4]:(class_Groups_Omonoid__mult(X4)=>X11=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),c_Groups_Oone__class_Oone(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__one__right)). 4.02/4.28 fof(fact_order__less__imp__le, axiom, ![X43, X13, X4]:(class_Orderings_Opreorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X43))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__imp__le)). 4.02/4.28 fof(fact_right__inverse__eq, axiom, ![X26, X25, X4]:(class_Rings_Odivision__ring(X4)=>((X25=X26<=>hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),X25)=c_Groups_Oone__class_Oone(X4))<=c_Groups_Ozero__class_Ozero(X4)!=X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_right__inverse__eq)). 4.02/4.28 fof(fact_wf__no__loop, axiom, ![X39, X4]:(c_Wellfounded_Owf(X4,X39)<=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X39),X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__no__loop)). 4.02/4.28 fof(fact_card__eq__0__iff, axiom, ![X3, X4]:((X3=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))|~(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))))<=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X4),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__eq__0__iff)). 4.02/4.28 fof(fact_type__definition_ORep__inverse, axiom, ![X9, X3, X170, X171, X7, X4]:(X9=hAPP(X170,hAPP(X171,X9))<=c_Typedef_Otype__definition(X4,X7,X171,X170,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_ORep__inverse)). 4.02/4.28 fof(fact_eval__eq, axiom, ![X123, X40, X24]:(c_Natural_Oevalc(X24,X40,X123)<=>?[X104]:c_Natural_Oevaln(X24,X40,X104,X123)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eval__eq)). 4.02/4.28 fof(fact_evaln__Suc, axiom, ![X158, X5, X159, X10]:(c_Natural_Oevaln(X10,X159,hAPP(c_Nat_OSuc,X5),X158)<=c_Natural_Oevaln(X10,X159,X5,X158)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evaln__Suc)). 4.02/4.28 fof(fact_sorted__sort, axiom, ![X32, X4]:(class_Orderings_Olinorder(X4)=>c_List_Olinorder__class_Osorted(X4,c_List_Olinorder__class_Osort__key(X4,X4,c_COMBI(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__sort)). 4.02/4.28 fof(fact_zle__antisym, axiom, ![X53, X29]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X53),X29))=>X29=X53)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29),X53))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__antisym)). 4.02/4.28 fof(fact_le__antisym, axiom, ![X5, X2]:((X2=X5<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X2)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__antisym)). 4.02/4.28 fof(fact_evalc_Oequations_I5_J, axiom, ![X66, X67, X65, X69, X70]:(((~(hBOOL(hAPP(X70,X67)))&c_Natural_Oevalc(X65,X67,X66))|(hBOOL(hAPP(X70,X67))&c_Natural_Oevalc(X69,X67,X66)))<=>c_Natural_Oevalc(c_Com_Ocom_OCond(X70,X69,X65),X67,X66)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evalc_Oequations_I5_J)). 4.02/4.28 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures, axiom, ![X17, X9]:(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X9,X17))<=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_SetInterval_Otransfer__nat__int__set__function__closures)). 4.02/4.28 fof(fact_power__power__power, axiom, ![X4]:(c_Power_Opower__class_Opower(X4)=c_Power_Opower_Opower(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Otimes__class_Otimes(X4))<=class_Power_Opower(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power__power__power)). 4.02/4.28 fof(fact_folding__image__simple_Oempty, axiom, ![X87, X76, X16, X22, X7, X4]:(c_Finite__Set_Ofolding__image__simple(X4,X7,X22,X16,X76,X87)=>X16=hAPP(X87,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__image__simple_Oempty)). 4.02/4.28 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J, axiom, ![X43, X13]:(c_Nat__Transfer_Ois__nat(X13)=>(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13),X43))<=c_Nat__Transfer_Ois__nat(X43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J)). 4.02/4.28 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J, axiom, ![X43, X13]:((c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13),X43))<=c_Nat__Transfer_Ois__nat(X43))<=c_Nat__Transfer_Ois__nat(X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J)). 4.02/4.28 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J, axiom, ![X43, X13]:((c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X13),X43))<=c_Nat__Transfer_Ois__nat(X43))<=c_Nat__Transfer_Ois__nat(X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Otransfer__int__nat__function__closures_I1_J)). 4.02/4.28 fof(fact_folding_Oempty, axiom, ![X87, X22, X7, X4]:(c_Fun_Oid(X7)=hAPP(X87,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))<=c_Finite__Set_Ofolding(X4,X7,X22,X87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding_Oempty)). 4.02/4.28 fof(fact_enum__UNIV, axiom, ![X4]:(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(c_List_Oset(X4),c_Enum_Oenum__class_Oenum(X4))<=class_Enum_Oenum(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__UNIV)). 4.02/4.28 fof(fact_min__max_Ole__iff__inf, axiom, ![X17, X9, X4]:((hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X9),X17)=X9<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X17)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ole__iff__inf)). 4.02/4.28 fof(fact_tsub__def, axiom, ![X13, X43]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X43),X13))=>c_Nat__Transfer_Otsub(X13,X43)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X13),X43))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Nat__Transfer_Otsub(X13,X43)<=~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X43),X13))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tsub__def)). 4.02/4.28 fof(fact_order__less__not__sym, axiom, ![X43, X13, X4]:(class_Orderings_Opreorder(X4)=>(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X43),X13)))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__not__sym)). 4.02/4.28 fof(fact_xt1_I9_J, axiom, ![X11, X12, X4]:(class_Orderings_Oorder(X4)=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X11))=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X12))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_xt1_I9_J)). 4.02/4.28 fof(fact_not__less__iff__gr__or__eq, axiom, ![X17, X9, X4]:((~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X9),X17)))<=>(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X17),X9))|X17=X9))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__less__iff__gr__or__eq)). 4.02/4.28 fof(fact_int__le__0__conv, axiom, ![X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__le__0__conv)). 4.02/4.28 fof(fact_elem__set, axiom, ![X35, X9, X4]:(X35=hAPP(c_Option_Ooption_OSome(X4),X9)<=>hBOOL(hAPP(hAPP(c_member(X4),X9),c_Option_Oset(X4,X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_elem__set)). 4.02/4.28 fof(fact_divmod__nat__rel__unique, axiom, ![X240, X200, X5, X2]:((hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X5),X240))=>X200=X240)<=hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X5),X200))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel__unique)). 4.02/4.28 fof(fact_Compl__eq__Compl__iff, axiom, ![X6, X3, X4]:(X6=X3<=>hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X6)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__eq__Compl__iff)). 4.02/4.28 fof(fact_nat__add__right__cancel, axiom, ![X20, X28, X21]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X28)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X28)<=>X20=X21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__right__cancel)). 4.02/4.28 fof(fact_nat__add__left__cancel, axiom, ![X20, X21, X28]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X20)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28),X21)<=>X21=X20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__left__cancel)). 4.02/4.28 fof(fact_le__less__Suc__eq, axiom, ![X20, X21]:((X21=X20<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,X21))))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21),X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__less__Suc__eq)). 4.02/4.28 fof(fact_diff__self, axiom, ![X11, X4]:(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X11),X11)=c_Groups_Ozero__class_Ozero(X4)<=class_Groups_Ogroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__self)). 4.02/4.28 fof(fact_min__ext__wf, axiom, ![X18, X4]:(c_Wellfounded_Owf(tc_fun(X4,tc_HOL_Obool),c_Wellfounded_Omin__ext(X4,X18))<=c_Wellfounded_Owf(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__ext__wf)). 4.02/4.28 fof(fact_max__ext__wf, axiom, ![X18, X4]:(c_Wellfounded_Owf(tc_fun(X4,tc_HOL_Obool),c_Wellfounded_Omax__ext(X4,X18))<=c_Wellfounded_Owf(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ext__wf)). 4.02/4.28 fof(fact_equal__int__def, axiom, ![X60, X28]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X28),X60)<=>hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X28),X60))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equal__int__def)). 4.02/4.28 fof(fact_evalc__elim__cases_I6_J, axiom, ![X187, X159, X209]:(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X209)),X159,X187)<=c_Natural_Oevalc(c_Com_Ocom_OBODY(X209),X159,X187)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evalc__elim__cases_I6_J)). 4.02/4.28 fof(fact_distinct1__rotate, axiom, ![X32, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X32))<=>hBOOL(hAPP(c_List_Odistinct(X4),hAPP(c_List_Orotate1(X4),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct1__rotate)). 4.02/4.28 fof(fact_distinct__rev, axiom, ![X32, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),hAPP(c_List_Orev(X4),X32)))<=>hBOOL(hAPP(c_List_Odistinct(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__rev)). 4.02/4.28 fof(fact_distinct__tl, axiom, ![X45, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X45))=>hBOOL(hAPP(c_List_Odistinct(X4),hAPP(c_List_Otl(X4),X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__tl)). 4.02/4.28 fof(fact_insert__absorb, axiom, ![X3, X26, X4]:(hBOOL(hAPP(hAPP(c_member(X4),X26),X3))=>hAPP(hAPP(c_Set_Oinsert(X4),X26),X3)=X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__absorb)). 4.02/4.28 fof(fact_bot__least, axiom, ![X13, X4]:(class_Orderings_Obot(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Orderings_Obot__class_Obot(X4)),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bot__least)). 4.02/4.28 fof(fact_top__greatest, axiom, ![X13, X4]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),c_Orderings_Otop__class_Otop(X4)))<=class_Orderings_Otop(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_top__greatest)). 4.02/4.28 fof(fact_exists__code, axiom, ![X56, X4]:(class_Enum_Oenum(X4)=>(?[X77]:hBOOL(hAPP(X56,X77))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X4),X56)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_exists__code)). 4.02/4.28 fof(fact_enum__ex, axiom, ![X56, X4]:((hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X4),X56))<=>?[X77]:hBOOL(hAPP(X56,X77)))<=class_Enum_Oenum(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__ex)). 4.02/4.28 fof(fact_list__ex__rev, axiom, ![X32, X56, X4]:(c_List_Olist__ex(X4,X56,X32)<=>c_List_Olist__ex(X4,X56,hAPP(c_List_Orev(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__rev)). 4.02/4.28 fof(fact_list__all__rev, axiom, ![X32, X56, X4]:(c_List_Olist__all(X4,X56,X32)<=>c_List_Olist__all(X4,X56,hAPP(c_List_Orev(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__rev)). 4.02/4.28 fof(fact_inj__on__imageI2, axiom, ![X3, X22, X274, X49, X7, X4]:(c_Fun_Oinj__on(X4,X49,X22,X3)<=c_Fun_Oinj__on(X4,X7,hAPP(c_Fun_Ocomp(X49,X7,X4,X274),X22),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__imageI2)). 4.02/4.28 fof(fact_replicate__eq__replicate, axiom, ![X17, X20, X9, X21, X4]:(((X17=X9<=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X21)&X21=X20)<=>c_List_Oreplicate(X4,X20,X17)=c_List_Oreplicate(X4,X21,X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__eq__replicate)). 4.02/4.28 fof(fact_zdiv__self, axiom, ![X11]:(c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X11)<=X11!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__self)). 4.02/4.28 fof(fact_not__None__eq, axiom, ![X4, X9]:(c_Option_Ooption_ONone(X4)!=X9<=>?[X34]:X9=hAPP(c_Option_Ooption_OSome(X4),X34)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__None__eq)). 4.02/4.28 fof(fact_not__Some__eq, axiom, ![X4, X9]:(X9=c_Option_Ooption_ONone(X4)<=>![X34]:hAPP(c_Option_Ooption_OSome(X4),X34)!=X9), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__Some__eq)). 4.02/4.28 fof(fact_Suc__lessD, axiom, ![X5, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X5))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__lessD)). 4.02/4.28 fof(fact_sort__key__simps_I1_J, axiom, ![X22, X4, X7]:(class_Orderings_Olinorder(X7)=>c_List_Olinorder__class_Osort__key(X4,X7,X22,c_List_Olist_ONil(X4))=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sort__key__simps_I1_J)). 4.02/4.28 fof(fact_not__square__less__zero, axiom, ![X11, X4]:(class_Rings_Olinordered__ring(X4)=>~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X11)),c_Groups_Ozero__class_Ozero(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__square__less__zero)). 4.02/4.28 fof(fact_list_Oinject, axiom, ![X264, X117, X224, X26, X4]:((X117=X26&X224=X264)<=>hAPP(hAPP(c_List_Olist_OCons(X4),X26),X224)=hAPP(hAPP(c_List_Olist_OCons(X4),X117),X264)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Oinject)). 4.02/4.28 fof(fact_append__same__eq, axiom, ![X30, X32, X31, X4]:(hAPP(hAPP(c_List_Oappend(X4),X30),X32)=hAPP(hAPP(c_List_Oappend(X4),X31),X32)<=>X31=X30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__same__eq)). 4.02/4.28 fof(fact_same__append__eq, axiom, ![X30, X31, X32, X4]:(hAPP(hAPP(c_List_Oappend(X4),X32),X31)=hAPP(hAPP(c_List_Oappend(X4),X32),X30)<=>X30=X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_same__append__eq)). 4.02/4.28 fof(fact_inf1D1, axiom, ![X9, X6, X3, X4]:(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6),X9))=>hBOOL(hAPP(X3,X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf1D1)). 4.02/4.28 fof(fact_acyclic__converse, axiom, ![X18, X4]:(c_Wellfounded_Oacyclic(X4,hAPP(c_Relation_Oconverse(X4,X4),X18))<=>c_Wellfounded_Oacyclic(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_acyclic__converse)). 4.02/4.28 fof(fact_inf1D2, axiom, ![X9, X6, X3, X4]:(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6),X9))=>hBOOL(hAPP(X6,X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf1D2)). 4.02/4.28 fof(fact_fun__upd__idem__iff, axiom, ![X17, X9, X22, X7, X4]:(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X7),X22),X9),X17)=X22<=>hAPP(X22,X9)=X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__idem__iff)). 4.02/4.28 fof(fact_fold__graph__imp__finite, axiom, ![X9, X3, X16, X22, X7, X4]:(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X7,X22,X16,X3),X9))=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph__imp__finite)). 4.02/4.28 fof(fact_of__nat__aux_Osimps_I1_J, axiom, ![X37, X306, X4]:(class_Rings_Osemiring__1(X4)=>X37=c_Nat_Osemiring__1__class_Oof__nat__aux(X4,X306,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__aux_Osimps_I1_J)). 4.02/4.28 fof(fact_folding__one__idem_Oidem, axiom, ![X9, X87, X22, X4]:(c_Finite__Set_Ofolding__one__idem(X4,X22,X87)=>hAPP(hAPP(X22,X9),X9)=X9), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_folding__one__idem_Oidem)). 4.02/4.28 fof(fact_sorted__tl, axiom, ![X45, X4]:((c_List_Olinorder__class_Osorted(X4,X45)=>c_List_Olinorder__class_Osorted(X4,hAPP(c_List_Otl(X4),X45)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__tl)). 4.02/4.28 fof(fact_finite__insert, axiom, ![X3, X26, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))<=>hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(hAPP(c_Set_Oinsert(X4),X26),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__insert)). 4.02/4.28 fof(fact_inf__eq__top__iff, axiom, ![X17, X9, X4]:((hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X9),X17)=c_Orderings_Otop__class_Otop(X4)<=>(c_Orderings_Otop__class_Otop(X4)=X17&c_Orderings_Otop__class_Otop(X4)=X9))<=class_Lattices_Obounded__lattice__top(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__eq__top__iff)). 4.02/4.28 fof(fact_mod__less, axiom, ![X5, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X5))=>X2=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__less)). 4.02/4.28 fof(fact_number__of__Min, axiom, ![X4]:(class_Int_Onumber__ring(X4)=>hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__Min)). 4.02/4.28 fof(fact_evalc_OBody, axiom, ![X187, X188, X189]:(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X189)),X188,X187)=>c_Natural_Oevalc(c_Com_Ocom_OBODY(X189),X188,X187)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_evalc_OBody)). 4.02/4.28 fof(fact_empty__fold__graphE, axiom, ![X9, X16, X22, X7, X4]:(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X7,X22,X16,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X9))=>X9=X16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__fold__graphE)). 4.02/4.28 fof(fact_wf__exp, axiom, ![X39, X20, X4]:(c_Wellfounded_Owf(X4,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X20),X39))=>c_Wellfounded_Owf(X4,X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__exp)). 4.02/4.28 fof(fact_sgn__sgn, axiom, ![X11, X4]:(class_Rings_Olinordered__idom(X4)=>c_Groups_Osgn__class_Osgn(X4,c_Groups_Osgn__class_Osgn(X4,X11))=c_Groups_Osgn__class_Osgn(X4,X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn__sgn)). 4.02/4.28 fof(fact_eq__number__of, axiom, ![X17, X9, X4]:((hAPP(c_Int_Onumber__class_Onumber__of(X4),X9)=hAPP(c_Int_Onumber__class_Onumber__of(X4),X17)<=>X17=X9)<=(class_Int_Onumber__ring(X4)&class_Int_Oring__char__0(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__number__of)). 4.02/4.28 fof(fact_mod__0, axiom, ![X11, X4]:(c_Groups_Ozero__class_Ozero(X4)=c_Divides_Odiv__class_Omod(X4,c_Groups_Ozero__class_Ozero(X4),X11)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__0)). 4.02/4.28 fof(fact_mod__by__1, axiom, ![X11, X4]:(class_Divides_Osemiring__div(X4)=>c_Groups_Ozero__class_Ozero(X4)=c_Divides_Odiv__class_Omod(X4,X11,c_Groups_Oone__class_Oone(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__by__1)). 4.02/4.28 fof(fact_sorted__remove1, axiom, ![X11, X45, X4]:((c_List_Olinorder__class_Osorted(X4,X45)=>c_List_Olinorder__class_Osorted(X4,c_List_Oremove1(X4,X11,X45)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__remove1)). 4.02/4.28 fof(fact_sorted__takeWhile, axiom, ![X56, X32, X4]:((c_List_Olinorder__class_Osorted(X4,X32)=>c_List_Olinorder__class_Osorted(X4,c_List_OtakeWhile(X4,X56,X32)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__takeWhile)). 4.02/4.28 fof(fact_wfP__accp__iff, axiom, ![X18, X4]:(c_Wellfounded_OwfP(X4,X18)<=>![X77]:hBOOL(hAPP(c_Wellfounded_Oaccp(X4,X18),X77))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wfP__accp__iff)). 4.02/4.28 fof(fact_type__definition_ORep__inject, axiom, ![X17, X9, X3, X170, X171, X7, X4]:((X9=X17<=>hAPP(X171,X17)=hAPP(X171,X9))<=c_Typedef_Otype__definition(X4,X7,X171,X170,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition_ORep__inject)). 4.02/4.28 fof(fact_upto__empty, axiom, ![X46, X135]:(c_List_Oupto(X46,X135)=c_List_Olist_ONil(tc_Int_Oint)<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X135),X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upto__empty)). 4.02/4.28 fof(fact_sup__eq__bot__iff, axiom, ![X17, X9, X4]:(((c_Orderings_Obot__class_Obot(X4)=X17&X9=c_Orderings_Obot__class_Obot(X4))<=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X9),X17)=c_Orderings_Obot__class_Obot(X4))<=class_Lattices_Obounded__lattice__bot(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__eq__bot__iff)). 4.02/4.28 fof(fact_field__power__not__zero, axiom, ![X5, X11, X4]:((c_Groups_Ozero__class_Ozero(X4)!=hAPP(hAPP(c_Power_Opower__class_Opower(X4),X11),X5)<=c_Groups_Ozero__class_Ozero(X4)!=X11)<=class_Rings_Oring__1__no__zero__divisors(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_field__power__not__zero)). 4.02/4.28 fof(fact_map__add__le__mapE, axiom, ![X48, X76, X22, X7, X4]:(c_Map_Omap__le(X4,X7,c_Map_Omap__add(X4,X7,X22,X76),X48)=>c_Map_Omap__le(X4,X7,X76,X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__le__mapE)). 4.02/4.28 fof(fact_wf__lenlex, axiom, ![X18, X4]:(c_Wellfounded_Owf(tc_List_Olist(X4),c_List_Olenlex(X4,X18))<=c_Wellfounded_Owf(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__lenlex)). 4.02/4.28 fof(fact_wf__lex, axiom, ![X18, X4]:(c_Wellfounded_Owf(tc_List_Olist(X4),c_List_Olex(X4,X18))<=c_Wellfounded_Owf(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__lex)). 4.02/4.28 fof(fact_finite__acyclic__wf, axiom, ![X18, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X4)),X18))=>(c_Wellfounded_Owf(X4,X18)<=c_Wellfounded_Oacyclic(X4,X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__acyclic__wf)). 4.02/4.28 fof(fact_inf__idem, axiom, ![X13, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X13)=X13<=class_Lattices_Osemilattice__inf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__idem)). 4.02/4.28 fof(fact_of__nat__less__0__iff, axiom, ![X2, X4]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X2)),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__less__0__iff)). 4.02/4.28 fof(fact_abs__not__less__zero, axiom, ![X11, X4]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X11)),c_Groups_Ozero__class_Ozero(X4))))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__not__less__zero)). 4.02/4.28 fof(fact_Inf__fin_Oidem, axiom, ![X13, X4]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4),X13),X13)=X13<=class_Lattices_Olattice(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inf__fin_Oidem)). 4.02/4.28 fof(fact_sup__idem, axiom, ![X13, X4]:(class_Lattices_Osemilattice__sup(X4)=>hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X13)=X13), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__idem)). 4.02/4.28 fof(fact_times_Oidem, axiom, ![X11, X4]:(class_Lattices_Oab__semigroup__idem__mult(X4)=>X11=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_times_Oidem)). 4.02/4.28 fof(fact_Sup__fin_Oidem, axiom, ![X13, X4]:(class_Lattices_Olattice(X4)=>X13=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4),X13),X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sup__fin_Oidem)). 4.02/4.28 fof(fact_mod__by__0, axiom, ![X11, X4]:(class_Divides_Osemiring__div(X4)=>c_Divides_Odiv__class_Omod(X4,X11,c_Groups_Ozero__class_Ozero(X4))=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__by__0)). 4.02/4.28 fof(fact_of__int__eq__iff, axiom, ![X16, X23, X4]:((hAPP(c_Int_Oring__1__class_Oof__int(X4),X16)=hAPP(c_Int_Oring__1__class_Oof__int(X4),X23)<=>X23=X16)<=class_Int_Oring__char__0(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__eq__iff)). 4.02/4.28 fof(fact_linorder__not__le, axiom, ![X17, X9, X4]:(class_Orderings_Olinorder(X4)=>(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X9),X17)))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X17),X9)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_linorder__not__le)). 4.02/4.28 fof(fact_of__nat__eq__iff, axiom, ![X20, X21, X4]:((X20=X21<=>hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X20)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X21))<=class_Nat_Osemiring__char__0(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__eq__iff)). 4.02/4.28 fof(fact_compl__eq__compl__iff, axiom, ![X17, X9, X4]:(class_Lattices_Oboolean__algebra(X4)=>(X9=X17<=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),X17)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__eq__compl__iff)). 4.02/4.28 fof(fact_neg__equal__iff__equal, axiom, ![X25, X26, X4]:(class_Groups_Ogroup__add(X4)=>(X25=X26<=>hAPP(c_Groups_Ouminus__class_Ouminus(X4),X25)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__equal__iff__equal)). 4.02/4.28 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J, axiom, ![X5, X13]:(c_Nat__Transfer_Ois__nat(X13)=>c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X13),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J)). 4.02/4.28 fof(fact_minus__zero, axiom, ![X4]:(hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Ozero__class_Ozero(X4))=c_Groups_Ozero__class_Ozero(X4)<=class_Groups_Ogroup__add(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__zero)). 4.02/4.28 fof(fact_some__eq__ex, axiom, ![X4, X56]:(hBOOL(hAPP(X56,c_Hilbert__Choice_OEps(X4,X56)))<=>?[X77]:hBOOL(hAPP(X56,X77))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_some__eq__ex)). 4.02/4.28 fof(fact_gr0__conv__Suc, axiom, ![X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20))<=>?[X50]:X20=hAPP(c_Nat_OSuc,X50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_gr0__conv__Suc)). 4.02/4.28 fof(fact_inj__uminus, axiom, ![X3, X4]:(class_Groups_Oordered__ab__group__add(X4)=>c_Fun_Oinj__on(X4,X4,c_Groups_Ouminus__class_Ouminus(X4),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__uminus)). 4.02/4.28 fof(fact_ext, axiom, ![X76, X22]:(![X19]:hAPP(X22,X19)=hAPP(X76,X19)=>X76=X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ext)). 4.02/4.28 fof(fact_compl__bot__eq, axiom, ![X4]:(c_Orderings_Otop__class_Otop(X4)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Orderings_Obot__class_Obot(X4))<=class_Lattices_Oboolean__algebra(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__bot__eq)). 4.02/4.28 fof(fact_number__of__eq, axiom, ![X107, X4]:(class_Int_Onumber__ring(X4)=>hAPP(c_Int_Oring__1__class_Oof__int(X4),X107)=hAPP(c_Int_Onumber__class_Onumber__of(X4),X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__eq)). 4.02/4.28 fof(fact_wf__in__rel, axiom, ![X39, X4]:(c_Wellfounded_OwfP(X4,c_FunDef_Oin__rel(X4,X4,X39))<=c_Wellfounded_Owf(X4,X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__in__rel)). 4.02/4.28 fof(fact_enum__all, axiom, ![X56, X4]:((![X77]:hBOOL(hAPP(X56,X77))<=>hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X4),X56)))<=class_Enum_Oenum(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__all)). 4.02/4.28 fof(fact_all__code, axiom, ![X56, X4]:((hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X4),X56))<=>![X77]:hBOOL(hAPP(X56,X77)))<=class_Enum_Oenum(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_all__code)). 4.02/4.28 fof(fact_wf__mlex, axiom, ![X22, X39, X4]:(c_Wellfounded_Owf(X4,c_Wellfounded_Omlex__prod(X4,X22,X39))<=c_Wellfounded_Owf(X4,X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__mlex)). 4.02/4.28 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J, axiom, ![X43, X13]:((c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X13,X43))<=c_Nat__Transfer_Ois__nat(X43))<=c_Nat__Transfer_Ois__nat(X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Otransfer__int__nat__function__closures_I2_J)). 4.02/4.28 fof(fact_compl__top__eq, axiom, ![X4]:(class_Lattices_Oboolean__algebra(X4)=>c_Orderings_Obot__class_Obot(X4)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Orderings_Otop__class_Otop(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_compl__top__eq)). 4.02/4.28 fof(fact_listsum__simps_I1_J, axiom, ![X4]:(class_Groups_Omonoid__add(X4)=>c_Groups_Ozero__class_Ozero(X4)=hAPP(c_List_Omonoid__add__class_Olistsum(X4),c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsum__simps_I1_J)). 4.02/4.28 fof(fact_not__neg__eq__ge__0, axiom, ![X9]:(~(hBOOL(hAPP(c_Nat__Numeral_Oneg,X9)))<=>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_not__neg__eq__ge__0)). 4.02/4.28 fof(fact_option__map__is__None, axiom, ![X140, X22, X4, X7]:(hAPP(hAPP(c_Option_Omap(X7,X4),X22),X140)=c_Option_Ooption_ONone(X4)<=>c_Option_Ooption_ONone(X7)=X140), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option__map__is__None)). 4.02/4.28 fof(fact_list__update__nonempty, axiom, ![X9, X28, X32, X4]:(c_List_Olist_ONil(X4)=X32<=>hAPP(hAPP(c_List_Olist__update(X4,X32),X28),X9)=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__nonempty)). 4.02/4.28 fof(fact_abs__zero, axiom, ![X4]:(class_Groups_Oordered__ab__group__add__abs(X4)=>c_Groups_Ozero__class_Ozero(X4)=hAPP(c_Groups_Oabs__class_Oabs(X4),c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__zero)). 4.02/4.28 fof(fact_Nil__is__map__conv, axiom, ![X32, X22, X7, X4]:(X32=c_List_Olist_ONil(X7)<=>c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Omap(X7,X4),X22),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nil__is__map__conv)). 4.02/4.28 fof(fact_greaterThan__eq__iff, axiom, ![X17, X9, X4]:((X17=X9<=>hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X17)=hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X9))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThan__eq__iff)). 4.02/4.28 fof(fact_abs__one, axiom, ![X4]:(c_Groups_Oone__class_Oone(X4)=hAPP(c_Groups_Oabs__class_Oabs(X4),c_Groups_Oone__class_Oone(X4))<=class_Rings_Olinordered__idom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__one)). 4.02/4.28 fof(fact_less__imp__le__nat, axiom, ![X5, X2]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X5))<=hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__imp__le__nat)). 4.02/4.28 fof(fact_lessThan__eq__iff, axiom, ![X17, X9, X4]:((hAPP(c_SetInterval_Oord__class_OlessThan(X4),X9)=hAPP(c_SetInterval_Oord__class_OlessThan(X4),X17)<=>X17=X9)<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessThan__eq__iff)). 4.02/4.28 fof(fact_atMost__eq__iff, axiom, ![X17, X9, X4]:((X9=X17<=>hAPP(c_SetInterval_Oord__class_OatMost(X4),X9)=hAPP(c_SetInterval_Oord__class_OatMost(X4),X17))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atMost__eq__iff)). 4.02/4.28 fof(fact_atLeast__eq__iff, axiom, ![X17, X9, X4]:(class_Orderings_Olinorder(X4)=>(X17=X9<=>hAPP(c_SetInterval_Oord__class_OatLeast(X4),X17)=hAPP(c_SetInterval_Oord__class_OatLeast(X4),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast__eq__iff)). 4.02/4.28 fof(fact_sorted__remdups, axiom, ![X47, X4]:((c_List_Olinorder__class_Osorted(X4,X47)=>c_List_Olinorder__class_Osorted(X4,c_List_Oremdups(X4,X47)))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__remdups)). 4.02/4.28 fof(fact_nat__le__0, axiom, ![X29]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,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_nat__le__0)). 4.02/4.28 fof(fact_min__max_Osup_Oidem, axiom, ![X11, X4]:(class_Orderings_Olinorder(X4)=>hAPP(hAPP(c_Orderings_Oord__class_Omax(X4),X11),X11)=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Osup_Oidem)). 4.02/4.28 fof(fact_Min_Oidem, axiom, ![X13, X4]:(class_Orderings_Olinorder(X4)=>X13=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4),X13),X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Min_Oidem)). 4.02/4.28 fof(fact_right__minus__eq, axiom, ![X25, X26, X4]:(class_Groups_Ogroup__add(X4)=>(X26=X25<=>hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X26),X25)=c_Groups_Ozero__class_Ozero(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_right__minus__eq)). 4.02/4.28 fof(fact_someI__ex, axiom, ![X4, X56]:(hBOOL(hAPP(X56,c_Hilbert__Choice_OEps(X4,X56)))<=?[X77]:hBOOL(hAPP(X56,X77))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_someI__ex)). 4.02/4.28 fof(fact_mod__self, axiom, ![X11, X4]:(c_Groups_Ozero__class_Ozero(X4)=c_Divides_Odiv__class_Omod(X4,X11,X11)<=class_Divides_Osemiring__div(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__self)). 4.02/4.28 fof(fact_pair__box_Oinject, axiom, ![X181, X117, X25, X26, X7, X4]:((X26=X117&X181=X25)<=>c_Nitpick_Opair__box_OPairBox(X4,X7,X117,X181)=c_Nitpick_Opair__box_OPairBox(X4,X7,X26,X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__box_Oinject)). 4.02/4.28 fof(fact_equal__refl, axiom, ![X13, X4]:(class_HOL_Oequal(X4)=>hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X4),X13),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equal__refl)). 4.02/4.28 fof(fact_order__refl, axiom, ![X13, X4]:(class_Orderings_Opreorder(X4)=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__refl)). 4.02/4.28 fof(fact_append__is__Nil__conv, axiom, ![X31, X32, X4]:(c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Oappend(X4),X32),X31)<=>(X32=c_List_Olist_ONil(X4)&X31=c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__is__Nil__conv)). 4.02/4.28 fof(fact_add__is__0, axiom, ![X20, X21]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X20&c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X21)<=>hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__is__0)). 4.02/4.28 fof(fact_neg__0__equal__iff__equal, axiom, ![X26, X4]:(class_Groups_Ogroup__add(X4)=>(c_Groups_Ozero__class_Ozero(X4)=X26<=>c_Groups_Ozero__class_Ozero(X4)=hAPP(c_Groups_Ouminus__class_Ouminus(X4),X26))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__0__equal__iff__equal)). 4.02/4.28 fof(fact_abs__eq__0, axiom, ![X26, X4]:((X26=c_Groups_Ozero__class_Ozero(X4)<=>c_Groups_Ozero__class_Ozero(X4)=hAPP(c_Groups_Oabs__class_Oabs(X4),X26))<=class_Groups_Oordered__ab__group__add__abs(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__eq__0)). 4.02/4.28 fof(fact_map__le__antisym, axiom, ![X76, X22, X7, X4]:((X22=X76<=c_Map_Omap__le(X4,X7,X76,X22))<=c_Map_Omap__le(X4,X7,X22,X76)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__le__antisym)). 4.02/4.28 fof(fact_nat__mult__eq__1__iff, axiom, ![X20, X21]:((X21=c_Groups_Oone__class_Oone(tc_Nat_Onat)&c_Groups_Oone__class_Oone(tc_Nat_Onat)=X20)<=>c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__eq__1__iff)). 4.02/4.28 fof(fact_nat__1__eq__mult__iff, axiom, ![X20, X21]:((c_Groups_Oone__class_Oone(tc_Nat_Onat)=X21&X20=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),X21),X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__1__eq__mult__iff)). 4.02/4.28 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures, axiom, ![X17, X9]:(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X9,X17))<=c_Nat__Transfer_Ois__nat(X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SetInterval_Otransfer__int__nat__set__function__closures)). 4.02/4.28 fof(fact_equal__eq, axiom, ![X17, X9, X4]:(class_HOL_Oequal(X4)=>(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X4),X9),X17))<=>X17=X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equal__eq)). 4.02/4.28 fof(fact_not__one__less__zero, axiom, ![X4]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__one__less__zero)). 4.02/4.28 fof(fact_WT_Oequations_I5_J, axiom, ![X67, X70, X69]:(hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X69,X70,X67)))<=>(hBOOL(hAPP(c_Com_OWT,X67))&hBOOL(hAPP(c_Com_OWT,X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WT_Oequations_I5_J)). 4.02/4.28 fof(fact_le__0__eq, axiom, ![X20]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<=>X20=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__0__eq)). 4.02/4.28 fof(fact_not__one__le__zero, axiom, ![X4]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Oone__class_Oone(X4)),c_Groups_Ozero__class_Ozero(X4))))<=class_Rings_Olinordered__semidom(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__one__le__zero)). 4.02/4.28 fof(fact_com__det, axiom, ![X106, X179, X159, X10]:(c_Natural_Oevalc(X10,X159,X179)=>(X106=X179<=c_Natural_Oevalc(X10,X159,X106))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com__det)). 4.02/4.28 fof(fact_rev__is__rev__conv, axiom, ![X31, X32, X4]:(X32=X31<=>hAPP(c_List_Orev(X4),X31)=hAPP(c_List_Orev(X4),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__is__rev__conv)). 4.02/4.28 fof(fact_option_Oinject, axiom, ![X117, X26, X4]:(X117=X26<=>hAPP(c_Option_Ooption_OSome(X4),X117)=hAPP(c_Option_Ooption_OSome(X4),X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Oinject)). 4.02/4.28 fof(fact_length__0__conv, axiom, ![X32, X4]:(X32=c_List_Olist_ONil(X4)<=>c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__0__conv)). 4.02/4.28 fof(fact_transfer__int__nat__relations_I1_J, axiom, ![X17, X9]:(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X9)<=>X9=X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__int__nat__relations_I1_J)). 4.02/4.28 fof(fact_WT_Oequations_I8_J, axiom, ![X69, X70, X67]:(hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X70)))<=>hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X67,X70,X69)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WT_Oequations_I8_J)). 4.02/4.28 fof(fact_reflpE, axiom, ![X9, X18, X4]:(hBOOL(hAPP(hAPP(X18,X9),X9))<=c_Predicate_Oreflp(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_reflpE)). 4.02/4.28 fof(fact_set__empty2, axiom, ![X32, X4]:(X32=c_List_Olist_ONil(X4)<=>hAPP(c_List_Oset(X4),X32)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__empty2)). 4.02/4.28 fof(fact_equivp__reflp, axiom, ![X9, X39, X4]:(hBOOL(hAPP(hAPP(X39,X9),X9))<=c_Equiv__Relations_Oequivp(X4,X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equivp__reflp)). 4.02/4.28 fof(fact_mem__def, axiom, ![X3, X9, X4]:(hBOOL(hAPP(X3,X9))<=>hBOOL(hAPP(hAPP(c_member(X4),X9),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mem__def)). 4.02/4.28 fof(fact_list__all2__Nil, axiom, ![X31, X56, X7, X4]:(c_List_Olist__all2(X4,X7,X56,c_List_Olist_ONil(X4),X31)<=>c_List_Olist_ONil(X7)=X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all2__Nil)). 4.02/4.28 fof(fact_fun__left__comm, axiom, ![X4]:(c_Finite__Set_Ofun__left__comm(X4,X4,c_Groups_Otimes__class_Otimes(X4))<=class_Groups_Oab__semigroup__mult(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm)). 4.02/4.28 fof(fact_min__max_Ofun__left__comm__idem__inf, axiom, ![X4]:(c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Orderings_Oord__class_Omin(X4))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofun__left__comm__idem__inf)). 4.02/4.28 fof(fact_fun__left__comm__idem__inf, axiom, ![X4]:(class_Lattices_Osemilattice__inf(X4)=>c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem__inf)). 4.02/4.28 fof(fact_fun__left__comm__idem, axiom, ![X4]:(class_Lattices_Oab__semigroup__idem__mult(X4)=>c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Groups_Otimes__class_Otimes(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem)). 4.02/4.28 fof(fact_min__max_Ofun__left__comm__idem__sup, axiom, ![X4]:(c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Orderings_Oord__class_Omax(X4))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__max_Ofun__left__comm__idem__sup)). 4.02/4.28 fof(fact_fun__left__comm__idem__sup, axiom, ![X4]:(c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4))<=class_Lattices_Osemilattice__sup(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem__sup)). 4.02/4.28 fof(fact_sgn0, axiom, ![X4]:(class_Groups_Osgn__if(X4)=>c_Groups_Osgn__class_Osgn(X4,c_Groups_Ozero__class_Ozero(X4))=c_Groups_Ozero__class_Ozero(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sgn0)). 4.02/4.28 fof(fact_com_Osimps_I2_J, axiom, ![X71, X72, X172, X120, X75, X121]:(c_Com_Ocom_OLocal(X121,X75,X120)=c_Com_Ocom_OLocal(X172,X72,X71)<=>((X71=X120&X75=X72)&X172=X121)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I2_J)). 4.02/4.28 fof(fact_lazy__sequence_Oinject, axiom, ![X116, X117, X118, X26, X4]:(c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X117,X116)=c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X26,X118)<=>(X116=X118&X26=X117)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Oinject)). 4.02/4.28 fof(fact_max__ord__max, axiom, ![X4]:(c_Orderings_Oord_Omax(X4,c_Orderings_Oord__class_Oless__eq(X4))=c_Orderings_Oord__class_Omax(X4)<=class_Orderings_Oord(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__ord__max)). 4.02/4.28 fof(fact_self__append__conv, axiom, ![X31, X4, X32]:(X31=c_List_Olist_ONil(X4)<=>hAPP(hAPP(c_List_Oappend(X4),X32),X31)=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_self__append__conv)). 4.02/4.28 fof(fact_self__append__conv2, axiom, ![X32, X4, X31]:(X32=c_List_Olist_ONil(X4)<=>X31=hAPP(hAPP(c_List_Oappend(X4),X32),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_self__append__conv2)). 4.02/4.28 fof(fact_add__eq__self__zero, axiom, ![X5, X2]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X5<=X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__eq__self__zero)). 4.02/4.28 fof(fact_enum__distinct, axiom, ![X4]:(class_Enum_Oenum(X4)=>hBOOL(hAPP(c_List_Odistinct(X4),c_Enum_Oenum__class_Oenum(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_enum__distinct)). 4.02/4.28 fof(fact_com_Osimps_I7_J, axiom, ![X72, X92, X93, X75, X94, X243]:(((X93=X243&X72=X75)&X92=X94)<=>c_Com_Ocom_OCall(X243,X94,X75)=c_Com_Ocom_OCall(X93,X92,X72)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I7_J)). 4.02/4.28 fof(fact_min__ord__min, axiom, ![X4]:(class_Orderings_Oord(X4)=>c_Orderings_Oord__class_Omin(X4)=c_Orderings_Oord_Omin(X4,c_Orderings_Oord__class_Oless__eq(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__ord__min)). 4.02/4.28 fof(fact_com_Osimps_I4_J, axiom, ![X151, X152, X72, X73, X74, X75]:(c_Com_Ocom_OCond(X72,X152,X151)=c_Com_Ocom_OCond(X75,X74,X73)<=>((X74=X152&X151=X73)&X72=X75)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I4_J)). 4.02/4.28 fof(fact_distinct__remdups__id, axiom, ![X45, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X45))=>X45=c_List_Oremdups(X4,X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__remdups__id)). 4.02/4.28 fof(fact_neg__def, axiom, ![X161]:(hBOOL(hAPP(c_Nat__Numeral_Oneg,X161))<=>hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X161),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__def)). 4.02/4.28 fof(fact_WTs__elim__cases_I7_J, axiom, ![X209]:(hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X209)))=>~(![X34]:hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X34)!=hAPP(c_Com_Obody,X209))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WTs__elim__cases_I7_J)). 4.02/4.28 fof(fact_WT_Oequations_I7_J, axiom, ![X26]:(hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X26)))<=>?[X34]:hAPP(c_Com_Obody,X26)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X34)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WT_Oequations_I7_J)). 4.02/4.28 fof(fact_of__nat__0, axiom, ![X4]:(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(X4)<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__0)). 4.02/4.28 fof(fact_of__int__0, axiom, ![X4]:(c_Groups_Ozero__class_Ozero(X4)=hAPP(c_Int_Oring__1__class_Oof__int(X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<=class_Rings_Oring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__0)). 4.02/4.28 fof(fact_of__int__1, axiom, ![X4]:(class_Rings_Oring__1(X4)=>c_Groups_Oone__class_Oone(X4)=hAPP(c_Int_Oring__1__class_Oof__int(X4),c_Groups_Oone__class_Oone(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__1)). 4.02/4.28 fof(fact_of__nat__1, axiom, ![X4]:(c_Groups_Oone__class_Oone(X4)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),c_Groups_Oone__class_Oone(tc_Nat_Onat))<=class_Rings_Osemiring__1(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__nat__1)). 4.02/4.28 fof(arity_prod__Smallcheck_Osmall, axiom, ![X155, X164]:((class_Smallcheck_Osmall(X155)&class_Smallcheck_Osmall(X164))=>class_Smallcheck_Osmall(tc_prod(X164,X155))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_prod__Smallcheck_Osmall)). 4.02/4.28 fof(fact_WT_OLocal, axiom, ![X26, X203, X24]:(hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X203,X26,X24)))<=hBOOL(hAPP(c_Com_OWT,X24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WT_OLocal)). 4.02/4.28 fof(fact_is__nat__def, axiom, ![X9]:(c_Nat__Transfer_Ois__nat(X9)<=>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_is__nat__def)). 4.02/4.28 fof(fact_int__eq__0__conv, axiom, ![X20]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20)<=>X20=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__eq__0__conv)). 4.02/4.28 fof(arity_fun__HOL_Oequal, axiom, ![X155, X164]:((class_HOL_Oequal(X155)&class_Enum_Oenum(X164))=>class_HOL_Oequal(tc_fun(X164,X155))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__HOL_Oequal)). 4.02/4.28 fof(arity_sum__Finite__Set_Ofinite, axiom, ![X155, X164]:(class_Finite__Set_Ofinite(tc_sum(X164,X155))<=(class_Finite__Set_Ofinite(X155)&class_Finite__Set_Ofinite(X164))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_sum__Finite__Set_Ofinite)). 4.02/4.28 fof(arity_prod__Finite__Set_Ofinite, axiom, ![X155, X164]:((class_Finite__Set_Ofinite(X155)&class_Finite__Set_Ofinite(X164))=>class_Finite__Set_Ofinite(tc_prod(X164,X155))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_prod__Finite__Set_Ofinite)). 4.02/4.28 fof(arity_fun__Finite__Set_Ofinite, axiom, ![X155, X164]:(class_Finite__Set_Ofinite(tc_fun(X164,X155))<=(class_Finite__Set_Ofinite(X155)&class_Finite__Set_Ofinite(X164))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Finite__Set_Ofinite)). 4.02/4.28 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J, axiom, ![X43, X13]:(c_Nat__Transfer_Ois__nat(X13)=>(c_Nat__Transfer_Ois__nat(X43)=>c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X13,X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J)). 4.02/4.28 fof(arity_prod__Lazy__Sequence_Osmall__lazy, axiom, ![X155, X164]:(class_Lazy__Sequence_Osmall__lazy(tc_prod(X164,X155))<=(class_Lazy__Sequence_Osmall__lazy(X164)&class_Lazy__Sequence_Osmall__lazy(X155))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_prod__Lazy__Sequence_Osmall__lazy)). 4.02/4.28 fof(arity_sum__Enum_Oenum, axiom, ![X155, X164]:(class_Enum_Oenum(tc_sum(X164,X155))<=(class_Enum_Oenum(X155)&class_Enum_Oenum(X164))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_sum__Enum_Oenum)). 4.02/4.28 fof(arity_prod__Enum_Oenum, axiom, ![X155, X164]:(class_Enum_Oenum(tc_prod(X164,X155))<=(class_Enum_Oenum(X155)&class_Enum_Oenum(X164))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_prod__Enum_Oenum)). 4.02/4.28 fof(arity_fun__Enum_Oenum, axiom, ![X155, X164]:((class_Enum_Oenum(X155)&class_Enum_Oenum(X164))=>class_Enum_Oenum(tc_fun(X164,X155))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Enum_Oenum)). 4.02/4.28 fof(fact_insort__not__Nil, axiom, ![X32, X26, X22, X4, X7]:(class_Orderings_Olinorder(X7)=>c_List_Olist_ONil(X4)!=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X7,X22),X26),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insort__not__Nil)). 4.02/4.28 fof(fact_finite, axiom, ![X3, X4]:(hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))<=class_Finite__Set_Ofinite(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite)). 4.02/4.28 fof(fact_replicate__empty, axiom, ![X9, X20, X4]:(c_List_Olist_ONil(X4)=c_List_Oreplicate(X4,X20,X9)<=>X20=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__empty)). 4.02/4.28 fof(fact_set__empty__eq, axiom, ![X35, X4]:(c_Option_Oset(X4,X35)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))<=>X35=c_Option_Ooption_ONone(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__empty__eq)). 4.02/4.28 fof(fact_remdups__id__iff__distinct, axiom, ![X32, X4]:(hBOOL(hAPP(c_List_Odistinct(X4),X32))<=>c_List_Oremdups(X4,X32)=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups__id__iff__distinct)). 4.02/4.28 fof(fact_WT_Oequations_I4_J, axiom, ![X67, X70]:(hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X70,X67)))<=>(hBOOL(hAPP(c_Com_OWT,X67))&hBOOL(hAPP(c_Com_OWT,X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WT_Oequations_I4_J)). 4.02/4.28 fof(fact_rotate1__is__Nil__conv, axiom, ![X32, X4]:(c_List_Olist_ONil(X4)=hAPP(c_List_Orotate1(X4),X32)<=>c_List_Olist_ONil(X4)=X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate1__is__Nil__conv)). 4.02/4.28 fof(fact_rev__is__Nil__conv, axiom, ![X32, X4]:(c_List_Olist_ONil(X4)=X32<=>c_List_Olist_ONil(X4)=hAPP(c_List_Orev(X4),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__is__Nil__conv)). 4.02/4.28 fof(fact_WTs__elim__cases_I8_J, axiom, ![X26, X56, X156]:(hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X56)))<=hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X156,X56,X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WTs__elim__cases_I8_J)). 4.02/4.28 fof(arity_fun__Lattices_Obounded__lattice__bot, axiom, ![X164, X155]:(class_Lattices_Obounded__lattice__bot(tc_fun(X164,X155))<=class_Lattices_Obounded__lattice(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Obounded__lattice__bot)). 4.02/4.28 fof(help_c__fconj__1, axiom, ![X112, X56]:(~(hBOOL(X56))|~(hBOOL(X112))|hBOOL(hAPP(hAPP(c_fconj,X56),X112))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fconj__1)). 4.02/4.28 fof(arity_fun__Orderings_Obot, axiom, ![X164, X155]:(class_Orderings_Obot(X155)=>class_Orderings_Obot(tc_fun(X164,X155))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Orderings_Obot)). 4.02/4.28 fof(arity_fun__Lattices_Odistrib__lattice, axiom, ![X164, X155]:(class_Lattices_Odistrib__lattice(tc_fun(X164,X155))<=class_Lattices_Odistrib__lattice(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Odistrib__lattice)). 4.02/4.28 fof(arity_fun__Groups_Ouminus, axiom, ![X164, X155]:(class_Groups_Ouminus(X155)=>class_Groups_Ouminus(tc_fun(X164,X155))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Groups_Ouminus)). 4.02/4.28 fof(arity_fun__Lattices_Obounded__lattice__top, axiom, ![X164, X155]:(class_Lattices_Obounded__lattice(X155)=>class_Lattices_Obounded__lattice__top(tc_fun(X164,X155))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Obounded__lattice__top)). 4.02/4.28 fof(arity_fun__Lattices_Obounded__lattice, axiom, ![X164, X155]:(class_Lattices_Obounded__lattice(tc_fun(X164,X155))<=class_Lattices_Obounded__lattice(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Obounded__lattice)). 4.02/4.28 fof(arity_fun__Groups_Ominus, axiom, ![X164, X155]:(class_Groups_Ominus(tc_fun(X164,X155))<=class_Groups_Ominus(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Groups_Ominus)). 4.02/4.28 fof(arity_fun__Lattices_Oboolean__algebra, axiom, ![X164, X155]:(class_Lattices_Oboolean__algebra(X155)=>class_Lattices_Oboolean__algebra(tc_fun(X164,X155))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Oboolean__algebra)). 4.02/4.28 fof(arity_fun__Orderings_Otop, axiom, ![X164, X155]:(class_Orderings_Otop(tc_fun(X164,X155))<=class_Orderings_Otop(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Orderings_Otop)). 4.02/4.28 fof(arity_fun__Orderings_Opreorder, axiom, ![X164, X155]:(class_Orderings_Opreorder(tc_fun(X164,X155))<=class_Orderings_Opreorder(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Orderings_Opreorder)). 4.02/4.28 fof(arity_fun__Orderings_Oorder, axiom, ![X164, X155]:(class_Orderings_Oorder(tc_fun(X164,X155))<=class_Orderings_Oorder(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Orderings_Oorder)). 4.02/4.28 fof(arity_fun__Complete__Lattice_Ocomplete__lattice, axiom, ![X164, X155]:(class_Complete__Lattice_Ocomplete__lattice(tc_fun(X164,X155))<=class_Complete__Lattice_Ocomplete__lattice(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Complete__Lattice_Ocomplete__lattice)). 4.02/4.28 fof(arity_fun__Lattices_Osemilattice__inf, axiom, ![X164, X155]:(class_Lattices_Osemilattice__inf(tc_fun(X164,X155))<=class_Lattices_Olattice(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Osemilattice__inf)). 4.02/4.28 fof(arity_fun__Orderings_Oord, axiom, ![X164, X155]:(class_Orderings_Oord(tc_fun(X164,X155))<=class_Orderings_Oord(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Orderings_Oord)). 4.05/4.28 fof(arity_fun__Lattices_Osemilattice__sup, axiom, ![X164, X155]:(class_Lattices_Olattice(X155)=>class_Lattices_Osemilattice__sup(tc_fun(X164,X155))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Osemilattice__sup)). 4.05/4.28 fof(arity_fun__Lattices_Olattice, axiom, ![X164, X155]:(class_Lattices_Olattice(tc_fun(X164,X155))<=class_Lattices_Olattice(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_fun__Lattices_Olattice)). 4.05/4.28 fof(fact_sorted_ONil, axiom, ![X4]:(c_List_Olinorder__class_Osorted(X4,c_List_Olist_ONil(X4))<=class_Orderings_Olinorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted_ONil)). 4.05/4.28 fof(fact_order__less__irrefl, axiom, ![X13, X4]:(~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),X13)))<=class_Orderings_Opreorder(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_order__less__irrefl)). 4.05/4.28 fof(fact_nat__list__def, axiom, ![X60]:(c_List_Onat__list(X60)<=>c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X60))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__list__def)). 4.05/4.28 fof(help_c__fimplies__1, axiom, ![X112, X56]:(hBOOL(X56)|hBOOL(hAPP(hAPP(c_fimplies,X56),X112))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fimplies__1)). 4.05/4.28 fof(fact_Rep__Integ__inject, axiom, ![X17, X9]:(hAPP(c_Int_ORep__Integ,X9)=hAPP(c_Int_ORep__Integ,X17)<=>X9=X17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Rep__Integ__inject)). 4.05/4.28 fof(fact_com_Osimps_I3_J, axiom, ![X151, X152, X73, X74]:(c_Com_Ocom_OSemi(X74,X73)=c_Com_Ocom_OSemi(X152,X151)<=>(X151=X73&X74=X152)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I3_J)). 4.05/4.28 fof(fact_com_Osimps_I5_J, axiom, ![X71, X72, X120, X75]:((X120=X71&X72=X75)<=>c_Com_Ocom_OWhile(X72,X71)=c_Com_Ocom_OWhile(X75,X120)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I5_J)). 4.05/4.28 fof(fact_Code__Numeral_Onat__of__inject, axiom, ![X60, X28]:(hAPP(c_Code__Numeral_Onat__of,X60)=hAPP(c_Code__Numeral_Onat__of,X28)<=>X28=X60), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Code__Numeral_Onat__of__inject)). 4.05/4.28 fof(fact_remdups__eq__nil__iff, axiom, ![X9, X4]:(c_List_Olist_ONil(X4)=c_List_Oremdups(X4,X9)<=>X9=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups__eq__nil__iff)). 4.05/4.28 fof(fact_nat_Oinject, axiom, ![X303, X242]:(X303=X242<=>hAPP(c_Nat_OSuc,X242)=hAPP(c_Nat_OSuc,X303)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat_Oinject)). 4.05/4.28 fof(fact_While, axiom, ![X25, X24]:(hBOOL(hAPP(c_Com_OWT,X24))=>hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X25,X24)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_While)). 4.05/4.28 fof(fact_WT_OBody, axiom, ![X189]:(c_Option_Ooption_ONone(tc_Com_Ocom)!=hAPP(c_Com_Obody,X189)=>hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X189)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WT_OBody)). 4.05/4.28 fof(help_c__fdisj__1, axiom, ![X112, X56]:(hBOOL(hAPP(hAPP(c_fdisj,X56),X112))|~(hBOOL(X56))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fdisj__1)). 4.05/4.28 fof(help_c__fdisj__2, axiom, ![X56, X112]:(~(hBOOL(X112))|hBOOL(hAPP(hAPP(c_fdisj,X56),X112))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fdisj__2)). 4.05/4.28 fof(help_c__fimplies__2, axiom, ![X56, X112]:(hBOOL(hAPP(hAPP(c_fimplies,X56),X112))|~(hBOOL(X112))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fimplies__2)). 4.05/4.28 fof(fact_WTs__elim__cases_I5_J, axiom, ![X248, X149, X25]:(hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X25,X149,X248)))=>~((~(hBOOL(hAPP(c_Com_OWT,X248)))<=hBOOL(hAPP(c_Com_OWT,X149))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WTs__elim__cases_I5_J)). 4.05/4.28 fof(fact_inf__min, axiom, ![X4]:((class_Orderings_Olinorder(X4)&class_Lattices_Osemilattice__inf(X4))=>c_Orderings_Oord__class_Omin(X4)=c_Lattices_Osemilattice__inf__class_Oinf(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inf__min)). 4.05/4.28 fof(fact_sup__max, axiom, ![X4]:((class_Lattices_Osemilattice__sup(X4)&class_Orderings_Olinorder(X4))=>c_Lattices_Osemilattice__sup__class_Osup(X4)=c_Orderings_Oord__class_Omax(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sup__max)). 4.05/4.28 fof(fact_WTs__elim__cases_I3_J, axiom, ![X24, X26, X203]:(hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X203,X26,X24)))=>hBOOL(hAPP(c_Com_OWT,X24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WTs__elim__cases_I3_J)). 4.05/4.28 fof(fact_nonzero__number__of__Min, axiom, ![X4]:(class_Int_Onumber__ring(X4)=>~(c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),c_Int_OMin)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nonzero__number__of__Min)). 4.05/4.28 fof(help_c__fdisj__3, axiom, ![X112, X56]:(hBOOL(X112)|hBOOL(X56)|~(hBOOL(hAPP(hAPP(c_fdisj,X56),X112)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fdisj__3)). 4.05/4.28 fof(fact_wf__acyclic, axiom, ![X18, X4]:(c_Wellfounded_Oacyclic(X4,X18)<=c_Wellfounded_Owf(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__acyclic)). 4.05/4.28 fof(fact_is__none__def, axiom, ![X9, X4]:(c_Option_Ois__none(X4,X9)<=>c_Option_Ooption_ONone(X4)=X9), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_is__none__def)). 4.05/4.28 fof(arity_Option__Ooption__Finite__Set_Ofinite, axiom, ![X155]:(class_Finite__Set_Ofinite(tc_Option_Ooption(X155))<=class_Finite__Set_Ofinite(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Option__Ooption__Finite__Set_Ofinite)). 4.05/4.28 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy, axiom, ![X155]:(class_Lazy__Sequence_Osmall__lazy(X155)=>class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X155))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_List__Olist__Lazy__Sequence_Osmall__lazy)). 4.05/4.28 fof(arity_Option__Ooption__Enum_Oenum, axiom, ![X155]:(class_Enum_Oenum(tc_Option_Ooption(X155))<=class_Enum_Oenum(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Option__Ooption__Enum_Oenum)). 4.05/4.28 fof(help_c__fequal__1, axiom, ![X17, X9]:(X9=X17|~(hBOOL(hAPP(hAPP(c_fequal,X9),X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fequal__1)). 4.05/4.28 fof(help_c__fimplies__3, axiom, ![X112, X56]:(hBOOL(X112)|~(hBOOL(X56))|~(hBOOL(hAPP(hAPP(c_fimplies,X56),X112)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fimplies__3)). 4.05/4.28 fof(fact_com_Osimps_I6_J, axiom, ![X92, X94]:(X94=X92<=>c_Com_Ocom_OBODY(X94)=c_Com_Ocom_OBODY(X92)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I6_J)). 4.05/4.28 fof(fact_WTs__elim__cases_I6_J, axiom, ![X24, X25]:(hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X25,X24)))=>hBOOL(hAPP(c_Com_OWT,X24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_WTs__elim__cases_I6_J)). 4.05/4.28 fof(fact_eq__equal, axiom, ![X4]:(class_HOL_Oequal(X4)=>c_fequal=c_HOL_Oequal__class_Oequal(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__equal)). 4.05/4.28 fof(help_c__fNot__2, axiom, ![X56]:(hBOOL(hAPP(c_fNot,X56))|~(~(hBOOL(X56)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fNot__2)). 4.05/4.28 fof(help_c__fconj__2, axiom, ![X112, X56]:(hBOOL(X56)|~(hBOOL(hAPP(hAPP(c_fconj,X56),X112)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fconj__2)). 4.05/4.28 fof(help_c__fconj__3, axiom, ![X112, X56]:(~(hBOOL(hAPP(hAPP(c_fconj,X56),X112)))|hBOOL(X112)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fconj__3)). 4.05/4.28 fof(fact_not__iszero__1, axiom, ![X4]:(class_Rings_Osemiring__1(X4)=>~(c_Int_Oiszero(X4,c_Groups_Oone__class_Oone(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__iszero__1)). 4.05/4.28 fof(fact_zero__neq__one, axiom, ![X4]:(c_Groups_Oone__class_Oone(X4)!=c_Groups_Ozero__class_Ozero(X4)<=class_Rings_Ozero__neq__one(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__neq__one)). 4.05/4.28 fof(help_c__fNot__1, axiom, ![X56]:(~(hBOOL(hAPP(c_fNot,X56)))|~(hBOOL(X56))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fNot__1)). 4.05/4.28 fof(fact_not__Nil__listrel1, axiom, ![X18, X32, X4]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_ONil(X4)),X32)),c_List_Olistrel1(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__Nil__listrel1)). 4.05/4.28 fof(fact_Nil__notin__lex, axiom, ![X18, X31, X4]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_ONil(X4)),X31)),c_List_Olex(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nil__notin__lex)). 4.05/4.28 fof(fact_not__listrel1__Nil, axiom, ![X18, X32, X4]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),c_List_Olist_ONil(X4))),c_List_Olistrel1(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__listrel1__Nil)). 4.05/4.28 fof(fact_Nil2__notin__lex, axiom, ![X18, X32, X4]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X32),c_List_Olist_ONil(X4))),c_List_Olex(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nil2__notin__lex)). 4.05/4.28 fof(fact_lexord__Nil__right, axiom, ![X18, X9, X4]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X9),c_List_Olist_ONil(X4))),c_List_Olexord(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexord__Nil__right)). 4.05/4.28 fof(fact_in__measures_I1_J, axiom, ![X17, X9, X4]:~(hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X17)),c_List_Omeasures(X4,c_List_Olist_ONil(tc_fun(X4,tc_Nat_Onat)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_in__measures_I1_J)). 4.05/4.28 fof(fact_map__upd__nonempty, axiom, ![X9, X28, X123, X7, X4]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X123),X28),hAPP(c_Option_Ooption_OSome(X7),X9))!=hAPP(c_COMBK(tc_Option_Ooption(X7),X4),c_Option_Ooption_ONone(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upd__nonempty)). 4.05/4.28 fof(fact_not__zle__0__negative, axiom, ![X5]:~(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,X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__zle__0__negative)). 4.05/4.28 fof(fact_not__int__zless__negative, axiom, ![X2, X5]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__int__zless__negative)). 4.05/4.28 fof(fact_not__psubset__empty, axiom, ![X3, X4]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__psubset__empty)). 4.05/4.28 fof(fact_Cantors__paradox, axiom, ![X3, X4]:~(?[X160]:hAPP(c_Set_OPow(X4),X3)=hAPP(c_Set_Oimage(X4,tc_fun(X4,tc_HOL_Obool),X160),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Cantors__paradox)). 4.05/4.28 fof(fact_bot2E, axiom, ![X17, X9, X7, X4]:~(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),X9),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bot2E)). 4.05/4.28 fof(fact_infinite__UNIV__listI, axiom, ![X4]:~(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X4)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X4),tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_infinite__UNIV__listI)). 4.05/4.28 fof(fact_not__add__less1, axiom, ![X135, X46]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X135)),X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__add__less1)). 4.05/4.28 fof(fact_not__add__less2, axiom, ![X46, X135]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X135),X46)),X46))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__add__less2)). 4.05/4.28 fof(fact_int__less__0__conv, axiom, ![X107]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X107)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__less__0__conv)). 4.05/4.28 fof(fact_empty__fold1SetE, axiom, ![X9, X22, X4]:~(hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,X22,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X9))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__fold1SetE)). 4.05/4.28 fof(fact_infinite__UNIV__int, axiom, ~(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_infinite__UNIV__int)). 4.05/4.28 fof(fact_infinite__UNIV__nat, axiom, ~(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_infinite__UNIV__nat)). 4.05/4.28 fof(fact_insert__not__empty, axiom, ![X3, X26, X4]:c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))!=hAPP(hAPP(c_Set_Oinsert(X4),X26),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__not__empty)). 4.05/4.28 fof(fact_Pow__not__empty, axiom, ![X3, X4]:c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))!=hAPP(c_Set_OPow(X4),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__not__empty)). 4.05/4.28 fof(fact_com_Osimps_I43_J, axiom, ![X120, X75, X121, X72, X92, X93]:c_Com_Ocom_OCall(X93,X92,X72)!=c_Com_Ocom_OLocal(X121,X75,X120), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I43_J)). 4.05/4.28 fof(fact_com_Osimps_I36_J, axiom, ![X151, X152, X72, X120, X75, X121]:c_Com_Ocom_OCond(X72,X152,X151)!=c_Com_Ocom_OLocal(X121,X75,X120), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I36_J)). 4.05/4.28 fof(fact_com_Osimps_I57_J, axiom, ![X73, X74, X75, X72, X92, X93]:c_Com_Ocom_OCond(X75,X74,X73)!=c_Com_Ocom_OCall(X93,X92,X72), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I57_J)). 4.05/4.28 fof(fact_UNIV__not__empty, axiom, ![X4]:c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__not__empty)). 4.05/4.28 fof(fact_list_Osimps_I2_J, axiom, ![X239, X111, X4]:c_List_Olist_ONil(X4)!=hAPP(hAPP(c_List_Olist_OCons(X4),X111),X239), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osimps_I2_J)). 4.05/4.28 fof(fact_not__less0, axiom, ![X5]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__less0)). 4.05/4.28 fof(fact_com_Osimps_I52_J, axiom, ![X71, X72, X73, X74, X75]:c_Com_Ocom_OCond(X75,X74,X73)!=c_Com_Ocom_OWhile(X72,X71), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I52_J)). 4.05/4.28 fof(fact_com_Osimps_I34_J, axiom, ![X151, X152, X120, X75, X121]:c_Com_Ocom_OSemi(X152,X151)!=c_Com_Ocom_OLocal(X121,X75,X120), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I34_J)). 4.05/4.28 fof(fact_com_Osimps_I51_J, axiom, ![X73, X74, X72, X92, X93]:c_Com_Ocom_OSemi(X74,X73)!=c_Com_Ocom_OCall(X93,X92,X72), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I51_J)). 4.05/4.28 fof(fact_com_Osimps_I45_J, axiom, ![X73, X74, X151, X152, X72]:c_Com_Ocom_OSemi(X74,X73)!=c_Com_Ocom_OCond(X72,X152,X151), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I45_J)). 4.05/4.28 fof(fact_com_Osimps_I39_J, axiom, ![X120, X75, X121, X71, X72]:c_Com_Ocom_OWhile(X72,X71)!=c_Com_Ocom_OLocal(X121,X75,X120), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I39_J)). 4.05/4.28 fof(fact_com_Osimps_I60_J, axiom, ![X72, X92, X93, X120, X75]:c_Com_Ocom_OWhile(X75,X120)!=c_Com_Ocom_OCall(X93,X92,X72), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I60_J)). 4.05/4.28 fof(fact_not__Cons__self, axiom, ![X13, X4, X45]:X45!=hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__Cons__self)). 4.05/4.28 fof(fact_option_Osimps_I2_J, axiom, ![X111, X4]:c_Option_Ooption_ONone(X4)!=hAPP(c_Option_Ooption_OSome(X4),X111), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Osimps_I2_J)). 4.05/4.28 fof(fact_com_Osimps_I41_J, axiom, ![X120, X75, X121, X92]:c_Com_Ocom_OBODY(X92)!=c_Com_Ocom_OLocal(X121,X75,X120), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I41_J)). 4.05/4.28 fof(fact_com_Osimps_I62_J, axiom, ![X72, X92, X93, X94]:c_Com_Ocom_OBODY(X94)!=c_Com_Ocom_OCall(X93,X92,X72), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I62_J)). 4.05/4.28 fof(fact_less__irrefl__nat, axiom, ![X5]:~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__irrefl__nat)). 4.05/4.28 fof(fact_com_Osimps_I55_J, axiom, ![X73, X74, X75, X92]:c_Com_Ocom_OBODY(X92)!=c_Com_Ocom_OCond(X75,X74,X73), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I55_J)). 4.05/4.28 fof(fact_com_Osimps_I47_J, axiom, ![X73, X74, X71, X72]:c_Com_Ocom_OWhile(X72,X71)!=c_Com_Ocom_OSemi(X74,X73), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I47_J)). 4.05/4.28 fof(fact_is__none__code_I2_J, axiom, ![X13, X7]:~(c_Option_Ois__none(X7,hAPP(c_Option_Ooption_OSome(X7),X13))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_is__none__code_I2_J)). 4.05/4.28 fof(fact_not__neg__int, axiom, ![X5]:~(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__neg__int)). 4.05/4.28 fof(fact_rel__simps_I7_J, axiom, ~(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I7_J)). 4.05/4.28 fof(fact_com_Osimps_I48_J, axiom, ![X256, X231, X232]:c_Com_Ocom_OSemi(X232,X231)!=c_Com_Ocom_OBODY(X256), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I48_J)). 4.05/4.28 fof(fact_com_Osimps_I59_J, axiom, ![X120, X75, X92]:c_Com_Ocom_OBODY(X92)!=c_Com_Ocom_OWhile(X75,X120), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osimps_I59_J)). 4.05/4.28 fof(fact_not__neg__0, axiom, ~(hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__neg__0)). 4.05/4.28 fof(fact_not__neg__1, axiom, ~(hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_not__neg__1)). 4.05/4.28 fof(fact_Zero__not__Suc, axiom, ![X2]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Zero__not__Suc)). 4.05/4.28 fof(fact_list__ex__simps_I2_J, axiom, ![X56, X4]:~(c_List_Olist__ex(X4,X56,c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex__simps_I2_J)). 4.05/4.28 fof(fact_list__ex1__simps_I1_J, axiom, ![X56, X4]:~(c_List_Olist__ex1(X4,X56,c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__ex1__simps_I1_J)). 4.05/4.28 fof(fact_rel__simps_I37_J, axiom, c_Int_OPls!=c_Int_OMin, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I37_J)). 4.05/4.28 fof(fact_Suc__n__not__n, axiom, ![X5]:X5!=hAPP(c_Nat_OSuc,X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Suc__n__not__n)). 4.05/4.28 fof(conj_0, hypothesis, c_Hoare__Mirabelle_Ostate__not__singleton, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_0)). 4.05/4.28 fof(help_c__fFalse__1, axiom, ~(hBOOL(c_fFalse)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fFalse__1)). 4.05/4.28 fof(fact_image__split__eq__Sigma, axiom, ![X3, X76, X22, X7, X4, X49]:hAPP(c_Set_Oimage(X49,tc_prod(X4,X7),hAPP(hAPP(c_COMBS(X49,X7,tc_prod(X4,X7)),hAPP(hAPP(c_COMBB(X4,tc_fun(X7,tc_prod(X4,X7)),X49),c_Product__Type_OPair(X4,X7)),X22)),X76)),X3)=hAPP(hAPP(c_Product__Type_OSigma(X4,X7),hAPP(c_Set_Oimage(X49,X4,X22),X3)),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X4),c_Set_Oimage(X49,X7,X76)),hAPP(hAPP(c_COMBC(X4,tc_fun(X49,tc_HOL_Obool),tc_fun(X49,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_HOL_Obool),tc_fun(tc_fun(X49,tc_HOL_Obool),tc_fun(X49,tc_HOL_Obool)),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X49,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X49,tc_HOL_Obool),X4),c_Set_Ovimage(X49,X4,X22)),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__split__eq__Sigma)). 4.05/4.28 fof(fact_sublist__shift__lemma__Suc, axiom, ![X263, X32, X56, X4]:hAPP(hAPP(c_List_Omap(tc_prod(X4,tc_Nat_Onat),X4),c_Product__Type_Ofst(X4,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X4,tc_Nat_Onat)),X56),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X4,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X4,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X4,tc_Nat_Onat),X32),X263)))=hAPP(hAPP(c_List_Omap(tc_prod(X4,tc_Nat_Onat),X4),c_Product__Type_Ofst(X4,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X4,tc_Nat_Onat)),X56),c_Product__Type_Osnd(X4,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X4,tc_Nat_Onat),X32),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X263)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__shift__lemma__Suc)). 4.05/4.28 fof(fact_INT__Int__distrib, axiom, ![X6, X3, X41, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X41),hAPP(hAPP(c_COMBS(X7,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X7),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool))),X3)),X6))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X41),X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X41),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__Int__distrib)). 4.05/4.28 fof(fact_scomp__scomp, axiom, ![X48, X76, X22, X177, X178, X7, X126, X49, X4]:hAPP(hAPP(c_Product__Type_Oscomp(X4,X178,X177,X7),X22),hAPP(hAPP(c_COMBC(X178,tc_fun(X49,tc_fun(X126,X7)),tc_fun(X177,X7)),hAPP(hAPP(c_COMBB(tc_fun(X177,tc_prod(X49,X126)),tc_fun(tc_fun(X49,tc_fun(X126,X7)),tc_fun(X177,X7)),X178),c_Product__Type_Oscomp(X177,X49,X126,X7)),X76)),X48))=hAPP(hAPP(c_Product__Type_Oscomp(X4,X49,X126,X7),hAPP(hAPP(c_Product__Type_Oscomp(X4,X178,X177,tc_prod(X49,X126)),X22),X76)),X48), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_scomp__scomp)). 4.05/4.28 fof(fact_UN__Un__distrib, axiom, ![X6, X3, X41, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X41),hAPP(hAPP(c_COMBS(X7,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X7),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool))),X3)),X6))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X41),X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X41),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__Un__distrib)). 4.05/4.28 fof(fact_Sigma__Diff__distrib2, axiom, ![X6, X3, X41, X7, X4]:hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X41),hAPP(hAPP(c_COMBS(X4,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool))),X3)),X6))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X41),X3)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X41),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Diff__distrib2)). 4.05/4.28 fof(fact_Sigma__Int__distrib2, axiom, ![X6, X3, X41, X7, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X41),X3)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X41),X6))=hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X41),hAPP(hAPP(c_COMBS(X4,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool))),X3)),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Int__distrib2)). 4.05/4.28 fof(fact_Sigma__Un__distrib2, axiom, ![X6, X3, X41, X7, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X41),X3)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X41),X6))=hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X41),hAPP(hAPP(c_COMBS(X4,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X4),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool))),X3)),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Un__distrib2)). 4.05/4.28 fof(fact_option__map__o__map__upd, axiom, ![X25, X26, X21, X22, X4, X7, X49]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X49),tc_Option_Ooption(X7),X4,hAPP(c_Option_Omap(X49,X7),X22)),X21)),X26),hAPP(c_Option_Ooption_OSome(X7),hAPP(X22,X25)))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X49),tc_Option_Ooption(X7),X4,hAPP(c_Option_Omap(X49,X7),X22)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X49)),X21),X26),hAPP(c_Option_Ooption_OSome(X49),X25))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option__map__o__map__upd)). 4.05/4.28 fof(fact_map__of__map__restrict, axiom, ![X257, X22, X7, X4]:c_Map_Orestrict__map(X4,X7,hAPP(c_Fun_Ocomp(X7,tc_Option_Ooption(X7),X4,c_Option_Ooption_OSome(X7)),X22),hAPP(c_List_Oset(X4),X257))=hAPP(c_Map_Omap__of(X4,X7),hAPP(hAPP(c_List_Omap(X4,tc_prod(X4,X7)),hAPP(hAPP(c_COMBS(X4,X7,tc_prod(X4,X7)),c_Product__Type_OPair(X4,X7)),X22)),X257)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__map__restrict)). 4.05/4.28 fof(fact_zip__update, axiom, ![X43, X59, X13, X46, X45, X7, X4]:hAPP(hAPP(c_List_Olist__update(tc_prod(X4,X7),hAPP(hAPP(c_List_Ozip(X4,X7),X45),X59)),X46),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X13),X43))=hAPP(hAPP(c_List_Ozip(X4,X7),hAPP(hAPP(c_List_Olist__update(X4,X45),X46),X13)),hAPP(hAPP(c_List_Olist__update(X7,X59),X46),X43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__update)). 4.05/4.28 fof(fact_map__pair_Ocompositionality, axiom, ![X290, X37, X48, X177, X178, X76, X22, X7, X126, X4, X49]:hAPP(c_Product__Type_Omap__pair(X49,X4,X126,X7,X22,X76),hAPP(c_Product__Type_Omap__pair(X178,X49,X177,X126,X48,X37),X290))=hAPP(c_Product__Type_Omap__pair(X178,X4,X177,X7,hAPP(c_Fun_Ocomp(X49,X4,X178,X22),X48),hAPP(c_Fun_Ocomp(X126,X7,X177,X76),X37)),X290), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair_Ocompositionality)). 4.05/4.28 fof(fact_UN__extend__simps_I10_J, axiom, ![X22, X6, X49, X3, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(X49,tc_fun(X4,tc_HOL_Obool),X7),X6),X22))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X49,X22),X3)),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__extend__simps_I10_J)). 4.05/4.28 fof(fact_INT__simps_I10_J, axiom, ![X6, X3, X22, X49, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X49,X7,X22),X3)),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X49,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(X7,tc_fun(X4,tc_HOL_Obool),X49),X6),X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__simps_I10_J)). 4.05/4.28 fof(fact_image__add__atLeastLessThan, axiom, ![X38, X37, X28]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),X28)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X38),X28))=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)),X28)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X37),X38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__add__atLeastLessThan)). 4.05/4.28 fof(fact_UN__o, axiom, ![X22, X76, X49, X3, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X49,X22),X3)),X76)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(c_Fun_Ocomp(X49,tc_fun(X4,tc_HOL_Obool),X7,X76),X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__o)). 4.05/4.28 fof(fact_zip__Cons__Cons, axiom, ![X59, X43, X45, X13, X7, X4]:hAPP(hAPP(c_List_Olist_OCons(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X13),X43)),hAPP(hAPP(c_List_Ozip(X4,X7),X45),X59))=hAPP(hAPP(c_List_Ozip(X4,X7),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)),hAPP(hAPP(c_List_Olist_OCons(X7),X43),X59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__Cons__Cons)). 4.05/4.28 fof(fact_fun__upd__comp, axiom, ![X17, X9, X76, X22, X4, X7, X49]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X7),hAPP(c_Fun_Ocomp(X49,X7,X4,X22),X76)),X9),hAPP(X22,X17))=hAPP(c_Fun_Ocomp(X49,X7,X4,X22),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X49),X76),X9),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__comp)). 4.05/4.28 fof(fact_image__add__atLeastAtMost, axiom, ![X38, X37, X28]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),X28),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X38),X28))=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)),X28)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X37,X38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__add__atLeastAtMost)). 4.05/4.28 fof(fact_INT__insert, axiom, ![X6, X3, X26, X4, X7]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(X6,X26)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X26),X3)),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__insert)). 4.05/4.28 fof(fact_split__comp, axiom, ![X9, X76, X22, X126, X4, X49, X7]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X49,X4),hAPP(c_Fun_Ocomp(X126,tc_fun(X49,X4),X7,X22),X76)),X9)=hAPP(hAPP(X22,hAPP(X76,hAPP(c_Product__Type_Ofst(X7,X49),X9))),hAPP(c_Product__Type_Osnd(X7,X49),X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__comp)). 4.05/4.28 fof(fact_UN__insert, axiom, ![X6, X3, X26, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7),X26),X3)),X6)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(X6,X26)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__insert)). 4.05/4.28 fof(fact_transpose__map__map, axiom, ![X32, X22, X7, X4]:c_List_Otranspose(X4,hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_List_Olist(X4)),hAPP(c_List_Omap(X7,X4),X22)),X32))=hAPP(hAPP(c_List_Omap(tc_List_Olist(X7),tc_List_Olist(X4)),hAPP(c_List_Omap(X7,X4),X22)),c_List_Otranspose(X7,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose__map__map)). 4.05/4.28 fof(fact_length__filter__map, axiom, ![X32, X22, X7, X56, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),hAPP(c_List_Ofilter(X7,hAPP(c_Fun_Ocomp(X4,tc_HOL_Obool,X7,X56),X22)),X32))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Ofilter(X4,X56),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__filter__map)). 4.05/4.28 fof(fact_fst__comp__map__pair, axiom, ![X76, X22, X7, X4, X126, X49]:hAPP(c_Fun_Ocomp(tc_prod(X49,X126),X49,tc_prod(X4,X7),c_Product__Type_Ofst(X49,X126)),c_Product__Type_Omap__pair(X4,X49,X7,X126,X22,X76))=hAPP(c_Fun_Ocomp(X4,X49,tc_prod(X4,X7),X22),c_Product__Type_Ofst(X4,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__comp__map__pair)). 4.05/4.28 fof(fact_snd__comp__map__pair, axiom, ![X76, X22, X7, X4, X49, X126]:hAPP(c_Fun_Ocomp(tc_prod(X126,X49),X49,tc_prod(X4,X7),c_Product__Type_Osnd(X126,X49)),c_Product__Type_Omap__pair(X4,X126,X7,X49,X22,X76))=hAPP(c_Fun_Ocomp(X7,X49,tc_prod(X4,X7),X76),c_Product__Type_Osnd(X4,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__comp__map__pair)). 4.05/4.28 fof(fact_restrict__complement__singleton__eq, axiom, ![X9, X22, X7, X4]:c_Map_Orestrict__map(X4,X7,X22,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X22),X9),c_Option_Ooption_ONone(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__complement__singleton__eq)). 4.05/4.28 fof(fact_Int__left__commute, axiom, ![X8, X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X6),X8))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__left__commute)). 4.05/4.28 fof(fact_Un__left__commute, axiom, ![X8, X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X6),X8))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__left__commute)). 4.05/4.28 fof(fact_zip__same__conv__map, axiom, ![X32, X4]:hAPP(hAPP(c_List_Omap(X4,tc_prod(X4,X4)),hAPP(hAPP(c_COMBS(X4,X4,tc_prod(X4,X4)),c_Product__Type_OPair(X4,X4)),c_COMBI(X4))),X32)=hAPP(hAPP(c_List_Ozip(X4,X4),X32),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__same__conv__map)). 4.05/4.28 fof(fact_Domain__Union, axiom, ![X86, X7, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X86),c_Relation_ODomain(X4,X7))=hAPP(c_Relation_ODomain(X4,X7),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),X86)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Union)). 4.05/4.28 fof(fact_Range__Union, axiom, ![X86, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X7,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X86),c_Relation_ORange(X7,X4))=hAPP(c_Relation_ORange(X7,X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X7,X4),tc_HOL_Obool),X86)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Union)). 4.05/4.28 fof(fact_map__update, axiom, ![X17, X28, X32, X22, X4, X7]:hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Omap(X7,X4),X22),X32)),X28),hAPP(X22,X17))=hAPP(hAPP(c_List_Omap(X7,X4),X22),hAPP(hAPP(c_List_Olist__update(X7,X32),X28),X17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__update)). 4.05/4.28 fof(fact_o__assoc, axiom, ![X48, X76, X126, X22, X4, X7, X49]:hAPP(c_Fun_Ocomp(X126,X7,X4,hAPP(c_Fun_Ocomp(X49,X7,X126,X22),X76)),X48)=hAPP(c_Fun_Ocomp(X49,X7,X4,X22),hAPP(c_Fun_Ocomp(X126,X49,X4,X76),X48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_o__assoc)). 4.05/4.28 fof(fact_Int__Union, axiom, ![X6, X3, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X6),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Union)). 4.05/4.28 fof(fact_Un__Inter, axiom, ![X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X6),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Inter)). 4.05/4.28 fof(fact_Option_Omap_Ocompositionality, axiom, ![X128, X76, X49, X22, X4, X7]:hAPP(hAPP(c_Option_Omap(X7,X4),X22),hAPP(hAPP(c_Option_Omap(X49,X7),X76),X128))=hAPP(hAPP(c_Option_Omap(X49,X4),hAPP(c_Fun_Ocomp(X7,X4,X49,X22),X76)),X128), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Option_Omap_Ocompositionality)). 4.05/4.28 fof(fact_image__Union, axiom, ![X86, X22, X4, X7]:hAPP(c_Set_Oimage(X7,X4,X22),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X86))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X7,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X86),c_Set_Oimage(X7,X4,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Union)). 4.05/4.28 fof(fact_map_Osimps_I2_J, axiom, ![X32, X9, X22, X4, X7]:hAPP(hAPP(c_List_Olist_OCons(X4),hAPP(X22,X9)),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32))=hAPP(hAPP(c_List_Omap(X7,X4),X22),hAPP(hAPP(c_List_Olist_OCons(X7),X9),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map_Osimps_I2_J)). 4.05/4.28 fof(fact_image__compose, axiom, ![X18, X76, X22, X49, X4, X7]:hAPP(c_Set_Oimage(X7,X4,hAPP(c_Fun_Ocomp(X49,X4,X7,X22),X76)),X18)=hAPP(c_Set_Oimage(X49,X4,X22),hAPP(c_Set_Oimage(X7,X49,X76),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__compose)). 4.05/4.28 fof(fact_image__insert, axiom, ![X6, X26, X22, X4, X7]:hAPP(c_Set_Oimage(X7,X4,X22),hAPP(hAPP(c_Set_Oinsert(X7),X26),X6))=hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X22,X26)),hAPP(c_Set_Oimage(X7,X4,X22),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__insert)). 4.05/4.28 fof(fact_foldl__Cons, axiom, ![X32, X9, X26, X22, X7, X4]:hAPP(c_List_Ofoldl(X4,X7,X22,X26),hAPP(hAPP(c_List_Olist_OCons(X7),X9),X32))=hAPP(c_List_Ofoldl(X4,X7,X22,hAPP(hAPP(X22,X26),X9)),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__Cons)). 4.05/4.28 fof(fact_drop__map, axiom, ![X32, X22, X7, X20, X4]:hAPP(hAPP(c_List_Omap(X7,X4),X22),hAPP(hAPP(c_List_Odrop(X7),X20),X32))=hAPP(hAPP(c_List_Odrop(X4),X20),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__map)). 4.05/4.28 fof(fact_take__map, axiom, ![X32, X22, X7, X20, X4]:hAPP(hAPP(c_List_Omap(X7,X4),X22),hAPP(hAPP(c_List_Otake(X7),X20),X32))=hAPP(hAPP(c_List_Otake(X4),X20),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__map)). 4.05/4.28 fof(fact_converse__inv__image, axiom, ![X22, X39, X7, X4]:hAPP(hAPP(c_Relation_Oinv__image(X7,X4),hAPP(c_Relation_Oconverse(X7,X7),X39)),X22)=hAPP(c_Relation_Oconverse(X4,X4),hAPP(hAPP(c_Relation_Oinv__image(X7,X4),X39),X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__inv__image)). 4.05/4.28 fof(fact_power_Opower_Opower__Suc, axiom, ![X20, X26, X168, X169, X4]:hAPP(hAPP(c_Power_Opower_Opower(X4,X169,X168),X26),hAPP(c_Nat_OSuc,X20))=hAPP(hAPP(X168,X26),hAPP(hAPP(c_Power_Opower_Opower(X4,X169,X168),X26),X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power_Opower_Opower__Suc)). 4.05/4.28 fof(fact_list__size__map, axiom, ![X32, X76, X7, X22, X4]:c_List_Olist_Olist__size(X7,hAPP(c_Fun_Ocomp(X4,tc_Nat_Onat,X7,X22),X76),X32)=c_List_Olist_Olist__size(X4,X22,hAPP(hAPP(c_List_Omap(X7,X4),X76),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__size__map)). 4.05/4.28 fof(fact_map__add__def, axiom, ![X9, X162, X163, X4, X7]:hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X4),X4,hAPP(X163,X9),c_Option_Ooption_OSome(X4)),hAPP(X162,X9))=hAPP(c_Map_Omap__add(X7,X4,X163,X162),X9), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__def)). 4.05/4.28 fof(fact_prod__case__beta, axiom, ![X51, X22, X4, X49, X7]:hAPP(hAPP(X22,hAPP(c_Product__Type_Ofst(X7,X49),X51)),hAPP(c_Product__Type_Osnd(X7,X49),X51))=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X49,X4),X22),X51), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_prod__case__beta)). 4.05/4.28 fof(fact_insert__commute, axiom, ![X3, X17, X9, X4]:hAPP(hAPP(c_Set_Oinsert(X4),X17),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3))=hAPP(hAPP(c_Set_Oinsert(X4),X9),hAPP(hAPP(c_Set_Oinsert(X4),X17),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__commute)). 4.05/4.28 fof(fact_map__replicate__const, axiom, ![X288, X28, X4, X7]:hAPP(hAPP(c_List_Omap(X7,X4),hAPP(c_COMBK(X4,X7),X28)),X288)=c_List_Oreplicate(X4,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X288),X28), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__replicate__const)). 4.05/4.28 fof(fact_map__tl, axiom, ![X32, X22, X4, X7]:hAPP(c_List_Otl(X4),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32))=hAPP(hAPP(c_List_Omap(X7,X4),X22),hAPP(c_List_Otl(X7),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__tl)). 4.05/4.28 fof(fact_rotate__simps, axiom, ![X45, X13, X7, X4]:(hAPP(hAPP(c_List_Oappend(X7),X45),hAPP(hAPP(c_List_Olist_OCons(X7),X13),c_List_Olist_ONil(X7)))=hAPP(c_List_Orotate1(X7),hAPP(hAPP(c_List_Olist_OCons(X7),X13),X45))&c_List_Olist_ONil(X4)=hAPP(c_List_Orotate1(X4),c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate__simps)). 4.05/4.28 fof(fact_zmult__div__cancel, axiom, ![X2, X5]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__div__cancel)). 4.05/4.28 fof(fact_mult__div__cancel, axiom, ![X2, X5]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__div__cancel)). 4.05/4.28 fof(fact_set__map, axiom, ![X32, X22, X7, X4]:hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32))=hAPP(c_Set_Oimage(X7,X4,X22),hAPP(c_List_Oset(X7),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__map)). 4.05/4.28 fof(fact_map__butlast, axiom, ![X32, X22, X4, X7]:c_List_Obutlast(X4,hAPP(hAPP(c_List_Omap(X7,X4),X22),X32))=hAPP(hAPP(c_List_Omap(X7,X4),X22),c_List_Obutlast(X7,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__butlast)). 4.05/4.28 fof(fact_nat__add__left__commute, axiom, ![X29, X43, X13]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X29))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__add__left__commute)). 4.05/4.28 fof(fact_nat__rec__Suc, axiom, ![X242, X129, X130, X4]:hAPP(hAPP(X129,X242),hAPP(c_Nat_Onat_Onat__rec(X4,X130,X129),X242))=hAPP(c_Nat_Onat_Onat__rec(X4,X130,X129),hAPP(c_Nat_OSuc,X242)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__rec__Suc)). 4.05/4.28 fof(fact_mult__Suc, axiom, ![X5, X2]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Suc)). 4.05/4.28 fof(fact_partition_Osimps_I1_J, axiom, ![X56, X4]:hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_List_Olist_ONil(X4))=c_List_Opartition(X4,X56,c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition_Osimps_I1_J)). 4.05/4.28 fof(help_c__COMBS__1, axiom, ![X39, X112, X56, X4, X49, X7]:hAPP(hAPP(X56,X39),hAPP(X112,X39))=hAPP(hAPP(hAPP(c_COMBS(X7,X49,X4),X56),X112),X39), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBS__1)). 4.05/4.28 fof(fact_mult__Suc__right, axiom, ![X5, X2]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__Suc__right)). 4.05/4.28 fof(fact_rev__filter, axiom, ![X32, X56, X4]:hAPP(c_List_Ofilter(X4,X56),hAPP(c_List_Orev(X4),X32))=hAPP(c_List_Orev(X4),hAPP(c_List_Ofilter(X4,X56),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__filter)). 4.05/4.28 fof(fact_split__Pair, axiom, ![X7, X4]:c_Fun_Oid(tc_prod(X4,X7))=hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_prod(X4,X7)),c_Product__Type_OPair(X4,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__Pair)). 4.05/4.28 fof(fact_n__lists_Osimps_I1_J, axiom, ![X45, X4]:c_Enum_On__lists(X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X45)=hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_List_Olist_ONil(tc_List_Olist(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_n__lists_Osimps_I1_J)). 4.05/4.28 fof(fact_lexn_Osimps_I1_J, axiom, ![X18, X4]:c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool))=hAPP(c_List_Olexn(X4,X18),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lexn_Osimps_I1_J)). 4.05/4.28 fof(fact_remove1__commute, axiom, ![X175, X43, X13, X4]:c_List_Oremove1(X4,X13,c_List_Oremove1(X4,X43,X175))=c_List_Oremove1(X4,X43,c_List_Oremove1(X4,X13,X175)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1__commute)). 4.05/4.28 fof(fact_New__DSequence_Opos__union__def, axiom, ![X37, X317, X143, X4]:hAPP(c_New__DSequence_Opos__union(X4,X143,X317),X37)=c_Lazy__Sequence_Oappend(X4,hAPP(X143,X37),hAPP(X317,X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__union__def)). 4.05/4.28 fof(fact_sublists_Osimps_I1_J, axiom, ![X4]:c_Enum_Osublists(X4,c_List_Olist_ONil(X4))=hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_List_Olist_ONil(tc_List_Olist(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublists_Osimps_I1_J)). 4.05/4.28 fof(fact_rp__inv__image__def, axiom, ![X7, X4]:c_FunDef_Orp__inv__image(X4,X7)=hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X7,X4),tc_prod(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X7,X4),tc_fun(tc_prod(X7,X7),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X7,X4),tc_prod(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X7,X4),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),tc_fun(tc_fun(X7,X4),tc_prod(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X7,X4),tc_fun(tc_prod(X7,X7),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_fun(X7,X4),tc_prod(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool))))),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X7,X4),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),tc_fun(tc_fun(X7,X4),tc_prod(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool))),tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,X4),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X7,X4),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),tc_fun(tc_fun(X7,X4),tc_prod(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)))),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_COMBS(tc_fun(X7,X4),tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7,X4),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)),tc_fun(tc_fun(X7,X4),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)))),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool))),tc_fun(X7,X4)),c_Product__Type_OPair(tc_fun(tc_prod(X7,X7),tc_HOL_Obool),tc_fun(tc_prod(X7,X7),tc_HOL_Obool)))),c_Relation_Oinv__image(X4,X7))))),c_Relation_Oinv__image(X4,X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rp__inv__image__def)). 4.05/4.28 fof(fact_minus__int__def, axiom, ![X16]: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,X16)),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),X16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__int__def)). 4.05/4.28 fof(fact_partition_Osimps_I2_J, axiom, ![X32, X9, X56, X4]:c_List_Opartition(X4,X56,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32))=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X4),tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))),tc_fun(tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))),tc_List_Olist(X4)),c_COMBS(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),tc_fun(tc_List_Olist(X4),tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))),tc_List_Olist(X4)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),tc_List_Olist(X4)),hAPP(c_If(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(X56,X9)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),tc_List_Olist(X4)),c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(c_List_Olist_OCons(X4),X9))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),tc_fun(tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),tc_fun(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)))),tc_List_Olist(X4)),c_COMBB(tc_List_Olist(X4),tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_List_Olist(X4))),c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)))),hAPP(c_List_Olist_OCons(X4),X9)))),c_List_Opartition(X4,X56,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition_Osimps_I2_J)). 4.05/4.28 fof(fact_map__upds__fold__map__upd, axiom, ![X284, X257, X21, X7, X4]:c_Map_Omap__upds(X4,X7,X21,X257,X284)=hAPP(c_List_Ofoldl(tc_fun(X4,tc_Option_Ooption(X7)),tc_prod(X4,X7),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X7,tc_fun(X4,tc_Option_Ooption(X7)))),tc_fun(tc_prod(X4,X7),tc_fun(X4,tc_Option_Ooption(X7))),tc_fun(X4,tc_Option_Ooption(X7))),c_Product__Type_Oprod_Oprod__case(X4,X7,tc_fun(X4,tc_Option_Ooption(X7)))),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_Option_Ooption(X7)),tc_fun(X7,tc_Option_Ooption(X7)),tc_fun(X4,tc_fun(X7,tc_fun(X4,tc_Option_Ooption(X7))))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(X7,tc_Option_Ooption(X7)),tc_fun(X7,tc_fun(X4,tc_Option_Ooption(X7))))),tc_fun(tc_fun(X7,tc_Option_Ooption(X7)),tc_fun(X4,tc_fun(X7,tc_fun(X4,tc_Option_Ooption(X7))))),tc_fun(X4,tc_Option_Ooption(X7))),c_COMBC(X4,tc_fun(X7,tc_Option_Ooption(X7)),tc_fun(X7,tc_fun(X4,tc_Option_Ooption(X7))))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_Option_Ooption(X7),tc_fun(X4,tc_Option_Ooption(X7)))),tc_fun(X4,tc_fun(tc_fun(X7,tc_Option_Ooption(X7)),tc_fun(X7,tc_fun(X4,tc_Option_Ooption(X7))))),tc_fun(X4,tc_Option_Ooption(X7))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X7),tc_fun(X4,tc_Option_Ooption(X7))),tc_fun(tc_fun(X7,tc_Option_Ooption(X7)),tc_fun(X7,tc_fun(X4,tc_Option_Ooption(X7)))),X4),c_COMBB(tc_Option_Ooption(X7),tc_fun(X4,tc_Option_Ooption(X7)),X7))),c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7))))),c_Option_Ooption_OSome(X7))),X21),hAPP(hAPP(c_List_Ozip(X4,X7),X257),X284)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__fold__map__upd)). 4.05/4.28 fof(fact_Sigma__def, axiom, ![X6, X3, X7, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X4,tc_fun(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X4),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool))),X6)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(tc_prod(X4,X7),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool))),X4),c_COMBC(X7,tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(tc_prod(X4,X7),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(tc_prod(X4,X7),tc_HOL_Obool))),X4),hAPP(c_COMBB(tc_prod(X4,X7),tc_fun(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X7),c_Set_Oinsert(tc_prod(X4,X7)))),c_Product__Type_OPair(X4,X7)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)))))=hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__def)). 4.05/4.28 fof(fact_zip__Cons, axiom, ![X31, X17, X32, X7, X4]:hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X4,X7)),X4,c_List_Olist_ONil(tc_prod(X4,X7)),hAPP(hAPP(c_COMBC(X4,tc_fun(tc_List_Olist(X4),tc_List_Olist(tc_prod(X4,X7))),tc_fun(tc_List_Olist(X4),tc_List_Olist(tc_prod(X4,X7)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X4,X7)),tc_List_Olist(tc_prod(X4,X7))),tc_fun(tc_fun(tc_List_Olist(X4),tc_List_Olist(tc_prod(X4,X7))),tc_fun(tc_List_Olist(X4),tc_List_Olist(tc_prod(X4,X7)))),X4),c_COMBB(tc_List_Olist(tc_prod(X4,X7)),tc_List_Olist(tc_prod(X4,X7)),tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_prod(X4,X7),tc_fun(tc_List_Olist(tc_prod(X4,X7)),tc_List_Olist(tc_prod(X4,X7))),X4),c_List_Olist_OCons(tc_prod(X4,X7))),hAPP(hAPP(c_COMBC(X4,X7,tc_prod(X4,X7)),c_Product__Type_OPair(X4,X7)),X17)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(X7),tc_List_Olist(tc_prod(X4,X7))),c_List_Ozip(X4,X7)),X31))),X32)=hAPP(hAPP(c_List_Ozip(X4,X7),X32),hAPP(hAPP(c_List_Olist_OCons(X7),X17),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__Cons)). 4.05/4.28 fof(fact_UN__Times__distrib, axiom, ![X87, X204, X6, X3, X7, X4, X126, X49]:hAPP(hAPP(c_Product__Type_OSigma(X4,X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,tc_fun(X4,tc_HOL_Obool)),X3),X204)),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X126,tc_fun(X7,tc_HOL_Obool)),X6),X87)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X49,X126),tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X49,X126),X3),hAPP(c_COMBK(tc_fun(X126,tc_HOL_Obool),X49),X6))),hAPP(c_Product__Type_Oprod_Oprod__case(X49,X126,tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X49,tc_fun(X126,tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),tc_fun(X126,tc_fun(tc_prod(X4,X7),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_fun(X7,tc_HOL_Obool)),tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),tc_fun(tc_fun(X126,tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),tc_fun(X126,tc_fun(tc_prod(X4,X7),tc_HOL_Obool))),X49),c_COMBB(tc_fun(X4,tc_fun(X7,tc_HOL_Obool)),tc_fun(tc_prod(X4,X7),tc_HOL_Obool),X126)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_fun(X7,tc_HOL_Obool)),tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X49),c_Product__Type_OSigma(X4,X7)),X204))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X4,tc_fun(X7,tc_HOL_Obool)),X126),c_COMBK(tc_fun(X7,tc_HOL_Obool),X4)),X87)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__Times__distrib)). 4.05/4.28 fof(fact_zip__Cons1, axiom, ![X31, X32, X9, X7, X4]:hAPP(hAPP(c_List_Ozip(X4,X7),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)),X31)=hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X4,X7)),X7,c_List_Olist_ONil(tc_prod(X4,X7)),hAPP(hAPP(c_COMBC(X7,tc_fun(tc_List_Olist(X7),tc_List_Olist(tc_prod(X4,X7))),tc_fun(tc_List_Olist(X7),tc_List_Olist(tc_prod(X4,X7)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X4,X7)),tc_List_Olist(tc_prod(X4,X7))),tc_fun(tc_fun(tc_List_Olist(X7),tc_List_Olist(tc_prod(X4,X7))),tc_fun(tc_List_Olist(X7),tc_List_Olist(tc_prod(X4,X7)))),X7),c_COMBB(tc_List_Olist(tc_prod(X4,X7)),tc_List_Olist(tc_prod(X4,X7)),tc_List_Olist(X7))),hAPP(hAPP(c_COMBB(tc_prod(X4,X7),tc_fun(tc_List_Olist(tc_prod(X4,X7)),tc_List_Olist(tc_prod(X4,X7))),X7),c_List_Olist_OCons(tc_prod(X4,X7))),hAPP(c_Product__Type_OPair(X4,X7),X9)))),hAPP(c_List_Ozip(X4,X7),X32))),X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__Cons1)). 4.05/4.28 fof(fact_Int__UN__distrib2, axiom, ![X6, X55, X49, X3, X41, X7, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X41),X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,tc_fun(X4,tc_HOL_Obool)),X55),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X41),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool),X7),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,tc_fun(X4,tc_HOL_Obool)),X55)),hAPP(hAPP(c_COMBC(X7,tc_fun(X49,tc_fun(X4,tc_HOL_Obool)),tc_fun(X49,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_fun(X49,tc_fun(X4,tc_HOL_Obool)),tc_fun(X49,tc_fun(X4,tc_HOL_Obool))),X7),c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X49)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X7),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool))),X3))),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__UN__distrib2)). 4.05/4.28 fof(fact_Un__INT__distrib2, axiom, ![X6, X55, X49, X3, X41, X7, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X41),X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X49,tc_fun(X4,tc_HOL_Obool)),X55),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X41),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool),X7),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X49,tc_fun(X4,tc_HOL_Obool)),X55)),hAPP(hAPP(c_COMBC(X7,tc_fun(X49,tc_fun(X4,tc_HOL_Obool)),tc_fun(X49,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_fun(X49,tc_fun(X4,tc_HOL_Obool)),tc_fun(X49,tc_fun(X4,tc_HOL_Obool))),X7),c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X49)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X7),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool))),X3))),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__INT__distrib2)). 4.05/4.28 fof(fact_map__zip__map2, axiom, ![X31, X76, X126, X32, X22, X4, X49, X7]:hAPP(hAPP(c_List_Omap(tc_prod(X7,X49),X4),X22),hAPP(hAPP(c_List_Ozip(X7,X49),X32),hAPP(hAPP(c_List_Omap(X126,X49),X76),X31)))=hAPP(hAPP(c_List_Omap(tc_prod(X7,X126),X4),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X126,X4),hAPP(hAPP(c_COMBB(tc_fun(X126,tc_prod(X7,X49)),tc_fun(X126,X4),X7),hAPP(c_COMBB(tc_prod(X7,X49),X4,X126),X22)),hAPP(hAPP(c_COMBC(X7,tc_fun(X126,X49),tc_fun(X126,tc_prod(X7,X49))),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_prod(X7,X49)),tc_fun(tc_fun(X126,X49),tc_fun(X126,tc_prod(X7,X49))),X7),c_COMBB(X49,tc_prod(X7,X49),X126)),c_Product__Type_OPair(X7,X49))),X76)))),hAPP(hAPP(c_List_Ozip(X7,X126),X32),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__zip__map2)). 4.05/4.28 fof(fact_min__weak__def, axiom, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool))))=c_FunDef_Omin__weak, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__weak__def)). 4.05/4.28 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)). 4.05/4.28 fof(fact_map__of__map, axiom, ![X32, X22, X49, X7, X4]:hAPP(c_Map_Omap__of(X4,X7),hAPP(hAPP(c_List_Omap(tc_prod(X4,X49),tc_prod(X4,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X49,tc_prod(X4,X7)),hAPP(hAPP(c_COMBC(X4,tc_fun(X49,X7),tc_fun(X49,tc_prod(X4,X7))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(tc_fun(X49,X7),tc_fun(X49,tc_prod(X4,X7))),X4),c_COMBB(X7,tc_prod(X4,X7),X49)),c_Product__Type_OPair(X4,X7))),X22))),X32))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X49),tc_Option_Ooption(X7),X4,hAPP(c_Option_Omap(X49,X7),X22)),hAPP(c_Map_Omap__of(X4,X49),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__map)). 4.05/4.28 fof(fact_zip__map2, axiom, ![X31, X22, X49, X32, X7, X4]:hAPP(hAPP(c_List_Omap(tc_prod(X4,X49),tc_prod(X4,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X49,tc_prod(X4,X7)),hAPP(hAPP(c_COMBC(X4,tc_fun(X49,X7),tc_fun(X49,tc_prod(X4,X7))),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(tc_fun(X49,X7),tc_fun(X49,tc_prod(X4,X7))),X4),c_COMBB(X7,tc_prod(X4,X7),X49)),c_Product__Type_OPair(X4,X7))),X22))),hAPP(hAPP(c_List_Ozip(X4,X49),X32),X31))=hAPP(hAPP(c_List_Ozip(X4,X7),X32),hAPP(hAPP(c_List_Omap(X49,X7),X22),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__map2)). 4.05/4.28 fof(fact_inj__graph, axiom, ![X7, X4]:c_Fun_Oinj__on(tc_fun(X4,X7),tc_fun(tc_prod(X4,X7),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X4,X7)),c_Set_OCollect(tc_prod(X4,X7))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X7,tc_HOL_Obool)),tc_fun(tc_prod(X4,X7),tc_HOL_Obool),tc_fun(X4,X7)),c_Product__Type_Oprod_Oprod__case(X4,X7,tc_HOL_Obool)),hAPP(c_COMBB(X7,tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_COMBC(X7,X7,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X4,X7),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__graph)). 4.05/4.28 fof(fact_neg__bind__def, axiom, ![X95, X96, X97, X22, X39, X4, X7]:hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X7,X4,X39,X22),X97),X96),X95)=c_New__DSequence_Oneg__bind(X7,X4,hAPP(hAPP(hAPP(X39,X97),X96),X95),hAPP(hAPP(c_COMBC(X7,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)))),hAPP(hAPP(c_COMBC(X7,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4))))),hAPP(hAPP(c_COMBC(X7,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)))))),X22),X97)),X96)),X95)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__bind__def)). 4.05/4.28 fof(fact_sublists_Osimps_I2_J, axiom, ![X32, X9, X4]:hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X4)),tc_List_Olist(tc_List_Olist(X4))),c_Enum_Osublists(X4,X32)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(X4)),tc_List_Olist(tc_List_Olist(X4)),tc_List_Olist(tc_List_Olist(X4))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(X4)),tc_fun(tc_List_Olist(tc_List_Olist(X4)),tc_List_Olist(tc_List_Olist(X4))),tc_List_Olist(tc_List_Olist(X4))),c_List_Oappend(tc_List_Olist(X4))),hAPP(c_List_Omap(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(c_List_Olist_OCons(X4),X9)))),c_COMBI(tc_List_Olist(tc_List_Olist(X4)))))=c_Enum_Osublists(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublists_Osimps_I2_J)). 4.05/4.28 fof(fact_New__Random__Sequence_Oneg__decr__bind__def, axiom, ![X95, X96, X97, X22, X39, X4, X7]:c_New__Random__Sequence_Oneg__decr__bind(X7,X4,X39,X22,X97,X96,X95)=c_New__DSequence_Oneg__decr__bind(X7,X4,hAPP(hAPP(hAPP(X39,X97),X96),X95),hAPP(hAPP(c_COMBC(X7,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)))),hAPP(hAPP(c_COMBC(X7,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4))))),hAPP(hAPP(c_COMBC(X7,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)))))),X22),X97)),X96)),X95)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__Random__Sequence_Oneg__decr__bind__def)). 4.05/4.28 fof(fact_map__zip__map, axiom, ![X31, X32, X76, X126, X22, X4, X49, X7]:hAPP(hAPP(c_List_Omap(tc_prod(X126,X49),X4),hAPP(c_Product__Type_Oprod_Oprod__case(X126,X49,X4),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_prod(X7,X49)),tc_fun(X49,X4),X126),hAPP(c_COMBB(tc_prod(X7,X49),X4,X49),X22)),hAPP(hAPP(c_COMBB(X7,tc_fun(X49,tc_prod(X7,X49)),X126),c_Product__Type_OPair(X7,X49)),X76)))),hAPP(hAPP(c_List_Ozip(X126,X49),X32),X31))=hAPP(hAPP(c_List_Omap(tc_prod(X7,X49),X4),X22),hAPP(hAPP(c_List_Ozip(X7,X49),hAPP(hAPP(c_List_Omap(X126,X7),X76),X32)),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__zip__map)). 4.05/4.28 fof(fact_pos__bind__def, axiom, ![X95, X96, X97, X22, X39, X4, X7]:hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X7,X4,X39,X22),X97),X96),X95)=c_New__DSequence_Opos__bind(X7,X4,hAPP(hAPP(hAPP(X39,X97),X96),X95),hAPP(hAPP(c_COMBC(X7,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4))),hAPP(hAPP(c_COMBC(X7,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4)))),hAPP(hAPP(c_COMBC(X7,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4))))),X22),X97)),X96)),X95)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__bind__def)). 4.05/4.28 fof(fact__02, axiom, ![X192, X148, X7, X4]:c_Lazy__Sequence_Oproduct(X4,X7,X148,X192)=hAPP(c_Lazy__Sequence_Obind(X4,tc_prod(X4,X7),X148),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X4,X7))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X4,X7)),X4),c_Lazy__Sequence_Obind(X7,tc_prod(X4,X7),X192)),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X4,X7))),X4),hAPP(c_COMBB(tc_prod(X4,X7),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X4,X7)),X7),c_Lazy__Sequence_Osingle(tc_prod(X4,X7)))),c_Product__Type_OPair(X4,X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact__02)). 4.05/4.28 fof(fact_New__Random__Sequence_Opos__decr__bind__def, axiom, ![X95, X96, X97, X22, X39, X4, X7]:c_New__Random__Sequence_Opos__decr__bind(X7,X4,X39,X22,X97,X96,X95)=c_New__DSequence_Opos__decr__bind(X7,X4,hAPP(hAPP(hAPP(X39,X97),X96),X95),hAPP(hAPP(c_COMBC(X7,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4))),hAPP(hAPP(c_COMBC(X7,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4)))),hAPP(hAPP(c_COMBC(X7,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4))))),X22),X97)),X96)),X95)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__Random__Sequence_Opos__decr__bind__def)). 4.05/4.28 fof(fact_rel__comp__UNION__distrib2, axiom, ![X40, X18, X41, X126, X7, X49, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X126,tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X41),hAPP(hAPP(c_COMBC(X126,tc_fun(tc_prod(X49,X7),tc_HOL_Obool),tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X4,X49),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X49,X7),tc_HOL_Obool),tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X126),c_Relation_Orel__comp(X4,X49,X7)),X18)),X40))=hAPP(hAPP(c_Relation_Orel__comp(X4,X49,X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X126,tc_fun(tc_prod(X4,X49),tc_HOL_Obool)),X41),X18)),X40), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__UNION__distrib2)). 4.05/4.28 fof(fact_map__filter__map__filter, axiom, ![X32, X56, X22, X4, X7]:hAPP(hAPP(c_List_Omap(X7,X4),X22),hAPP(c_List_Ofilter(X7,X56),X32))=c_List_Omap__filter(X7,X4,hAPP(hAPP(c_COMBC(X7,tc_Option_Ooption(X4),tc_Option_Ooption(X4)),hAPP(hAPP(c_COMBS(X7,tc_Option_Ooption(X4),tc_fun(tc_Option_Ooption(X4),tc_Option_Ooption(X4))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X4),tc_fun(tc_Option_Ooption(X4),tc_Option_Ooption(X4))),X7),c_If(tc_Option_Ooption(X4))),X56)),hAPP(hAPP(c_COMBB(X4,tc_Option_Ooption(X4),X7),c_Option_Ooption_OSome(X4)),X22))),c_Option_Ooption_ONone(X4)),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__filter__map__filter)). 4.05/4.28 fof(fact_Id__on__def_H, axiom, ![X3, X4]:c_Relation_OId__on(X4,X3)=hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X4,tc_HOL_Obool)),X4),c_COMBC(X4,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj)),c_fequal))),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__def_H)). 4.05/4.28 fof(fact_insert__times__insert, axiom, ![X6, X25, X3, X26, X7, X4]:hAPP(hAPP(c_Set_Oinsert(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X26),X25)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),hAPP(hAPP(c_Set_Oinsert(X7),X25),X6)))),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),hAPP(hAPP(c_Set_Oinsert(X4),X26),X3)),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),X6))))=hAPP(hAPP(c_Product__Type_OSigma(X4,X7),hAPP(hAPP(c_Set_Oinsert(X4),X26),X3)),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),hAPP(hAPP(c_Set_Oinsert(X7),X25),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__times__insert)). 4.05/4.28 fof(fact_measures__def, axiom, ![X278, X4]:hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),X4),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(X4,tc_List_Olist(tc_fun(X4,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(X4,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),X4),c_List_Omap(tc_fun(X4,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(X4,tc_Nat_Onat),X4,tc_Nat_Onat),c_COMBI(tc_fun(X4,tc_Nat_Onat))))),X278))=c_List_Omeasures(X4,X278), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_measures__def)). 4.05/4.28 fof(fact_select__weight__def, axiom, ![X32, X4]:hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X4),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X4)),X32)))),hAPP(hAPP(c_COMBB(X4,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X4,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X4,X32)))=c_Random_Oselect__weight(X4,X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__weight__def)). 4.05/4.28 fof(fact_INT__extend__simps_I9_J, axiom, ![X8, X6, X49, X3, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X49,tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X49,tc_HOL_Obool)),X3),X6)),X8)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X7,tc_fun(X49,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X49,tc_HOL_Obool),tc_fun(tc_fun(X49,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),X7),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X49,tc_fun(X4,tc_HOL_Obool))),X6)),X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__extend__simps_I9_J)). 4.05/4.28 fof(fact_fun__left__comm__idem__remove, axiom, ![X4]:c_Finite__Set_Ofun__left__comm__idem(X4,tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem__remove)). 4.05/4.28 fof(fact_INT__extend__simps_I6_J, axiom, ![X6, X3, X8, X7, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBC(X7,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X7),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool))),X3)),X6))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X8),X3)),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__extend__simps_I6_J)). 4.05/4.28 fof(fact_UN__extend__simps_I6_J, axiom, ![X6, X3, X8, X7, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBC(X7,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X7),c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool))),X3)),X6))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X8),X3)),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__extend__simps_I6_J)). 4.05/4.28 fof(fact_UN__extend__simps_I4_J, axiom, ![X6, X3, X8, X7, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBC(X7,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X7),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool))),X3)),X6))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X8),X3)),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__extend__simps_I4_J)). 4.05/4.28 fof(fact_UN__Pow__subset, axiom, ![X6, X3, X7, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),X7),c_Set_OPow(X4)),X6))),hAPP(c_Set_OPow(X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__Pow__subset)). 4.05/4.28 fof(fact_swap__product, axiom, ![X6, X3, X4, X7]:hAPP(c_Set_Oimage(tc_prod(X7,X4),tc_prod(X4,X7),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X4,tc_prod(X4,X7)),hAPP(c_COMBC(X4,X7,tc_prod(X4,X7)),c_Product__Type_OPair(X4,X7)))),hAPP(hAPP(c_Product__Type_OSigma(X7,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X7),X6)))=hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X6),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_swap__product)). 4.05/4.28 fof(fact_zip__map1, axiom, ![X31, X32, X22, X49, X7, X4]:hAPP(hAPP(c_List_Ozip(X4,X7),hAPP(hAPP(c_List_Omap(X49,X4),X22),X32)),X31)=hAPP(hAPP(c_List_Omap(tc_prod(X49,X7),tc_prod(X4,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X49,X7,tc_prod(X4,X7)),hAPP(hAPP(c_COMBB(X4,tc_fun(X7,tc_prod(X4,X7)),X49),c_Product__Type_OPair(X4,X7)),X22))),hAPP(hAPP(c_List_Ozip(X49,X7),X32),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__map1)). 4.05/4.28 fof(fact_rotate1__def, axiom, ![X32, X4]:hAPP(c_List_Olist_Olist__case(tc_List_Olist(X4),X4,c_List_Olist_ONil(X4),hAPP(hAPP(c_COMBB(tc_List_Olist(X4),tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),X4),hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Oappend(X4))),hAPP(hAPP(c_COMBC(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)),c_List_Olist_ONil(X4)))),X32)=hAPP(c_List_Orotate1(X4),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rotate1__def)). 4.05/4.28 fof(fact_Image__INT__subset, axiom, ![X6, X3, X49, X18, X7, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X4,X18),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X49,tc_fun(X7,tc_HOL_Obool)),X3),X6))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X49,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X49),c_Relation_OImage(X7,X4,X18)),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__INT__subset)). 4.05/4.28 fof(fact_zip__append2, axiom, ![X175, X59, X45, X7, X4]:hAPP(hAPP(c_List_Oappend(tc_prod(X4,X7)),hAPP(hAPP(c_List_Ozip(X4,X7),hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X59)),X45)),X59)),hAPP(hAPP(c_List_Ozip(X4,X7),hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X59)),X45)),X175))=hAPP(hAPP(c_List_Ozip(X4,X7),X45),hAPP(hAPP(c_List_Oappend(X7),X59),X175)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__append2)). 4.05/4.28 fof(fact_zip__append1, axiom, ![X175, X59, X45, X7, X4]:hAPP(hAPP(c_List_Oappend(tc_prod(X4,X7)),hAPP(hAPP(c_List_Ozip(X4,X7),X45),hAPP(hAPP(c_List_Otake(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),X175))),hAPP(hAPP(c_List_Ozip(X4,X7),X59),hAPP(hAPP(c_List_Odrop(X7),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),X175)))=hAPP(hAPP(c_List_Ozip(X4,X7),hAPP(hAPP(c_List_Oappend(X4),X45),X59)),X175), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__append1)). 4.05/4.28 fof(fact_foldl__map, axiom, ![X32, X22, X49, X26, X76, X7, X4]:hAPP(c_List_Ofoldl(X4,X49,hAPP(hAPP(c_COMBC(X4,tc_fun(X49,X7),tc_fun(X49,X4)),hAPP(hAPP(c_COMBB(tc_fun(X7,X4),tc_fun(tc_fun(X49,X7),tc_fun(X49,X4)),X4),c_COMBB(X7,X4,X49)),X76)),X22),X26),X32)=hAPP(c_List_Ofoldl(X4,X7,X76,X26),hAPP(hAPP(c_List_Omap(X49,X7),X22),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__map)). 4.05/4.28 fof(fact_rel__comp__UNION__distrib, axiom, ![X18, X41, X126, X40, X7, X49, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X126,tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X41),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X49,X7),tc_HOL_Obool),tc_fun(tc_prod(X4,X7),tc_HOL_Obool),X126),hAPP(c_Relation_Orel__comp(X4,X49,X7),X40)),X18))=hAPP(hAPP(c_Relation_Orel__comp(X4,X49,X7),X40),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X126,tc_fun(tc_prod(X49,X7),tc_HOL_Obool)),X41),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__UNION__distrib)). 4.05/4.28 fof(fact_split__comp__eq, axiom, ![X76, X22, X126, X49, X7, X4]:hAPP(hAPP(c_COMBS(tc_prod(X4,X7),X7,X49),hAPP(hAPP(c_COMBB(X126,tc_fun(X7,X49),tc_prod(X4,X7)),X22),hAPP(hAPP(c_COMBB(X4,X126,tc_prod(X4,X7)),X76),c_Product__Type_Ofst(X4,X7)))),c_Product__Type_Osnd(X4,X7))=hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,X49),hAPP(hAPP(c_COMBB(X126,tc_fun(X7,X49),X4),X22),X76)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__comp__eq)). 4.05/4.28 fof(fact_split__twice, axiom, ![X51, X76, X178, X126, X22, X4, X49, X7]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X126,X178,X4),hAPP(hAPP(c_COMBB(tc_fun(X178,tc_prod(X7,X49)),tc_fun(X178,X4),X126),hAPP(c_COMBB(tc_prod(X7,X49),X4,X178),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X49,X4),X22))),X76)),X51)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X49,X4),X22),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X126,X178,tc_prod(X7,X49)),X76),X51)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__twice)). 4.05/4.28 fof(fact_restrict__upd__same, axiom, ![X17, X9, X21, X7, X4]:c_Map_Orestrict__map(X4,X7,X21,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=c_Map_Orestrict__map(X4,X7,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X21),X9),hAPP(c_Option_Ooption_OSome(X7),X17)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__upd__same)). 4.05/4.28 fof(fact_Sigma__Union, axiom, ![X6, X156, X7, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X156),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_fun(X7,tc_HOL_Obool)),tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),c_Product__Type_OSigma(X4,X7)),X6))=hAPP(hAPP(c_Product__Type_OSigma(X4,X7),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X156)),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Union)). 4.05/4.28 fof(fact_list__update_Osimps_I2_J, axiom, ![X64, X37, X32, X9, X4]:c_Nat_Onat_Onat__case(tc_List_Olist(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X64),X32),hAPP(hAPP(c_COMBB(tc_List_Olist(X4),tc_List_Olist(X4),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X4),X9)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X4,tc_List_Olist(X4)),c_List_Olist__update(X4,X32)),X64)),X37)=hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)),X37),X64), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update_Osimps_I2_J)). 4.05/4.28 fof(fact_INT__extend__simps_I8_J, axiom, ![X6, X3, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X3)),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X7,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool))),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__extend__simps_I8_J)). 4.05/4.28 fof(fact_UN__simps_I8_J, axiom, ![X6, X3, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),X3)),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X7,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_fun(X4,tc_HOL_Obool)),tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool))),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I8_J)). 4.05/4.28 fof(fact_wmin__emptyI, axiom, ![X156]: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)),X156),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wmin__emptyI)). 4.05/4.28 fof(fact_Union__Int__subset, axiom, ![X6, X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X3),X6))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X3)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__Int__subset)). 4.05/4.28 fof(fact_Inter__Un__subset, axiom, ![X6, X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X3)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X6))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__Un__subset)). 4.05/4.28 fof(fact_converse__INTER, axiom, ![X18, X86, X49, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X49,tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X86),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X7,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X7),tc_HOL_Obool),X49),c_Relation_Oconverse(X7,X4)),X18))=hAPP(c_Relation_Oconverse(X7,X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X49,tc_fun(tc_prod(X7,X4),tc_HOL_Obool)),X86),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__INTER)). 4.05/4.28 fof(fact_converse__UNION, axiom, ![X18, X86, X49, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X86),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X7,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X7),tc_HOL_Obool),X49),c_Relation_Oconverse(X7,X4)),X18))=hAPP(c_Relation_Oconverse(X7,X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,tc_fun(tc_prod(X7,X4),tc_HOL_Obool)),X86),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__UNION)). 4.05/4.28 fof(fact_image__diff__subset, axiom, ![X6, X3, X22, X7, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X4,X22),X3)),hAPP(c_Set_Oimage(X7,X4,X22),X6))),hAPP(c_Set_Oimage(X7,X4,X22),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7,tc_HOL_Obool)),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__diff__subset)). 4.05/4.28 fof(fact_Image__Int__subset, axiom, ![X6, X3, X39, X7, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X4,X39),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X3),X6))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X4,X39),X3)),hAPP(c_Relation_OImage(X7,X4,X39),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__Int__subset)). 4.05/4.28 fof(fact_image__Int__subset, axiom, ![X6, X3, X22, X7, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X4,X22),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X3),X6))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X7,X4,X22),X3)),hAPP(c_Set_Oimage(X7,X4,X22),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Int__subset)). 4.05/4.28 fof(fact_rtrancl__is__UN__rel__pow, axiom, ![X39, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X4,X4),tc_HOL_Obool),tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool)),X39))=c_Transitive__Closure_Ortrancl(X4,X39), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__is__UN__rel__pow)). 4.05/4.28 fof(fact_take__Cons, axiom, ![X32, X9, X20, X4]:c_Nat_Onat_Onat__case(tc_List_Olist(X4),c_List_Olist_ONil(X4),hAPP(hAPP(c_COMBB(tc_List_Olist(X4),tc_List_Olist(X4),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X4),X9)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Otake(X4)),X32)),X20)=hAPP(hAPP(c_List_Otake(X4),X20),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Cons)). 4.05/4.28 fof(fact_tl__append, axiom, ![X31, X32, X4]:hAPP(c_List_Otl(X4),hAPP(hAPP(c_List_Oappend(X4),X32),X31))=hAPP(c_List_Olist_Olist__case(tc_List_Olist(X4),X4,hAPP(c_List_Otl(X4),X31),hAPP(c_COMBK(tc_fun(tc_List_Olist(X4),tc_List_Olist(X4)),X4),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Oappend(X4)),X31))),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl__append)). 4.05/4.28 fof(fact_Ex__inj__on__UNION__Sigma, axiom, ![X3, X41, X7, X4]:?[X160]:(c_Fun_Oinj__on(X4,tc_prod(X7,X4),X160,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X41),X3))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7,X4),tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,tc_prod(X7,X4),X160),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X41),X3))),hAPP(hAPP(c_Product__Type_OSigma(X7,X4),X41),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Ex__inj__on__UNION__Sigma)). 4.05/4.28 fof(fact_Range__Int__subset, axiom, ![X6, X3, X7, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ORange(X7,X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X4),tc_HOL_Obool)),X3),X6))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ORange(X7,X4),X3)),hAPP(c_Relation_ORange(X7,X4),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Int__subset)). 4.05/4.28 fof(fact_Domain__Int__subset, axiom, ![X6, X3, X7, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X4,X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X3),X6))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X4,X7),X3)),hAPP(c_Relation_ODomain(X4,X7),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Int__subset)). 4.05/4.28 fof(fact_Range__Diff__subset, axiom, ![X6, X3, X7, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ORange(X7,X4),X3)),hAPP(c_Relation_ORange(X7,X4),X6))),hAPP(c_Relation_ORange(X7,X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X7,X4),tc_HOL_Obool)),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Diff__subset)). 4.05/4.28 fof(fact_Int__Union2, axiom, ![X3, X6, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X6),hAPP(hAPP(c_COMBC(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool))),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X6)),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Union2)). 4.05/4.28 fof(fact_Domain__Diff__subset, axiom, ![X6, X3, X7, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X4,X7),X3)),hAPP(c_Relation_ODomain(X4,X7),X6))),hAPP(c_Relation_ODomain(X4,X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Diff__subset)). 4.05/4.28 fof(fact_rtrancl__Un__subset, axiom, ![X86, X39, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X39)),c_Transitive__Closure_Ortrancl(X4,X86))),c_Transitive__Closure_Ortrancl(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X39),X86)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__Un__subset)). 4.05/4.28 fof(fact_Compl__Times__UNIV2, axiom, ![X3, X7, X4]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))))=hAPP(hAPP(c_Product__Type_OSigma(X4,X7),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X3)),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__Times__UNIV2)). 4.05/4.28 fof(fact_Compl__Times__UNIV1, axiom, ![X3, X7, X4]:hAPP(hAPP(c_Product__Type_OSigma(X4,X7),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X3)))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__Times__UNIV1)). 4.05/4.28 fof(fact_INT__simps_I7_J, axiom, ![X6, X3, X8, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X7),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3)),X6))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X8),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__simps_I7_J)). 4.05/4.28 fof(fact_Eps__split, axiom, ![X56, X7, X4]:c_Hilbert__Choice_OEps(tc_prod(X4,X7),hAPP(hAPP(c_COMBS(tc_prod(X4,X7),X7,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X4,tc_fun(X7,tc_HOL_Obool),tc_prod(X4,X7)),X56),c_Product__Type_Ofst(X4,X7))),c_Product__Type_Osnd(X4,X7)))=c_Hilbert__Choice_OEps(tc_prod(X4,X7),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_HOL_Obool),X56)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Eps__split)). 4.05/4.28 fof(fact_UN__extend__simps_I5_J, axiom, ![X6, X8, X7, X3, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X7),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3)),X6))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X8),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__extend__simps_I5_J)). 4.05/4.28 fof(fact_UN__simps_I7_J, axiom, ![X6, X3, X8, X4, X7]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X8),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X7),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3)),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__simps_I7_J)). 4.05/4.28 fof(fact_update__zip, axiom, ![X270, X46, X59, X45, X7, X4]:hAPP(hAPP(c_List_Ozip(X4,X7),hAPP(hAPP(c_List_Olist__update(X4,X45),X46),hAPP(c_Product__Type_Ofst(X4,X7),X270))),hAPP(hAPP(c_List_Olist__update(X7,X59),X46),hAPP(c_Product__Type_Osnd(X4,X7),X270)))=hAPP(hAPP(c_List_Olist__update(tc_prod(X4,X7),hAPP(hAPP(c_List_Ozip(X4,X7),X45),X59)),X46),X270), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_update__zip)). 4.05/4.28 fof(fact_Un__Pow__subset, axiom, ![X6, X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X4),X3)),hAPP(c_Set_OPow(X4),X6))),hAPP(c_Set_OPow(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Pow__subset)). 4.05/4.28 fof(fact_rel__comp__distrib2, axiom, ![X39, X105, X86, X7, X49, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X49,X7),X86),X39)),hAPP(hAPP(c_Relation_Orel__comp(X4,X49,X7),X105),X39))=hAPP(hAPP(c_Relation_Orel__comp(X4,X49,X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X49),tc_HOL_Obool)),X86),X105)),X39), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__distrib2)). 4.05/4.28 fof(fact_rel__comp__distrib, axiom, ![X105, X86, X39, X7, X49, X4]:hAPP(hAPP(c_Relation_Orel__comp(X4,X49,X7),X39),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X49,X7),tc_HOL_Obool)),X86),X105))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4,X49,X7),X39),X86)),hAPP(hAPP(c_Relation_Orel__comp(X4,X49,X7),X39),X105)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__distrib)). 4.05/4.28 fof(fact_UN__Un, axiom, ![X54, X6, X3, X4, X7]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),X54)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X6),X54))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3),X6)),X54), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__Un)). 4.05/4.28 fof(fact_INT__Un, axiom, ![X54, X6, X3, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3),X6)),X54)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X3),X54)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X6),X54)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__Un)). 4.05/4.28 fof(fact_zdiv__zmult1__eq, axiom, ![X10, X12, X11]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12),X10))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X10))),X10))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X12)),X10), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zmult1__eq)). 4.05/4.28 fof(fact_div__mult1__eq, axiom, ![X10, X12, X11]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X12)),X10)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X12),X10))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X12,X10))),X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult1__eq)). 4.05/4.28 fof(fact_Pow__INT__eq, axiom, ![X6, X3, X7, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),X7),c_Set_OPow(X4)),X6))=hAPP(c_Set_OPow(X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__INT__eq)). 4.05/4.28 fof(fact_map__filter__simps_I1_J, axiom, ![X32, X9, X22, X4, X7]:c_List_Omap__filter(X7,X4,X22,hAPP(hAPP(c_List_Olist_OCons(X7),X9),X32))=hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(X4),X4,c_List_Omap__filter(X7,X4,X22,X32),hAPP(hAPP(c_COMBC(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)),c_List_Omap__filter(X7,X4,X22,X32))),hAPP(X22,X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__filter__simps_I1_J)). 4.05/4.28 fof(fact_Compl__INT, axiom, ![X6, X3, X7, X4]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X7),c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool))),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__INT)). 4.05/4.28 fof(fact_Compl__UN, axiom, ![X6, X3, X7, X4]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X7),c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool))),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__UN)). 4.05/4.28 fof(fact_rel__pow__add, axiom, ![X39, X20, X21, X4]:hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20)),X39)=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X21),X39)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X20),X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__add)). 4.05/4.28 fof(fact_map__pair_Ocomp, axiom, ![X37, X48, X76, X22, X7, X4, X126, X49, X177, X178]:c_Product__Type_Omap__pair(X4,X49,X7,X126,hAPP(c_Fun_Ocomp(X178,X49,X4,X22),X48),hAPP(c_Fun_Ocomp(X177,X126,X7,X76),X37))=hAPP(c_Fun_Ocomp(tc_prod(X178,X177),tc_prod(X49,X126),tc_prod(X4,X7),c_Product__Type_Omap__pair(X178,X49,X177,X126,X22,X76)),c_Product__Type_Omap__pair(X4,X178,X7,X177,X48,X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair_Ocomp)). 4.05/4.28 fof(fact_select__weigth__drop__zero, axiom, ![X32, X4]:c_Random_Oselect__weight(X4,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X4),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X4)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X32))=c_Random_Oselect__weight(X4,X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__weigth__drop__zero)). 4.05/4.28 fof(fact_pick__drop__zero, axiom, ![X32, X4]:c_Random_Opick(X4,X32)=c_Random_Opick(X4,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X4),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X4)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pick__drop__zero)). 4.05/4.28 fof(fact_Pow__insert, axiom, ![X3, X26, X4]:hAPP(c_Set_OPow(X4),hAPP(hAPP(c_Set_Oinsert(X4),X26),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X4),X3)),hAPP(c_Set_Oimage(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),hAPP(c_Set_Oinsert(X4),X26)),hAPP(c_Set_OPow(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__insert)). 4.05/4.28 fof(fact_INT__extend__simps_I5_J, axiom, ![X6, X8, X7, X26, X4]:hAPP(hAPP(c_Set_Oinsert(X4),X26),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X8),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X8),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X7),hAPP(c_Set_Oinsert(X4),X26)),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__extend__simps_I5_J)). 4.05/4.28 fof(fact_map__of_Osimps_I2_J, axiom, ![X113, X51, X7, X4]:hAPP(c_Map_Omap__of(X4,X7),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X4,X7)),X51),X113))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),hAPP(c_Map_Omap__of(X4,X7),X113)),hAPP(c_Product__Type_Ofst(X4,X7),X51)),hAPP(c_Option_Ooption_OSome(X7),hAPP(c_Product__Type_Osnd(X4,X7),X51))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of_Osimps_I2_J)). 4.05/4.28 fof(fact_Image__UN, axiom, ![X6, X3, X49, X18, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X49),c_Relation_OImage(X7,X4,X18)),X6))=hAPP(c_Relation_OImage(X7,X4,X18),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,tc_fun(X7,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__UN)). 4.05/4.28 fof(fact_image__UN, axiom, ![X6, X3, X49, X22, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X49),c_Set_Oimage(X7,X4,X22)),X6))=hAPP(c_Set_Oimage(X7,X4,X22),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X49,tc_fun(X7,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__UN)). 4.05/4.28 fof(fact_Un__Diff, axiom, ![X8, X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X8)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X6),X8))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)),X8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Diff)). 4.05/4.28 fof(fact_Int__Un__distrib2, axiom, ![X3, X8, X6, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X6),X8)),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X6),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X8),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Un__distrib2)). 4.05/4.28 fof(fact_Un__Int__distrib2, axiom, ![X3, X8, X6, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X6),X8)),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X6),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X8),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Int__distrib2)). 4.05/4.28 fof(fact_Int__Un__distrib, axiom, ![X8, X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X8))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X6),X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__Un__distrib)). 4.05/4.28 fof(fact_Diff__Int, axiom, ![X8, X6, X3, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X6),X8))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Int)). 4.05/4.28 fof(fact_Un__Int__distrib, axiom, ![X8, X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X6),X8))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Int__distrib)). 4.05/4.28 fof(fact_dom__option__map, axiom, ![X21, X22, X49, X7, X4]:c_Map_Odom(X4,X7,hAPP(hAPP(c_COMBS(X4,tc_Option_Ooption(X49),tc_Option_Ooption(X7)),hAPP(hAPP(c_COMBB(tc_fun(X49,X7),tc_fun(tc_Option_Ooption(X49),tc_Option_Ooption(X7)),X4),c_Option_Omap(X49,X7)),X22)),X21))=c_Map_Odom(X4,X49,X21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__option__map)). 4.05/4.28 fof(fact_Diff__insert, axiom, ![X6, X26, X3, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),X6))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__insert)). 4.05/4.28 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J, axiom, ![X6, X3]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X3),X6)=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)),X3)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J)). 4.05/4.28 fof(fact_Sigma__Int__distrib1, axiom, ![X8, X55, X41, X7, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X41),X8)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X55),X8))=hAPP(hAPP(c_Product__Type_OSigma(X4,X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X41),X55)),X8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Int__distrib1)). 4.05/4.28 fof(fact_Sigma__Diff__distrib1, axiom, ![X8, X55, X41, X7, X4]:hAPP(hAPP(c_Product__Type_OSigma(X4,X7),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X41),X55)),X8)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X41),X8)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X55),X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Diff__distrib1)). 4.05/4.28 fof(fact_Sigma__Un__distrib1, axiom, ![X8, X55, X41, X7, X4]:hAPP(hAPP(c_Product__Type_OSigma(X4,X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X41),X55)),X8)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X41),X8)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X55),X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__Un__distrib1)). 4.05/4.28 fof(fact_product_Osimps_I2_J, axiom, ![X31, X32, X9, X7, X4]:hAPP(hAPP(c_List_Oappend(tc_prod(X4,X7)),hAPP(hAPP(c_List_Omap(X7,tc_prod(X4,X7)),hAPP(c_Product__Type_OPair(X4,X7),X9)),X31)),c_Enum_Oproduct(X4,X7,X32,X31))=c_Enum_Oproduct(X4,X7,hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32),X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_product_Osimps_I2_J)). 4.05/4.28 fof(fact_pair__leq__def, axiom, 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)))=c_FunDef_Opair__leq, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__leq__def)). 4.05/4.28 fof(fact_drop__append, axiom, ![X59, X45, X5, X4]:hAPP(hAPP(c_List_Odrop(X4),X5),hAPP(hAPP(c_List_Oappend(X4),X45),X59))=hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Odrop(X4),X5),X45)),hAPP(hAPP(c_List_Odrop(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45))),X59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__append)). 4.05/4.28 fof(fact_take__append, axiom, ![X59, X45, X5, X4]:hAPP(hAPP(c_List_Otake(X4),X5),hAPP(hAPP(c_List_Oappend(X4),X45),X59))=hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Otake(X4),X5),X45)),hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45))),X59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__append)). 4.05/4.28 fof(fact_neg__map__def, axiom, ![X56, X22, X4, X7]:c_New__Random__Sequence_Oneg__bind(X7,X4,X56,hAPP(c_Fun_Ocomp(X4,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)))))),X7,c_New__Random__Sequence_Oneg__single(X4)),X22))=c_New__Random__Sequence_Oneg__map(X7,X4,X22,X56), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__map__def)). 4.05/4.28 fof(fact_split__eta, axiom, ![X22, X49, X7, X4]:hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,X49),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_prod(X4,X7)),tc_fun(X7,X49),X4),hAPP(c_COMBB(tc_prod(X4,X7),X49,X7),X22)),c_Product__Type_OPair(X4,X7)))=X22, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__eta)). 4.05/4.28 fof(fact_dom__map__upds, axiom, ![X31, X32, X21, X7, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),X31)),X32))),c_Map_Odom(X4,X7,X21))=c_Map_Odom(X4,X7,c_Map_Omap__upds(X4,X7,X21,X32,X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__map__upds)). 4.05/4.28 fof(fact_pos__map__def, axiom, ![X56, X22, X4, X7]:c_New__Random__Sequence_Opos__bind(X7,X4,X56,hAPP(c_Fun_Ocomp(X4,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4))))),X7,c_New__Random__Sequence_Opos__single(X4)),X22))=c_New__Random__Sequence_Opos__map(X7,X4,X22,X56), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__map__def)). 4.05/4.28 fof(fact_hb__flat_Osimps_I2_J, axiom, ![X292, X143, X4]:c_Lazy__Sequence_Oappend(tc_Option_Ooption(X4),hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)),tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)),c_Lazy__Sequence_Ohit__bound(X4),c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4)))),X143),c_Lazy__Sequence_Ohb__flat(X4,X292))=c_Lazy__Sequence_Ohb__flat(X4,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4))),X143,X292)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hb__flat_Osimps_I2_J)). 4.05/4.28 fof(fact_zip__takeWhile__fst, axiom, ![X31, X32, X56, X7, X4]:c_List_OtakeWhile(tc_prod(X4,X7),hAPP(c_Fun_Ocomp(X4,tc_HOL_Obool,tc_prod(X4,X7),X56),c_Product__Type_Ofst(X4,X7)),hAPP(hAPP(c_List_Ozip(X4,X7),X32),X31))=hAPP(hAPP(c_List_Ozip(X4,X7),c_List_OtakeWhile(X4,X56,X32)),X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__takeWhile__fst)). 4.05/4.28 fof(fact_zip__takeWhile__snd, axiom, ![X31, X56, X32, X7, X4]:hAPP(hAPP(c_List_Ozip(X4,X7),X32),c_List_OtakeWhile(X7,X56,X31))=c_List_OtakeWhile(tc_prod(X4,X7),hAPP(c_Fun_Ocomp(X7,tc_HOL_Obool,tc_prod(X4,X7),X56),c_Product__Type_Osnd(X4,X7)),hAPP(hAPP(c_List_Ozip(X4,X7),X32),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__takeWhile__snd)). 4.05/4.28 fof(fact_drop__Cons, axiom, ![X32, X9, X20, X4]:hAPP(hAPP(c_List_Odrop(X4),X20),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32))=c_Nat_Onat_Onat__case(tc_List_Olist(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Odrop(X4)),X32),X20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Cons)). 4.05/4.28 fof(fact_Un__Image, axiom, ![X3, X86, X39, X4, X7]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X4,X39),X3)),hAPP(c_Relation_OImage(X7,X4,X86),X3))=hAPP(c_Relation_OImage(X7,X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X4),tc_HOL_Obool)),X39),X86)),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Image)). 4.05/4.28 fof(fact_converse__Int, axiom, ![X40, X18, X4, X7]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X7,X4),X18)),hAPP(c_Relation_Oconverse(X7,X4),X40))=hAPP(c_Relation_Oconverse(X7,X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X7,X4),tc_HOL_Obool)),X18),X40)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__Int)). 4.05/4.28 fof(fact_converse__Un, axiom, ![X40, X18, X4, X7]:hAPP(c_Relation_Oconverse(X7,X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X4),tc_HOL_Obool)),X18),X40))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X7,X4),X18)),hAPP(c_Relation_Oconverse(X7,X4),X40)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__Un)). 4.05/4.28 fof(fact_inj__singleton, axiom, ![X4]:c_Fun_Oinj__on(X4,tc_fun(X4,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__singleton)). 4.05/4.28 fof(fact_image__add__int__atLeastLessThan, axiom, ![X115, X60]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X60),X115)=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)),X60)),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),X115),X60))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__add__int__atLeastLessThan)). 4.05/4.28 fof(fact_map__add__upd, axiom, ![X17, X9, X76, X22, X7, X4]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),c_Map_Omap__add(X4,X7,X22,X76)),X9),hAPP(c_Option_Ooption_OSome(X7),X17))=c_Map_Omap__add(X4,X7,X22,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X76),X9),hAPP(c_Option_Ooption_OSome(X7),X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__upd)). 4.05/4.28 fof(fact_list__update__length, axiom, ![X43, X59, X13, X45, X4]:hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Oappend(X4),X45),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X59))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),X43)=hAPP(hAPP(c_List_Oappend(X4),X45),hAPP(hAPP(c_List_Olist_OCons(X4),X43),X59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__length)). 4.05/4.28 fof(fact_Image__Un, axiom, ![X6, X3, X39, X4, X7]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7,X4,X39),X3)),hAPP(c_Relation_OImage(X7,X4,X39),X6))=hAPP(c_Relation_OImage(X7,X4,X39),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__Un)). 4.05/4.28 fof(fact_partition__filter__conv, axiom, ![X32, X22, X4]:hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),hAPP(c_List_Ofilter(X4,X22),X32)),hAPP(c_List_Ofilter(X4,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X4,c_fNot),X22)),X32))=c_List_Opartition(X4,X22,X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition__filter__conv)). 4.05/4.28 fof(fact_pred__nat__def, axiom, hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc)))=c_Wellfounded_Opred__nat, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pred__nat__def)). 4.05/4.28 fof(fact_funpow__add, axiom, ![X22, X20, X21, X4]:hAPP(c_Fun_Ocomp(X4,X4,X4,hAPP(hAPP(c_Nat_Ocompow(X4,X4),X21),X22)),hAPP(hAPP(c_Nat_Ocompow(X4,X4),X20),X22))=hAPP(hAPP(c_Nat_Ocompow(X4,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20)),X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_funpow__add)). 4.05/4.28 fof(fact_product__list__set, axiom, ![X31, X32, X7, X4]:hAPP(c_List_Oset(tc_prod(X4,X7)),c_Enum_Oproduct(X4,X7,X32,X31))=hAPP(hAPP(c_Product__Type_OSigma(X4,X7),hAPP(c_List_Oset(X4),X32)),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),hAPP(c_List_Oset(X7),X31))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_product__list__set)). 4.05/4.28 fof(fact_UN__singleton, axiom, ![X3, X4]:X3=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),c_Set_Oinsert(X4)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__singleton)). 4.05/4.28 fof(fact_card__cartesian__product, axiom, ![X6, X3, X7, X4]:hAPP(c_Finite__Set_Ocard(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OSigma(X4,X7),X3),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),X6)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X3)),hAPP(c_Finite__Set_Ocard(X7),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__cartesian__product)). 4.05/4.28 fof(fact_swap__inj__on, axiom, ![X3, X7, X4]:c_Fun_Oinj__on(tc_prod(X4,X7),tc_prod(X7,X4),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,tc_prod(X7,X4)),hAPP(c_COMBC(X7,X4,tc_prod(X7,X4)),c_Product__Type_OPair(X7,X4))),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_swap__inj__on)). 4.05/4.28 fof(fact_Option_Omap_Ocomp, axiom, ![X76, X22, X4, X7, X49]:hAPP(c_Fun_Ocomp(tc_Option_Ooption(X49),tc_Option_Ooption(X7),tc_Option_Ooption(X4),hAPP(c_Option_Omap(X49,X7),X22)),hAPP(c_Option_Omap(X4,X49),X76))=hAPP(c_Option_Omap(X4,X7),hAPP(c_Fun_Ocomp(X49,X7,X4,X22),X76)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Option_Omap_Ocomp)). 4.05/4.28 fof(fact_map__comp__map, axiom, ![X76, X22, X4, X7, X49]:hAPP(c_Fun_Ocomp(tc_List_Olist(X49),tc_List_Olist(X7),tc_List_Olist(X4),hAPP(c_List_Omap(X49,X7),X22)),hAPP(c_List_Omap(X4,X49),X76))=hAPP(c_List_Omap(X4,X7),hAPP(c_Fun_Ocomp(X49,X7,X4,X22),X76)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__comp__map)). 4.05/4.28 fof(fact_Id__on__subset__Times, axiom, ![X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Relation_OId__on(X4,X3)),hAPP(hAPP(c_Product__Type_OSigma(X4,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__subset__Times)). 4.05/4.28 fof(fact_Domain__Un__eq, axiom, ![X6, X3, X7, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X4,X7),X3)),hAPP(c_Relation_ODomain(X4,X7),X6))=hAPP(c_Relation_ODomain(X4,X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Un__eq)). 4.05/4.28 fof(fact_Range__Un__eq, axiom, ![X6, X3, X4, X7]:hAPP(c_Relation_ORange(X7,X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7,X4),tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ORange(X7,X4),X3)),hAPP(c_Relation_ORange(X7,X4),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Un__eq)). 4.05/4.28 fof(fact_insert__inter__insert, axiom, ![X6, X3, X26, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X4),X26),X3)),hAPP(hAPP(c_Set_Oinsert(X4),X26),X6))=hAPP(hAPP(c_Set_Oinsert(X4),X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__inter__insert)). 4.05/4.28 fof(fact_drop__zip, axiom, ![X59, X45, X5, X7, X4]:hAPP(hAPP(c_List_Odrop(tc_prod(X4,X7)),X5),hAPP(hAPP(c_List_Ozip(X4,X7),X45),X59))=hAPP(hAPP(c_List_Ozip(X4,X7),hAPP(hAPP(c_List_Odrop(X4),X5),X45)),hAPP(hAPP(c_List_Odrop(X7),X5),X59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__zip)). 4.05/4.28 fof(fact_rtrancl__Un__rtrancl, axiom, ![X86, X39, X4]:c_Transitive__Closure_Ortrancl(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X39),X86))=c_Transitive__Closure_Ortrancl(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X39)),c_Transitive__Closure_Ortrancl(X4,X86))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__Un__rtrancl)). 4.05/4.28 fof(fact_converse__meet, axiom, ![X40, X18, X4, X7]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),c_Predicate_Oconversep(X7,X4,X18)),c_Predicate_Oconversep(X7,X4,X40))=c_Predicate_Oconversep(X7,X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_fun(X4,tc_HOL_Obool))),X18),X40)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__meet)). 4.05/4.28 fof(fact_converse__join, axiom, ![X40, X18, X4, X7]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_fun(X7,tc_HOL_Obool))),c_Predicate_Oconversep(X7,X4,X18)),c_Predicate_Oconversep(X7,X4,X40))=c_Predicate_Oconversep(X7,X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_fun(X4,tc_HOL_Obool))),X18),X40)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__join)). 4.05/4.28 fof(fact_set__update__subset__insert, axiom, ![X9, X37, X32, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist__update(X4,X32),X37),X9))),hAPP(hAPP(c_Set_Oinsert(X4),X9),hAPP(c_List_Oset(X4),X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__update__subset__insert)). 4.05/4.28 fof(fact_zadd__int__left, axiom, ![X29, X5, X2]: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),X2),X5))),X29)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5)),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__int__left)). 4.05/4.28 fof(fact_map__upds__def, axiom, ![X31, X32, X21, X7, X4]:c_Map_Omap__add(X4,X7,X21,hAPP(c_Map_Omap__of(X4,X7),hAPP(c_List_Orev(tc_prod(X4,X7)),hAPP(hAPP(c_List_Ozip(X4,X7),X32),X31))))=c_Map_Omap__upds(X4,X7,X21,X32,X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__def)). 4.05/4.28 fof(fact_UNIV__Times__UNIV, axiom, ![X7, X4]:hAPP(hAPP(c_Product__Type_OSigma(X4,X7),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X4),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))=c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__Times__UNIV)). 4.05/4.28 fof(fact_filter__map, axiom, ![X32, X22, X7, X56, X4]:hAPP(hAPP(c_List_Omap(X7,X4),X22),hAPP(c_List_Ofilter(X7,hAPP(c_Fun_Ocomp(X4,tc_HOL_Obool,X7,X56),X22)),X32))=hAPP(c_List_Ofilter(X4,X56),hAPP(hAPP(c_List_Omap(X7,X4),X22),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__map)). 4.05/4.28 fof(fact_insert__Diff__single, axiom, ![X3, X26, X4]:hAPP(hAPP(c_Set_Oinsert(X4),X26),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))=hAPP(hAPP(c_Set_Oinsert(X4),X26),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__Diff__single)). 4.05/4.28 fof(fact_Range__insert, axiom, ![X18, X25, X26, X4, X7]:hAPP(c_Relation_ORange(X7,X4),hAPP(hAPP(c_Set_Oinsert(tc_prod(X7,X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X4),X26),X25)),X18))=hAPP(hAPP(c_Set_Oinsert(X4),X25),hAPP(c_Relation_ORange(X7,X4),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__insert)). 4.05/4.28 fof(fact_Domain__insert, axiom, ![X18, X25, X26, X7, X4]:hAPP(c_Relation_ODomain(X4,X7),hAPP(hAPP(c_Set_Oinsert(tc_prod(X4,X7)),hAPP(hAPP(c_Product__Type_OPair(X4,X7),X26),X25)),X18))=hAPP(hAPP(c_Set_Oinsert(X4),X26),hAPP(c_Relation_ODomain(X4,X7),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__insert)). 4.05/4.28 fof(fact_listrel_ONil, axiom, ![X18, X4]:hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_List_Olist_ONil(X4))),c_List_Olistrel(X4,X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel_ONil)). 4.05/4.28 fof(fact_rel__pow__0__I, axiom, ![X39, X9, X4]:hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X9),X9)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X39))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__0__I)). 4.05/4.28 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1, axiom, ![X18, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool)),c_List_Olistrel1(X4,c_Transitive__Closure_Ortrancl(X4,X18))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__rtrancl__subset__rtrancl__listrel1)). 4.05/4.28 fof(fact_converse__rel__comp, axiom, ![X40, X18, X49, X4, X7]:hAPP(c_Relation_Oconverse(X7,X4),hAPP(hAPP(c_Relation_Orel__comp(X7,X49,X4),X18),X40))=hAPP(hAPP(c_Relation_Orel__comp(X4,X49,X7),hAPP(c_Relation_Oconverse(X49,X4),X40)),hAPP(c_Relation_Oconverse(X7,X49),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__rel__comp)). 4.05/4.28 fof(fact_Pow__Int__eq, axiom, ![X6, X3, X4]:hAPP(c_Set_OPow(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X4),X3)),hAPP(c_Set_OPow(X4),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__Int__eq)). 4.05/4.28 fof(fact_replicate__app__Cons__same, axiom, ![X45, X13, X5, X4]:hAPP(hAPP(c_List_Oappend(X4),c_List_Oreplicate(X4,X5,X13)),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45))=hAPP(hAPP(c_List_Olist_OCons(X4),X13),hAPP(hAPP(c_List_Oappend(X4),c_List_Oreplicate(X4,X5,X13)),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__app__Cons__same)). 4.05/4.28 fof(fact_rev__take, axiom, ![X45, X46, X4]:hAPP(hAPP(c_List_Odrop(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),X46)),hAPP(c_List_Orev(X4),X45))=hAPP(c_List_Orev(X4),hAPP(hAPP(c_List_Otake(X4),X46),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__take)). 4.05/4.28 fof(fact_rev__drop, axiom, ![X45, X46, X4]:hAPP(c_List_Orev(X4),hAPP(hAPP(c_List_Odrop(X4),X46),X45))=hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),X46)),hAPP(c_List_Orev(X4),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__drop)). 4.05/4.28 fof(fact_splice_Osimps_I3_J, axiom, ![X59, X43, X45, X13, X4]:c_List_Osplice(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45),hAPP(hAPP(c_List_Olist_OCons(X4),X43),X59))=hAPP(hAPP(c_List_Olist_OCons(X4),X13),hAPP(hAPP(c_List_Olist_OCons(X4),X43),c_List_Osplice(X4,X45,X59))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_splice_Osimps_I3_J)). 4.05/4.28 fof(fact_nth__append__length__plus, axiom, ![X5, X59, X45, X4]:hAPP(hAPP(c_List_Onth(X4),X59),X5)=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Oappend(X4),X45),X59)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__append__length__plus)). 4.05/4.28 fof(fact_UNIV__option__conv, axiom, ![X4]:hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(X4)),c_Option_Ooption_ONone(X4)),hAPP(c_Set_Oimage(X4,tc_Option_Ooption(X4),c_Option_Ooption_OSome(X4)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))=c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X4),tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__option__conv)). 4.05/4.28 fof(fact_Un__Diff__Int, axiom, ![X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6))=X3, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Diff__Int)). 4.05/4.28 fof(fact_Field__Un, axiom, ![X40, X18, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_OField(X4),X18)),hAPP(c_Relation_OField(X4),X40))=hAPP(c_Relation_OField(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X18),X40)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__Un)). 4.05/4.28 fof(fact_restrict__map__insert, axiom, ![X3, X26, X22, X7, X4]:c_Map_Orestrict__map(X4,X7,X22,hAPP(hAPP(c_Set_Oinsert(X4),X26),X3))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),c_Map_Orestrict__map(X4,X7,X22,X3)),X26),hAPP(X22,X26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__map__insert)). 4.05/4.28 fof(fact_takeWhile__map, axiom, ![X32, X22, X7, X56, X4]:hAPP(hAPP(c_List_Omap(X7,X4),X22),c_List_OtakeWhile(X7,hAPP(c_Fun_Ocomp(X4,tc_HOL_Obool,X7,X56),X22),X32))=c_List_OtakeWhile(X4,X56,hAPP(hAPP(c_List_Omap(X7,X4),X22),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__map)). 4.05/4.28 fof(fact_UN__empty2, axiom, ![X3, X4, X7]:c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X7),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__empty2)). 4.05/4.28 fof(fact_fun__upd__upd, axiom, ![X16, X17, X9, X22, X7, X4]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X7),X22),X9),X16)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X7),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X7),X22),X9),X17)),X9),X16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__upd)). 4.05/4.28 fof(fact_lex__def, axiom, ![X18, X4]:c_List_Olex(X4,X18)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lex__def)). 4.05/4.28 fof(fact_take__drop, axiom, ![X45, X2, X5, X4]:hAPP(hAPP(c_List_Otake(X4),X5),hAPP(hAPP(c_List_Odrop(X4),X2),X45))=hAPP(hAPP(c_List_Odrop(X4),X2),hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X2)),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__drop)). 4.05/4.28 fof(fact_zdiff__zmult__distrib, axiom, ![X53, X216, X217]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X217),X53)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X216),X53))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X217),X216)),X53), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__zmult__distrib)). 4.05/4.28 fof(fact_zadd__zmult__distrib, axiom, ![X53, X216, X217]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X217),X216)),X53)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X217),X53)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X216),X53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__zmult__distrib)). 4.05/4.28 fof(fact_diff__mult__distrib, axiom, ![X107, X5, X2]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5)),X107)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X107)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__mult__distrib)). 4.05/4.28 fof(fact_add__mult__distrib, axiom, ![X107, X5, X2]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X5)),X107)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X107)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__mult__distrib)). 4.05/4.28 fof(fact_drop__take, axiom, ![X45, X2, X5, X4]:hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5)),hAPP(hAPP(c_List_Odrop(X4),X5),X45))=hAPP(hAPP(c_List_Odrop(X4),X5),hAPP(hAPP(c_List_Otake(X4),X2),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__take)). 4.05/4.28 fof(fact_zdiff__zmult__distrib2, axiom, ![X216, X217, X53]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),X217)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),X216))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X217),X216)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__zmult__distrib2)). 4.05/4.28 fof(fact_diff__mult__distrib2, axiom, ![X5, X2, X107]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__mult__distrib2)). 4.05/4.28 fof(fact_zpower__zadd__distrib, axiom, ![X29, X43, X13]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X13),X43)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X13),X29))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zpower__zadd__distrib)). 4.05/4.28 fof(fact_add__mult__distrib2, axiom, ![X5, X2, X107]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_add__mult__distrib2)). 4.05/4.28 fof(fact_comp__funpow, axiom, ![X22, X20, X7, X4]:hAPP(hAPP(c_Nat_Ocompow(tc_fun(X4,X7),tc_fun(X4,X7)),X20),c_Fun_Ocomp(X7,X7,X4,X22))=c_Fun_Ocomp(X7,X7,X4,hAPP(hAPP(c_Nat_Ocompow(X7,X7),X20),X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_comp__funpow)). 4.05/4.28 fof(fact_sublists__powset, axiom, ![X32, X4]:hAPP(c_Set_Oimage(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool),c_List_Oset(X4)),hAPP(c_List_Oset(tc_List_Olist(X4)),c_Enum_Osublists(X4,X32)))=hAPP(c_Set_OPow(X4),hAPP(c_List_Oset(X4),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublists__powset)). 4.05/4.28 fof(fact_listrel__subset__rtrancl__listrel1, axiom, ![X18, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4)),tc_HOL_Obool)),c_List_Olistrel(X4,X18)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__subset__rtrancl__listrel1)). 4.05/4.28 fof(fact_int__setprod, axiom, ![X3, X22, X4]:hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X4),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X22)),X3)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,tc_Nat_Onat),X22),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__setprod)). 4.05/4.28 fof(fact_int__setsum, axiom, ![X3, X22, X4]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X22),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X4),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X22)),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__setsum)). 4.05/4.28 fof(fact_map__pair__simp, axiom, ![X25, X26, X76, X22, X7, X126, X4, X49]:hAPP(hAPP(c_Product__Type_OPair(X4,X7),hAPP(X22,X26)),hAPP(X76,X25))=hAPP(c_Product__Type_Omap__pair(X49,X4,X126,X7,X22,X76),hAPP(hAPP(c_Product__Type_OPair(X49,X126),X26),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair__simp)). 4.05/4.28 fof(fact_New__DSequence_Opos__bind__def, axiom, ![X37, X22, X9, X4, X7]:hAPP(c_New__DSequence_Opos__bind(X7,X4,X9,X22),X37)=hAPP(c_Lazy__Sequence_Obind(X7,X4,hAPP(X9,X37)),hAPP(hAPP(c_COMBC(X7,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4)),X22),X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__bind__def)). 4.05/4.28 fof(fact_rev__foldl__cons, axiom, ![X32, X4]:hAPP(c_List_Orev(X4),X32)=hAPP(c_List_Ofoldl(tc_List_Olist(X4),X4,hAPP(c_COMBC(X4,tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olist_OCons(X4)),c_List_Olist_ONil(X4)),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__foldl__cons)). 4.05/4.28 fof(fact_list__update__code_I3_J, axiom, ![X43, X46, X45, X13, X4]:hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)),hAPP(c_Nat_OSuc,X46)),X43)=hAPP(hAPP(c_List_Olist_OCons(X4),X13),hAPP(hAPP(c_List_Olist__update(X4,X45),X46),X43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__code_I3_J)). 4.05/4.28 fof(fact_listsp__inf__eq, axiom, ![X6, X3, X4]:c_List_Olistsp(X4,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)),c_List_Olistsp(X4,X3)),c_List_Olistsp(X4,X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp__inf__eq)). 4.05/4.28 fof(fact_hb__map_Osimps_I2_J, axiom, ![X143, X9, X22, X4, X7]:c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X4),hAPP(hAPP(c_Option_Omap(X7,X4),X22),X9),c_Lazy__Sequence_Ohb__map(X7,X4,X22,X143))=c_Lazy__Sequence_Ohb__map(X7,X4,X22,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X7),X9,X143)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hb__map_Osimps_I2_J)). 4.05/4.28 fof(fact_empty__upd__none, axiom, ![X154, X9, X4, X7]:hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,tc_Option_Ooption(X4)),hAPP(c_COMBK(tc_Option_Ooption(X4),X7),c_Option_Ooption_ONone(X4))),X9),c_Option_Ooption_ONone(X4)),X154)=c_Option_Ooption_ONone(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__upd__none)). 4.05/4.28 fof(fact_Diff__idemp, axiom, ![X6, X3, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__idemp)). 4.05/4.28 fof(fact_Un__Diff__cancel, axiom, ![X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X6),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__Diff__cancel)). 4.05/4.28 fof(fact_Int__left__absorb, axiom, ![X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__left__absorb)). 4.05/4.28 fof(fact_Option_Omap__def, axiom, ![X22, X7, X4]:c_Option_Ooption_Ooption__case(tc_Option_Ooption(X7),X4,c_Option_Ooption_ONone(X7),hAPP(hAPP(c_COMBB(X7,tc_Option_Ooption(X7),X4),c_Option_Ooption_OSome(X7)),X22))=hAPP(c_Option_Omap(X4,X7),X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Option_Omap__def)). 4.05/4.28 fof(fact_Un__left__absorb, axiom, ![X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__left__absorb)). 4.05/4.28 fof(fact_funpow__mult, axiom, ![X22, X21, X20, X4]:hAPP(hAPP(c_Nat_Ocompow(X4,X4),X20),hAPP(hAPP(c_Nat_Ocompow(X4,X4),X21),X22))=hAPP(hAPP(c_Nat_Ocompow(X4,X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X20)),X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_funpow__mult)). 4.05/4.28 fof(fact_map__of__append, axiom, ![X31, X32, X7, X4]:hAPP(c_Map_Omap__of(X4,X7),hAPP(hAPP(c_List_Oappend(tc_prod(X4,X7)),X32),X31))=c_Map_Omap__add(X4,X7,hAPP(c_Map_Omap__of(X4,X7),X31),hAPP(c_Map_Omap__of(X4,X7),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of__append)). 4.05/4.28 fof(fact_filter__append, axiom, ![X31, X32, X56, X4]:hAPP(hAPP(c_List_Oappend(X4),hAPP(c_List_Ofilter(X4,X56),X32)),hAPP(c_List_Ofilter(X4,X56),X31))=hAPP(c_List_Ofilter(X4,X56),hAPP(hAPP(c_List_Oappend(X4),X32),X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter__append)). 4.05/4.28 fof(fact_tl__take, axiom, ![X45, X5, X4]:hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X4),X45))=hAPP(c_List_Otl(X4),hAPP(hAPP(c_List_Otake(X4),X5),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl__take)). 4.05/4.28 fof(fact_divmod__nat__rel, axiom, ![X5, X2]:hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X5),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X5)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_divmod__nat__rel)). 4.05/4.28 fof(fact_finite__range__map__of, axiom, ![X145, X7, X4]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X4)),hAPP(c_Set_Oimage(X7,tc_Option_Ooption(X4),hAPP(c_Map_Omap__of(X7,X4),X145)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__range__map__of)). 4.05/4.28 fof(fact_foldl__append, axiom, ![X31, X32, X26, X22, X7, X4]:hAPP(c_List_Ofoldl(X4,X7,X22,X26),hAPP(hAPP(c_List_Oappend(X7),X32),X31))=hAPP(c_List_Ofoldl(X4,X7,X22,hAPP(c_List_Ofoldl(X4,X7,X22,X26),X32)),X31), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__append)). 4.05/4.28 fof(fact_mod__mult__distrib, axiom, ![X107, X5, X2]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5)),X107)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X107),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__distrib)). 4.05/4.28 fof(fact_mod__mult__distrib2, axiom, ![X5, X2, X107]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__distrib2)). 4.05/4.28 fof(fact_mod__mult__self4, axiom, ![X2, X5, X107]: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),X107),X5)),X2)),X5)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self4)). 4.05/4.28 fof(fact_nth__append__length, axiom, ![X59, X13, X45, X4]:hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Oappend(X4),X45),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X59))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45))=X13, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__append__length)). 4.05/4.28 fof(fact_select__weight__cons__zero, axiom, ![X32, X9, X4]:c_Random_Oselect__weight(X4,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X4)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X4),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X9)),X32))=c_Random_Oselect__weight(X4,X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_select__weight__cons__zero)). 4.05/4.28 fof(fact_dom__map__add, axiom, ![X20, X21, X7, X4]:c_Map_Odom(X4,X7,c_Map_Omap__add(X4,X7,X21,X20))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X7,X20)),c_Map_Odom(X4,X7,X21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__map__add)). 4.05/4.28 fof(fact_set__drop__subset, axiom, ![X32, X20, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Odrop(X4),X20),X32))),hAPP(c_List_Oset(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__drop__subset)). 4.05/4.28 fof(fact_set__take__subset, axiom, ![X32, X20, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Otake(X4),X20),X32))),hAPP(c_List_Oset(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__take__subset)). 4.05/4.28 fof(fact__01, axiom, ![X250, X13, X4]:hAPP(c_Option_Ooption_OSome(tc_prod(X4,tc_Lazy__Sequence_Olazy__sequence(X4))),hAPP(hAPP(c_Product__Type_OPair(X4,tc_Lazy__Sequence_Olazy__sequence(X4)),X13),X250))=hAPP(c_Lazy__Sequence_Oyield(X4),c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X13,X250)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact__01)). 4.05/4.28 fof(fact_INTER__eq__Inter__image, axiom, ![X6, X3, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),X3),X6)=c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),hAPP(c_Set_Oimage(X7,tc_fun(X4,tc_HOL_Obool),X6),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INTER__eq__Inter__image)). 4.05/4.28 fof(fact_funpow_Osimps_I2_J, axiom, ![X22, X20, X4]:hAPP(hAPP(c_Nat_Ocompow(X4,X4),hAPP(c_Nat_OSuc,X20)),X22)=hAPP(c_Fun_Ocomp(X4,X4,X4,X22),hAPP(hAPP(c_Nat_Ocompow(X4,X4),X20),X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_funpow_Osimps_I2_J)). 4.05/4.28 fof(fact_snd__def, axiom, ![X51, X4, X7]:hAPP(c_Product__Type_Osnd(X7,X4),X51)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X4,X4),hAPP(c_COMBK(tc_fun(X4,X4),X7),c_COMBI(X4))),X51), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__def)). 4.05/4.28 fof(fact_replicate__length__filter, axiom, ![X32, X9, X4]:hAPP(c_List_Ofilter(X4,hAPP(c_fequal,X9)),X32)=c_List_Oreplicate(X4,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Ofilter(X4,hAPP(c_fequal,X9)),X32)),X9), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__length__filter)). 4.05/4.28 fof(fact_take__Suc__Cons, axiom, ![X45, X13, X5, X4]:hAPP(hAPP(c_List_Olist_OCons(X4),X13),hAPP(hAPP(c_List_Otake(X4),X5),X45))=hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_OSuc,X5)),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Suc__Cons)). 4.05/4.28 fof(fact_length__filter__le, axiom, ![X32, X56, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Ofilter(X4,X56),X32))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__filter__le)). 4.05/4.28 fof(fact_subset__Pow__Union, axiom, ![X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_Set_OPow(X4),c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__Pow__Union)). 4.05/4.28 fof(fact_zpower__zmod, axiom, ![X43, X2, X13]: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,X13,X2)),X43),X2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X13),X43),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zpower__zmod)). 4.05/4.28 fof(fact_zdiff__zmod__left, axiom, ![X43, X2, X13]: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,X13,X2)),X43),X2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X13),X43),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__zmod__left)). 4.05/4.28 fof(fact_zdiff__zmod__right, axiom, ![X2, X43, X13]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X13),c_Divides_Odiv__class_Omod(tc_Int_Oint,X43,X2)),X2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X13),X43),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiff__zmod__right)). 4.05/4.28 fof(fact_zmod__simps_I3_J, axiom, ![X10, X12, X11]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12,X10)),X10)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X12),X10), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__simps_I3_J)). 4.05/4.28 fof(fact_Field__def, axiom, ![X18, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X4,X4),X18)),hAPP(c_Relation_ORange(X4,X4),X18))=hAPP(c_Relation_OField(X4),X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__def)). 4.05/4.28 fof(fact_Inter__def, axiom, ![X86, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X86),c_COMBI(tc_fun(X4,tc_HOL_Obool)))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),X86), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__def)). 4.05/4.28 fof(fact_Union__def, axiom, ![X86, X4]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X86),c_COMBI(tc_fun(X4,tc_HOL_Obool)))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),X86), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__def)). 4.05/4.28 fof(fact_diff__cancel2, axiom, ![X5, X107, X2]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X107)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X107))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__cancel2)). 4.05/4.28 fof(fact_diff__cancel, axiom, ![X5, X2, X107]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X107),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X107),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__cancel)). 4.05/4.28 fof(fact_Diff__Compl, axiom, ![X6, X3, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X6))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__Compl)). 4.05/4.28 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J, axiom, ![X20, X21]: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),X21),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X21,X20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_SetInterval_Otransfer__nat__int__set__functions_I2_J)). 4.05/4.28 fof(fact_rel__comp__empty1, axiom, ![X39, X7, X49, X4]:hAPP(hAPP(c_Relation_Orel__comp(X4,X49,X7),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X49),tc_HOL_Obool))),X39)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X7),tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__empty1)). 4.05/4.28 fof(fact_rel__comp__empty2, axiom, ![X39, X7, X49, X4]:c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X7),tc_HOL_Obool))=hAPP(hAPP(c_Relation_Orel__comp(X4,X49,X7),X39),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X49,X7),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__comp__empty2)). 4.05/4.28 fof(fact_set__remove1__subset, axiom, ![X32, X9, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),c_List_Oremove1(X4,X9,X32))),hAPP(c_List_Oset(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__remove1__subset)). 4.05/4.28 fof(fact_set__sublist__subset, axiom, ![X41, X32, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_List_Oset(X4),c_List_Osublist(X4,X32,X41))),hAPP(c_List_Oset(X4),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__sublist__subset)). 4.05/4.28 fof(fact_length__takeWhile__le, axiom, ![X32, X56, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X56,X32))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__takeWhile__le)). 4.05/4.28 fof(fact_sorted__transpose, axiom, ![X32, X4]:c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X4),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X4))),c_List_Otranspose(X4,X32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__transpose)). 4.05/4.28 fof(fact_replicate__add, axiom, ![X13, X2, X5, X4]:c_List_Oreplicate(X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X2),X13)=hAPP(hAPP(c_List_Oappend(X4),c_List_Oreplicate(X4,X5,X13)),c_List_Oreplicate(X4,X2,X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__add)). 4.05/4.28 fof(fact_Diff__disjoint, axiom, ![X6, X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X6),X3))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__disjoint)). 4.05/4.28 fof(fact_butlast__conv__take, axiom, ![X45, X4]:hAPP(hAPP(c_List_Otake(X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X45)=c_List_Obutlast(X4,X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast__conv__take)). 4.05/4.28 fof(fact_diff__Suc, axiom, ![X20, X21]: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),X21),X20))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21),hAPP(c_Nat_OSuc,X20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__Suc)). 4.05/4.28 fof(fact_partition__filter2, axiom, ![X32, X56, X4]:hAPP(c_List_Ofilter(X4,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X4,c_fNot),X56)),X32)=hAPP(c_Product__Type_Osnd(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Opartition(X4,X56,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition__filter2)). 4.05/4.28 fof(fact_list__update__overwrite, axiom, ![X43, X13, X46, X45, X4]:hAPP(hAPP(c_List_Olist__update(X4,X45),X46),X43)=hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Olist__update(X4,X45),X46),X13)),X46),X43), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__overwrite)). 4.05/4.28 fof(fact_div__mod__code__numeral__def, axiom, ![X2, X5]:c_Code__Numeral_Odiv__mod__code__numeral(X5,X2)=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),X5),X2)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X5,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mod__code__numeral__def)). 4.05/4.28 fof(fact_rev__append, axiom, ![X59, X45, X4]:hAPP(c_List_Orev(X4),hAPP(hAPP(c_List_Oappend(X4),X45),X59))=hAPP(hAPP(c_List_Oappend(X4),hAPP(c_List_Orev(X4),X59)),hAPP(c_List_Orev(X4),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__append)). 4.05/4.28 fof(fact_funpow__swap1, axiom, ![X9, X20, X4, X22]:hAPP(X22,hAPP(hAPP(hAPP(c_Nat_Ocompow(X4,X4),X20),X22),X9))=hAPP(hAPP(hAPP(c_Nat_Ocompow(X4,X4),X20),X22),hAPP(X22,X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_funpow__swap1)). 4.05/4.28 fof(fact_append__assoc, axiom, ![X175, X59, X45, X4]:hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Oappend(X4),X45),X59)),X175)=hAPP(hAPP(c_List_Oappend(X4),X45),hAPP(hAPP(c_List_Oappend(X4),X59),X175)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__assoc)). 4.05/4.28 fof(fact_append__Cons, axiom, ![X59, X45, X13, X4]:hAPP(hAPP(c_List_Olist_OCons(X4),X13),hAPP(hAPP(c_List_Oappend(X4),X45),X59))=hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)),X59), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__Cons)). 4.05/4.28 fof(fact_drop__drop, axiom, ![X45, X2, X5, X4]:hAPP(hAPP(c_List_Odrop(X4),X5),hAPP(hAPP(c_List_Odrop(X4),X2),X45))=hAPP(hAPP(c_List_Odrop(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X2)),X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__drop)). 4.05/4.28 fof(fact_zpower__zpower, axiom, ![X29, X43, X13]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X13),X43)),X29)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zpower__zpower)). 4.05/4.28 fof(fact_nat__mult__assoc, axiom, ![X107, X5, X2]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)),X107)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__assoc)). 4.05/4.28 fof(fact_zmult__assoc, axiom, ![X259, X216, X217]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X217),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X216),X259))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X217),X216)),X259), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__assoc)). 4.05/4.28 fof(fact_div__mult2__eq, axiom, ![X10, X12, X11]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),X10))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X11),X12)),X10), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__mult2__eq)). 4.05/4.28 fof(fact_zmult__int, axiom, ![X5, X2]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(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),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__int)). 4.05/4.28 fof(fact_snd__prod__fun, axiom, ![X9, X76, X22, X126, X49, X4, X7]:hAPP(c_Product__Type_Osnd(X7,X4),hAPP(c_Product__Type_Omap__pair(X49,X7,X126,X4,X22,X76),X9))=hAPP(X76,hAPP(c_Product__Type_Osnd(X49,X126),X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_snd__prod__fun)). 4.05/4.28 fof(fact_fst__map__pair, axiom, ![X9, X76, X22, X126, X49, X7, X4]:hAPP(X22,hAPP(c_Product__Type_Ofst(X49,X126),X9))=hAPP(c_Product__Type_Ofst(X4,X7),hAPP(c_Product__Type_Omap__pair(X49,X4,X126,X7,X22,X76),X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__map__pair)). 4.05/4.28 fof(fact_zadd__int, axiom, ![X5, X2]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(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),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zadd__int)). 4.05/4.28 fof(fact_Divides_Otransfer__int__nat__functions_I1_J, axiom, ![X43, X13]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X13),X43))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X13)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Otransfer__int__nat__functions_I1_J)). 4.05/4.28 fof(fact_rtrancl_Ortrancl__refl, axiom, ![X18, X26, X4]:hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X26),X26)),c_Transitive__Closure_Ortrancl(X4,X18))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl_Ortrancl__refl)). 4.05/4.28 fof(fact_scomp__apply, axiom, ![X9, X76, X22, X4, X126, X49, X7]:hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X7,X49,X126,X4),X22),X76),X9)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X49,X126,X4),X76),hAPP(X22,X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_scomp__apply)). 4.05/4.28 fof(fact_remdups__map__remdups, axiom, ![X32, X22, X7, X4]:c_List_Oremdups(X4,hAPP(hAPP(c_List_Omap(X7,X4),X22),X32))=c_List_Oremdups(X4,hAPP(hAPP(c_List_Omap(X7,X4),X22),c_List_Oremdups(X7,X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups__map__remdups)). 4.05/4.28 fof(fact_mod__mult__self3, axiom, ![X2, X5, X107]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5)=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),X107),X5)),X2),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__mult__self3)). 4.05/4.28 fof(fact_dom__const, axiom, ![X22, X7, X4]:c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=c_Map_Odom(X4,X7,hAPP(hAPP(c_COMBB(X7,tc_Option_Ooption(X7),X4),c_Option_Ooption_OSome(X7)),X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__const)). 4.05/4.28 fof(fact_split__conv, axiom, ![X25, X26, X22, X4, X49, X7]:hAPP(hAPP(X22,X26),X25)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X49,X4),X22),hAPP(hAPP(c_Product__Type_OPair(X7,X49),X26),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_split__conv)). 4.05/4.28 fof(fact_converse__pred__comp, axiom, ![X40, X18, X49, X4, X7]:c_Predicate_Opred__comp(X4,X49,X7,c_Predicate_Oconversep(X49,X4,X40),c_Predicate_Oconversep(X7,X49,X18))=c_Predicate_Oconversep(X7,X4,c_Predicate_Opred__comp(X7,X49,X4,X18,X40)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__pred__comp)). 4.05/4.28 fof(fact_UNIV__Plus__UNIV, axiom, ![X7, X4]:c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X4,X7),tc_HOL_Obool))=c_Sum__Type_OPlus(X4,X7,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__Plus__UNIV)). 4.05/4.28 fof(fact_list__update__code_I2_J, axiom, ![X43, X45, X13, X4]:hAPP(hAPP(c_List_Olist_OCons(X4),X43),X45)=hAPP(hAPP(c_List_Olist__update(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X43), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__code_I2_J)). 4.05/4.28 fof(fact_negative__zless, axiom, ![X2, X5]: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,X5)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negative__zless)). 4.05/4.28 fof(fact_takeWhile__eq__take, axiom, ![X32, X56, X4]:hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X56,X32))),X32)=c_List_OtakeWhile(X4,X56,X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile__eq__take)). 4.05/4.28 fof(fact_card__length, axiom, ![X32, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),hAPP(c_List_Oset(X4),X32))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X32))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__length)). 4.05/4.28 fof(fact_length__n__lists, axiom, ![X45, X5, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X4))),c_Enum_On__lists(X4,X5,X45))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__n__lists)). 4.05/4.28 fof(fact_Compl__partition, axiom, ![X3, X4]:c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__partition)). 4.05/4.28 fof(fact_take__tl, axiom, ![X45, X5, X4]:hAPP(c_List_Otl(X4),hAPP(hAPP(c_List_Otake(X4),hAPP(c_Nat_OSuc,X5)),X45))=hAPP(hAPP(c_List_Otake(X4),X5),hAPP(c_List_Otl(X4),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__tl)). 4.05/4.28 fof(fact_take__1__Cons, axiom, ![X45, X13, X4]:hAPP(hAPP(c_List_Otake(X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45))=hAPP(hAPP(c_List_Olist_OCons(X4),X13),c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__1__Cons)). 4.05/4.28 fof(fact_Diff__subset, axiom, ![X6, X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X6)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__subset)). 4.05/4.28 fof(fact_Int__lower1, axiom, ![X6, X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__lower1)). 4.05/4.28 fof(fact_Int__lower2, axiom, ![X6, X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__lower2)). 4.05/4.28 fof(fact_Un__upper1, axiom, ![X6, X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__upper1)). 4.05/4.28 fof(fact_Un__upper2, axiom, ![X3, X6, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__upper2)). 4.05/4.28 fof(fact_restrict__restrict, axiom, ![X6, X3, X21, X7, X4]:c_Map_Orestrict__map(X4,X7,c_Map_Orestrict__map(X4,X7,X21,X3),X6)=c_Map_Orestrict__map(X4,X7,X21,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__restrict)). 4.05/4.28 fof(fact_upd__None__map__le, axiom, ![X9, X22, X7, X4]:c_Map_Omap__le(X4,X7,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,tc_Option_Ooption(X7)),X22),X9),c_Option_Ooption_ONone(X7)),X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_upd__None__map__le)). 4.05/4.28 fof(fact_zminus__zmod, axiom, ![X2, X13]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X13),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,X13,X2)),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zminus__zmod)). 4.05/4.28 fof(fact_nth__Cons__Suc, axiom, ![X5, X45, X13, X4]:hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)),hAPP(c_Nat_OSuc,X5))=hAPP(hAPP(c_List_Onth(X4),X45),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__Cons__Suc)). 4.05/4.28 fof(fact_drop__Suc__Cons, axiom, ![X45, X13, X5, X4]:hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_OSuc,X5)),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45))=hAPP(hAPP(c_List_Odrop(X4),X5),X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Suc__Cons)). 4.05/4.28 fof(fact_append__take__drop__id, axiom, ![X45, X5, X4]:hAPP(hAPP(c_List_Oappend(X4),hAPP(hAPP(c_List_Otake(X4),X5),X45)),hAPP(hAPP(c_List_Odrop(X4),X5),X45))=X45, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__take__drop__id)). 4.05/4.28 fof(fact_pair__collapse, axiom, ![X15, X7, X4]:X15=hAPP(hAPP(c_Product__Type_OPair(X4,X7),hAPP(c_Product__Type_Ofst(X4,X7),X15)),hAPP(c_Product__Type_Osnd(X4,X7),X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__collapse)). 4.05/4.28 fof(fact_INT__empty, axiom, ![X6, X4, X7]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),X6)=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_INT__empty)). 4.05/4.28 fof(fact_Compl__eq__Diff__UNIV, axiom, ![X3, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X3)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__eq__Diff__UNIV)). 4.05/4.28 fof(fact_prod_Orecs, axiom, ![X25, X26, X130, X4, X49, X7]:hAPP(hAPP(X130,X26),X25)=c_Product__Type_Oprod_Oprod__rec(X7,X49,X4,X130,hAPP(hAPP(c_Product__Type_OPair(X7,X49),X26),X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_prod_Orecs)). 4.05/4.28 fof(fact_restrict__map__empty, axiom, ![X9, X61, X4, X7]:hAPP(c_Map_Orestrict__map(X7,X4,hAPP(c_COMBK(tc_Option_Ooption(X4),X7),c_Option_Ooption_ONone(X4)),X61),X9)=c_Option_Ooption_ONone(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__map__empty)). 4.05/4.28 fof(fact_wf__less, axiom, c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__less)). 4.05/4.28 fof(fact_Pow__bottom, axiom, ![X6, X4]:hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),hAPP(c_Set_OPow(X4),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__bottom)). 4.05/4.28 fof(fact_set__replicate__Suc, axiom, ![X9, X20, X4]:hAPP(c_List_Oset(X4),c_List_Oreplicate(X4,hAPP(c_Nat_OSuc,X20),X9))=hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__replicate__Suc)). 4.05/4.28 fof(fact_zmod__zminus2, axiom, ![X12, X11]:c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12))=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),X11),X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zminus2)). 4.05/4.28 fof(fact_length__tl, axiom, ![X45, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Otl(X4),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__tl)). 4.05/4.28 fof(fact_zmod__zminus__zminus, axiom, ![X12, X11]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zminus__zminus)). 4.05/4.28 fof(fact_drop__replicate, axiom, ![X13, X107, X46, X4]:hAPP(hAPP(c_List_Odrop(X4),X46),c_List_Oreplicate(X4,X107,X13))=c_List_Oreplicate(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X107),X46),X13), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__replicate)). 4.05/4.28 fof(fact_Divides_Otransfer__int__nat__functions_I2_J, axiom, ![X43, X13]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X13,X43))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X13),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Divides_Otransfer__int__nat__functions_I2_J)). 4.05/4.28 fof(fact_le__cube, axiom, ![X2]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__cube)). 4.05/4.28 fof(fact_Pair__scomp, axiom, ![X22, X9, X7, X49, X4]:hAPP(hAPP(c_Product__Type_Oscomp(X4,X49,X4,X7),hAPP(c_Product__Type_OPair(X49,X4),X9)),X22)=hAPP(X22,X9), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pair__scomp)). 4.05/4.28 fof(fact_list_Osimps_I5_J, axiom, ![X224, X26, X129, X130, X7, X4]:hAPP(c_List_Olist_Olist__case(X4,X7,X130,X129),hAPP(hAPP(c_List_Olist_OCons(X7),X26),X224))=hAPP(hAPP(X129,X26),X224), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osimps_I5_J)). 4.05/4.28 fof(fact_map__add__upds, axiom, ![X31, X32, X162, X163, X7, X4]:c_Map_Omap__upds(X4,X7,c_Map_Omap__add(X4,X7,X163,X162),X32,X31)=c_Map_Omap__add(X4,X7,X163,c_Map_Omap__upds(X4,X7,X162,X32,X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__upds)). 4.05/4.28 fof(fact_nth_Osimps, axiom, ![X20, X32, X9, X4]:hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X9),X32)),X20)=c_Nat_Onat_Onat__case(X4,X9,hAPP(c_List_Onth(X4),X32),X20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth_Osimps)). 4.05/4.28 fof(fact_image__Suc__atLeastAtMost, axiom, ![X38, X37]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X37),hAPP(c_Nat_OSuc,X38))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X37,X38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__Suc__atLeastAtMost)). 4.05/4.28 fof(fact_negative__zless__0, axiom, ![X5]: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,X5)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negative__zless__0)). 4.05/4.28 fof(fact_negative__zle, axiom, ![X2, X5]: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),X5))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negative__zle)). 4.05/4.28 fof(fact_zero__le__zpower__abs, axiom, ![X5, X13]: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),X13)),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__zpower__abs)). 4.05/4.28 fof(fact_rtrancl__idemp__self__comp, axiom, ![X39, X4]:c_Transitive__Closure_Ortrancl(X4,X39)=hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),c_Transitive__Closure_Ortrancl(X4,X39)),c_Transitive__Closure_Ortrancl(X4,X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__idemp__self__comp)). 4.05/4.28 fof(fact_Sigma__empty1, axiom, ![X6, X7, X4]:c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X7),tc_HOL_Obool))=hAPP(hAPP(c_Product__Type_OSigma(X4,X7),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Sigma__empty1)). 4.05/4.28 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J, axiom, ![X43, X13]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13),X43))=c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X13),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J)). 4.05/4.28 fof(fact_card__eq__setsum, axiom, ![X3, X4]:hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X4),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)=hAPP(c_Finite__Set_Ocard(X4),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__eq__setsum)). 4.05/4.28 fof(fact_length__butlast, axiom, ![X45, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Obutlast(X4,X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__butlast)). 4.05/4.28 fof(fact_small__int__def, axiom, ![X102, X22]:hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),X22),X102)=c_Smallcheck_Osmall_H(X22,hAPP(c_Code__Numeral_Oint__of,X102),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X102))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__int__def)). 4.05/4.28 fof(fact_scomp__Pair, axiom, ![X9, X49, X7, X4]:X9=hAPP(hAPP(c_Product__Type_Oscomp(X4,X7,X49,tc_prod(X7,X49)),X9),c_Product__Type_OPair(X7,X49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_scomp__Pair)). 4.05/4.28 fof(fact_empty__Diff, axiom, ![X3, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X3)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__Diff)). 4.05/4.28 fof(fact_dom__restrict, axiom, ![X3, X21, X7, X4]:c_Map_Odom(X4,X7,c_Map_Orestrict__map(X4,X7,X21,X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X7,X21)),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_dom__restrict)). 4.05/4.28 fof(fact_Int__empty__left, axiom, ![X6, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X6)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__empty__left)). 4.05/4.28 fof(fact_Un__UNIV__left, axiom, ![X6, X4]:c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__UNIV__left)). 4.05/4.28 fof(fact_Diff__UNIV, axiom, ![X3, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__UNIV)). 4.05/4.28 fof(fact_Un__UNIV__right, axiom, ![X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__UNIV__right)). 4.05/4.28 fof(fact_Int__empty__right, axiom, ![X3, X4]:c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__empty__right)). 4.05/4.28 fof(fact_Inter__UNIV, axiom, ![X4]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__UNIV)). 4.05/4.28 fof(fact_Union__UNIV, axiom, ![X4]:c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__UNIV)). 4.05/4.28 fof(fact_Inter__empty, axiom, ![X4]:c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X4,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Inter__empty)). 4.05/4.28 fof(fact_Union__empty, axiom, ![X4]:c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__empty)). 4.05/4.28 fof(fact_length__list__update, axiom, ![X13, X46, X45, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(hAPP(c_List_Olist__update(X4,X45),X46),X13))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__list__update)). 4.05/4.28 fof(fact_listrel1__converse, axiom, ![X18, X4]:c_List_Olistrel1(X4,hAPP(c_Relation_Oconverse(X4,X4),X18))=hAPP(c_Relation_Oconverse(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Olistrel1(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel1__converse)). 4.05/4.28 fof(fact_zpower__int, axiom, ![X5, X2]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X5))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zpower__int)). 4.05/4.28 fof(fact_zmult__zminus, axiom, ![X53, X29]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),X53))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29)),X53), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__zminus)). 4.05/4.28 fof(fact_zdiv__zminus2, axiom, ![X12, X11]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X12))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11)),X12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zminus2)). 4.05/4.28 fof(fact_inj__on__add__nat, axiom, ![X176, X28]: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)),X28),X176), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__add__nat)). 4.05/4.28 fof(fact_map__replicate, axiom, ![X9, X20, X22, X4, X7]:c_List_Oreplicate(X4,X20,hAPP(X22,X9))=hAPP(hAPP(c_List_Omap(X7,X4),X22),c_List_Oreplicate(X7,X20,X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__replicate)). 4.05/4.28 fof(fact_partition__filter1, axiom, ![X32, X56, X4]:hAPP(c_Product__Type_Ofst(tc_List_Olist(X4),tc_List_Olist(X4)),c_List_Opartition(X4,X56,X32))=hAPP(c_List_Ofilter(X4,X56),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_partition__filter1)). 4.05/4.28 fof(fact_insert__absorb2, axiom, ![X3, X9, X4]:hAPP(hAPP(c_Set_Oinsert(X4),X9),X3)=hAPP(hAPP(c_Set_Oinsert(X4),X9),hAPP(hAPP(c_Set_Oinsert(X4),X9),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__absorb2)). 4.05/4.28 fof(fact_refl__on__empty, axiom, ![X4]:c_Relation_Orefl__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__empty)). 4.05/4.28 fof(fact_fold__image__empty, axiom, ![X16, X76, X22, X7, X4]:X16=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X7,X22),X76),X16),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__image__empty)). 4.05/4.28 fof(fact_mod__Suc__eq__Suc__mod, axiom, ![X5, X2]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5)),X5)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__Suc__eq__Suc__mod)). 4.05/4.28 fof(fact_map__add__assoc, axiom, ![X235, X162, X163, X7, X4]:c_Map_Omap__add(X4,X7,X163,c_Map_Omap__add(X4,X7,X162,X235))=c_Map_Omap__add(X4,X7,c_Map_Omap__add(X4,X7,X163,X162),X235), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__assoc)). 4.05/4.28 fof(fact_fold1__singleton, axiom, ![X26, X22, X4]:X26=hAPP(c_Finite__Set_Ofold1(X4,X22),hAPP(hAPP(c_Set_Oinsert(X4),X26),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold1__singleton)). 4.05/4.28 fof(fact_full__small__int__def, axiom, ![X102, X22]:c_Smallcheck_Ofull__small_H(X22,hAPP(c_Code__Numeral_Oint__of,X102),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X102)))=c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,X22,X102), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_full__small__int__def)). 4.05/4.28 fof(fact_ran__empty, axiom, ![X4, X7]:c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=c_Map_Oran(X7,X4,hAPP(c_COMBK(tc_Option_Ooption(X4),X7),c_Option_Ooption_ONone(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_ran__empty)). 4.05/4.28 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int, axiom, ![X115, X60]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X60,X115)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X60),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X115),c_Groups_Oone__class_Oone(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastLessThanPlusOne__atLeastAtMost__int)). 4.05/4.28 fof(fact_fst__def, axiom, ![X51, X7, X4]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X7,X4),c_COMBK(X4,X7)),X51)=hAPP(c_Product__Type_Ofst(X4,X7),X51), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fst__def)). 4.05/4.28 fof(fact_Image__Id__on, axiom, ![X6, X3, X4]:hAPP(c_Relation_OImage(X4,X4,c_Relation_OId__on(X4,X3)),X6)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__Id__on)). 4.05/4.28 fof(fact_subset__insertI, axiom, ![X26, X6, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X6),hAPP(hAPP(c_Set_Oinsert(X4),X26),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__insertI)). 4.05/4.28 fof(fact_negative__zle__0, axiom, ![X5]: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),X5))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_negative__zle__0)). 4.05/4.28 fof(fact_option__map__Some, axiom, ![X9, X22, X4, X7]:hAPP(c_Option_Ooption_OSome(X4),hAPP(X22,X9))=hAPP(hAPP(c_Option_Omap(X7,X4),X22),hAPP(c_Option_Ooption_OSome(X7),X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option__map__Some)). 4.05/4.28 fof(fact_int__Suc, axiom, ![X2]: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),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__Suc)). 4.05/4.28 fof(fact_replicate__Suc, axiom, ![X13, X5, X4]:c_List_Oreplicate(X4,hAPP(c_Nat_OSuc,X5),X13)=hAPP(hAPP(c_List_Olist_OCons(X4),X13),c_List_Oreplicate(X4,X5,X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__Suc)). 4.05/4.28 fof(fact_New__DSequence_Oneg__union__def, axiom, ![X37, X17, X9, X4]:c_Lazy__Sequence_Oappend(tc_Option_Ooption(X4),hAPP(X9,X37),hAPP(X17,X37))=hAPP(c_New__DSequence_Oneg__union(X4,X9,X17),X37), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Oneg__union__def)). 4.05/4.28 fof(fact_butlast__drop, axiom, ![X45, X5, X4]:hAPP(hAPP(c_List_Odrop(X4),X5),c_List_Obutlast(X4,X45))=c_List_Obutlast(X4,hAPP(hAPP(c_List_Odrop(X4),X5),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast__drop)). 4.05/4.28 fof(fact_List_Oset__insert, axiom, ![X32, X9, X4]:hAPP(c_List_Oset(X4),c_List_Oinsert(X4,X9,X32))=hAPP(hAPP(c_Set_Oinsert(X4),X9),hAPP(c_List_Oset(X4),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Oset__insert)). 4.05/4.28 fof(fact_fold__graph_OemptyI, axiom, ![X16, X22, X7, X4]:hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X7,X22,X16,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph_OemptyI)). 4.05/4.28 fof(fact_Rep__Integ, axiom, ![X9]:hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X9)),c_Int_OInteg)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Rep__Integ)). 4.05/4.28 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J, axiom, ![X3]:hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X3)=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)),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J)). 4.05/4.28 fof(fact_pair__box_Orecs, axiom, ![X25, X26, X130, X4, X49, X7]:hAPP(hAPP(X130,X26),X25)=c_Nitpick_Opair__box_Opair__box__rec(X7,X49,X4,X130,c_Nitpick_Opair__box_OPairBox(X7,X49,X26,X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__box_Orecs)). 4.05/4.28 fof(fact_pair__box_Osimps_I2_J, axiom, ![X25, X26, X130, X4, X49, X7]:hAPP(hAPP(X130,X26),X25)=c_Nitpick_Opair__box_Opair__box__case(X7,X49,X4,X130,c_Nitpick_Opair__box_OPairBox(X7,X49,X26,X25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__box_Osimps_I2_J)). 4.05/4.28 fof(help_c__COMBB__1, axiom, ![X39, X112, X56, X49, X4, X7]:hAPP(hAPP(hAPP(c_COMBB(X7,X4,X49),X56),X112),X39)=hAPP(X56,hAPP(X112,X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBB__1)). 4.05/4.28 fof(help_c__COMBC__1, axiom, ![X39, X112, X56, X4, X49, X7]:hAPP(hAPP(X56,X39),X112)=hAPP(hAPP(hAPP(c_COMBC(X7,X49,X4),X56),X112),X39), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBC__1)). 4.05/4.28 fof(fact_empty__map__add, axiom, ![X21, X7, X4]:c_Map_Omap__add(X4,X7,hAPP(c_COMBK(tc_Option_Ooption(X7),X4),c_Option_Ooption_ONone(X7)),X21)=X21, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__map__add)). 4.05/4.28 fof(fact_map__add__empty, axiom, ![X21, X7, X4]:c_Map_Omap__add(X4,X7,X21,hAPP(c_COMBK(tc_Option_Ooption(X7),X4),c_Option_Ooption_ONone(X7)))=X21, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__add__empty)). 4.05/4.28 fof(fact_Field__empty, axiom, ![X4]:hAPP(c_Relation_OField(X4),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__empty)). 4.05/4.28 fof(fact_Image__empty, axiom, ![X39, X4, X7]:hAPP(c_Relation_OImage(X7,X4,X39),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Image__empty)). 4.05/4.28 fof(fact_Compl__UNIV__eq, axiom, ![X4]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__UNIV__eq)). 4.05/4.28 fof(fact_Compl__empty__eq, axiom, ![X4]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Compl__empty__eq)). 4.05/4.28 fof(fact_eq__comp__r, axiom, ![X39, X4]:c_Predicate_Opred__comp(X4,X4,X4,c_fequal,c_Predicate_Opred__comp(X4,X4,X4,X39,c_fequal))=X39, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__comp__r)). 4.05/4.28 fof(fact_listset_Osimps_I2_J, axiom, ![X150, X3, X4]:c_List_Oset__Cons(X4,X3,c_List_Olistset(X4,X150))=c_List_Olistset(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_HOL_Obool)),X3),X150)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listset_Osimps_I2_J)). 4.05/4.28 fof(fact_subtract__code__numeral__def, axiom, c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral)=c_Code__Numeral_Osubtract__code__numeral, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subtract__code__numeral__def)). 4.05/4.28 fof(fact_transpose_Osimps_I2_J, axiom, ![X265, X4]:c_List_Otranspose(X4,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),X265))=c_List_Otranspose(X4,X265), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose_Osimps_I2_J)). 4.05/4.28 fof(fact_Range__def, axiom, ![X18, X4, X7]:hAPP(c_Relation_ODomain(X4,X7),hAPP(c_Relation_Oconverse(X7,X4),X18))=hAPP(c_Relation_ORange(X7,X4),X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__def)). 4.05/4.28 fof(fact_Range__converse, axiom, ![X18, X4, X7]:hAPP(c_Relation_ODomain(X4,X7),X18)=hAPP(c_Relation_ORange(X7,X4),hAPP(c_Relation_Oconverse(X4,X7),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__converse)). 4.05/4.28 fof(fact_Abs__Integ__cases, axiom, ![X9]:~(![X34]:(hAPP(c_Int_OAbs__Integ,X34)=X9=>~(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X34),c_Int_OInteg))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Abs__Integ__cases)). 4.05/4.28 fof(fact_restrict__map__to__empty, axiom, ![X9, X21, X4, X7]:hAPP(c_Map_Orestrict__map(X7,X4,X21,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),X9)=c_Option_Ooption_ONone(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_restrict__map__to__empty)). 4.05/4.28 fof(fact_pair__box_Osize_I2_J, axiom, ![X12, X11, X7, X4]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X4,X7)),c_Nitpick_Opair__box_OPairBox(X4,X7,X11,X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__box_Osize_I2_J)). 4.05/4.28 fof(fact_empty__subsetI, axiom, ![X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_empty__subsetI)). 4.05/4.28 fof(fact_subset__UNIV, axiom, ![X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__UNIV)). 4.05/4.28 fof(fact_diff__less__Suc, axiom, ![X5, X2]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5)),hAPP(c_Nat_OSuc,X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__less__Suc)). 4.05/4.28 fof(fact_less__add__Suc2, axiom, ![X2, X46]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X46)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_less__add__Suc2)). 4.05/4.28 fof(fact_map__pair_Oidentity, axiom, ![X7, X4]:c_Product__Type_Omap__pair(X4,X4,X7,X7,c_COMBI(X4),c_COMBI(X7))=c_Fun_Oid(tc_prod(X4,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__pair_Oidentity)). 4.05/4.28 fof(fact_lazy__sequence_Osimps_I5_J, axiom, ![X118, X26, X129, X130, X7, X4]:c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X4,X7,X130,X129,c_Lazy__Sequence_Olazy__sequence_OInsert(X7,X26,X118))=hAPP(hAPP(X129,X26),X118), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lazy__sequence_Osimps_I5_J)). 4.05/4.28 fof(fact_option_Osimps_I5_J, axiom, ![X26, X129, X130, X7, X4]:hAPP(c_Option_Ooption_Ooption__case(X4,X7,X130,X129),hAPP(c_Option_Ooption_OSome(X7),X26))=hAPP(X129,X26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Osimps_I5_J)). 4.05/4.28 fof(fact_fold__empty, axiom, ![X16, X22, X4, X7]:X16=hAPP(hAPP(c_Finite__Set_Ofold(X7,X4,X22),X16),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__empty)). 4.05/4.28 fof(fact_nth__Cons__0, axiom, ![X45, X13, X4]:X13=hAPP(hAPP(c_List_Onth(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nth__Cons__0)). 4.05/4.28 fof(fact_Int__UNIV__left, axiom, ![X6, X4]:X6=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__UNIV__left)). 4.05/4.28 fof(fact_the__elem__eq, axiom, ![X9, X4]:X9=c_Set_Othe__elem(X4,hAPP(hAPP(c_Set_Oinsert(X4),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the__elem__eq)). 4.05/4.28 fof(fact_Diff__empty, axiom, ![X3, X4]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=X3, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__empty)). 4.05/4.28 fof(fact_map__le__empty, axiom, ![X76, X7, X4]:c_Map_Omap__le(X4,X7,hAPP(c_COMBK(tc_Option_Ooption(X7),X4),c_Option_Ooption_ONone(X7)),X76), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__le__empty)). 4.05/4.28 fof(fact_Int__UNIV__right, axiom, ![X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=X3, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__UNIV__right)). 4.05/4.28 fof(fact_double__complement, axiom, ![X3, X4]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X3))=X3, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_double__complement)). 4.05/4.28 fof(fact_rtrancl__converse, axiom, ![X18, X4]:hAPP(c_Relation_Oconverse(X4,X4),c_Transitive__Closure_Ortrancl(X4,X18))=c_Transitive__Closure_Ortrancl(X4,hAPP(c_Relation_Oconverse(X4,X4),X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__converse)). 4.05/4.28 fof(fact_remdups__filter, axiom, ![X32, X56, X4]:c_List_Oremdups(X4,hAPP(c_List_Ofilter(X4,X56),X32))=hAPP(c_List_Ofilter(X4,X56),c_List_Oremdups(X4,X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups__filter)). 4.05/4.28 fof(fact_list__update__id, axiom, ![X46, X45, X4]:X45=hAPP(hAPP(c_List_Olist__update(X4,X45),X46),hAPP(hAPP(c_List_Onth(X4),X45),X46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__id)). 4.05/4.28 fof(fact_drop__1__Cons, axiom, ![X45, X13, X4]:X45=hAPP(hAPP(c_List_Odrop(X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__1__Cons)). 4.05/4.28 fof(fact_Pow__UNIV, axiom, ![X4]:hAPP(c_Set_OPow(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__UNIV)). 4.05/4.28 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int, axiom, ![X115, X60]:c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X60,X115)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X60),c_Groups_Oone__class_Oone(tc_Int_Oint))),X115), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastPlusOneLessThan__greaterThanLessThan__int)). 4.05/4.28 fof(fact_map__of_Osimps_I1_J, axiom, ![X52, X7, X4]:c_Option_Ooption_ONone(X7)=hAPP(hAPP(c_Map_Omap__of(X4,X7),c_List_Olist_ONil(tc_prod(X4,X7))),X52), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__of_Osimps_I1_J)). 4.05/4.28 fof(fact_diff__add__0, axiom, ![X2, X5]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__add__0)). 4.05/4.28 fof(fact_card__atLeastLessThan, axiom, ![X115, X60]:hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X60),X115))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X115),X60), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__atLeastLessThan)). 4.05/4.28 fof(fact_Pow__top, axiom, ![X3, X4]:hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(c_Set_OPow(X4),X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Pow__top)). 4.05/4.28 fof(fact_option_Orecs_I2_J, axiom, ![X26, X129, X130, X7, X4]:c_Option_Ooption_Ooption__rec(X4,X7,X130,X129,hAPP(c_Option_Ooption_OSome(X7),X26))=hAPP(X129,X26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Orecs_I2_J)). 4.05/4.28 fof(fact_neg__single__def, axiom, ![X95, X96, X97, X9, X4]:hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X4),X9),X97),X96),X95)=c_New__DSequence_Oneg__single(X4,X9), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__single__def)). 4.05/4.28 fof(fact_pos__single__def, axiom, ![X95, X96, X97, X9, X4]:c_New__DSequence_Opos__single(X4,X9)=hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X4),X9),X97),X96),X95), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pos__single__def)). 4.05/4.28 fof(fact__03, axiom, ![X249, X250, X13, X4]:c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X13,c_Lazy__Sequence_Oappend(X4,X250,X249))=c_Lazy__Sequence_Oappend(X4,c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X13,X250),X249), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact__03)). 4.05/4.28 fof(fact_Id__on__empty, axiom, ![X4]:c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))=c_Relation_OId__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Id__on__empty)). 4.05/4.28 fof(fact_length__rev, axiom, ![X45, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Orev(X4),X45))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__rev)). 4.05/4.28 fof(fact_length__rotate1, axiom, ![X45, X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X45)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),hAPP(c_List_Orotate1(X4),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__rotate1)). 4.05/4.28 fof(fact_transfer__morphism__int__nat, axiom, c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__morphism__int__nat)). 4.05/4.28 fof(fact_lists_ONil, axiom, ![X3, X4]:hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),c_List_Olist_ONil(X4)),c_List_Olists(X4,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists_ONil)). 4.05/4.28 fof(fact_div__int__def, axiom, ![X12, X11]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),X12)=hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X11,X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__int__def)). 4.05/4.28 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)). 4.05/4.28 fof(fact_override__on__emptyset, axiom, ![X76, X22, X7, X4]:X22=c_Fun_Ooverride__on(X4,X7,X22,X76,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_override__on__emptyset)). 4.05/4.28 fof(fact_fun__upd__same, axiom, ![X17, X9, X22, X4, X7]:X17=hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7,X4),X22),X9),X17),X9), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__same)). 4.05/4.28 fof(fact_diff__add__inverse2, axiom, ![X5, X2]:X2=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X5)),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__add__inverse2)). 4.05/4.28 fof(fact_diff__add__inverse, axiom, ![X2, X5]:X2=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X2)),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__add__inverse)). 4.05/4.28 fof(fact_fun__upd__triv, axiom, ![X9, X22, X7, X4]:X22=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X7),X22),X9),hAPP(X22,X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__upd__triv)). 4.05/4.28 fof(fact_fold__graph_H_Oequations_I1_J, axiom, ![X67, X70, X7, X4]:c_Nitpick_Ofold__graph_H(X4,X7,X70,X67,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),X67), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fold__graph_H_Oequations_I1_J)). 4.05/4.28 fof(fact_rel__pow__1, axiom, ![X39, X4]:X39=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X39), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__pow__1)). 4.05/4.28 fof(fact_Diff__cancel, axiom, ![X3, X4]:c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Diff__cancel)). 4.05/4.28 fof(fact_zip__Nil, axiom, ![X59, X7, X4]:c_List_Olist_ONil(tc_prod(X4,X7))=hAPP(hAPP(c_List_Ozip(X4,X7),c_List_Olist_ONil(X4)),X59), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip__Nil)). 4.05/4.28 fof(fact_zip_Osimps_I1_J, axiom, ![X45, X7, X4]:c_List_Olist_ONil(tc_prod(X4,X7))=hAPP(hAPP(c_List_Ozip(X4,X7),X45),c_List_Olist_ONil(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zip_Osimps_I1_J)). 4.05/4.28 fof(fact_diff__le__self, axiom, ![X5, X2]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X5)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__le__self)). 4.05/4.28 fof(fact_div__le__dividend, axiom, ![X5, X2]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X5)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_div__le__dividend)). 4.05/4.28 fof(fact_type__definition__code__numeral, axiom, c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition__code__numeral)). 4.05/4.28 fof(fact_neg__zminus__int, axiom, ![X5]: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,X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__zminus__int)). 4.05/4.28 fof(fact_insertI1, axiom, ![X6, X26, X4]:hBOOL(hAPP(hAPP(c_member(X4),X26),hAPP(hAPP(c_Set_Oinsert(X4),X26),X6))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insertI1)). 4.05/4.28 fof(fact_le__square, axiom, ![X2]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__square)). 4.05/4.28 fof(fact_le__add1, axiom, ![X2, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__add1)). 4.05/4.28 fof(fact_zmod__zdiv__trivial, axiom, ![X12, X11]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)),X12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zdiv__trivial)). 4.05/4.28 fof(fact_le__add2, axiom, ![X2, X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__add2)). 4.05/4.28 fof(fact_Field__converse, axiom, ![X18, X4]:hAPP(c_Relation_OField(X4),hAPP(c_Relation_Oconverse(X4,X4),X18))=hAPP(c_Relation_OField(X4),X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Field__converse)). 4.05/4.28 fof(fact_posDivAlg__0, axiom, ![X12]:c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)=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)). 4.05/4.28 fof(fact_lists__UNIV, axiom, ![X4]:c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X4),tc_HOL_Obool))=c_List_Olists(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lists__UNIV)). 4.05/4.28 fof(fact_refl__rtrancl, axiom, ![X18, X4]:c_Relation_Orefl__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__rtrancl)). 4.05/4.28 fof(fact_zero__zle__int, axiom, ![X5]: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),X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__zle__int)). 4.05/4.28 fof(fact_rev__replicate, axiom, ![X13, X5, X4]:hAPP(c_List_Orev(X4),c_List_Oreplicate(X4,X5,X13))=c_List_Oreplicate(X4,X5,X13), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev__replicate)). 4.05/4.28 fof(fact_mod__int__def, axiom, ![X12, X11]:c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X12)=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X11,X12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__int__def)). 4.05/4.28 fof(fact_insert__remdups, axiom, ![X45, X13, X4]:c_List_Oremdups(X4,c_List_Oinsert(X4,X13,X45))=c_List_Oinsert(X4,X13,c_List_Oremdups(X4,X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__remdups)). 4.05/4.28 fof(fact_Range__rtrancl, axiom, ![X39, X4]:hAPP(c_Relation_ORange(X4,X4),c_Transitive__Closure_Ortrancl(X4,X39))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__rtrancl)). 4.05/4.28 fof(fact_Domain__rtrancl, axiom, ![X39, X4]:c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Relation_ODomain(X4,X4),c_Transitive__Closure_Ortrancl(X4,X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__rtrancl)). 4.05/4.28 fof(fact_insert__Nil, axiom, ![X13, X4]:hAPP(hAPP(c_List_Olist_OCons(X4),X13),c_List_Olist_ONil(X4))=c_List_Oinsert(X4,X13,c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_insert__Nil)). 4.05/4.28 fof(fact_mod__less__eq__dividend, axiom, ![X5, X2]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X5)),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mod__less__eq__dividend)). 4.05/4.28 fof(fact_UNIV__I, axiom, ![X9, X4]:hBOOL(hAPP(hAPP(c_member(X4),X9),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UNIV__I)). 4.05/4.28 fof(fact_power_Opower_Opower__0, axiom, ![X26, X168, X169, X4]:hAPP(hAPP(c_Power_Opower_Opower(X4,X169,X168),X26),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X169, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_power_Opower_Opower__0)). 4.05/4.28 fof(fact_converse__converse, axiom, ![X18, X4, X7]:hAPP(c_Relation_Oconverse(X7,X4),hAPP(c_Relation_Oconverse(X4,X7),X18))=X18, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__converse)). 4.05/4.28 fof(fact_converse__Id__on, axiom, ![X3, X4]:c_Relation_OId__on(X4,X3)=hAPP(c_Relation_Oconverse(X4,X4),c_Relation_OId__on(X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_converse__Id__on)). 4.05/4.28 fof(fact_list__update__code_I1_J, axiom, ![X43, X46, X4]:c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Olist__update(X4,c_List_Olist_ONil(X4)),X46),X43), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__update__code_I1_J)). 4.05/4.28 fof(fact_sublist__empty, axiom, ![X32, X4]:c_List_Osublist(X4,X32,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_List_Olist_ONil(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__empty)). 4.05/4.28 fof(fact_funpow_Osimps_I1_J, axiom, ![X22, X4]:hAPP(hAPP(c_Nat_Ocompow(X4,X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22)=c_Fun_Oid(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_funpow_Osimps_I1_J)). 4.05/4.28 fof(fact_option__map__None, axiom, ![X22, X4, X7]:c_Option_Ooption_ONone(X4)=hAPP(hAPP(c_Option_Omap(X7,X4),X22),c_Option_Ooption_ONone(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option__map__None)). 4.05/4.28 fof(fact_wf__empty, axiom, ![X4]:c_Wellfounded_Owf(X4,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__empty)). 4.05/4.28 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1, axiom, ![X18, X4]:c_List_Olistrel(X4,c_Transitive__Closure_Ortrancl(X4,X18))=c_Transitive__Closure_Ortrancl(tc_List_Olist(X4),c_List_Olistrel1(X4,X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrel__rtrancl__eq__rtrancl__listrel1)). 4.05/4.28 fof(fact_Nitpick_Ofrac__def, axiom, ![X12, X11, X4]:c_Nitpick_OAbs__Frac(X4,c_Nitpick_Onorm__frac(X11,X12))=hAPP(hAPP(c_Nitpick_Ofrac(X4),X11),X12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_Ofrac__def)). 4.05/4.28 fof(fact_set__rev, axiom, ![X32, X4]:hAPP(c_List_Oset(X4),hAPP(c_List_Orev(X4),X32))=hAPP(c_List_Oset(X4),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__rev)). 4.05/4.28 fof(fact_set__rotate1, axiom, ![X32, X4]:hAPP(c_List_Oset(X4),X32)=hAPP(c_List_Oset(X4),hAPP(c_List_Orotate1(X4),X32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__rotate1)). 4.05/4.28 fof(fact_option_Osize_I4_J, axiom, ![X11, X4]:hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X4)),hAPP(c_Option_Ooption_OSome(X4),X11))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Osize_I4_J)). 4.05/4.28 fof(fact_abs__int__eq, axiom, ![X2]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)=hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_abs__int__eq)). 4.05/4.28 fof(fact_product_Osimps_I1_J, axiom, ![X280, X7, X4]:c_Enum_Oproduct(X4,X7,c_List_Olist_ONil(X4),X280)=c_List_Olist_ONil(tc_prod(X4,X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_product_Osimps_I1_J)). 4.05/4.28 fof(fact_id__o, axiom, ![X76, X4, X7]:hAPP(c_Fun_Ocomp(X7,X7,X4,c_Fun_Oid(X7)),X76)=X76, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_id__o)). 4.05/4.28 fof(fact_list_Osimps_I4_J, axiom, ![X129, X130, X7, X4]:hAPP(c_List_Olist_Olist__case(X4,X7,X130,X129),c_List_Olist_ONil(X7))=X130, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osimps_I4_J)). 4.05/4.28 fof(fact_foldl__Nil, axiom, ![X26, X22, X7, X4]:hAPP(c_List_Ofoldl(X4,X7,X22,X26),c_List_Olist_ONil(X7))=X26, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_foldl__Nil)). 4.05/4.28 fof(fact_o__id, axiom, ![X22, X7, X4]:hAPP(c_Fun_Ocomp(X4,X7,X4,X22),c_Fun_Oid(X4))=X22, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_o__id)). 4.05/4.28 fof(fact_option_Osimps_I4_J, axiom, ![X129, X130, X7, X4]:X130=hAPP(c_Option_Ooption_Ooption__case(X4,X7,X130,X129),c_Option_Ooption_ONone(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Osimps_I4_J)). 4.05/4.28 fof(fact_nat__case__Suc, axiom, ![X242, X129, X130, X4]:hAPP(X129,X242)=c_Nat_Onat_Onat__case(X4,X130,X129,hAPP(c_Nat_OSuc,X242)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__case__Suc)). 4.05/4.28 fof(fact_length__replicate, axiom, ![X13, X5, X4]:X5=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Oreplicate(X4,X5,X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_length__replicate)). 4.05/4.28 fof(fact_map__le__map__add, axiom, ![X76, X22, X7, X4]:c_Map_Omap__le(X4,X7,X22,c_Map_Omap__add(X4,X7,X76,X22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__le__map__add)). 4.05/4.28 fof(fact_hd_Osimps, axiom, ![X45, X13, X4]:X13=hAPP(c_List_Ohd(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_hd_Osimps)). 4.05/4.28 fof(fact_tl_Osimps_I2_J, axiom, ![X45, X13, X4]:X45=hAPP(c_List_Otl(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl_Osimps_I2_J)). 4.05/4.28 fof(fact_diff__Suc__1, axiom, ![X5]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X5)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X5, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__Suc__1)). 4.05/4.28 fof(fact_inj__on__empty, axiom, ![X22, X7, X4]:c_Fun_Oinj__on(X4,X7,X22,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__empty)). 4.05/4.28 fof(fact_inj__on__rev, axiom, ![X3, X4]:c_Fun_Oinj__on(tc_List_Olist(X4),tc_List_Olist(X4),c_List_Orev(X4),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__rev)). 4.05/4.28 fof(fact_Union__Pow__eq, axiom, ![X3, X4]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(c_Set_OPow(X4),X3))=X3, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Union__Pow__eq)). 4.05/4.28 fof(fact_atLeastSucLessThan__greaterThanLessThan, axiom, ![X115, X60]:c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X60,X115)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X60)),X115), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeastSucLessThan__greaterThanLessThan)). 4.05/4.28 fof(fact_number__of__code__numeral__def, axiom, c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral)=hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_number__of__code__numeral__def)). 4.05/4.28 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J, axiom, ![X8]: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)),X8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J)). 4.05/4.28 fof(fact_set__remdups, axiom, ![X32, X4]:hAPP(c_List_Oset(X4),c_List_Oremdups(X4,X32))=hAPP(c_List_Oset(X4),X32), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_set__remdups)). 4.05/4.28 fof(fact_Un__absorb, axiom, ![X3, X4]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X3)=X3, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Un__absorb)). 4.05/4.28 fof(fact_Int__absorb, axiom, ![X3, X4]:X3=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X3),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Int__absorb)). 4.05/4.28 fof(fact_zero__less__Suc, axiom, ![X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__less__Suc)). 4.05/4.28 fof(fact_subset__refl, axiom, ![X3, X4]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_subset__refl)). 4.05/4.28 fof(fact_finite__atLeastLessThan__int, axiom, ![X115, X60]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X60),X115))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__atLeastLessThan__int)). 4.05/4.28 fof(fact_finite__atLeastLessThan, axiom, ![X115, X60]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X60),X115))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__atLeastLessThan)). 4.05/4.28 fof(fact_map__upds__Nil1, axiom, ![X108, X21, X7, X4]:c_Map_Omap__upds(X4,X7,X21,c_List_Olist_ONil(X4),X108)=X21, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__Nil1)). 4.05/4.28 fof(fact_map__upds__Nil2, axiom, ![X109, X21, X7, X4]:c_Map_Omap__upds(X4,X7,X21,X109,c_List_Olist_ONil(X7))=X21, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__upds__Nil2)). 4.05/4.28 fof(fact_option_Orecs_I1_J, axiom, ![X129, X130, X7, X4]:X130=c_Option_Ooption_Ooption__rec(X4,X7,X130,X129,c_Option_Ooption_ONone(X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Orecs_I1_J)). 4.05/4.28 fof(fact_small__lazy__int__def, axiom, ![X44]:c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X44)=c_Lazy__Sequence_Osmall__lazy_H(X44,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X44)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_small__lazy__int__def)). 4.05/4.28 fof(fact_List_Omap_Oid, axiom, ![X4]:hAPP(c_List_Omap(X4,X4),c_Fun_Oid(X4))=c_Fun_Oid(tc_List_Olist(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Omap_Oid)). 4.05/4.28 fof(fact_conversep__conversep, axiom, ![X18, X4, X7]:c_Predicate_Oconversep(X7,X4,c_Predicate_Oconversep(X4,X7,X18))=X18, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conversep__conversep)). 4.05/4.28 fof(fact_Option_Omap_Oid, axiom, ![X4]:hAPP(c_Option_Omap(X4,X4),c_Fun_Oid(X4))=c_Fun_Oid(tc_Option_Ooption(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Option_Omap_Oid)). 4.05/4.28 fof(fact_Option_Omap_Oidentity, axiom, ![X4]:c_Fun_Oid(tc_Option_Ooption(X4))=hAPP(c_Option_Omap(X4,X4),c_COMBI(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Option_Omap_Oidentity)). 4.05/4.28 fof(fact_List_Omap_Oidentity, axiom, ![X4]:c_Fun_Oid(tc_List_Olist(X4))=hAPP(c_List_Omap(X4,X4),c_COMBI(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Omap_Oidentity)). 4.05/4.28 fof(fact_com_Osize_I16_J, axiom, ![X75, X94, X243]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(X243,X94,X75)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I16_J)). 4.05/4.28 fof(fact_map__filter__simps_I2_J, axiom, ![X22, X4, X7]:c_List_Omap__filter(X7,X4,X22,c_List_Olist_ONil(X7))=c_List_Olist_ONil(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__filter__simps_I2_J)). 4.05/4.28 fof(fact_take__0, axiom, ![X45, X4]:hAPP(hAPP(c_List_Otake(X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X45)=c_List_Olist_ONil(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__0)). 4.05/4.28 fof(fact_drop__Nil, axiom, ![X5, X4]:c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Odrop(X4),X5),c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__Nil)). 4.05/4.28 fof(fact_total__on__empty, axiom, ![X18, X4]:c_Relation_Ototal__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_total__on__empty)). 4.05/4.28 fof(fact_fun__left__comm__idem__insert, axiom, ![X4]:c_Finite__Set_Ofun__left__comm__idem(X4,tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_fun__left__comm__idem__insert)). 4.05/4.28 fof(fact_take__Nil, axiom, ![X5, X4]:c_List_Olist_ONil(X4)=hAPP(hAPP(c_List_Otake(X4),X5),c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_take__Nil)). 4.05/4.28 fof(fact_diff__0__eq__0, axiom, ![X5]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__0__eq__0)). 4.05/4.28 fof(fact_finite__atLeastAtMost__int, axiom, ![X115, X60]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X60,X115))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__atLeastAtMost__int)). 4.05/4.28 fof(fact_zdiv__zero, axiom, ![X12]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zdiv__zero)). 4.05/4.28 fof(fact_finite__atLeastAtMost, axiom, ![X115, X60]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X60,X115))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__atLeastAtMost)). 4.05/4.28 fof(fact_finite_Oequations_I1_J, axiom, ![X4]:hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite_Oequations_I1_J)). 4.05/4.28 fof(fact_DIVISION__BY__ZERO, axiom, ![X11]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11),c_Groups_Ozero__class_Ozero(tc_Int_Oint))&c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_DIVISION__BY__ZERO)). 4.05/4.28 fof(fact_nat__of__number, axiom, ![X107]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X107)=hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__of__number)). 4.05/4.28 fof(fact_image__ident, axiom, ![X203, X4]:hAPP(c_Set_Oimage(X4,X4,c_COMBI(X4)),X203)=X203, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__ident)). 4.05/4.28 fof(fact_inj__Some, axiom, ![X3, X4]:c_Fun_Oinj__on(X4,tc_Option_Ooption(X4),c_Option_Ooption_OSome(X4),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__Some)). 4.05/4.28 fof(fact_listrelp_Oequations_I1_J, axiom, ![X18, X4]:c_List_Olistrelp(X4,X18,c_List_Olist_ONil(X4),c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listrelp_Oequations_I1_J)). 4.05/4.28 fof(fact_image__id, axiom, ![X203, X4]:X203=hAPP(c_Set_Oimage(X4,X4,c_Fun_Oid(X4)),X203), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_image__id)). 4.05/4.28 fof(fact_nat__rec__0, axiom, ![X129, X130, X4]:hAPP(c_Nat_Onat_Onat__rec(X4,X130,X129),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X130, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__rec__0)). 4.05/4.28 fof(fact_Domain__Id__on, axiom, ![X3, X4]:hAPP(c_Relation_ODomain(X4,X4),c_Relation_OId__on(X4,X3))=X3, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Domain__Id__on)). 4.05/4.28 fof(fact_Range__Id__on, axiom, ![X3, X4]:X3=hAPP(c_Relation_ORange(X4,X4),c_Relation_OId__on(X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Range__Id__on)). 4.05/4.28 fof(fact_List_Oset_Osimps_I1_J, axiom, ![X4]:hAPP(c_List_Oset(X4),c_List_Olist_ONil(X4))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_List_Oset_Osimps_I1_J)). 4.05/4.28 fof(fact_rtrancl__idemp, axiom, ![X18, X4]:c_Transitive__Closure_Ortrancl(X4,c_Transitive__Closure_Ortrancl(X4,X18))=c_Transitive__Closure_Ortrancl(X4,X18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rtrancl__idemp)). 4.05/4.28 fof(fact_remdups__remdups, axiom, ![X45, X4]:c_List_Oremdups(X4,X45)=c_List_Oremdups(X4,c_List_Oremdups(X4,X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups__remdups)). 4.05/4.28 fof(fact_transpose_Osimps_I1_J, axiom, ![X4]:c_List_Otranspose(X4,c_List_Olist_ONil(tc_List_Olist(X4)))=c_List_Olist_ONil(tc_List_Olist(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transpose_Osimps_I1_J)). 4.05/4.28 fof(fact_New__DSequence_Opos__single__def, axiom, ![X202, X13, X4]:hAPP(c_Lazy__Sequence_Osingle(X4),X13)=hAPP(c_New__DSequence_Opos__single(X4,X13),X202), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__single__def)). 4.05/4.28 fof(fact_filter_Osimps_I1_J, axiom, ![X56, X4]:c_List_Olist_ONil(X4)=hAPP(c_List_Ofilter(X4,X56),c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_filter_Osimps_I1_J)). 4.05/4.28 fof(fact_list_Osize_I3_J, axiom, ![X4]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_Olist_ONil(X4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osize_I3_J)). 4.05/4.28 fof(fact_option_Osize_I3_J, axiom, ![X4]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X4)),c_Option_Ooption_ONone(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Osize_I3_J)). 4.05/4.28 fof(fact_code__numeral_Osimps_I4_J, axiom, ![X129, X130, X4]:c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X4,X130,X129,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=X130, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osimps_I4_J)). 4.05/4.28 fof(fact_nat__case__0, axiom, ![X129, X130, X4]:X130=c_Nat_Onat_Onat__case(X4,X130,X129,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__case__0)). 4.05/4.28 fof(help_c__COMBK__1, axiom, ![X262, X209, X7, X4]:X209=hAPP(hAPP(c_COMBK(X4,X7),X209),X262), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBK__1)). 4.05/4.28 fof(fact_append__Nil, axiom, ![X59, X4]:hAPP(hAPP(c_List_Oappend(X4),c_List_Olist_ONil(X4)),X59)=X59, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__Nil)). 4.05/4.28 fof(fact_drop__0, axiom, ![X45, X4]:X45=hAPP(hAPP(c_List_Odrop(X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X45), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_drop__0)). 4.05/4.28 fof(fact_append__Nil2, axiom, ![X45, X4]:hAPP(hAPP(c_List_Oappend(X4),X45),c_List_Olist_ONil(X4))=X45, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_append__Nil2)). 4.05/4.28 fof(fact_zmult__1, axiom, ![X29]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X29)=X29, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__1)). 4.05/4.28 fof(fact_plus__nat_Oadd__0, axiom, ![X5]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5)=X5, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_plus__nat_Oadd__0)). 4.05/4.28 fof(fact_nat__mult__1, axiom, ![X5]:X5=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__1)). 4.05/4.28 fof(fact_minus__nat_Odiff__0, axiom, ![X2]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_minus__nat_Odiff__0)). 4.05/4.28 fof(fact_zmult__1__right, axiom, ![X29]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X29),c_Groups_Oone__class_Oone(tc_Int_Oint))=X29, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmult__1__right)). 4.05/4.28 fof(fact_nat__mult__1__right, axiom, ![X5]:X5=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),c_Groups_Oone__class_Oone(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__mult__1__right)). 4.05/4.28 fof(fact_lessI, axiom, ![X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_OSuc,X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_lessI)). 4.05/4.28 fof(fact_zminus__zminus, axiom, ![X29]:X29=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zminus__zminus)). 4.05/4.28 fof(fact_Option_Oset_Osimps_I1_J, axiom, ![X4]:c_Option_Oset(X4,c_Option_Ooption_ONone(X4))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Option_Oset_Osimps_I1_J)). 4.05/4.28 fof(fact_New__DSequence_Oneg__single__def, axiom, ![X202, X13, X4]:c_Lazy__Sequence_Ohb__single(X4,X13)=hAPP(c_New__DSequence_Oneg__single(X4,X13),X202), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Oneg__single__def)). 4.05/4.28 fof(fact_inj__on__id2, axiom, ![X3, X4]:c_Fun_Oinj__on(X4,X4,c_COMBI(X4),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__id2)). 4.05/4.28 fof(fact_inj__on__id, axiom, ![X3, X4]:c_Fun_Oinj__on(X4,X4,c_Fun_Oid(X4),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__on__id)). 4.05/4.28 fof(fact_com_Osize_I8_J, axiom, ![X75, X94, X243]:c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(X243,X94,X75))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I8_J)). 4.05/4.28 fof(fact_refl__on__Id__on, axiom, ![X3, X4]:c_Relation_Orefl__on(X4,X3,c_Relation_OId__on(X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_refl__on__Id__on)). 4.05/4.28 fof(fact_top1I, axiom, ![X9, X4]:hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_top1I)). 4.05/4.28 fof(fact_single__valued__Id__on, axiom, ![X3, X4]:c_Relation_Osingle__valued(X4,X4,c_Relation_OId__on(X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_single__valued__Id__on)). 4.05/4.28 fof(fact_takeWhile_Osimps_I1_J, axiom, ![X56, X4]:c_List_OtakeWhile(X4,X56,c_List_Olist_ONil(X4))=c_List_Olist_ONil(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_takeWhile_Osimps_I1_J)). 4.05/4.28 fof(fact_listsp_ONil, axiom, ![X3, X4]:hBOOL(hAPP(c_List_Olistsp(X4,X3),c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_listsp_ONil)). 4.05/4.28 fof(fact_distinct__remdups, axiom, ![X45, X4]:hBOOL(hAPP(c_List_Odistinct(X4),c_List_Oremdups(X4,X45))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__remdups)). 4.05/4.28 fof(fact_distinct__upto, axiom, ![X135, X46]:hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X46,X135))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct__upto)). 4.05/4.28 fof(fact_sublist__nil, axiom, ![X3, X4]:c_List_Olist_ONil(X4)=c_List_Osublist(X4,c_List_Olist_ONil(X4),X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sublist__nil)). 4.05/4.28 fof(fact_remove1_Osimps_I1_J, axiom, ![X13, X4]:c_List_Olist_ONil(X4)=c_List_Oremove1(X4,X13,c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remove1_Osimps_I1_J)). 4.05/4.28 fof(fact_list_Osize_I1_J, axiom, ![X228, X4]:c_List_Olist_Olist__size(X4,X228,c_List_Olist_ONil(X4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list_Osize_I1_J)). 4.05/4.28 fof(fact_option_Osize_I1_J, axiom, ![X228, X4]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Option_Ooption_Ooption__size(X4,X228,c_Option_Ooption_ONone(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_option_Osize_I1_J)). 4.05/4.28 fof(fact_replicate__0, axiom, ![X13, X4]:c_List_Oreplicate(X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X13)=c_List_Olist_ONil(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_replicate__0)). 4.05/4.28 fof(fact_zmod__zero, axiom, ![X12]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__zero)). 4.05/4.28 fof(fact_diff__self__eq__0, axiom, ![X2]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_diff__self__eq__0)). 4.05/4.28 fof(fact_wf__finite__psubset, axiom, ![X4]:c_Wellfounded_Owf(tc_fun(X4,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__finite__psubset)). 4.05/4.28 fof(fact_rev_Osimps_I1_J, axiom, ![X4]:hAPP(c_List_Orev(X4),c_List_Olist_ONil(X4))=c_List_Olist_ONil(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rev_Osimps_I1_J)). 4.05/4.28 fof(fact_tl_Osimps_I1_J, axiom, ![X4]:c_List_Olist_ONil(X4)=hAPP(c_List_Otl(X4),c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tl_Osimps_I1_J)). 4.05/4.28 fof(fact_splice_Osimps_I1_J, axiom, ![X59, X4]:c_List_Osplice(X4,c_List_Olist_ONil(X4),X59)=X59, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_splice_Osimps_I1_J)). 4.05/4.28 fof(fact_the_Osimps, axiom, ![X13, X4]:hAPP(c_Option_Othe(X4),hAPP(c_Option_Ooption_OSome(X4),X13))=X13, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_the_Osimps)). 4.05/4.28 fof(fact_splice__Nil2, axiom, ![X45, X4]:X45=c_List_Osplice(X4,X45,c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_splice__Nil2)). 4.05/4.28 fof(fact_inj__Suc, axiom, ![X176]:c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X176), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__Suc)). 4.05/4.28 fof(fact_zmod__self, axiom, ![X11]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X11,X11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zmod__self)). 4.05/4.28 fof(fact_list__all__simps_I2_J, axiom, ![X56, X4]:c_List_Olist__all(X4,X56,c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_list__all__simps_I2_J)). 4.05/4.28 fof(fact_wf__measures, axiom, ![X278, X4]:c_Wellfounded_Owf(X4,c_List_Omeasures(X4,X278)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__measures)). 4.05/4.28 fof(fact_sorted__upto, axiom, ![X135, X46]:c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X46,X135)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_sorted__upto)). 4.05/4.28 fof(fact_eq__int__refl, axiom, ![X107]:hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X107),X107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_eq__int__refl)). 4.05/4.28 fof(fact_zle__refl, axiom, ![X53]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X53),X53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zle__refl)). 4.05/4.28 fof(fact_le__refl, axiom, ![X5]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_le__refl)). 4.05/4.28 fof(fact_rel__simps_I6_J, axiom, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I6_J)). 4.05/4.28 fof(fact_com_Osize_I15_J, axiom, ![X294]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OBODY(X294)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I15_J)). 4.05/4.28 fof(fact_rel__simps_I23_J, axiom, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_rel__simps_I23_J)). 4.05/4.28 fof(fact_neg__number__of__Min, axiom, hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_neg__number__of__Min)). 4.05/4.28 fof(fact_butlast_Osimps_I1_J, axiom, ![X4]:c_List_Obutlast(X4,c_List_Olist_ONil(X4))=c_List_Olist_ONil(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_butlast_Osimps_I1_J)). 4.05/4.28 fof(fact_distinct_Osimps_I1_J, axiom, ![X4]:hBOOL(hAPP(c_List_Odistinct(X4),c_List_Olist_ONil(X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_distinct_Osimps_I1_J)). 4.05/4.28 fof(fact_remdups_Osimps_I1_J, axiom, ![X4]:c_List_Olist_ONil(X4)=c_List_Oremdups(X4,c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_remdups_Osimps_I1_J)). 4.05/4.28 fof(fact_some__sym__eq__trivial, axiom, ![X9, X4]:c_Hilbert__Choice_OEps(X4,hAPP(c_fequal,X9))=X9, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_some__sym__eq__trivial)). 4.05/4.28 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J, axiom, ![X29]:c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J)). 4.05/4.28 fof(fact_New__DSequence_Opos__empty__def, axiom, ![X202, X4]:hAPP(c_New__DSequence_Opos__empty(X4),X202)=c_Lazy__Sequence_Oempty(X4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_New__DSequence_Opos__empty__def)). 4.05/4.28 fof(fact_map__le__refl, axiom, ![X22, X7, X4]:c_Map_Omap__le(X4,X7,X22,X22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_map__le__refl)). 4.05/4.28 fof(fact_zero__code__numeral__code, axiom, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls)=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__code__numeral__code)). 4.05/4.28 fof(fact_conversep__eq, axiom, ![X4]:c_fequal=c_Predicate_Oconversep(X4,X4,c_fequal), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_conversep__eq)). 4.05/4.28 fof(fact_Rep__Integ__inverse, axiom, ![X9]:X9=hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Rep__Integ__inverse)). 4.05/4.28 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)). 4.05/4.28 fof(arity_Nitpick__Opair____box__HOL_Oequal, axiom, ![X155, X164]:class_HOL_Oequal(tc_Nitpick_Opair__box(X164,X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nitpick__Opair____box__HOL_Oequal)). 4.05/4.28 fof(arity_sum__HOL_Oequal, axiom, ![X155, X164]:class_HOL_Oequal(tc_sum(X164,X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_sum__HOL_Oequal)). 4.05/4.28 fof(arity_prod__HOL_Oequal, axiom, ![X155, X164]:class_HOL_Oequal(tc_prod(X164,X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_prod__HOL_Oequal)). 4.05/4.28 fof(arity_Nitpick__Opair____box__Nat_Osize, axiom, ![X155, X164]:class_Nat_Osize(tc_Nitpick_Opair__box(X164,X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nitpick__Opair____box__Nat_Osize)). 4.05/4.28 fof(arity_sum__Nat_Osize, axiom, ![X155, X164]:class_Nat_Osize(tc_sum(X164,X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_sum__Nat_Osize)). 4.05/4.28 fof(arity_prod__Nat_Osize, axiom, ![X155, X164]:class_Nat_Osize(tc_prod(X164,X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_prod__Nat_Osize)). 4.05/4.28 fof(fact_is__none__code_I1_J, axiom, ![X4]:c_Option_Ois__none(X4,c_Option_Ooption_ONone(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_is__none__code_I1_J)). 4.05/4.28 fof(fact_wf__int__ge__less__than2, axiom, ![X102]:c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X102)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__int__ge__less__than2)). 4.05/4.28 fof(fact_wf__int__ge__less__than, axiom, ![X102]:c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X102)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__int__ge__less__than)). 4.05/4.28 fof(help_c__COMBI__1, axiom, ![X209, X4]:X209=hAPP(c_COMBI(X4),X209), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__COMBI__1)). 4.05/4.28 fof(fact_id__def, axiom, ![X52, X4]:X52=hAPP(c_Fun_Oid(X4),X52), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_id__def)). 4.05/4.28 fof(fact_nat__size, axiom, ![X5]:X5=hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat__size)). 4.05/4.28 fof(fact_com_Osize_I7_J, axiom, ![X294]:c_Com_Ocom_Ocom__size(c_Com_Ocom_OBODY(X294))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_com_Osize_I7_J)). 4.05/4.28 fof(fact_identity__equivp, axiom, ![X4]:c_Equiv__Relations_Oequivp(X4,c_fequal), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_identity__equivp)). 4.05/4.28 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal, axiom, ![X155]:class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal)). 4.05/4.28 fof(arity_Option__Ooption__HOL_Oequal, axiom, ![X155]:class_HOL_Oequal(tc_Option_Ooption(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Option__Ooption__HOL_Oequal)). 4.05/4.28 fof(arity_List__Olist__HOL_Oequal, axiom, ![X155]:class_HOL_Oequal(tc_List_Olist(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_List__Olist__HOL_Oequal)). 4.05/4.28 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize, axiom, ![X155]:class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Lazy____Sequence__Olazy____sequence__Nat_Osize)). 4.05/4.28 fof(arity_Option__Ooption__Nat_Osize, axiom, ![X155]:class_Nat_Osize(tc_Option_Ooption(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Option__Ooption__Nat_Osize)). 4.05/4.28 fof(arity_List__Olist__Nat_Osize, axiom, ![X155]:class_Nat_Osize(tc_List_Olist(X155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_List__Olist__Nat_Osize)). 4.05/4.28 fof(fact_int__0__neq__1, axiom, 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__neq__1)). 4.05/4.28 fof(fact_Nitpick_OFrac__def, axiom, hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Nitpick_OFrac, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nitpick_OFrac__def)). 4.05/4.28 fof(fact_max__rpair__set, axiom, c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__rpair__set)). 4.05/4.28 fof(fact_min__rpair__set, axiom, c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_min__rpair__set)). 4.05/4.28 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)). 4.05/4.28 fof(fact_UN__lessThan__UNIV, axiom, c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__lessThan__UNIV)). 4.05/4.28 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)). 4.05/4.28 fof(fact_UN__atLeast__UNIV, axiom, c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_UN__atLeast__UNIV)). 4.05/4.28 fof(fact_Integ__def, axiom, c_Int_OInteg=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), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Integ__def)). 4.05/4.28 fof(fact_equiv__intrel, axiom, c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_equiv__intrel)). 4.05/4.28 fof(fact_type__definition__Integ, axiom, c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_type__definition__Integ)). 4.05/4.28 fof(fact_greaterThan__0, axiom, hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_greaterThan__0)). 4.05/4.28 fof(fact_inj__int, axiom, c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_inj__int)). 4.05/4.28 fof(fact_transfer__morphism__nat__int, axiom, c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_transfer__morphism__nat__int)). 4.05/4.28 fof(fact_code__numeral__zero__minus__one, axiom, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral__zero__minus__one)). 4.05/4.28 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)). 4.05/4.28 fof(fact_card__UNIV__unit, axiom, c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_card__UNIV__unit)). 4.05/4.28 fof(fact_int__0__less__1, axiom, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__0__less__1)). 4.05/4.28 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, axiom, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J)). 4.05/4.28 fof(fact_atLeast__0, axiom, 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)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_atLeast__0)). 4.05/4.28 fof(fact_pair__less__def, axiom, c_FunDef_Opair__less=c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_pair__less__def)). 4.05/4.28 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)). 4.05/4.28 fof(fact_code__numeral_Osize_I3_J, axiom, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osize_I3_J)). 4.05/4.28 fof(conj_3, hypothesis, hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_3)). 4.05/4.28 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)). 4.05/4.28 fof(fact_max__strict__def, axiom, c_FunDef_Omax__strict=c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_max__strict__def)). 4.05/4.28 fof(fact_int__1, axiom, c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_int__1)). 4.05/4.28 fof(fact_finite__dom__body, axiom, hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_finite__dom__body)). 4.05/4.28 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J, axiom, c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J)). 4.05/4.28 fof(fact_wf__pair__less, axiom, c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__pair__less)). 4.05/4.28 fof(fact_bool_Osize_I4_J, axiom, hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bool_Osize_I4_J)). 4.05/4.28 fof(fact_bool_Osize_I3_J, axiom, hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bool_Osize_I3_J)). 4.05/4.28 fof(fact_body__def, axiom, c_Com_Obody=hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_body__def)). 4.05/4.28 fof(fact_wf__less__than, axiom, c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__less__than)). 4.05/4.28 fof(fact_wf__pred__nat, axiom, c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_wf__pred__nat)). 4.05/4.28 fof(fact_code__numeral_Osize_I1_J, axiom, c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_code__numeral_Osize_I1_J)). 4.05/4.28 fof(fact_nat_Osize_I1_J, axiom, c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_nat_Osize_I1_J)). 4.05/4.28 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J, axiom, c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J)). 4.05/4.28 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J, axiom, c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J)). 4.05/4.28 fof(fact_bool_Osize_I2_J, axiom, c_HOL_Obool_Obool__size(c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bool_Osize_I2_J)). 4.05/4.28 fof(fact_bool_Osize_I1_J, axiom, c_HOL_Obool_Obool__size(c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_bool_Osize_I1_J)). 4.05/4.28 fof(fact_of__int__eq__id, axiom, c_Fun_Oid(tc_Int_Oint)=c_Int_Oring__1__class_Oof__int(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_of__int__eq__id)). 4.05/4.28 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)). 4.05/4.28 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, axiom, class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__comm__semiring__strict)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict, axiom, class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict)). 4.05/4.28 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict, axiom, class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict)). 4.05/4.28 fof(arity_Int__Oint__Groups_Oabs__if, axiom, class_Groups_Oabs__if(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oabs__if)). 4.05/4.28 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot, axiom, class_Lattices_Obounded__lattice__bot(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Obounded__lattice__bot)). 4.05/4.28 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add, axiom, class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ocancel__ab__semigroup__add)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add, axiom, class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add)). 4.05/4.28 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, axiom, class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add)). 4.05/4.28 fof(arity_Int__Oint__Groups_Oab__semigroup__add, axiom, class_Groups_Oab__semigroup__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oab__semigroup__add)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add, axiom, class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add)). 4.05/4.28 fof(arity_Nat__Onat__Groups_Oab__semigroup__add, axiom, class_Groups_Oab__semigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oab__semigroup__add)). 4.05/4.28 fof(arity_Int__Oint__Rings_Olinordered__semiring, axiom, class_Rings_Olinordered__semiring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__semiring)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring, axiom, class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring)). 4.05/4.28 fof(arity_Nat__Onat__Rings_Olinordered__semiring, axiom, class_Rings_Olinordered__semiring(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Olinordered__semiring)). 4.05/4.28 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors, axiom, class_Rings_Oring__no__zero__divisors(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oring__no__zero__divisors)). 4.05/4.28 fof(arity_Nat__Onat__Orderings_Owellorder, axiom, class_Orderings_Owellorder(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Orderings_Owellorder)). 4.05/4.28 fof(arity_Int__Oint__Rings_Ocomm__ring__1, axiom, class_Rings_Ocomm__ring__1(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ocomm__ring__1)). 4.05/4.28 fof(arity_Int__Oint__Groups_Osgn__if, axiom, class_Groups_Osgn__if(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Osgn__if)). 4.05/4.28 fof(arity_Int__Oint__Rings_Oidom, axiom, class_Rings_Oidom(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oidom)). 4.05/4.28 fof(arity_Product____Type__Ounit__Smallcheck_Osmall, axiom, class_Smallcheck_Osmall(tc_Product__Type_Ounit), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Product____Type__Ounit__Smallcheck_Osmall)). 4.05/4.28 fof(arity_Int__Oint__Smallcheck_Osmall, axiom, class_Smallcheck_Osmall(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Smallcheck_Osmall)). 4.05/4.28 fof(arity_Int__Oint__Int_Oring__char__0, axiom, class_Int_Oring__char__0(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Int_Oring__char__0)). 4.05/4.28 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, axiom, class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le, axiom, class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le)). 4.05/4.28 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le, axiom, class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le)). 4.05/4.28 fof(arity_Int__Oint__Rings_Ocomm__semiring, axiom, class_Rings_Ocomm__semiring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ocomm__semiring)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring, axiom, class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring)). 4.05/4.28 fof(arity_Nat__Onat__Rings_Ocomm__semiring, axiom, class_Rings_Ocomm__semiring(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Ocomm__semiring)). 4.05/4.28 fof(arity_HOL__Obool__Orderings_Obot, axiom, class_Orderings_Obot(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Orderings_Obot)). 4.05/4.28 fof(arity_Nat__Onat__Orderings_Obot, axiom, class_Orderings_Obot(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Orderings_Obot)). 4.05/4.28 fof(arity_Int__Oint__Lattices_Odistrib__lattice, axiom, class_Lattices_Odistrib__lattice(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Lattices_Odistrib__lattice)). 4.05/4.28 fof(arity_HOL__Obool__Lattices_Odistrib__lattice, axiom, class_Lattices_Odistrib__lattice(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Odistrib__lattice)). 4.05/4.28 fof(arity_Nat__Onat__Lattices_Odistrib__lattice, axiom, class_Lattices_Odistrib__lattice(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Lattices_Odistrib__lattice)). 4.05/4.28 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add, axiom, class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Olinordered__ab__semigroup__add)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add, axiom, class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add)). 4.05/4.28 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add, axiom, class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add)). 4.05/4.28 fof(arity_Int__Oint__Groups_Osemigroup__add, axiom, class_Groups_Osemigroup__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Osemigroup__add)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add, axiom, class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add)). 4.05/4.28 fof(arity_Nat__Onat__Groups_Osemigroup__add, axiom, class_Groups_Osemigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Osemigroup__add)). 4.05/4.28 fof(arity_Int__Oint__Rings_Olinordered__ring__strict, axiom, class_Rings_Olinordered__ring__strict(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__ring__strict)). 4.05/4.28 fof(arity_Int__Oint__Groups_Ouminus, axiom, class_Groups_Ouminus(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ouminus)). 4.05/4.28 fof(arity_HOL__Obool__Groups_Ouminus, axiom, class_Groups_Ouminus(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Groups_Ouminus)). 4.05/4.28 fof(arity_Int__Oint__Rings_Ono__zero__divisors, axiom, class_Rings_Ono__zero__divisors(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ono__zero__divisors)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors, axiom, class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors)). 4.05/4.28 fof(arity_Nat__Onat__Rings_Ono__zero__divisors, axiom, class_Rings_Ono__zero__divisors(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Ono__zero__divisors)). 4.05/4.28 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top, axiom, class_Lattices_Obounded__lattice__top(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Obounded__lattice__top)). 4.05/4.28 fof(arity_Int__Oint__Rings_Oordered__ring__abs, axiom, class_Rings_Oordered__ring__abs(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oordered__ring__abs)). 4.05/4.28 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add, axiom, class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add, axiom, class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add)). 4.05/4.28 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add, axiom, class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add)). 4.05/4.28 fof(arity_Int__Oint__Groups_Oab__semigroup__mult, axiom, class_Groups_Oab__semigroup__mult(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oab__semigroup__mult)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult, axiom, class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult)). 4.05/4.28 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult, axiom, class_Groups_Oab__semigroup__mult(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oab__semigroup__mult)). 4.05/4.28 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, axiom, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct)). 4.05/4.28 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, axiom, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct)). 4.05/4.28 fof(arity_Int__Oint__Rings_Oordered__comm__semiring, axiom, class_Rings_Oordered__comm__semiring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oordered__comm__semiring)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring, axiom, class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring)). 4.05/4.28 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring, axiom, class_Rings_Oordered__comm__semiring(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Oordered__comm__semiring)). 4.05/4.28 fof(arity_Int__Oint__Groups_Omonoid__add, axiom, class_Groups_Omonoid__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Omonoid__add)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add, axiom, class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add)). 4.05/4.28 fof(arity_Nat__Onat__Groups_Omonoid__add, axiom, class_Groups_Omonoid__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Omonoid__add)). 4.05/4.28 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring, axiom, class_Rings_Oordered__cancel__semiring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oordered__cancel__semiring)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring, axiom, class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring)). 4.05/4.28 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring, axiom, class_Rings_Oordered__cancel__semiring(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Oordered__cancel__semiring)). 4.05/4.28 fof(arity_Int__Oint__Groups_Omonoid__mult, axiom, class_Groups_Omonoid__mult(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Omonoid__mult)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult, axiom, class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult)). 4.05/4.28 fof(arity_Nat__Onat__Groups_Omonoid__mult, axiom, class_Groups_Omonoid__mult(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Omonoid__mult)). 4.05/4.28 fof(arity_Int__Oint__Groups_Oone, axiom, class_Groups_Oone(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oone)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone, axiom, class_Groups_Oone(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Oone)). 4.05/4.28 fof(arity_Nat__Onat__Groups_Oone, axiom, class_Groups_Oone(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oone)). 4.05/4.28 fof(arity_Product____Type__Ounit__HOL_Oequal, axiom, class_HOL_Oequal(tc_Product__Type_Ounit), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Product____Type__Ounit__HOL_Oequal)). 4.05/4.28 fof(arity_Code____Evaluation__Oterm__HOL_Oequal, axiom, class_HOL_Oequal(tc_Code__Evaluation_Oterm), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Evaluation__Oterm__HOL_Oequal)). 4.05/4.28 fof(arity_Com__Ostate__HOL_Oequal, axiom, class_HOL_Oequal(tc_Com_Ostate), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Com__Ostate__HOL_Oequal)). 4.05/4.28 fof(arity_Com__Ovname__HOL_Oequal, axiom, class_HOL_Oequal(tc_Com_Ovname), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Com__Ovname__HOL_Oequal)). 4.05/4.28 fof(arity_Int__Oint__HOL_Oequal, axiom, class_HOL_Oequal(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__HOL_Oequal)). 4.05/4.28 fof(arity_HOL__Obool__HOL_Oequal, axiom, class_HOL_Oequal(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__HOL_Oequal)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal, axiom, class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__HOL_Oequal)). 4.05/4.28 fof(arity_Nat__Onat__HOL_Oequal, axiom, class_HOL_Oequal(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__HOL_Oequal)). 4.05/4.28 fof(arity_HOL__Obool__Lattices_Obounded__lattice, axiom, class_Lattices_Obounded__lattice(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Obounded__lattice)). 4.05/4.28 fof(arity_Int__Oint__Nat_Osemiring__char__0, axiom, class_Nat_Osemiring__char__0(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Nat_Osemiring__char__0)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0, axiom, class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0)). 4.05/4.28 fof(arity_Nat__Onat__Nat_Osemiring__char__0, axiom, class_Nat_Osemiring__char__0(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Nat_Osemiring__char__0)). 4.05/4.28 fof(arity_Int__Oint__Groups_Ominus, axiom, class_Groups_Ominus(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ominus)). 4.05/4.28 fof(arity_HOL__Obool__Groups_Ominus, axiom, class_Groups_Ominus(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Groups_Ominus)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus, axiom, class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Ominus)). 4.05/4.28 fof(arity_Nat__Onat__Groups_Ominus, axiom, class_Groups_Ominus(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ominus)). 4.05/4.28 fof(arity_Int__Oint__Rings_Oordered__ring, axiom, class_Rings_Oordered__ring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oordered__ring)). 4.05/4.28 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add, axiom, class_Groups_Oordered__comm__monoid__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__comm__monoid__add)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add, axiom, class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add)). 4.05/4.28 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add, axiom, class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oordered__comm__monoid__add)). 4.05/4.28 fof(arity_Int__Oint__Rings_Oordered__semiring, axiom, class_Rings_Oordered__semiring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oordered__semiring)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring, axiom, class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring)). 4.05/4.28 fof(arity_Nat__Onat__Rings_Oordered__semiring, axiom, class_Rings_Oordered__semiring(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Oordered__semiring)). 4.05/4.28 fof(arity_Int__Oint__Rings_Olinordered__ring, axiom, class_Rings_Olinordered__ring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__ring)). 4.05/4.28 fof(arity_Int__Oint__Rings_Omult__zero, axiom, class_Rings_Omult__zero(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Omult__zero)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero, axiom, class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero)). 4.05/4.28 fof(arity_Nat__Onat__Rings_Omult__zero, axiom, class_Rings_Omult__zero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Omult__zero)). 4.05/4.28 fof(arity_HOL__Obool__Lattices_Oboolean__algebra, axiom, class_Lattices_Oboolean__algebra(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Oboolean__algebra)). 4.05/4.28 fof(arity_Int__Oint__Rings_Ozero__neq__one, axiom, class_Rings_Ozero__neq__one(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ozero__neq__one)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one, axiom, class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one)). 4.05/4.28 fof(arity_Nat__Onat__Rings_Ozero__neq__one, axiom, class_Rings_Ozero__neq__one(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Ozero__neq__one)). 4.05/4.28 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors, axiom, class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oring__1__no__zero__divisors)). 4.05/4.28 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite, axiom, class_Finite__Set_Ofinite(tc_Product__Type_Ounit), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Product____Type__Ounit__Finite__Set_Ofinite)). 4.05/4.28 fof(arity_HOL__Obool__Finite__Set_Ofinite, axiom, class_Finite__Set_Ofinite(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Finite__Set_Ofinite)). 4.05/4.28 fof(arity_Int__Oint__Rings_Oring, axiom, class_Rings_Oring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oring)). 4.05/4.28 fof(arity_HOL__Obool__Orderings_Otop, axiom, class_Orderings_Otop(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Orderings_Otop)). 4.05/4.28 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add, axiom, class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__ab__semigroup__add)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add, axiom, class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add)). 4.05/4.28 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add, axiom, class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Oordered__ab__semigroup__add)). 4.05/4.28 fof(arity_Int__Oint__Rings_Osemiring, axiom, class_Rings_Osemiring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Osemiring)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring, axiom, class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Osemiring)). 4.05/4.28 fof(arity_Nat__Onat__Rings_Osemiring, axiom, class_Rings_Osemiring(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Osemiring)). 4.05/4.28 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add, axiom, class_Groups_Olinordered__ab__group__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Olinordered__ab__group__add)). 4.05/4.28 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add, axiom, class_Groups_Ocancel__semigroup__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ocancel__semigroup__add)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add, axiom, class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add)). 4.05/4.28 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add, axiom, class_Groups_Ocancel__semigroup__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ocancel__semigroup__add)). 4.05/4.28 fof(arity_Int__Oint__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Orderings_Opreorder)). 4.05/4.28 fof(arity_HOL__Obool__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Orderings_Opreorder)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder)). 4.05/4.28 fof(arity_Nat__Onat__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Orderings_Opreorder)). 4.05/4.28 fof(arity_Product____Type__Ounit__Nat_Osize, axiom, class_Nat_Osize(tc_Product__Type_Ounit), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Product____Type__Ounit__Nat_Osize)). 4.05/4.28 fof(arity_Code____Evaluation__Oterm__Nat_Osize, axiom, class_Nat_Osize(tc_Code__Evaluation_Oterm), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Evaluation__Oterm__Nat_Osize)). 4.05/4.28 fof(arity_Com__Ostate__Nat_Osize, axiom, class_Nat_Osize(tc_Com_Ostate), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Com__Ostate__Nat_Osize)). 4.05/4.28 fof(arity_Com__Ovname__Nat_Osize, axiom, class_Nat_Osize(tc_Com_Ovname), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Com__Ovname__Nat_Osize)). 4.05/4.28 fof(arity_HOL__Obool__Nat_Osize, axiom, class_Nat_Osize(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Nat_Osize)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize, axiom, class_Nat_Osize(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Nat_Osize)). 4.05/4.28 fof(arity_Nat__Onat__Nat_Osize, axiom, class_Nat_Osize(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Nat_Osize)). 4.05/4.28 fof(arity_Int__Oint__Divides_Oring__div, axiom, class_Divides_Oring__div(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Divides_Oring__div)). 4.05/4.28 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict, axiom, class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__semiring__1__strict)). 4.05/4.28 fof(arity_Int__Oint__Rings_Olinordered__semidom, axiom, class_Rings_Olinordered__semidom(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__semidom)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom, axiom, class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom)). 4.05/4.28 fof(arity_Nat__Onat__Rings_Olinordered__semidom, axiom, class_Rings_Olinordered__semidom(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Olinordered__semidom)). 4.05/4.28 fof(arity_Int__Oint__Groups_Ozero, axiom, class_Groups_Ozero(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ozero)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero, axiom, class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Ozero)). 4.05/4.28 fof(arity_Nat__Onat__Groups_Ozero, axiom, class_Groups_Ozero(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ozero)). 4.05/4.28 fof(arity_Int__Oint__Rings_Olinordered__semiring__1, axiom, class_Rings_Olinordered__semiring__1(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__semiring__1)). 4.05/4.28 fof(arity_Int__Oint__Rings_Osemiring__1, axiom, class_Rings_Osemiring__1(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Osemiring__1)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1, axiom, class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1)). 4.05/4.28 fof(arity_Nat__Onat__Rings_Osemiring__1, axiom, class_Rings_Osemiring__1(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Osemiring__1)). 4.05/4.28 fof(arity_Int__Oint__Rings_Osemiring__0, axiom, class_Rings_Osemiring__0(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Osemiring__0)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0, axiom, class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0)). 4.05/4.28 fof(arity_Nat__Onat__Rings_Osemiring__0, axiom, class_Rings_Osemiring__0(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Osemiring__0)). 4.05/4.28 fof(arity_Int__Oint__Rings_Olinordered__idom, axiom, class_Rings_Olinordered__idom(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__idom)). 4.05/4.28 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy, axiom, class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy)). 4.05/4.28 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy, axiom, class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Lazy__Sequence_Osmall__lazy)). 4.05/4.28 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs, axiom, class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__ab__group__add__abs)). 4.05/4.28 fof(arity_Product____Type__Ounit__Enum_Oenum, axiom, class_Enum_Oenum(tc_Product__Type_Ounit), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Product____Type__Ounit__Enum_Oenum)). 4.05/4.28 fof(arity_HOL__Obool__Enum_Oenum, axiom, class_Enum_Oenum(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Enum_Oenum)). 4.05/4.28 fof(arity_Int__Oint__Rings_Oring__1, axiom, class_Rings_Oring__1(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Oring__1)). 4.05/4.28 fof(arity_Int__Oint__Int_Onumber__ring, axiom, class_Int_Onumber__ring(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Int_Onumber__ring)). 4.05/4.28 fof(arity_Int__Oint__Orderings_Oorder, axiom, class_Orderings_Oorder(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Orderings_Oorder)). 4.05/4.28 fof(arity_HOL__Obool__Orderings_Oorder, axiom, class_Orderings_Oorder(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Orderings_Oorder)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder, axiom, class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Orderings_Oorder)). 4.05/4.28 fof(arity_Nat__Onat__Orderings_Oorder, axiom, class_Orderings_Oorder(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Orderings_Oorder)). 4.05/4.28 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult, axiom, class_Groups_Ocomm__monoid__mult(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ocomm__monoid__mult)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult, axiom, class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult)). 4.05/4.28 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult, axiom, class_Groups_Ocomm__monoid__mult(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ocomm__monoid__mult)). 4.05/4.28 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict, axiom, class_Rings_Olinordered__semiring__strict(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Olinordered__semiring__strict)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict, axiom, class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict)). 4.05/4.28 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict, axiom, class_Rings_Olinordered__semiring__strict(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Olinordered__semiring__strict)). 4.05/4.28 fof(arity_Int__Oint__Groups_Oordered__ab__group__add, axiom, class_Groups_Oordered__ab__group__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oordered__ab__group__add)). 4.05/4.28 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice, axiom, class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice)). 4.05/4.28 fof(arity_Int__Oint__Groups_Ogroup__add, axiom, class_Groups_Ogroup__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ogroup__add)). 4.05/4.28 fof(arity_Int__Oint__Lattices_Osemilattice__inf, axiom, class_Lattices_Osemilattice__inf(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Lattices_Osemilattice__inf)). 4.05/4.28 fof(arity_HOL__Obool__Lattices_Osemilattice__inf, axiom, class_Lattices_Osemilattice__inf(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Osemilattice__inf)). 4.05/4.28 fof(arity_Nat__Onat__Lattices_Osemilattice__inf, axiom, class_Lattices_Osemilattice__inf(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Lattices_Osemilattice__inf)). 4.05/4.28 fof(arity_Int__Oint__Orderings_Oord, axiom, class_Orderings_Oord(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Orderings_Oord)). 4.05/4.28 fof(arity_HOL__Obool__Orderings_Oord, axiom, class_Orderings_Oord(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Orderings_Oord)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord, axiom, class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Orderings_Oord)). 4.05/4.28 fof(arity_Nat__Onat__Orderings_Oord, axiom, class_Orderings_Oord(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Orderings_Oord)). 4.05/4.28 fof(arity_Int__Oint__Lattices_Osemilattice__sup, axiom, class_Lattices_Osemilattice__sup(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Lattices_Osemilattice__sup)). 4.05/4.28 fof(arity_HOL__Obool__Lattices_Osemilattice__sup, axiom, class_Lattices_Osemilattice__sup(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Osemilattice__sup)). 4.05/4.28 fof(arity_Nat__Onat__Lattices_Osemilattice__sup, axiom, class_Lattices_Osemilattice__sup(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Lattices_Osemilattice__sup)). 4.05/4.28 fof(arity_Int__Oint__Int_Onumber, axiom, class_Int_Onumber(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Int_Onumber)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber, axiom, class_Int_Onumber(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Int_Onumber)). 4.05/4.28 fof(arity_Nat__Onat__Int_Onumber, axiom, class_Int_Onumber(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Int_Onumber)). 4.05/4.28 fof(arity_Int__Oint__Groups_Ocomm__monoid__add, axiom, class_Groups_Ocomm__monoid__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Ocomm__monoid__add)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add, axiom, class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add)). 4.05/4.28 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add, axiom, class_Groups_Ocomm__monoid__add(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Groups_Ocomm__monoid__add)). 4.05/4.28 fof(arity_Int__Oint__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Rings_Ocomm__semiring__1)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1)). 4.05/4.28 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Rings_Ocomm__semiring__1)). 4.05/4.28 fof(arity_Int__Oint__Orderings_Olinorder, axiom, class_Orderings_Olinorder(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Orderings_Olinorder)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder, axiom, class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder)). 4.05/4.28 fof(arity_Nat__Onat__Orderings_Olinorder, axiom, class_Orderings_Olinorder(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Orderings_Olinorder)). 4.05/4.28 fof(arity_Int__Oint__Power_Opower, axiom, class_Power_Opower(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Power_Opower)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower, axiom, class_Power_Opower(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Power_Opower)). 4.05/4.28 fof(arity_Nat__Onat__Power_Opower, axiom, class_Power_Opower(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Power_Opower)). 4.05/4.28 fof(arity_Int__Oint__Groups_Oab__group__add, axiom, class_Groups_Oab__group__add(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Groups_Oab__group__add)). 4.05/4.28 fof(arity_Int__Oint__Lattices_Olattice, axiom, class_Lattices_Olattice(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Lattices_Olattice)). 4.05/4.28 fof(arity_HOL__Obool__Lattices_Olattice, axiom, class_Lattices_Olattice(tc_HOL_Obool), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_HOL__Obool__Lattices_Olattice)). 4.05/4.28 fof(arity_Nat__Onat__Lattices_Olattice, axiom, class_Lattices_Olattice(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Lattices_Olattice)). 4.05/4.28 fof(arity_Int__Oint__Divides_Osemiring__div, axiom, class_Divides_Osemiring__div(tc_Int_Oint), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Int__Oint__Divides_Osemiring__div)). 4.05/4.28 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div, axiom, class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div)). 4.05/4.28 fof(arity_Nat__Onat__Divides_Osemiring__div, axiom, class_Divides_Osemiring__div(tc_Nat_Onat), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Nat__Onat__Divides_Osemiring__div)). 4.05/4.28 fof(conj_2, hypothesis, hBOOL(hAPP(c_Com_OWT,v_c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_2)). 4.05/4.28 fof(arity_Com__Ocom__HOL_Oequal, axiom, class_HOL_Oequal(tc_Com_Ocom), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Com__Ocom__HOL_Oequal)). 4.05/4.28 fof(arity_Com__Ocom__Nat_Osize, axiom, class_Nat_Osize(tc_Com_Ocom), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Com__Ocom__Nat_Osize)). 4.05/4.28 fof(help_c__fTrue__1, axiom, hBOOL(c_fTrue), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', help_c__fTrue__1)). 4.05/4.28 fof(c_0_4420, plain, ![X9601]:c_Int_Osucc(X9601)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9601),c_Int_OMin), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I2_J])). 4.05/4.28 cnf(c_0_4421, plain, (c_Int_OPls=c_Int_Osucc(c_Int_OMin)), inference(split_conjunct,[status(thm)],[fact_succ__Min])). 4.05/4.28 cnf(c_0_4422, 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_4420])). 4.05/4.28 fof(c_0_4423, plain, ![X11903]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11903),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Int_Osucc(X11903), inference(variable_rename,[status(thm)],[fact_succ__def])). 4.05/4.28 fof(c_0_4424, plain, ![X17323]:c_Int_Osucc(c_Int_Opred(X17323))=X17323, inference(variable_rename,[status(thm)],[fact_succ__pred])). 4.05/4.28 fof(c_0_4425, plain, ![X2658]:c_Int_Opred(X2658)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2658),c_Int_OMin), inference(variable_rename,[status(thm)],[fact_add__Min__right])). 4.05/4.28 cnf(c_0_4426, plain, (c_Int_OPls=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)), inference(rw,[status(thm)],[c_0_4421, c_0_4422])). 4.05/4.28 cnf(c_0_4427, plain, (c_Int_OPls=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[fact_Pls__def]), ['final']). 4.05/4.28 cnf(c_0_4428, 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_4423])). 4.05/4.28 fof(c_0_4429, plain, ![X9261]:c_Int_Opred(X9261)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X9261), inference(variable_rename,[status(thm)],[fact_add__Min])). 4.05/4.28 fof(c_0_4430, plain, ![X4068]:c_Int_OMin!=c_Int_OBit0(X4068), inference(variable_rename,[status(thm)],[fact_rel__simps_I42_J])). 4.05/4.28 fof(c_0_4431, plain, ![X13923]:c_Int_OBit0(X13923)=c_Int_Opred(c_Int_OBit1(X13923)), inference(variable_rename,[status(thm)],[fact_pred__Bit1])). 4.05/4.28 fof(c_0_4432, plain, ![X12556]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X12556)),X12556)=c_Int_OBit1(X12556), inference(variable_rename,[status(thm)],[fact_Bit1__def])). 4.05/4.28 cnf(c_0_4433, plain, (c_Int_Osucc(c_Int_Opred(X1))=X1), inference(split_conjunct,[status(thm)],[c_0_4424])). 4.05/4.28 cnf(c_0_4434, plain, (c_Int_Opred(X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)), inference(split_conjunct,[status(thm)],[c_0_4425])). 4.05/4.28 fof(c_0_4435, plain, ![X2401]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X2401))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X2401)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I4_J])). 4.05/4.28 fof(c_0_4436, plain, ![X6420]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6420),X6420)=c_Int_OBit0(X6420), inference(variable_rename,[status(thm)],[fact_Bit0__def])). 4.05/4.28 fof(c_0_4437, plain, ![X5811]:X5811=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5811),c_Int_OPls), inference(variable_rename,[status(thm)],[fact_add__Pls__right])). 4.05/4.28 cnf(c_0_4438, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_4426, c_0_4427])). 4.05/4.28 cnf(c_0_4439, 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_4428, c_0_4422]), ['final']). 4.05/4.28 cnf(c_0_4440, plain, (c_Int_Opred(X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X1)), inference(split_conjunct,[status(thm)],[c_0_4429])). 4.05/4.28 fof(c_0_4441, plain, ![X4335]:c_List_Oupt(X4335,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_List_Olist_ONil(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_upt__0])). 4.05/4.28 fof(c_0_4442, plain, ![X6811, X6812]:c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6812),X6811))=c_List_Oupt(X6812,X6811), inference(variable_rename,[status(thm)],[fact_sorted__list__of__set__range])). 4.05/4.28 fof(c_0_4443, plain, ![X3003, X3004, X3005, X3006]:hAPP(c_Set_Ovimage(X3006,X3005,X3004),hAPP(c_Set_OCollect(X3005),X3003))=hAPP(c_Set_OCollect(X3006),hAPP(hAPP(c_COMBB(X3005,tc_HOL_Obool,X3006),X3003),X3004)), inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq])). 4.05/4.28 fof(c_0_4444, plain, ![X17067, X17068]:hAPP(c_Set_OCollect(X17068),X17067)=X17067, inference(variable_rename,[status(thm)],[fact_Collect__def])). 4.05/4.28 fof(c_0_4445, plain, ![X1632, X1633]:X1632=hAPP(c_Set_OCollect(X1633),hAPP(hAPP(c_COMBC(X1633,tc_fun(X1633,tc_HOL_Obool),tc_HOL_Obool),c_member(X1633)),X1632)), inference(variable_rename,[status(thm)],[fact_Collect__mem__eq])). 4.05/4.28 fof(c_0_4446, plain, ![X980, X981, X982, X983]:hAPP(c_Set_OCollect(tc_prod(X983,X982)),hAPP(c_Product__Type_Oprod_Oprod__case(X983,X982,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X983,tc_fun(X982,tc_HOL_Obool),tc_fun(X982,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X982,tc_HOL_Obool),tc_fun(X982,tc_HOL_Obool)),X983),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X982)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X983),c_fconj),X981))),X980)))=hAPP(hAPP(c_Product__Type_OSigma(X983,X982),hAPP(c_Set_OCollect(X983),X981)),hAPP(c_COMBK(tc_fun(X982,tc_HOL_Obool),X983),hAPP(c_Set_OCollect(X982),X980))), inference(variable_rename,[status(thm)],[fact_Collect__split])). 4.05/4.28 fof(c_0_4447, plain, ![X8972, X8973]:((c_Groups_Oone__class_Oone(X8973)!=hAPP(hAPP(c_Power_Opower__class_Opower(X8973),X8972),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|(hAPP(c_Groups_Ouminus__class_Ouminus(X8973),c_Groups_Oone__class_Oone(X8973))=X8972|c_Groups_Oone__class_Oone(X8973)=X8972)|~class_Rings_Oring__1__no__zero__divisors(X8973))&((hAPP(c_Groups_Ouminus__class_Ouminus(X8973),c_Groups_Oone__class_Oone(X8973))!=X8972|c_Groups_Oone__class_Oone(X8973)=hAPP(hAPP(c_Power_Opower__class_Opower(X8973),X8972),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(X8973))&(c_Groups_Oone__class_Oone(X8973)!=X8972|c_Groups_Oone__class_Oone(X8973)=hAPP(hAPP(c_Power_Opower__class_Opower(X8973),X8972),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(X8973)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__1__iff])])])). 4.05/4.28 fof(c_0_4448, plain, ![X6891, X6892]:((X6891=c_Groups_Ozero__class_Ozero(X6892)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6892),c_Groups_Ozero__class_Ozero(X6892)),hAPP(hAPP(c_Power_Opower__class_Opower(X6892),X6891),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|~class_Rings_Olinordered__idom(X6892))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6892),c_Groups_Ozero__class_Ozero(X6892)),hAPP(hAPP(c_Power_Opower__class_Opower(X6892),X6891),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|X6891!=c_Groups_Ozero__class_Ozero(X6892)|~class_Rings_Olinordered__idom(X6892))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power2])])])). 4.05/4.28 fof(c_0_4449, plain, ![X17373]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17373),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X17373|X17373=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__2__cases])])). 4.05/4.28 fof(c_0_4450, plain, ![X2719, X2720]:(~class_Rings_Olinordered__idom(X2720)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2720),hAPP(hAPP(c_Power_Opower__class_Opower(X2720),X2719),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X2720)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power2__less__0])])])). 4.05/4.28 fof(c_0_4451, plain, ![X8531]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8531)=hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8531)), inference(variable_rename,[status(thm)],[fact_nat__number__of])). 4.05/4.28 fof(c_0_4452, plain, ![X6105]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X6105)=X6105, inference(variable_rename,[status(thm)],[fact_number__of__is__id])). 4.05/4.28 fof(c_0_4453, plain, ![X8944]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X8944),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Int_Opred(X8944), inference(variable_rename,[status(thm)],[fact_pred__def])). 4.05/4.28 fof(c_0_4454, plain, ![X15241, X15242]:hAPP(c_Set_OCollect(X15242),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X15242),c_fNot),X15241))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X15242,tc_HOL_Obool)),hAPP(c_Set_OCollect(X15242),X15241)), inference(variable_rename,[status(thm)],[fact_Collect__neg__eq])). 4.05/4.28 fof(c_0_4455, plain, ![X4289, X4290, X4291, X4292]:(hBOOL(hAPP(X4292,X4291))|hAPP(c_List_Ofilter(X4290,X4292),X4289)=hAPP(c_List_OremoveAll(X4290,X4291),hAPP(c_List_Ofilter(X4290,X4292),X4289))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_removeAll__filter__not])])])). 4.05/4.28 fof(c_0_4456, plain, ![X2026, X2027]:c_List_Ofilter(X2027,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2027),c_fNot),hAPP(c_fequal,X2026)))=c_List_OremoveAll(X2027,X2026), inference(variable_rename,[status(thm)],[fact_removeAll__filter__not__eq])). 4.05/4.28 fof(c_0_4457, plain, ![X17033, X17034, X17035]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17035,tc_HOL_Obool)),hAPP(c_Set_OCollect(X17035),X17034)),hAPP(c_Set_OCollect(X17035),X17033))=hAPP(c_Set_OCollect(X17035),hAPP(hAPP(c_COMBS(X17035,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17035),c_fconj),X17034)),X17033)), inference(variable_rename,[status(thm)],[fact_Collect__conj__eq])). 4.05/4.28 fof(c_0_4458, plain, ![X16578]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X16578)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X16578)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X16578))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X16578))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J])])). 4.05/4.28 fof(c_0_4459, plain, ![X1249]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1249))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1249))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1249)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1249)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J])])). 4.05/4.28 fof(c_0_4460, plain, ![X10084]:((~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X10084))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X10084))))&(~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X10084)))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X10084)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I3_J])])). 4.05/4.28 fof(c_0_4461, plain, ![X4916]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4916),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X4916)),c_Int_OPls)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X4916)),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4916),c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J])])). 4.05/4.28 fof(c_0_4462, plain, ![X7437]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X7437)),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7437),c_Int_OPls)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7437),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X7437)),c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J])])). 4.05/4.28 fof(c_0_4463, plain, ![X1679]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1679))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1679))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1679)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1679)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I25_J])])). 4.05/4.28 fof(c_0_4464, plain, ![X1061]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1061))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1061))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1061)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1061)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I8_J])])). 4.05/4.28 fof(c_0_4465, plain, ![X10015]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X10015)),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10015),c_Int_OMin)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10015),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X10015)),c_Int_OMin)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I28_J])])). 4.05/4.28 fof(c_0_4466, plain, ![X13438]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X13438)),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13438),c_Int_OMin)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13438),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X13438)),c_Int_OMin)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I11_J])])). 4.05/4.28 fof(c_0_4467, plain, ![X13479]:((c_Int_OBit0(X13479)!=c_Int_OPls|X13479=c_Int_OPls)&(X13479!=c_Int_OPls|c_Int_OBit0(X13479)=c_Int_OPls)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I44_J])])). 4.05/4.28 fof(c_0_4468, plain, ![X3732]:((~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X3732),c_Int_OPls))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X3732)),c_Int_OPls)))&(~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X3732)),c_Int_OPls))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X3732),c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I9_J])])). 4.05/4.28 fof(c_0_4469, plain, ![X15468]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X15468))))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15468))))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15468)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X15468)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit0])])). 4.05/4.28 fof(c_0_4470, plain, ![X4641, X4642]:c_Int_OBit0(X4642)!=c_Int_OBit1(X4641), inference(variable_rename,[status(thm)],[fact_rel__simps_I49_J])). 4.05/4.28 fof(c_0_4471, plain, ![X13363]:~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X13363))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__int__code_I7_J])])). 4.05/4.28 fof(c_0_4472, plain, ![X2269]:~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X2269)),c_Int_OMin)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__int__code_I11_J])])). 4.05/4.28 cnf(c_0_4473, plain, (c_Int_OMin!=c_Int_OBit0(X1)), inference(split_conjunct,[status(thm)],[c_0_4430])). 4.05/4.28 cnf(c_0_4474, plain, (c_Int_OBit0(X1)=c_Int_Opred(c_Int_OBit1(X1))), inference(split_conjunct,[status(thm)],[c_0_4431])). 4.05/4.28 cnf(c_0_4475, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)=c_Int_OBit1(X1)), inference(split_conjunct,[status(thm)],[c_0_4432])). 4.05/4.28 fof(c_0_4476, plain, ![X16698]:~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X16698))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__int__code_I4_J])])). 4.05/4.28 fof(c_0_4477, plain, ![X15285]:~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X15285)),c_Int_OPls)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__int__code_I10_J])])). 4.05/4.28 fof(c_0_4478, plain, ![X11513]:c_Int_OPls!=c_Int_OBit1(X11513), inference(variable_rename,[status(thm)],[fact_rel__simps_I46_J])). 4.05/4.28 fof(c_0_4479, plain, ![X8253, X8254]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X8254))),c_List_Otranspose(X8254,X8253))=c_List_Ofoldr(tc_List_Olist(X8254),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X8254)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X8254))),X8253,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_length__transpose])). 4.05/4.28 fof(c_0_4480, plain, ![X9909, X9910, X9911, X9912, X9913]:c_List_Ofoldr(X9913,X9912,X9911,X9910,X9909)=hAPP(c_List_Ofoldl(X9912,X9913,hAPP(c_COMBC(X9913,X9912,X9912),X9911),X9909),hAPP(c_List_Orev(X9913),X9910)), inference(variable_rename,[status(thm)],[fact_foldr__foldl])). 4.05/4.28 fof(c_0_4481, plain, ![X13974, X13975]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X13975)),X13974)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13975),X13974)), inference(variable_rename,[status(thm)],[fact_add__Suc])). 4.05/4.28 fof(c_0_4482, plain, ![X5000, X5001]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X5001)),X5000)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5001),hAPP(c_Nat_OSuc,X5000)), inference(variable_rename,[status(thm)],[fact_add__Suc__shift])). 4.05/4.28 fof(c_0_4483, plain, ![X15399, X15400]:hAPP(hAPP(c_List_Omap(tc_List_Olist(X15400),X15400),c_List_Ohd(X15400)),hAPP(c_List_Ofilter(tc_List_Olist(X15400),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X15400)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X15400),tc_List_Olist(X15400),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X15400)))),X15399))=c_List_Oconcat(X15400,hAPP(hAPP(c_List_Omap(tc_List_Olist(X15400),tc_List_Olist(X15400)),c_List_Olist_Olist__case(tc_List_Olist(X15400),X15400,c_List_Olist_ONil(X15400),hAPP(hAPP(c_COMBB(tc_List_Olist(X15400),tc_fun(tc_List_Olist(X15400),tc_List_Olist(X15400)),X15400),c_COMBK(tc_List_Olist(X15400),tc_List_Olist(X15400))),hAPP(hAPP(c_COMBC(X15400,tc_List_Olist(X15400),tc_List_Olist(X15400)),c_List_Olist_OCons(X15400)),c_List_Olist_ONil(X15400))))),X15399)), inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__head])). 4.05/4.28 fof(c_0_4484, plain, ![X3610, X3611]:hAPP(c_List_Ofoldl(tc_List_Olist(X3611),tc_List_Olist(X3611),c_List_Oappend(X3611),c_List_Olist_ONil(X3611)),X3610)=c_List_Oconcat(X3611,X3610), inference(variable_rename,[status(thm)],[fact_concat__conv__foldl])). 4.05/4.28 fof(c_0_4485, plain, ![X3412, X3413]:hAPP(hAPP(c_Set_Oinsert(X3413),X3412),c_Orderings_Obot__class_Obot(tc_fun(X3413,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X3413),hAPP(hAPP(c_COMBC(X3413,X3413,tc_HOL_Obool),c_fequal),X3412)), inference(variable_rename,[status(thm)],[fact_singleton__conv])). 4.05/4.28 fof(c_0_4486, plain, ![X10101, X10102]:hAPP(hAPP(c_Set_Oinsert(X10102),X10101),c_Orderings_Obot__class_Obot(tc_fun(X10102,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X10102),hAPP(c_fequal,X10101)), inference(variable_rename,[status(thm)],[fact_singleton__conv2])). 4.05/4.28 fof(c_0_4487, plain, ![X1442, X1443]:hAPP(hAPP(c_List_Omap(tc_List_Olist(X1443),tc_List_Olist(X1443)),c_List_Otl(X1443)),hAPP(c_List_Ofilter(tc_List_Olist(X1443),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1443)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X1443),tc_List_Olist(X1443),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X1443)))),X1442))=c_List_Oconcat(tc_List_Olist(X1443),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1443),tc_List_Olist(tc_List_Olist(X1443))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1443)),X1443,c_List_Olist_ONil(tc_List_Olist(X1443)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1443),tc_List_Olist(tc_List_Olist(X1443))),X1443),hAPP(hAPP(c_COMBC(tc_List_Olist(X1443),tc_List_Olist(tc_List_Olist(X1443)),tc_List_Olist(tc_List_Olist(X1443))),c_List_Olist_OCons(tc_List_Olist(X1443))),c_List_Olist_ONil(tc_List_Olist(X1443)))))),X1442)), inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__tail])). 4.05/4.28 fof(c_0_4488, plain, ![X4452, X4453]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4453),X4452))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X4453)),c_Int_OBit0(X4452)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I9_J])). 4.05/4.28 cnf(c_0_4489, 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_4433, c_0_4422]), c_0_4434])). 4.05/4.28 fof(c_0_4490, plain, ![X5986, X5987]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5987),X5986)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5986),X5987), inference(variable_rename,[status(thm)],[fact_zadd__commute])). 4.05/4.28 fof(c_0_4491, plain, ![X17350]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X17350))=c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X17350)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I5_J])). 4.05/4.28 cnf(c_0_4492, 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_4435])). 4.05/4.28 fof(c_0_4493, plain, ![X8496, X8497, X8498]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8498),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8497),X8496))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8498),X8497)),X8496), inference(variable_rename,[status(thm)],[fact_zadd__assoc])). 4.05/4.28 cnf(c_0_4494, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)=c_Int_OBit0(X1)), inference(split_conjunct,[status(thm)],[c_0_4436])). 4.05/4.28 fof(c_0_4495, plain, ![X13769, X13770, X13771, X13772]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13772,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13772,tc_HOL_Obool)),X13771),X13770)),X13769)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13772,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13772,tc_HOL_Obool)),X13771),X13769)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13772,tc_HOL_Obool)),X13770),X13769)), inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib2])). 4.05/4.28 fof(c_0_4496, plain, ![X12946, X12947, X12948, X12949]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12949,tc_HOL_Obool)),X12948),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12949,tc_HOL_Obool)),X12947),X12946))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12949,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12949,tc_HOL_Obool)),X12948),X12947)),X12946), inference(variable_rename,[status(thm)],[fact_Int__Diff])). 4.05/4.28 fof(c_0_4497, plain, ![X11067, X11068]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X11068|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(X11068,X11067))&((X11067=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,X11067))),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)),X11067)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11068))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11067),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11068),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X11068,X11067)),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),X11067))))),c_Divides_Opdivmod(X11068,X11067))))=c_Divides_Odivmod__int(X11068,X11067)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11068)&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X11067|hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11068)=c_Divides_Odivmod__int(X11068,X11067)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11068))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__pdivmod])])])])). 4.05/4.28 fof(c_0_4498, plain, ![X17289, X17290, X17291, X17292]:c_Product__Type_Oapsnd(X17292,X17291,X17290,X17289)=c_Product__Type_Omap__pair(X17290,X17290,X17292,X17291,c_Fun_Oid(X17290),X17289), inference(variable_rename,[status(thm)],[fact_apsnd__def])). 4.05/4.28 fof(c_0_4499, plain, ![X13430, X13431]:((X13431!=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(X13431,X13430))&((X13430!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odivmod__int(X13431,X13430)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13431)|X13431=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(X13430=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odivmod__int(X13431,X13430)=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,X13430))),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,X13431)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X13430))),c_Divides_Opdivmod(X13431,X13430)),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),X13430))))),c_Divides_Opdivmod(X13431,X13430))))|X13431=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__code])])])])). 4.05/4.28 fof(c_0_4500, plain, ![X3081, X3082]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3081),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Groups_Ouminus__class_Ouminus(X3082),hAPP(c_Int_Oring__1__class_Oof__int(X3082),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3081)))=hAPP(c_Int_Oring__1__class_Oof__int(X3082),X3081)|X3081=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~class_Rings_Oring__1(X3082))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3081),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X3082),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X3082,X3082)),tc_fun(tc_Int_Oint,X3082)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3082,X3082),X3082),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X3082,X3082)),tc_fun(tc_Int_Oint,X3082)),tc_Int_Oint),c_COMBB(tc_fun(X3082,X3082),X3082,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X3082,tc_fun(tc_fun(X3082,X3082),X3082),tc_Int_Oint),c_HOL_OLet(X3082,X3082)),c_Int_Oring__1__class_Oof__int(X3082)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X3082,X3082),tc_fun(X3082,X3082)),hAPP(hAPP(c_COMBB(tc_fun(X3082,tc_fun(X3082,X3082)),tc_fun(tc_fun(X3082,X3082),tc_fun(X3082,X3082)),tc_Int_Oint),c_COMBS(X3082,X3082,X3082)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X3082,X3082),tc_fun(X3082,tc_fun(X3082,X3082))),hAPP(hAPP(c_COMBB(tc_fun(X3082,tc_fun(X3082,X3082)),tc_fun(tc_fun(X3082,X3082),tc_fun(X3082,tc_fun(X3082,X3082))),tc_Int_Oint),c_COMBB(X3082,tc_fun(X3082,X3082),X3082)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3082,tc_fun(X3082,X3082)),tc_Int_Oint),c_If(X3082)),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(X3082,X3082,X3082),c_Groups_Oplus__class_Oplus(X3082)),c_COMBI(X3082))))),hAPP(hAPP(c_COMBC(X3082,X3082,X3082),hAPP(hAPP(c_COMBB(X3082,tc_fun(X3082,X3082),X3082),c_Groups_Oplus__class_Oplus(X3082)),hAPP(hAPP(c_COMBS(X3082,X3082,X3082),c_Groups_Oplus__class_Oplus(X3082)),c_COMBI(X3082)))),c_Groups_Oone__class_Oone(X3082))))),c_Divides_Odivmod__int(X3081,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=hAPP(c_Int_Oring__1__class_Oof__int(X3082),X3081)|X3081=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~class_Rings_Oring__1(X3082)))&(X3081!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(c_Int_Oring__1__class_Oof__int(X3082),X3081)=c_Groups_Ozero__class_Ozero(X3082)|~class_Rings_Oring__1(X3082))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__num])])])])). 4.05/4.28 fof(c_0_4501, plain, ![X11394, X11395, X11396]:(~class_Int_Onumber__ring(X11396)|hAPP(hAPP(c_Power_Opower__class_Opower(X11396),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X11396),X11395),X11394)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X11396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11396),hAPP(hAPP(c_Power_Opower__class_Opower(X11396),X11395),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(X11396),X11394),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(X11396),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11396),hAPP(c_Int_Onumber__class_Onumber__of(X11396),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X11395)),X11394))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__diff])])). 4.05/4.28 cnf(c_0_4502, plain, (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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[fact_numeral__2__eq__2])). 4.05/4.28 cnf(c_0_4503, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OPls)), inference(split_conjunct,[status(thm)],[c_0_4437])). 4.05/4.28 cnf(c_0_4504, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_4438, c_0_4439])). 4.05/4.28 cnf(c_0_4505, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X1)), inference(rw,[status(thm)],[c_0_4440, c_0_4434])). 4.05/4.28 fof(c_0_4506, plain, ![X5763, X5764, X5765]:(~class_Int_Onumber__ring(X5765)|hAPP(hAPP(c_Power_Opower__class_Opower(X5765),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5765),X5764),X5763)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5765),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5765),hAPP(hAPP(c_Power_Opower__class_Opower(X5765),X5764),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(X5765),X5763),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(X5765),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5765),hAPP(c_Int_Onumber__class_Onumber__of(X5765),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X5764)),X5763))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__sum])])). 4.05/4.28 fof(c_0_4507, plain, ![X5251, X5252]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5252),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),X5251),c_Groups_Oone__class_Oone(tc_Int_Oint)),X5252))),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)))),X5251)),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)))),X5252))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__zmod__mult__2])])])). 4.05/4.28 fof(c_0_4508, plain, ![X11188, X11189]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11189))|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)))),X11188)),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)))),X11189))=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,X11188,X11189)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__zmod__mult__2])])])). 4.05/4.28 fof(c_0_4509, plain, ![X10537]:((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X10537|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(c_Code__Numeral_Oint__of,X10537))&((c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X10537,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|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),X10537),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))=hAPP(c_Code__Numeral_Oint__of,X10537)|X10537=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))&(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X10537,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hAPP(c_Code__Numeral_Oint__of,X10537)=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),X10537),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|X10537=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__of__code])])])])). 4.05/4.28 fof(c_0_4510, plain, ![X14118, X14119]:((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),X14119)))|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),X14118)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X14119)))),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(X14118)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X14119))))&(~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),X14119)))|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),X14118),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X14119)))),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(X14118)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X14119))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmod__number__of__Bit1])])])). 4.05/4.28 fof(c_0_4511, plain, ![X7817, X7818]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7818),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X7817))),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)))),X7818))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7817),c_Groups_Oone__class_Oone(tc_Int_Oint))),X7818)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__zdiv__mult__2])])). 4.05/4.28 fof(c_0_4512, plain, ![X17494, X17495]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17495))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X17494),X17495)=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)))),X17494))),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)))),X17495))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__zdiv__mult__2])])])). 4.05/4.28 fof(c_0_4513, plain, ![X17376, X17377, X17378]:((X17376!=c_Groups_Ozero__class_Ozero(X17378)|X17377!=c_Groups_Ozero__class_Ozero(X17378)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17378),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17378),hAPP(hAPP(c_Power_Opower__class_Opower(X17378),X17377),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(X17378),X17376),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X17378)))|~class_Rings_Olinordered__idom(X17378))&((X17376=c_Groups_Ozero__class_Ozero(X17378)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17378),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17378),hAPP(hAPP(c_Power_Opower__class_Opower(X17378),X17377),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(X17378),X17376),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X17378)))|~class_Rings_Olinordered__idom(X17378))&(X17377=c_Groups_Ozero__class_Ozero(X17378)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17378),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17378),hAPP(hAPP(c_Power_Opower__class_Opower(X17378),X17377),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(X17378),X17376),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X17378)))|~class_Rings_Olinordered__idom(X17378)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff])])])). 4.05/4.28 fof(c_0_4514, plain, ![X16410, X16411, X16412]:(((X16411=c_Groups_Ozero__class_Ozero(X16412)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16412),c_Groups_Ozero__class_Ozero(X16412)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16412),hAPP(hAPP(c_Power_Opower__class_Opower(X16412),X16411),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(X16412),X16410),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))|~class_Rings_Olinordered__idom(X16412))&(X16410=c_Groups_Ozero__class_Ozero(X16412)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16412),c_Groups_Ozero__class_Ozero(X16412)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16412),hAPP(hAPP(c_Power_Opower__class_Opower(X16412),X16411),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(X16412),X16410),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))|~class_Rings_Olinordered__idom(X16412)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16412),c_Groups_Ozero__class_Ozero(X16412)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16412),hAPP(hAPP(c_Power_Opower__class_Opower(X16412),X16411),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(X16412),X16410),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))|(X16411!=c_Groups_Ozero__class_Ozero(X16412)|X16410!=c_Groups_Ozero__class_Ozero(X16412))|~class_Rings_Olinordered__idom(X16412))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sum__power2__gt__zero__iff])])])])). 4.05/4.28 fof(c_0_4515, plain, ![X8073, X8074, X8075]:(~class_Rings_Olinordered__idom(X8075)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8075),c_Groups_Ozero__class_Ozero(X8075)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8075),hAPP(hAPP(c_Power_Opower__class_Opower(X8075),X8074),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(X8075),X8073),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__ge__zero])])). 4.05/4.28 fof(c_0_4516, plain, ![X8388, X8389, X8390]:(((X8388=c_Groups_Ozero__class_Ozero(X8390)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8390),hAPP(hAPP(c_Power_Opower__class_Opower(X8390),X8389),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(X8390),X8388),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))!=c_Groups_Ozero__class_Ozero(X8390)|~class_Rings_Olinordered__idom(X8390))&(X8389=c_Groups_Ozero__class_Ozero(X8390)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8390),hAPP(hAPP(c_Power_Opower__class_Opower(X8390),X8389),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(X8390),X8388),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))!=c_Groups_Ozero__class_Ozero(X8390)|~class_Rings_Olinordered__idom(X8390)))&(X8388!=c_Groups_Ozero__class_Ozero(X8390)|X8389!=c_Groups_Ozero__class_Ozero(X8390)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8390),hAPP(hAPP(c_Power_Opower__class_Opower(X8390),X8389),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(X8390),X8388),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_Groups_Ozero__class_Ozero(X8390)|~class_Rings_Olinordered__idom(X8390))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff])])])). 4.05/4.28 fof(c_0_4517, plain, ![X12704, X12705, X12706]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk391_3(X12704,X12705,X12706)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X12705))),X12706)))|hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X12705)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X12705)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X12705),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X12705)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X12705)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X12705),hAPP(hAPP(c_COMBB(tc_List_Olist(X12705),tc_fun(tc_Nat_Onat,X12705),tc_Nat_Onat),c_List_Onth(X12705)),hAPP(c_List_Onth(tc_List_Olist(X12705)),X12706))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X12705))),X12706)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12704))=c_List_Otranspose(X12705,X12706)|c_List_Olist_ONil(tc_List_Olist(X12705))=X12706)&(X12704!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12705)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X12705)),X12706),esk391_3(X12704,X12705,X12706)))|hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X12705)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X12705)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X12705),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X12705)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X12705)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X12705),hAPP(hAPP(c_COMBB(tc_List_Olist(X12705),tc_fun(tc_Nat_Onat,X12705),tc_Nat_Onat),c_List_Onth(X12705)),hAPP(c_List_Onth(tc_List_Olist(X12705)),X12706))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X12705))),X12706)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12704))=c_List_Otranspose(X12705,X12706)|c_List_Olist_ONil(tc_List_Olist(X12705))=X12706))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk391_3(X12704,X12705,X12706)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X12705))),X12706)))|hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X12705)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X12705)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X12705),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X12705)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X12705)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X12705),hAPP(hAPP(c_COMBB(tc_List_Olist(X12705),tc_fun(tc_Nat_Onat,X12705),tc_Nat_Onat),c_List_Onth(X12705)),hAPP(c_List_Onth(tc_List_Olist(X12705)),X12706))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X12705))),X12706)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12704))=c_List_Otranspose(X12705,X12706)|X12704!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(X12704!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12705)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X12705)),X12706),esk391_3(X12704,X12705,X12706)))|hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X12705)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X12705)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X12705),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X12705)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X12705)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X12705),hAPP(hAPP(c_COMBB(tc_List_Olist(X12705),tc_fun(tc_Nat_Onat,X12705),tc_Nat_Onat),c_List_Onth(X12705)),hAPP(c_List_Onth(tc_List_Olist(X12705)),X12706))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X12705))),X12706)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12704))=c_List_Otranspose(X12705,X12706)|X12704!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transpose__rectangle])])])])])). 4.05/4.28 cnf(c_0_4518, 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_4441])). 4.05/4.28 cnf(c_0_4519, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))=c_List_Oupt(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4442])). 4.05/4.28 fof(c_0_4520, plain, ![X11524]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X11524),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_atLeastLessThan0])). 4.05/4.28 fof(c_0_4521, plain, ![X10234, X10235, X10236, X10237]:hAPP(c_Set_OCollect(X10237),hAPP(hAPP(c_COMBC(X10237,tc_fun(X10236,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X10236,tc_fun(tc_fun(X10236,tc_HOL_Obool),tc_HOL_Obool),X10237),c_member(X10236)),X10235)),X10234))=hAPP(c_Set_Ovimage(X10237,X10236,X10235),X10234), inference(variable_rename,[status(thm)],[fact_vimage__def])). 4.05/4.28 cnf(c_0_4522, plain, (hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Set_OCollect(X2),X4))=hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_4443])). 4.05/4.28 cnf(c_0_4523, plain, (hAPP(c_Set_OCollect(X1),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_4444]), ['final']). 4.05/4.28 fof(c_0_4524, plain, ![X15863, X15864]:c_List_Olists(X15864,X15863)=hAPP(c_Set_OCollect(tc_List_Olist(X15864)),hAPP(hAPP(c_COMBC(tc_List_Olist(X15864),tc_fun(X15864,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X15864,tc_HOL_Obool),tc_fun(tc_fun(X15864,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X15864)),c_Orderings_Oord__class_Oless__eq(tc_fun(X15864,tc_HOL_Obool))),c_List_Oset(X15864))),X15863)), inference(variable_rename,[status(thm)],[fact_lists__eq__set])). 4.05/4.28 fof(c_0_4525, plain, ![X16188, X16189, X16190]:(~class_Groups_Omonoid__mult(X16190)|hAPP(hAPP(c_Power_Opower__class_Opower(X16190),X16189),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)))),X16188)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16190),X16189),hAPP(hAPP(c_Power_Opower__class_Opower(X16190),hAPP(hAPP(c_Power_Opower__class_Opower(X16190),X16189),X16188)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__odd__eq])])). 4.05/4.28 fof(c_0_4526, plain, ![X6859, X6860, X6861]:((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),esk214_3(X6859,X6860,X6861)),esk215_3(X6859,X6860,X6861))))|hBOOL(hAPP(hAPP(X6859,X6861),X6860))|~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),X6861),X6860))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk215_3(X6859,X6860,X6861)),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),esk214_3(X6859,X6860,X6861)),esk215_3(X6859,X6860,X6861))))|hBOOL(hAPP(hAPP(X6859,esk214_3(X6859,X6860,X6861)),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)))),esk215_3(X6859,X6860,X6861))))|hBOOL(hAPP(hAPP(X6859,X6861),X6860))|~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),X6861),X6860))))&(~hBOOL(hAPP(hAPP(X6859,esk214_3(X6859,X6860,X6861)),esk215_3(X6859,X6860,X6861)))|hBOOL(hAPP(hAPP(X6859,X6861),X6860))|~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),X6861),X6860)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_negDivAlg_Opinduct])])])])])). 4.05/4.28 fof(c_0_4527, plain, ![X5589, X5590, X5591]:(~class_Rings_Oring__1(X5591)|hAPP(hAPP(c_Power_Opower__class_Opower(X5591),hAPP(c_Groups_Ouminus__class_Ouminus(X5591),X5590)),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)))),X5589))=hAPP(hAPP(c_Power_Opower__class_Opower(X5591),X5590),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)))),X5589))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus__even])])). 4.05/4.28 fof(c_0_4528, plain, ![X6021, X6022]:(~class_Complete__Lattice_Ocomplete__lattice(X6022)|c_Complete__Lattice_OSup__class_OSup(X6022,X6021)=c_Complete__Lattice_OInf__class_OInf(X6022,hAPP(c_Set_OCollect(X6022),hAPP(hAPP(c_COMBB(tc_fun(X6022,tc_HOL_Obool),tc_HOL_Obool,X6022),c_HOL_OAll(X6022)),hAPP(hAPP(c_COMBB(tc_fun(X6022,tc_HOL_Obool),tc_fun(X6022,tc_HOL_Obool),X6022),hAPP(c_COMBS(X6022,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6022),c_fimplies),hAPP(hAPP(c_COMBC(X6022,tc_fun(X6022,tc_HOL_Obool),tc_HOL_Obool),c_member(X6022)),X6021)))),hAPP(c_COMBC(X6022,X6022,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X6022))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__Inf])])). 4.05/4.28 cnf(c_0_4529, plain, (X1=hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1))), inference(split_conjunct,[status(thm)],[c_0_4445])). 4.05/4.28 fof(c_0_4530, plain, ![X11985, X11986, X11987, X11988]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11987,tc_fun(X11988,tc_HOL_Obool)),X11986),hAPP(hAPP(c_COMBB(tc_fun(X11988,tc_HOL_Obool),tc_fun(X11988,tc_HOL_Obool),X11987),c_Set_OCollect(X11988)),hAPP(c_COMBC(X11988,X11987,tc_HOL_Obool),X11985)))=hAPP(c_Set_OCollect(X11988),hAPP(hAPP(c_COMBB(tc_fun(X11987,tc_HOL_Obool),tc_HOL_Obool,X11988),c_HOL_OAll(X11987)),hAPP(hAPP(c_COMBB(tc_fun(X11987,tc_HOL_Obool),tc_fun(X11987,tc_HOL_Obool),X11988),hAPP(c_COMBS(X11987,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X11987),c_fimplies),hAPP(hAPP(c_COMBC(X11987,tc_fun(X11987,tc_HOL_Obool),tc_HOL_Obool),c_member(X11987)),X11986)))),X11985))), inference(variable_rename,[status(thm)],[fact_Collect__ball__eq])). 4.05/4.28 fof(c_0_4531, plain, ![X1569, X1570]:(~class_Complete__Lattice_Ocomplete__lattice(X1570)|c_Complete__Lattice_OSup__class_OSup(X1570,hAPP(c_Set_OCollect(X1570),hAPP(hAPP(c_COMBB(tc_fun(X1570,tc_HOL_Obool),tc_HOL_Obool,X1570),c_HOL_OAll(X1570)),hAPP(hAPP(c_COMBB(tc_fun(X1570,tc_HOL_Obool),tc_fun(X1570,tc_HOL_Obool),X1570),hAPP(c_COMBS(X1570,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1570),c_fimplies),hAPP(hAPP(c_COMBC(X1570,tc_fun(X1570,tc_HOL_Obool),tc_HOL_Obool),c_member(X1570)),X1569)))),c_Orderings_Oord__class_Oless__eq(X1570)))))=c_Complete__Lattice_OInf__class_OInf(X1570,X1569)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__Sup])])])). 4.05/4.28 fof(c_0_4532, plain, ![X3166, X3167]:((hAPP(c_Nat_OSuc,X3167)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3166)|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(X3166))),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)),X3167))))))&(~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(X3166))),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)),X3167)))))|hAPP(c_Nat_OSuc,X3167)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3166))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__eq__number__of])])). 4.05/4.28 fof(c_0_4533, plain, ![X4251, X4252, X4253]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4253,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4253,tc_HOL_Obool)),hAPP(c_Set_OCollect(X4253),X4252))),hAPP(c_Set_OCollect(X4253),X4251))=hAPP(c_Set_OCollect(X4253),hAPP(hAPP(c_COMBS(X4253,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4253),c_fimplies),X4252)),X4251)), inference(variable_rename,[status(thm)],[fact_Collect__imp__eq])). 4.05/4.28 fof(c_0_4534, plain, ![X17664, X17665, X17666]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17666,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17666,tc_HOL_Obool)),X17665)),X17664)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17666,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17666,tc_HOL_Obool)),X17665),X17664)), inference(variable_rename,[status(thm)],[fact_Compl__Diff__eq])). 4.05/4.28 fof(c_0_4535, plain, ![X16760, X16761, X16762]:((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),esk499_3(X16760,X16761,X16762)),esk500_3(X16760,X16761,X16762))))|hBOOL(hAPP(hAPP(X16760,X16762),X16761))|~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),X16762),X16761))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk499_3(X16760,X16761,X16762)),esk500_3(X16760,X16761,X16762)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X16760,X16761,X16762)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X16760,esk499_3(X16760,X16761,X16762)),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)))),esk500_3(X16760,X16761,X16762))))|hBOOL(hAPP(hAPP(X16760,X16762),X16761))|~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),X16762),X16761))))&(~hBOOL(hAPP(hAPP(X16760,esk499_3(X16760,X16761,X16762)),esk500_3(X16760,X16761,X16762)))|hBOOL(hAPP(hAPP(X16760,X16762),X16761))|~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),X16762),X16761)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_posDivAlg_Opinduct])])])])])). 4.05/4.28 fof(c_0_4536, plain, ![X9462, X9463, X9464, X9465]:hAPP(c_Set_OCollect(tc_prod(X9465,X9464)),hAPP(c_Product__Type_Oprod_Oprod__case(X9465,X9464,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X9465,tc_fun(X9464,tc_HOL_Obool),tc_fun(X9464,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X9464,tc_HOL_Obool),tc_fun(X9464,tc_HOL_Obool)),X9465),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X9464)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X9465),c_fconj),hAPP(hAPP(c_COMBC(X9465,tc_fun(X9465,tc_HOL_Obool),tc_HOL_Obool),c_member(X9465)),X9463)))),hAPP(hAPP(c_COMBC(X9464,tc_fun(X9464,tc_HOL_Obool),tc_HOL_Obool),c_member(X9464)),X9462))))=c_Nitpick_Oprod(X9465,X9464,X9463,X9462), inference(variable_rename,[status(thm)],[fact_Nitpick_Oprod__def])). 4.05/4.28 cnf(c_0_4537, 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_4446])). 4.05/4.28 fof(c_0_4538, plain, ![X11640, X11641, X11642]:(~class_Groups_Omonoid__mult(X11642)|hAPP(hAPP(c_Power_Opower__class_Opower(X11642),hAPP(hAPP(c_Power_Opower__class_Opower(X11642),X11641),X11640)),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(X11642),X11641),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)))),X11640))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__even__eq])])). 4.05/4.28 fof(c_0_4539, plain, ![X1895, X1896]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1896)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1895)))|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(X1895))),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),X1896)),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(X1895))),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),X1896)),c_Int_Onat)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1896)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1895))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__number__of])])). 4.05/4.28 fof(c_0_4540, plain, ![X4544, X4545]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4545)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4544)))|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(X4544))),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),X4545)),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(X4544))),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),X4545)),c_Int_Onat)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4545)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4544))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__number__of])])). 4.05/4.28 fof(c_0_4541, plain, ![X15434, X15435]:(~class_Rings_Olinordered__idom(X15435)|hAPP(c_Groups_Oabs__class_Oabs(X15435),hAPP(hAPP(c_Power_Opower__class_Opower(X15435),X15434),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(X15435),X15434),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__power2])])])). 4.05/4.28 fof(c_0_4542, plain, ![X13454, X13455]:(~class_Rings_Olinordered__idom(X13455)|hAPP(hAPP(c_Power_Opower__class_Opower(X13455),hAPP(c_Groups_Oabs__class_Oabs(X13455),X13454)),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(X13455),X13454),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power2__abs])])])). 4.05/4.28 fof(c_0_4543, plain, ![X6039, X6040]:(~class_Rings_Oring__1(X6040)|hAPP(hAPP(c_Power_Opower__class_Opower(X6040),X6039),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(X6040),hAPP(c_Groups_Ouminus__class_Ouminus(X6040),X6039)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__minus])])). 4.05/4.28 fof(c_0_4544, plain, ![X5376, X5377, X5378]:(~class_Rings_Ocomm__semiring__1(X5378)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5378),X5377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5378),hAPP(hAPP(c_Power_Opower__class_Opower(X5378),X5377),X5376)),hAPP(hAPP(c_Power_Opower__class_Opower(X5378),X5377),X5376)))=hAPP(hAPP(c_Power_Opower__class_Opower(X5378),X5377),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)))),X5376)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J])])])). 4.05/4.28 fof(c_0_4545, plain, ![X13805]:((~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,X13805,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,X13805,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,X13805,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)|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,X13805,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod2__gr__0])])). 4.05/4.28 fof(c_0_4546, plain, ![X17169, X17170, X17171, X17172, X17173, X17174, X17175, X17176]:(((~hBOOL(hAPP(hAPP(c_member(tc_prod(X17171,X17171)),X17172),X17169))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X17171,X17171,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X17171,tc_fun(X17171,tc_HOL_Obool),tc_fun(X17171,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X17171,tc_HOL_Obool),tc_fun(X17171,tc_HOL_Obool)),X17171),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X17171)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17171),c_fconj),hAPP(hAPP(c_COMBC(X17171,tc_fun(X17171,tc_HOL_Obool),tc_HOL_Obool),c_member(X17171)),X17170)))),hAPP(hAPP(c_COMBC(X17171,tc_fun(X17171,tc_HOL_Obool),tc_HOL_Obool),c_member(X17171)),X17170))),X17172))|~c_Relation_Orefl__on(X17171,X17170,X17169))&(~hBOOL(hAPP(hAPP(c_member(X17171),X17173),X17170))|hBOOL(hAPP(hAPP(c_member(tc_prod(X17171,X17171)),hAPP(hAPP(c_Product__Type_OPair(X17171,X17171),X17173),X17173)),X17169))|~c_Relation_Orefl__on(X17171,X17170,X17169)))&(((hBOOL(hAPP(hAPP(c_member(X17176),esk515_3(X17174,X17175,X17176)),X17175))|hBOOL(hAPP(hAPP(c_member(tc_prod(X17176,X17176)),esk514_3(X17174,X17175,X17176)),X17174))|c_Relation_Orefl__on(X17176,X17175,X17174))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X17176,X17176)),hAPP(hAPP(c_Product__Type_OPair(X17176,X17176),esk515_3(X17174,X17175,X17176)),esk515_3(X17174,X17175,X17176))),X17174))|hBOOL(hAPP(hAPP(c_member(tc_prod(X17176,X17176)),esk514_3(X17174,X17175,X17176)),X17174))|c_Relation_Orefl__on(X17176,X17175,X17174)))&((hBOOL(hAPP(hAPP(c_member(X17176),esk515_3(X17174,X17175,X17176)),X17175))|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X17176,X17176,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X17176,tc_fun(X17176,tc_HOL_Obool),tc_fun(X17176,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X17176,tc_HOL_Obool),tc_fun(X17176,tc_HOL_Obool)),X17176),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X17176)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17176),c_fconj),hAPP(hAPP(c_COMBC(X17176,tc_fun(X17176,tc_HOL_Obool),tc_HOL_Obool),c_member(X17176)),X17175)))),hAPP(hAPP(c_COMBC(X17176,tc_fun(X17176,tc_HOL_Obool),tc_HOL_Obool),c_member(X17176)),X17175))),esk514_3(X17174,X17175,X17176)))|c_Relation_Orefl__on(X17176,X17175,X17174))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X17176,X17176)),hAPP(hAPP(c_Product__Type_OPair(X17176,X17176),esk515_3(X17174,X17175,X17176)),esk515_3(X17174,X17175,X17176))),X17174))|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X17176,X17176,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X17176,tc_fun(X17176,tc_HOL_Obool),tc_fun(X17176,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X17176,tc_HOL_Obool),tc_fun(X17176,tc_HOL_Obool)),X17176),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X17176)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17176),c_fconj),hAPP(hAPP(c_COMBC(X17176,tc_fun(X17176,tc_HOL_Obool),tc_HOL_Obool),c_member(X17176)),X17175)))),hAPP(hAPP(c_COMBC(X17176,tc_fun(X17176,tc_HOL_Obool),tc_HOL_Obool),c_member(X17176)),X17175))),esk514_3(X17174,X17175,X17176)))|c_Relation_Orefl__on(X17176,X17175,X17174))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__on__def_H])])])])])])])). 4.05/4.28 fof(c_0_4547, plain, ![X1142, X1143, X1144]:(~hBOOL(hAPP(c_List_Odistinct(X1144),X1143))|(~hBOOL(hAPP(hAPP(c_member(X1144),X1142),hAPP(c_List_Oset(X1144),X1143)))|hAPP(hAPP(c_List_Olist_OCons(X1144),X1142),hAPP(c_List_Orev(X1144),c_List_OtakeWhile(X1144,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1144),c_fNot),hAPP(hAPP(c_COMBC(X1144,X1144,tc_HOL_Obool),c_fequal),X1142)),X1143)))=c_List_OdropWhile(X1144,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1144),c_fNot),hAPP(hAPP(c_COMBC(X1144,X1144,tc_HOL_Obool),c_fequal),X1142)),hAPP(c_List_Orev(X1144),X1143)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dropWhile__neq__rev])])). 4.05/4.28 fof(c_0_4548, plain, ![X16895, X16896, X16897]:c_List_OdropWhile(X16897,X16896,X16895)=hAPP(hAPP(c_List_Odrop(X16897),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16897)),c_List_OtakeWhile(X16897,X16896,X16895))),X16895), inference(variable_rename,[status(thm)],[fact_dropWhile__eq__drop])). 4.05/4.28 fof(c_0_4549, plain, ![X4507, X4508]:(~class_Rings_Osemiring__1(X4508)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4507))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4508),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4508),hAPP(c_Int_Onat,X4507))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4508),hAPP(c_Int_Onat,X4507)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4508),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)))),X4507))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__double])])])). 4.05/4.28 fof(c_0_4550, plain, ![X6975, X6976, X6977]:(~class_Rings_Olinordered__idom(X6977)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6977),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6977),hAPP(hAPP(c_Power_Opower__class_Opower(X6977),X6976),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(X6977),X6975),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X6977)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__sum__power2__lt__zero])])])). 4.05/4.28 fof(c_0_4551, plain, ![X15772, X15773]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15772),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),X15773),X15772)))|c_Divides_OnegDivAlg(X15773,X15772)=hAPP(c_Divides_Oadjust(X15772),c_Divides_OnegDivAlg(X15773,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)))),X15772))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15772),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15773),X15772))=c_Divides_OnegDivAlg(X15773,X15772))&(~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),X15773),X15772)))|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),X15773),X15772))=c_Divides_OnegDivAlg(X15773,X15772)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_negDivAlg_Osimps])])])])). 4.05/4.28 fof(c_0_4552, plain, ![X16213, X16214, X16215]:(~class_Rings_Ocomm__semiring__1(X16215)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16215),hAPP(hAPP(c_Power_Opower__class_Opower(X16215),X16214),X16213)),hAPP(hAPP(c_Power_Opower__class_Opower(X16215),X16214),X16213))=hAPP(hAPP(c_Power_Opower__class_Opower(X16215),X16214),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)))),X16213))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J])])])). 4.05/4.28 fof(c_0_4553, plain, ![X14905, X14906]:((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),X14905),X14906)))|hAPP(c_Divides_Oadjust(X14906),c_Divides_OnegDivAlg(X14905,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)))),X14906)))=c_Divides_OnegDivAlg(X14905,X14906)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14906)))&(~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),X14905),X14906)))|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),X14905),X14906))=c_Divides_OnegDivAlg(X14905,X14906)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14906)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn])])])])). 4.05/4.28 fof(c_0_4554, plain, ![X15026, X15027]:((~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(X15027))),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)),X15026))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15027)),hAPP(c_Nat_OSuc,X15026))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15027)),hAPP(c_Nat_OSuc,X15026)))|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(X15027))),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)),X15026)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__Suc])])). 4.05/4.28 fof(c_0_4555, plain, ![X12388, X12389]:((~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(X12389))),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)),X12388))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12389)),hAPP(c_Nat_OSuc,X12388))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12389)),hAPP(c_Nat_OSuc,X12388)))|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(X12389))),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)),X12388)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of__Suc])])). 4.05/4.28 fof(c_0_4556, plain, ![X4281, X4282]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4282),X4281))|c_Divides_OposDivAlg(X4282,X4281)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4282))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4281),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Divides_OposDivAlg(X4282,X4281)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4282)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4281),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4282),X4281))|c_Divides_OposDivAlg(X4282,X4281)=hAPP(c_Divides_Oadjust(X4281),c_Divides_OposDivAlg(X4282,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)))),X4281))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_posDivAlg_Osimps])])])])). 4.05/4.28 fof(c_0_4557, plain, ![X9157, X9158, X9159]:(~class_Rings_Olinordered__idom(X9159)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9159),X9158),c_Groups_Ozero__class_Ozero(X9159)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9159),hAPP(hAPP(c_Power_Opower__class_Opower(X9159),X9158),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)))),X9157)))),c_Groups_Ozero__class_Ozero(X9159))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__power__less__zero])])). 4.05/4.28 fof(c_0_4558, plain, ![X5464, X5465]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5464),X5465))|c_Divides_OposDivAlg(X5464,X5465)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5464)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5465)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5464),X5465))|c_Divides_OposDivAlg(X5464,X5465)=hAPP(c_Divides_Oadjust(X5465),c_Divides_OposDivAlg(X5464,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)))),X5465)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5465)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn])])])])). 4.05/4.28 fof(c_0_4559, plain, ![X12708, X12709]:(~class_Rings_Oring__1(X12709)|hAPP(hAPP(c_Power_Opower__class_Opower(X12709),hAPP(c_Groups_Ouminus__class_Ouminus(X12709),c_Groups_Oone__class_Oone(X12709))),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)))),X12708)))=hAPP(c_Groups_Ouminus__class_Ouminus(X12709),c_Groups_Oone__class_Oone(X12709))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus1__odd])])). 4.05/4.28 fof(c_0_4560, plain, ![X17601]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17601))|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),X17601),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])])])). 4.05/4.28 fof(c_0_4561, plain, ![X2363, X2364]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2364)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2363))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2364),X2363)), inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib])). 4.05/4.28 fof(c_0_4562, plain, ![X4796, X4797]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4797),X4796)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4797),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4796)), inference(variable_rename,[status(thm)],[fact_diff__int__def])). 4.05/4.28 fof(c_0_4563, plain, ![X13980, X13981]:(~class_Int_Onumber__ring(X13981)|hAPP(c_Int_Onumber__class_Onumber__of(X13981),c_Int_OMin)=hAPP(hAPP(c_Power_Opower__class_Opower(X13981),hAPP(c_Int_Onumber__class_Onumber__of(X13981),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)))),X13980)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__m1__odd])])])). 4.05/4.28 fof(c_0_4564, plain, ![X8015, X8016, X8017, X8018]:(~c_Fun_Oinj__on(X8018,X8017,X8016,c_Orderings_Otop__class_Otop(tc_fun(X8018,tc_HOL_Obool)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8018,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X8018,X8017,X8016),hAPP(hAPP(c_Set_Oinsert(X8017),X8015),c_Orderings_Obot__class_Obot(tc_fun(X8017,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X8018),c_HOL_OThe(X8018,hAPP(hAPP(c_COMBC(X8018,X8017,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X8017,tc_fun(X8017,tc_HOL_Obool),X8018),c_fequal),X8016)),X8015))),c_Orderings_Obot__class_Obot(tc_fun(X8018,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__vimage__singleton])])])). 4.05/4.28 fof(c_0_4565, plain, ![X584, X585]:c_Enum_Oenum__the(X585,X584)=c_HOL_OThe(X585,X584), inference(variable_rename,[status(thm)],[fact_enum__the__def])). 4.05/4.28 fof(c_0_4566, plain, ![X1567, X1568]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1568),c_Groups_Ozero__class_Ozero(X1568)),X1567))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1568),c_Groups_Ozero__class_Ozero(X1568)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1568),X1567),hAPP(c_Int_Onumber__class_Onumber__of(X1568),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|(~class_Int_Onumber__ring(X1568)|~class_Fields_Olinordered__field__inverse__zero(X1568)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1568),c_Groups_Ozero__class_Ozero(X1568)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1568),X1567),hAPP(c_Int_Onumber__class_Onumber__of(X1568),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1568),c_Groups_Ozero__class_Ozero(X1568)),X1567))|(~class_Int_Onumber__ring(X1568)|~class_Fields_Olinordered__field__inverse__zero(X1568)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_half__gt__zero__iff])])])])). 4.05/4.28 fof(c_0_4567, plain, ![X17538, X17539]:(~class_Rings_Oring__1(X17539)|hAPP(hAPP(c_Power_Opower__class_Opower(X17539),hAPP(c_Groups_Ouminus__class_Ouminus(X17539),c_Groups_Oone__class_Oone(X17539))),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)))),X17538))=c_Groups_Oone__class_Oone(X17539)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__minus1__even])])])). 4.05/4.28 fof(c_0_4568, plain, ![X4867, X4868, X4869]:(~hBOOL(hAPP(c_List_Odistinct(X4869),X4868))|(~hBOOL(hAPP(hAPP(c_member(X4869),X4867),hAPP(c_List_Oset(X4869),X4868)))|c_List_OtakeWhile(X4869,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4869),c_fNot),hAPP(hAPP(c_COMBC(X4869,X4869,tc_HOL_Obool),c_fequal),X4867)),hAPP(c_List_Orev(X4869),X4868))=hAPP(c_List_Orev(X4869),hAPP(c_List_Otl(X4869),c_List_OdropWhile(X4869,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4869),c_fNot),hAPP(hAPP(c_COMBC(X4869,X4869,tc_HOL_Obool),c_fequal),X4867)),X4868))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile__neq__rev])])])). 4.05/4.28 fof(c_0_4569, plain, ![X4578, X4579, X4580]:hAPP(c_List_Otl(X4580),hAPP(hAPP(c_List_Odrop(X4580),X4579),X4578))=hAPP(hAPP(c_List_Odrop(X4580),X4579),hAPP(c_List_Otl(X4580),X4578)), inference(variable_rename,[status(thm)],[fact_drop__tl])). 4.05/4.28 fof(c_0_4570, plain, ![X13935, X13936, X13937]:hAPP(hAPP(c_List_Odrop(X13937),X13936),hAPP(c_List_Otl(X13937),X13935))=hAPP(hAPP(c_List_Odrop(X13937),hAPP(c_Nat_OSuc,X13936)),X13935), inference(variable_rename,[status(thm)],[fact_drop__Suc])). 4.05/4.28 fof(c_0_4571, plain, ![X2941, X2942, X2943]:(~class_Rings_Olinordered__idom(X2943)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2943),c_Groups_Ozero__class_Ozero(X2943)),hAPP(hAPP(c_Power_Opower__class_Opower(X2943),X2942),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)))),X2941))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__even__power_H])])])). 4.05/4.28 fof(c_0_4572, plain, ![X2067, X2068]:((~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),X2068)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2067)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2068))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X2067))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X2068))))&(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),X2068)))|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),X2067)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2068))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X2067))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X2068))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__number__of__Bit1])])])). 4.05/4.28 fof(c_0_4573, plain, ![X10997, X10998, X10999]:((~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),X10998)))|hAPP(hAPP(c_HOL_OLet(X10999,X10999),hAPP(hAPP(c_Power_Opower__class_Opower(X10999),X10997),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X10998))),hAPP(hAPP(c_COMBS(X10999,X10999,X10999),hAPP(hAPP(c_COMBB(X10999,tc_fun(X10999,X10999),X10999),c_Groups_Otimes__class_Otimes(X10999)),hAPP(c_Groups_Otimes__class_Otimes(X10999),X10997))),c_COMBI(X10999)))=hAPP(hAPP(c_Power_Opower__class_Opower(X10999),X10997),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X10998)))|~class_Int_Onumber__ring(X10999))&(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),X10998)))|hAPP(hAPP(c_Power_Opower__class_Opower(X10999),X10997),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X10998)))=c_Groups_Oone__class_Oone(X10999)|~class_Int_Onumber__ring(X10999))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__number__of__odd])])])])). 4.05/4.28 fof(c_0_4574, plain, ![X17008, X17009]:(~class_Int_Onumber__ring(X17009)|hAPP(hAPP(c_Power_Opower__class_Opower(X17009),hAPP(c_Int_Onumber__class_Onumber__of(X17009),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)))),X17008))=c_Groups_Oone__class_Oone(X17009)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__even])])). 4.05/4.28 fof(c_0_4575, plain, ![X901]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X901))|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),X901),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])])). 4.05/4.28 fof(c_0_4576, plain, ![X2952, X2953]:((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),X2953)))|c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2952),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X2953))))&(~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),X2953)))|hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2952),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2953))),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),X2952))),c_COMBI(tc_Int_Oint)))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2952),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X2953))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zpower__number__of__odd])])])). 4.05/4.28 fof(c_0_4577, plain, ![X16334, X16335]:(~class_Rings_Olinordered__idom(X16335)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16335),c_Groups_Ozero__class_Ozero(X16335)),hAPP(hAPP(c_Power_Opower__class_Opower(X16335),X16334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__power2])])])). 4.05/4.28 fof(c_0_4578, plain, ![X16003, X16004]:(~class_Int_Onumber__ring(X16004)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16004),X16003),X16003)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16004),hAPP(c_Int_Onumber__class_Onumber__of(X16004),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X16003)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2])])). 4.05/4.28 fof(c_0_4579, plain, ![X8741, X8742, X8743]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8743)),X8741)),X8742)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8743)),hAPP(hAPP(c_List_Otake(X8743),X8742),X8741)), inference(variable_rename,[status(thm)],[fact_length__take])). 4.05/4.28 fof(c_0_4580, plain, ![X10733, X10734]:(~class_Int_Onumber__ring(X10734)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10734),X10733),X10733)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10734),X10733),hAPP(c_Int_Onumber__class_Onumber__of(X10734),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])])). 4.05/4.28 fof(c_0_4581, plain, ![X2528, X2529]:(~class_Rings_Ocomm__semiring__1(X2529)|hAPP(hAPP(c_Power_Opower__class_Opower(X2529),X2528),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(X2529),X2528),X2528)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J])])])). 4.05/4.28 fof(c_0_4582, plain, ![X11208, X11209]:(~class_Groups_Omonoid__mult(X11209)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11209),X11208),X11208)=hAPP(hAPP(c_Power_Opower__class_Opower(X11209),X11208),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__eq__square])])])). 4.05/4.28 fof(c_0_4583, plain, ![X14404, X14405]:(~class_Groups_Omonoid__mult(X14405)|hAPP(hAPP(c_Power_Opower__class_Opower(X14405),X14404),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14405),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14405),X14404),X14404)),X14404)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power3__eq__cube])])])). 4.05/4.28 cnf(c_0_4584, 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])). 4.05/4.28 fof(c_0_4585, plain, ![X1024, X1025, X1026, X1027, X1028]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X1028,X1028)),hAPP(hAPP(c_Product__Type_OPair(X1028,X1028),X1027),X1026)),c_Transitive__Closure_Otrancl(X1028,X1025)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X1028,X1028)),hAPP(hAPP(c_Product__Type_OPair(X1028,X1028),X1026),X1024)),c_Transitive__Closure_Otrancl(X1028,X1025)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1028,X1028)),hAPP(hAPP(c_Product__Type_OPair(X1028,X1028),X1027),X1024)),c_Transitive__Closure_Otrancl(X1028,X1025))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__trans])])])). 4.05/4.28 fof(c_0_4586, plain, ![X12211, X12212]:c_Transitive__Closure_Otrancl(X12212,X12211)=hAPP(hAPP(c_Relation_Orel__comp(X12212,X12212,X12212),c_Transitive__Closure_Ortrancl(X12212,X12211)),X12211), inference(variable_rename,[status(thm)],[fact_trancl__unfold__right])). 4.05/4.28 fof(c_0_4587, plain, ![X4713]:(~class_Int_Onumber__ring(X4713)|hAPP(c_Int_Onumber__class_Onumber__of(X4713),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4713),c_Groups_Oone__class_Oone(X4713)),c_Groups_Oone__class_Oone(X4713))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_one__add__one__is__two])])])). 4.05/4.28 fof(c_0_4588, plain, ![X6015, X6016, X6017]:(~class_Int_Onumber__ring(X6017)|hAPP(hAPP(c_HOL_OLet(X6017,X6017),hAPP(hAPP(c_Power_Opower__class_Opower(X6017),X6016),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6015))),hAPP(hAPP(c_COMBS(X6017,X6017,X6017),c_Groups_Otimes__class_Otimes(X6017)),c_COMBI(X6017)))=hAPP(hAPP(c_Power_Opower__class_Opower(X6017),X6016),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X6015)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__number__of__even])])). 4.05/4.28 fof(c_0_4589, plain, ![X1057, X1058]:c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1058,X1057))=c_Divides_Odivmod__nat(X1058,X1057), inference(variable_rename,[status(thm)],[fact_divmod__nat__def])). 4.05/4.28 fof(c_0_4590, plain, ![X1561, X1562]:((c_Groups_Ozero__class_Ozero(X1562)!=X1561|c_Groups_Ozero__class_Ozero(X1562)=hAPP(hAPP(c_Power_Opower__class_Opower(X1562),X1561),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(X1562))&(c_Groups_Ozero__class_Ozero(X1562)!=hAPP(hAPP(c_Power_Opower__class_Opower(X1562),X1561),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|c_Groups_Ozero__class_Ozero(X1562)=X1561|~class_Rings_Oring__1__no__zero__divisors(X1562))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__eq__power2])])])). 4.05/4.28 fof(c_0_4591, plain, ![X15321, X15322, X15323, X15324, X15325]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15325,X15325)),hAPP(hAPP(c_Product__Type_OPair(X15325,X15325),X15324),X15323)),c_Transitive__Closure_Ortrancl(X15325,X15322)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15325,X15325)),hAPP(hAPP(c_Product__Type_OPair(X15325,X15325),X15323),X15321)),c_Transitive__Closure_Otrancl(X15325,X15322)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X15325,X15325)),hAPP(hAPP(c_Product__Type_OPair(X15325,X15325),X15324),X15321)),c_Transitive__Closure_Otrancl(X15325,X15322))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__trancl__trancl])])])). 4.05/4.28 fof(c_0_4592, plain, ![X13485, X13486, X13487, X13488, X13489]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13489,X13489)),hAPP(hAPP(c_Product__Type_OPair(X13489,X13489),X13488),X13487)),c_Transitive__Closure_Otrancl(X13489,X13486)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13489,X13489)),hAPP(hAPP(c_Product__Type_OPair(X13489,X13489),X13487),X13485)),c_Transitive__Closure_Ortrancl(X13489,X13486)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X13489,X13489)),hAPP(hAPP(c_Product__Type_OPair(X13489,X13489),X13488),X13485)),c_Transitive__Closure_Otrancl(X13489,X13486))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__rtrancl__trancl])])])). 4.05/4.28 fof(c_0_4593, plain, ![X2700]:(~class_Rings_Osemiring__1(X2700)|hAPP(hAPP(c_Power_Opower__class_Opower(X2700),c_Groups_Ozero__class_Ozero(X2700)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Ozero__class_Ozero(X2700)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__power2])])])). 4.05/4.28 fof(c_0_4594, plain, ![X10540]:(~class_Rings_Osemiring__1(X10540)|hAPP(hAPP(c_Power_Opower__class_Opower(X10540),c_Groups_Oone__class_Oone(X10540)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oone__class_Oone(X10540)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__power2])])). 4.05/4.28 fof(c_0_4595, plain, ![X756, X757, X758, X759, X760]:(~c_Fun_Oinj__on(X760,X759,X758,hAPP(hAPP(c_Set_Oinsert(X760),X757),hAPP(c_List_Oset(X760),X756)))|hAPP(hAPP(c_List_Omap(X760,X759),X758),hAPP(c_List_OremoveAll(X760,X757),X756))=hAPP(c_List_OremoveAll(X759,hAPP(X758,X757)),hAPP(hAPP(c_List_Omap(X760,X759),X758),X756))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__removeAll__inj__on])])). 4.05/4.28 fof(c_0_4596, plain, ![X9753, X9754, X9755, X9756, X9757]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9757,X9757)),hAPP(hAPP(c_Product__Type_OPair(X9757,X9757),X9756),X9755)),X9754))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9757,X9757)),hAPP(hAPP(c_Product__Type_OPair(X9757,X9757),X9755),X9753)),c_Transitive__Closure_Otrancl(X9757,X9754)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9757,X9757)),hAPP(hAPP(c_Product__Type_OPair(X9757,X9757),X9756),X9753)),c_Transitive__Closure_Otrancl(X9757,X9754))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__trancl2])])). 4.05/4.28 fof(c_0_4597, plain, ![X9187, X9188, X9189, X9190, X9191]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9191,X9191)),hAPP(hAPP(c_Product__Type_OPair(X9191,X9191),X9190),X9189)),c_Transitive__Closure_Otrancl(X9191,X9188)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9191,X9191)),hAPP(hAPP(c_Product__Type_OPair(X9191,X9191),X9189),X9187)),X9188))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9191,X9191)),hAPP(hAPP(c_Product__Type_OPair(X9191,X9191),X9190),X9187)),c_Transitive__Closure_Otrancl(X9191,X9188))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Transitive__Closure_Otrancl__into__trancl])])). 4.05/4.28 fof(c_0_4598, plain, ![X5729, X5730, X5731, X5732, X5733]:(~c_Fun_Oinj__on(X5733,X5732,X5731,c_Orderings_Otop__class_Otop(tc_fun(X5733,tc_HOL_Obool)))|hAPP(c_List_OremoveAll(X5732,hAPP(X5731,X5730)),hAPP(hAPP(c_List_Omap(X5733,X5732),X5731),X5729))=hAPP(hAPP(c_List_Omap(X5733,X5732),X5731),hAPP(c_List_OremoveAll(X5733,X5730),X5729))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__removeAll__inj])])])). 4.05/4.28 fof(c_0_4599, plain, ![X9127, X9128, X9129]:(~class_Rings_Oring__1(X9129)|~class_Rings_Oinverse(X9129)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9129),hAPP(c_Int_Oring__1__class_Oof__int(X9129),hAPP(c_Nitpick_Onum(X9128),X9127))),hAPP(c_Int_Oring__1__class_Oof__int(X9129),hAPP(c_Nitpick_Odenom(X9128),X9127)))=c_Nitpick_Oof__frac(X9128,X9129,X9127)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oof__frac__def])])). 4.05/4.28 fof(c_0_4600, plain, ![X3214]:hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X3214,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X3214))=c_Nitpick_Onum(X3214), inference(variable_rename,[status(thm)],[fact_Nitpick_Onum__def])). 4.05/4.28 fof(c_0_4601, plain, ![X2402]:hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X2402,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X2402))=c_Nitpick_Odenom(X2402), inference(variable_rename,[status(thm)],[fact_Nitpick_Odenom__def])). 4.05/4.28 fof(c_0_4602, plain, ![X11666]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X11666)))|hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X11666)),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(X11666)))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X11666)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X11666)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__number__of__Bit1])])])). 4.05/4.28 fof(c_0_4603, plain, ![X1804, X1805, X1806]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1806,X1806),tc_HOL_Obool)),X1805),hAPP(hAPP(c_Product__Type_OSigma(X1806,X1806),X1804),hAPP(c_COMBK(tc_fun(X1806,tc_HOL_Obool),X1806),X1804))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1806,X1806),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X1806,X1805)),hAPP(hAPP(c_Product__Type_OSigma(X1806,X1806),X1804),hAPP(c_COMBK(tc_fun(X1806,tc_HOL_Obool),X1806),X1804))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__subset__Sigma])])])). 4.05/4.28 fof(c_0_4604, plain, ![X17634, X17635, X17636]:(~class_Rings_Olinordered__idom(X17636)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17636),c_Groups_Ozero__class_Ozero(X17636)),hAPP(hAPP(c_Power_Opower__class_Opower(X17636),X17635),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)))),X17634)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17636),c_Groups_Ozero__class_Ozero(X17636)),X17635)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__0__le__power__imp__0__le])])). 4.05/4.28 fof(c_0_4605, plain, ![X3436, X3437, X3438]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3438,tc_HOL_Obool)),X3437),hAPP(hAPP(c_Set_Oinsert(X3438),X3436),c_Orderings_Obot__class_Obot(tc_fun(X3438,tc_HOL_Obool)))))|c_HOL_OThe(X3438,hAPP(hAPP(c_COMBC(X3438,tc_fun(X3438,tc_HOL_Obool),tc_HOL_Obool),c_member(X3438)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3438,tc_HOL_Obool)),X3437),hAPP(hAPP(c_Set_Oinsert(X3438),X3436),c_Orderings_Obot__class_Obot(tc_fun(X3438,tc_HOL_Obool))))))=c_Partial__Function_Oflat__lub(X3438,X3436,X3437))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3438,tc_HOL_Obool)),X3437),hAPP(hAPP(c_Set_Oinsert(X3438),X3436),c_Orderings_Obot__class_Obot(tc_fun(X3438,tc_HOL_Obool)))))|X3436=c_Partial__Function_Oflat__lub(X3438,X3436,X3437))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_flat__lub__def])])])). 4.05/4.28 fof(c_0_4606, plain, ![X12184, X12185, X12186, X12187, X12188]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X12188,X12188)),hAPP(hAPP(c_Product__Type_OPair(X12188,X12188),X12187),X12186)),c_Transitive__Closure_Ortrancl(X12188,X12185)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X12188,X12188)),hAPP(hAPP(c_Product__Type_OPair(X12188,X12188),X12186),X12184)),X12185))|hBOOL(hAPP(hAPP(c_member(tc_prod(X12188,X12188)),hAPP(hAPP(c_Product__Type_OPair(X12188,X12188),X12187),X12184)),c_Transitive__Closure_Otrancl(X12188,X12185))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__into__trancl1])])])). 4.05/4.28 cnf(c_0_4607, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))=X2|c_Groups_Oone__class_Oone(X1)=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),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_4447])). 4.05/4.28 cnf(c_0_4608, 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))))))|X2!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4448])). 4.05/4.28 cnf(c_0_4609, 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),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), inference(split_conjunct,[status(thm)],[c_0_4449])). 4.05/4.28 cnf(c_0_4610, 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_4450])). 4.05/4.28 fof(c_0_4611, plain, ![X11836, X11837, X11838, X11839, X11840]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X11840,X11840)),hAPP(hAPP(c_Product__Type_OPair(X11840,X11840),X11839),X11838)),X11837))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X11840,X11840)),hAPP(hAPP(c_Product__Type_OPair(X11840,X11840),X11838),X11836)),X11837))|hBOOL(hAPP(hAPP(c_member(tc_prod(X11840,X11840)),hAPP(hAPP(c_Product__Type_OPair(X11840,X11840),X11839),X11836)),c_Transitive__Closure_Otrancl(X11840,X11837))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_r__r__into__trancl])])])). 4.05/4.28 fof(c_0_4612, plain, ![X16127, X16128, X16129, X16130]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16130),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16129)),c_List_OdropWhile(X16129,X16128,X16127))))|hAPP(hAPP(c_List_Onth(X16129),X16127),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16130),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16129)),c_List_OtakeWhile(X16129,X16128,X16127))))=hAPP(hAPP(c_List_Onth(X16129),c_List_OdropWhile(X16129,X16128,X16127)),X16130)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dropWhile__nth])])])). 4.05/4.28 fof(c_0_4613, plain, ![X9609, X9610, X9611, X9612]:((X9611!=X9612|hAPP(c_List_OremoveAll(X9610,X9612),hAPP(hAPP(c_List_Olist_OCons(X9610),X9611),X9609))=hAPP(c_List_OremoveAll(X9610,X9612),X9609))&(X9611=X9612|hAPP(c_List_OremoveAll(X9610,X9612),hAPP(hAPP(c_List_Olist_OCons(X9610),X9611),X9609))=hAPP(hAPP(c_List_Olist_OCons(X9610),X9611),hAPP(c_List_OremoveAll(X9610,X9612),X9609)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_removeAll_Osimps_I2_J])])])). 4.05/4.28 fof(c_0_4614, plain, ![X448, X449, X450]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X450,X450),tc_HOL_Obool)),X449),X448))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X450,X450),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X450,X450,X450),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X450,X450),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X450,X449)),X448)),X449)),X448))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X450,X450),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X450,X449)),X448)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__Int__subset])])). 4.05/4.28 fof(c_0_4615, plain, ![X12476, X12477]:((~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X12477),X12476))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X12477)),c_Int_OBit0(X12476))))&(~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X12477)),c_Int_OBit0(X12476)))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X12477),X12476)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I13_J])])). 4.05/4.28 fof(c_0_4616, plain, ![X10402, X10403]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10403),X10402))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X10403)),c_Int_OBit0(X10402))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X10403)),c_Int_OBit0(X10402)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10403),X10402)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I14_J])])). 4.05/4.28 fof(c_0_4617, plain, ![X580, X581]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X581)),c_Int_OBit0(X580)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X581),X580)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X581),X580))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X581)),c_Int_OBit0(X580))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J])])). 4.05/4.28 fof(c_0_4618, plain, ![X2743, X2744]:(~class_Int_Onumber__ring(X2744)|hAPP(c_Int_Onumber__class_Onumber__of(X2744),c_Int_OBit0(X2743))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2744),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2744),c_Groups_Ozero__class_Ozero(X2744)),hAPP(c_Int_Onumber__class_Onumber__of(X2744),X2743))),hAPP(c_Int_Onumber__class_Onumber__of(X2744),X2743))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_number__of__Bit0])])])). 4.05/4.28 fof(c_0_4619, plain, ![X5617, X5618, X5619]:hAPP(c_Set_OCollect(X5619),hAPP(hAPP(c_COMBS(X5619,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5619),c_fdisj),X5618)),X5617))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5619,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5619),X5618)),hAPP(c_Set_OCollect(X5619),X5617)), inference(variable_rename,[status(thm)],[fact_Collect__disj__eq])). 4.05/4.28 fof(c_0_4620, plain, ![X4810, X4811]:(~class_Int_Onumber__ring(X4811)|hAPP(c_Int_Onumber__class_Onumber__of(X4811),c_Int_OBit0(X4810))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4811),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4811),c_Groups_Oone__class_Oone(X4811)),c_Groups_Oone__class_Oone(X4811))),hAPP(c_Int_Onumber__class_Onumber__of(X4811),X4810))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_double__number__of__Bit0])])])). 4.05/4.28 fof(c_0_4621, plain, ![X6232, X6233, X6234, X6235]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X6235,X6235)),hAPP(hAPP(c_Product__Type_OPair(X6235,X6235),esk187_4(X6232,X6233,X6234,X6235)),X6233)),c_Transitive__Closure_Ortrancl(X6235,X6232)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6235,X6235)),hAPP(hAPP(c_Product__Type_OPair(X6235,X6235),X6234),X6233)),c_Transitive__Closure_Otrancl(X6235,X6232))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X6235,X6235)),hAPP(hAPP(c_Product__Type_OPair(X6235,X6235),X6234),esk187_4(X6232,X6233,X6234,X6235))),X6232))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6235,X6235)),hAPP(hAPP(c_Product__Type_OPair(X6235,X6235),X6234),X6233)),c_Transitive__Closure_Otrancl(X6235,X6232))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclD])])])])). 4.05/4.28 fof(c_0_4622, plain, ![X6034, X6035, X6036, X6037]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X6037,X6037)),hAPP(hAPP(c_Product__Type_OPair(X6037,X6037),esk185_4(X6034,X6035,X6036,X6037)),X6035)),X6034))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6037,X6037)),hAPP(hAPP(c_Product__Type_OPair(X6037,X6037),X6036),X6035)),c_Transitive__Closure_Otrancl(X6037,X6034))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X6037,X6037)),hAPP(hAPP(c_Product__Type_OPair(X6037,X6037),X6036),esk185_4(X6034,X6035,X6036,X6037))),c_Transitive__Closure_Ortrancl(X6037,X6034)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6037,X6037)),hAPP(hAPP(c_Product__Type_OPair(X6037,X6037),X6036),X6035)),c_Transitive__Closure_Otrancl(X6037,X6034))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclD2])])])])). 4.05/4.28 fof(c_0_4623, plain, ![X9499, X9500, X9501, X9502]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9502,X9502)),X9501),c_Transitive__Closure_Otrancl(X9502,X9500)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X9502,X9502),tc_HOL_Obool)),X9500),X9499))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9502,X9502)),X9501),c_Transitive__Closure_Otrancl(X9502,X9499))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__mono])])])). 4.05/4.28 fof(c_0_4624, plain, ![X3311, X3312]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X3312),X3311)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3312),X3311)),X3311), inference(variable_rename,[status(thm)],[fact_nat__minus__add__max])). 4.05/4.28 fof(c_0_4625, plain, ![X2323, X2324]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2323),X2324)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2324),X2323), inference(variable_rename,[status(thm)],[fact_nat__add__commute])). 4.05/4.28 fof(c_0_4626, plain, ![X3205, X3206]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X3206)),c_Int_OBit1(X3205)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3206),X3205)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3206),X3205))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X3206)),c_Int_OBit1(X3205))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I15_J])])). 4.05/4.28 fof(c_0_4627, plain, ![X2361, X2362]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2362),X2361))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X2362)),c_Int_OBit1(X2361))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X2362)),c_Int_OBit1(X2361)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2362),X2361)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J])])). 4.05/4.28 fof(c_0_4628, plain, ![X5749, X5750]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X5750)),c_Int_OBit0(X5749)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5750),X5749)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5750),X5749))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X5750)),c_Int_OBit0(X5749))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I16_J])])). 4.05/4.28 fof(c_0_4629, plain, ![X562, X563]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X563)),c_Int_OBit0(X562)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X563),X562)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X563),X562))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X563)),c_Int_OBit0(X562))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J])])). 4.05/4.28 fof(c_0_4630, plain, ![X7485, X7486]:(~class_Int_Onumber__ring(X7486)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7486),hAPP(c_Int_Onumber__class_Onumber__of(X7486),X7485)),c_Groups_Oone__class_Oone(X7486))=hAPP(c_Int_Onumber__class_Onumber__of(X7486),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7485),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__special_I2_J])])). 4.05/4.28 fof(c_0_4631, plain, ![X10852, X10853]:(~class_Int_Onumber__ring(X10853)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10853),c_Groups_Oone__class_Oone(X10853)),hAPP(c_Int_Onumber__class_Onumber__of(X10853),X10852))=hAPP(c_Int_Onumber__class_Onumber__of(X10853),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),X10852)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__special_I1_J])])). 4.05/4.28 fof(c_0_4632, plain, ![X9985, X9986, X9987, X9988]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X9988,X9988)),hAPP(hAPP(c_Product__Type_OPair(X9988,X9988),X9987),X9986)),c_Transitive__Closure_Otrancl(X9988,X9985)))|X9987=X9986|~hBOOL(hAPP(hAPP(c_member(tc_prod(X9988,X9988)),hAPP(hAPP(c_Product__Type_OPair(X9988,X9988),X9987),X9986)),c_Transitive__Closure_Ortrancl(X9988,X9985))))&(X9986!=X9987|X9987=X9986|~hBOOL(hAPP(hAPP(c_member(tc_prod(X9988,X9988)),hAPP(hAPP(c_Product__Type_OPair(X9988,X9988),X9987),X9986)),c_Transitive__Closure_Ortrancl(X9988,X9985))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtranclD])])])])). 4.05/4.28 fof(c_0_4633, plain, ![X1137, X1138]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X1138))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1137),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1138),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1137)),X1138)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__eq__diff__pred])])). 4.05/4.28 cnf(c_0_4634, 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_4451])). 4.05/4.28 cnf(c_0_4635, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)=X1), inference(split_conjunct,[status(thm)],[c_0_4452]), ['final']). 4.05/4.28 fof(c_0_4636, plain, ![X12036]:c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X12036)=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),X12036),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(variable_rename,[status(thm)],[fact_negDivAlg__minus1])). 4.05/4.28 cnf(c_0_4637, 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_4453])). 4.05/4.28 fof(c_0_4638, plain, ![X2270, X2271, X2272, X2273, X2274]:(hAPP(c_Product__Type_Ofst(X2274,X2273),hAPP(hAPP(c_Product__Type_OPair(X2274,X2273),X2272),X2271))!=X2270|X2270=X2272), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fst__eqD])])). 4.05/4.28 fof(c_0_4639, plain, ![X919, X920, X921, X923, X924, X925, X926]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk23_3(X919,X920,X921)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X921,X921)),X920),c_Transitive__Closure_Otrancl(X921,X919))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X921,X921)),X920),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X921,X921),tc_HOL_Obool),esk23_3(X919,X920,X921)),X919)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X921,X921)),X920),c_Transitive__Closure_Otrancl(X921,X919)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X926))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X925,X925)),X924),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X925,X925),tc_HOL_Obool),X926),X923)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X925,X925)),X924),c_Transitive__Closure_Otrancl(X925,X923))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__power])])])])])])). 4.05/4.28 fof(c_0_4640, plain, ![X4008, X4009]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X4009,X4009)),hAPP(hAPP(c_Product__Type_OPair(X4009,X4009),esk125_2(X4008,X4009)),esk125_2(X4008,X4009))),c_Transitive__Closure_Otrancl(X4009,X4008)))|c_Wellfounded_Oacyclic(X4009,X4008)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acyclicI])])])])). 4.05/4.28 fof(c_0_4641, plain, ![X4002, X4003, X4005, X4006, X4007]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X4003,X4003)),hAPP(hAPP(c_Product__Type_OPair(X4003,X4003),esk124_2(X4002,X4003)),esk124_2(X4002,X4003))),c_Transitive__Closure_Otrancl(X4003,X4002)))|c_Wellfounded_Oacyclic(X4003,X4002))&(~c_Wellfounded_Oacyclic(X4006,X4005)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4006,X4006)),hAPP(hAPP(c_Product__Type_OPair(X4006,X4006),X4007),X4007)),c_Transitive__Closure_Otrancl(X4006,X4005))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acyclic__def])])])])])])). 4.05/4.28 fof(c_0_4642, plain, ![X13892, X13893, X13894, X13895, X13896]:(X13892!=hAPP(c_Product__Type_Osnd(X13896,X13895),hAPP(hAPP(c_Product__Type_OPair(X13896,X13895),X13894),X13893))|X13892=X13893), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_snd__eqD])])])). 4.05/4.28 fof(c_0_4643, plain, ![X6175, X6176, X6177]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X6177),c_Nitpick_Oplus__frac(X6177,X6176,c_Nitpick_Ouminus__frac(X6177,X6175)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Nitpick_Oless__frac(X6177,X6176,X6175))&(~c_Nitpick_Oless__frac(X6177,X6176,X6175)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X6177),c_Nitpick_Oplus__frac(X6177,X6176,c_Nitpick_Ouminus__frac(X6177,X6175)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__frac__def])])). 4.05/4.28 fof(c_0_4644, plain, ![X12230, X12231, X12232]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X12232),c_Nitpick_Oplus__frac(X12232,X12231,c_Nitpick_Ouminus__frac(X12232,X12230)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Nitpick_Oless__eq__frac(X12232,X12231,X12230))&(~c_Nitpick_Oless__eq__frac(X12232,X12231,X12230)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X12232),c_Nitpick_Oplus__frac(X12232,X12231,c_Nitpick_Ouminus__frac(X12232,X12230)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__eq__frac__def])])). 4.05/4.28 fof(c_0_4645, plain, ![X16801, X16802]:(~class_Int_Onumber__ring(X16802)|hAPP(c_Int_Onumber__class_Onumber__of(X16802),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X16801))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16802),c_Groups_Oone__class_Oone(X16802)),hAPP(c_Int_Onumber__class_Onumber__of(X16802),X16801))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I2_J])])). 4.05/4.28 fof(c_0_4646, plain, ![X4756, X4757]:(~class_Int_Onumber__ring(X4757)|hAPP(c_Int_Onumber__class_Onumber__of(X4757),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4756),c_Int_OBit1(c_Int_OPls)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4757),hAPP(c_Int_Onumber__class_Onumber__of(X4757),X4756)),c_Groups_Oone__class_Oone(X4757))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__special_I3_J])])])). 4.05/4.28 fof(c_0_4647, plain, ![X962, X963, X964, X965]:((((hBOOL(hAPP(hAPP(c_member(X965),X963),X962))|~hBOOL(hAPP(hAPP(c_member(X965),X963),X962))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),X962))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),X962))|~hBOOL(hAPP(hAPP(c_member(X965),X963),X962))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),X962)))))&((((hBOOL(hAPP(hAPP(c_member(X965),X963),X962))|(~hBOOL(hAPP(hAPP(c_member(X965),X963),X964))|hBOOL(hAPP(hAPP(c_member(X965),X963),X964)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),X962))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),X962))|(~hBOOL(hAPP(hAPP(c_member(X965),X963),X964))|hBOOL(hAPP(hAPP(c_member(X965),X963),X964)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),X962)))))&((hBOOL(hAPP(hAPP(c_member(X965),X963),X962))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X965,tc_HOL_Obool)),X964),X962))|hBOOL(hAPP(hAPP(c_member(X965),X963),X964)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),X962))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),X962))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X965,tc_HOL_Obool)),X964),X962))|hBOOL(hAPP(hAPP(c_member(X965),X963),X964)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),X962))))))&(((hBOOL(hAPP(hAPP(c_member(X965),X963),X962))|(~hBOOL(hAPP(hAPP(c_member(X965),X963),X964))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),c_Orderings_Obot__class_Obot(tc_fun(X965,tc_HOL_Obool))))),X962)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),X962))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),X962))|(~hBOOL(hAPP(hAPP(c_member(X965),X963),X964))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),c_Orderings_Obot__class_Obot(tc_fun(X965,tc_HOL_Obool))))),X962)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),X962)))))&((hBOOL(hAPP(hAPP(c_member(X965),X963),X962))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X965,tc_HOL_Obool)),X964),X962))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),c_Orderings_Obot__class_Obot(tc_fun(X965,tc_HOL_Obool))))),X962)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),X962))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),X962))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X965,tc_HOL_Obool)),X964),X962))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),c_Orderings_Obot__class_Obot(tc_fun(X965,tc_HOL_Obool))))),X962)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),X962))))))))&(((~hBOOL(hAPP(hAPP(c_member(X965),X963),X964))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),c_Orderings_Obot__class_Obot(tc_fun(X965,tc_HOL_Obool))))),X962))|hBOOL(hAPP(hAPP(c_member(X965),X963),X962))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),X962))))&(hBOOL(hAPP(hAPP(c_member(X965),X963),X964))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X965,tc_HOL_Obool)),X964),X962))|hBOOL(hAPP(hAPP(c_member(X965),X963),X962))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),X962)))))&(~hBOOL(hAPP(hAPP(c_member(X965),X963),X962))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),X962))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X965,tc_HOL_Obool)),X964),hAPP(hAPP(c_Set_Oinsert(X965),X963),X962)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_psubset__insert__iff])])])])). 4.05/4.28 fof(c_0_4648, plain, ![X7550, X7551, X7552]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7552,tc_HOL_Obool)),X7551),X7550))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7552,tc_HOL_Obool)),X7551),X7550)))&(X7550!=X7551|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7552,tc_HOL_Obool)),X7551),X7550))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7552,tc_HOL_Obool)),X7551),X7550))|X7550=X7551|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7552,tc_HOL_Obool)),X7551),X7550)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])])). 4.05/4.28 fof(c_0_4649, plain, ![X16558, X16559]:((~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X16559)),c_Int_OBit1(X16558)))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X16559),X16558)))&(~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X16559),X16558))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X16559)),c_Int_OBit1(X16558))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I16_J])])). 4.05/4.28 fof(c_0_4650, plain, ![X984, X985]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X985)),c_Int_OBit1(X984)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X985),X984)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X985),X984))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X985)),c_Int_OBit1(X984))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J])])). 4.05/4.29 fof(c_0_4651, plain, ![X2441, X2442]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2442),X2441))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X2442)),c_Int_OBit1(X2441))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X2442)),c_Int_OBit1(X2441)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2442),X2441)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I16_J])])). 4.05/4.29 fof(c_0_4652, plain, ![X12583, X12584, X12585, X12586]:(((hBOOL(hAPP(X12585,X12584))|c_List_Olist__ex1(X12586,X12585,X12583)|~c_List_Olist__ex1(X12586,X12585,hAPP(hAPP(c_List_Olist_OCons(X12586),X12584),X12583)))&(~hBOOL(hAPP(X12585,X12584))|c_List_Olist__all(X12586,hAPP(hAPP(c_COMBS(X12586,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12586),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12586),c_fNot),X12585))),hAPP(c_fequal,X12584)),X12583)|~c_List_Olist__ex1(X12586,X12585,hAPP(hAPP(c_List_Olist_OCons(X12586),X12584),X12583))))&(((hBOOL(hAPP(X12585,X12584))|~hBOOL(hAPP(X12585,X12584))|c_List_Olist__ex1(X12586,X12585,hAPP(hAPP(c_List_Olist_OCons(X12586),X12584),X12583)))&(~c_List_Olist__all(X12586,hAPP(hAPP(c_COMBS(X12586,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12586),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12586),c_fNot),X12585))),hAPP(c_fequal,X12584)),X12583)|~hBOOL(hAPP(X12585,X12584))|c_List_Olist__ex1(X12586,X12585,hAPP(hAPP(c_List_Olist_OCons(X12586),X12584),X12583))))&((hBOOL(hAPP(X12585,X12584))|~c_List_Olist__ex1(X12586,X12585,X12583)|c_List_Olist__ex1(X12586,X12585,hAPP(hAPP(c_List_Olist_OCons(X12586),X12584),X12583)))&(~c_List_Olist__all(X12586,hAPP(hAPP(c_COMBS(X12586,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12586),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12586),c_fNot),X12585))),hAPP(c_fequal,X12584)),X12583)|~c_List_Olist__ex1(X12586,X12585,X12583)|c_List_Olist__ex1(X12586,X12585,hAPP(hAPP(c_List_Olist_OCons(X12586),X12584),X12583)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__ex1__simps_I2_J])])])])). 4.05/4.29 cnf(c_0_4653, 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_4454])). 4.05/4.29 cnf(c_0_4654, 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_4455])). 4.05/4.29 cnf(c_0_4655, 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_4456])). 4.05/4.29 fof(c_0_4656, plain, ![X7478, X7479, X7480, X7481]:hAPP(c_List_Ofilter(X7481,hAPP(hAPP(c_COMBS(X7481,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7481),c_fconj),X7479)),X7480)),X7478)=hAPP(c_List_Ofilter(X7481,X7480),hAPP(c_List_Ofilter(X7481,X7479),X7478)), inference(variable_rename,[status(thm)],[fact_filter__filter])). 4.05/4.29 cnf(c_0_4657, plain, (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))=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))), inference(split_conjunct,[status(thm)],[c_0_4457])). 4.05/4.29 fof(c_0_4658, plain, ![X10604, X10605, X10606]:((~hBOOL(hAPP(X10606,X10605))|hAPP(c_Set_OCollect(X10604),hAPP(hAPP(c_COMBS(X10604,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10604),c_fconj),hAPP(c_fequal,X10605))),X10606))=hAPP(hAPP(c_Set_Oinsert(X10604),X10605),c_Orderings_Obot__class_Obot(tc_fun(X10604,tc_HOL_Obool))))&(hBOOL(hAPP(X10606,X10605))|c_Orderings_Obot__class_Obot(tc_fun(X10604,tc_HOL_Obool))=hAPP(c_Set_OCollect(X10604),hAPP(hAPP(c_COMBS(X10604,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10604),c_fconj),hAPP(c_fequal,X10605))),X10606)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Collect__conv__if2])])])). 4.05/4.29 fof(c_0_4659, plain, ![X13572, X13573]:((~c_Int_Oiszero(X13573,hAPP(c_Int_Onumber__class_Onumber__of(X13573),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),X13572))))|c_Groups_Oone__class_Oone(X13573)=hAPP(c_Int_Onumber__class_Onumber__of(X13573),X13572)|~class_Int_Onumber__ring(X13573))&(c_Groups_Oone__class_Oone(X13573)!=hAPP(c_Int_Onumber__class_Onumber__of(X13573),X13572)|c_Int_Oiszero(X13573,hAPP(c_Int_Onumber__class_Onumber__of(X13573),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),X13572))))|~class_Int_Onumber__ring(X13573))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__special_I2_J])])])])). 4.05/4.29 fof(c_0_4660, plain, ![X5682, X5683]:((hAPP(c_Int_Onumber__class_Onumber__of(X5683),X5682)!=c_Groups_Oone__class_Oone(X5683)|c_Int_Oiszero(X5683,hAPP(c_Int_Onumber__class_Onumber__of(X5683),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5682),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))|~class_Int_Onumber__ring(X5683))&(~c_Int_Oiszero(X5683,hAPP(c_Int_Onumber__class_Onumber__of(X5683),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5682),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))|hAPP(c_Int_Onumber__class_Onumber__of(X5683),X5682)=c_Groups_Oone__class_Oone(X5683)|~class_Int_Onumber__ring(X5683))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I4_J])])])). 4.05/4.29 fof(c_0_4661, plain, ![X3142, X3143]:(~class_Int_Onumber__ring(X3143)|hAPP(c_Int_Onumber__class_Onumber__of(X3143),c_Int_OBit1(X3142))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3143),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3143),c_Groups_Oone__class_Oone(X3143)),hAPP(c_Int_Onumber__class_Onumber__of(X3143),X3142))),hAPP(c_Int_Onumber__class_Onumber__of(X3143),X3142))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit1])])). 4.05/4.29 fof(c_0_4662, plain, ![X7356, X7357, X7358, X7359]:(~class_Groups_Ocomm__monoid__add(X7359)|hAPP(c_List_Omonoid__add__class_Olistsum(X7359),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X7359),X7358),c_List_Oupt(X7357,X7356)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7359),X7358),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X7357,X7356)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__set__upt__conv__listsum__nat])])). 4.05/4.29 fof(c_0_4663, plain, ![X10210, X10211]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X10211),X10210)=hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X10211,X10210)), inference(variable_rename,[status(thm)],[fact_set__upt])). 4.05/4.29 fof(c_0_4664, plain, ![X3017, X3018]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3018),X3017))|c_List_Oupt(X3018,hAPP(c_Nat_OSuc,X3017))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X3018,X3017)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X3017),c_List_Olist_ONil(tc_Nat_Onat)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__Suc__append])])). 4.05/4.29 fof(c_0_4665, plain, ![X5670, X5671]:((~c_Int_Oiszero(X5671,hAPP(c_Int_Onumber__class_Onumber__of(X5671),X5670))|c_Int_Oiszero(X5671,hAPP(c_Int_Onumber__class_Onumber__of(X5671),c_Int_OBit0(X5670)))|(~class_Int_Oring__char__0(X5671)|~class_Int_Onumber__ring(X5671)))&(~c_Int_Oiszero(X5671,hAPP(c_Int_Onumber__class_Onumber__of(X5671),c_Int_OBit0(X5670)))|c_Int_Oiszero(X5671,hAPP(c_Int_Onumber__class_Onumber__of(X5671),X5670))|(~class_Int_Oring__char__0(X5671)|~class_Int_Onumber__ring(X5671)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_iszero__number__of__Bit0])])])])). 4.05/4.29 fof(c_0_4666, plain, ![X15263, X15264]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15264),c_Groups_Oone__class_Oone(X15264)),hAPP(c_Int_Onumber__class_Onumber__of(X15264),X15263)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X15263))|(~class_Int_Onumber__ring(X15264)|~class_Rings_Olinordered__idom(X15264)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X15263))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15264),c_Groups_Oone__class_Oone(X15264)),hAPP(c_Int_Onumber__class_Onumber__of(X15264),X15263)))|(~class_Int_Onumber__ring(X15264)|~class_Rings_Olinordered__idom(X15264)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I2_J])])])). 4.05/4.29 fof(c_0_4667, plain, ![X3377, X3378]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3378),c_Groups_Oone__class_Oone(X3378)),hAPP(c_Int_Onumber__class_Onumber__of(X3378),X3377)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X3377))|(~class_Rings_Olinordered__idom(X3378)|~class_Int_Onumber__ring(X3378)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X3377))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3378),c_Groups_Oone__class_Oone(X3378)),hAPP(c_Int_Onumber__class_Onumber__of(X3378),X3377)))|(~class_Rings_Olinordered__idom(X3378)|~class_Int_Onumber__ring(X3378)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I2_J])])])). 4.05/4.29 fof(c_0_4668, plain, ![X16888, X16889]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16888),c_Int_OBit1(c_Int_OPls)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16889),hAPP(c_Int_Onumber__class_Onumber__of(X16889),X16888)),c_Groups_Oone__class_Oone(X16889)))|(~class_Int_Onumber__ring(X16889)|~class_Rings_Olinordered__idom(X16889)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16889),hAPP(c_Int_Onumber__class_Onumber__of(X16889),X16888)),c_Groups_Oone__class_Oone(X16889)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16888),c_Int_OBit1(c_Int_OPls)))|(~class_Int_Onumber__ring(X16889)|~class_Rings_Olinordered__idom(X16889)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__special_I4_J])])])])). 4.05/4.29 fof(c_0_4669, plain, ![X7271, X7272]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7272),hAPP(c_Int_Onumber__class_Onumber__of(X7272),X7271)),c_Groups_Oone__class_Oone(X7272)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7271),c_Int_OBit1(c_Int_OPls)))|(~class_Int_Onumber__ring(X7272)|~class_Rings_Olinordered__idom(X7272)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7271),c_Int_OBit1(c_Int_OPls)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7272),hAPP(c_Int_Onumber__class_Onumber__of(X7272),X7271)),c_Groups_Oone__class_Oone(X7272)))|(~class_Int_Onumber__ring(X7272)|~class_Rings_Olinordered__idom(X7272)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__special_I4_J])])])])). 4.05/4.29 fof(c_0_4670, plain, ![X11762, X11763]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X11763)))|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X11763)),X11762))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X11762))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X11763)))|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X11763)),X11762))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X11763))),X11762))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of__add])])])). 4.05/4.29 fof(c_0_4671, plain, ![X16673, X16674, X16675, X16676]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16676),X16675))|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X16674),X16673)!=c_List_Oupt(X16676,X16675))&(X16673=c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16676),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X16675)|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X16674),X16673)!=c_List_Oupt(X16676,X16675)))&(X16676=X16674|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X16674),X16673)!=c_List_Oupt(X16676,X16675)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16676),X16675))|X16673!=c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16676),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X16675)|X16676!=X16674|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X16674),X16673)=c_List_Oupt(X16676,X16675))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__eq__Cons__conv])])])). 4.05/4.29 fof(c_0_4672, plain, ![X9478, X9479, X9480, X9481]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9481,X9481)),hAPP(hAPP(c_Product__Type_OPair(X9481,X9481),X9480),X9479)),c_Transitive__Closure_Otrancl(X9481,X9478)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9481,X9481)),hAPP(hAPP(c_Product__Type_OPair(X9481,X9481),X9480),X9479)),c_Transitive__Closure_Ortrancl(X9481,X9478)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__into__rtrancl])])])). 4.05/4.29 fof(c_0_4673, plain, ![X1788, X1789, X1790]:hAPP(c_Set_Oimage(tc_prod(X1790,X1789),X1790,c_Product__Type_Ofst(X1790,X1789)),hAPP(c_List_Oset(tc_prod(X1790,X1789)),X1788))=c_Map_Odom(X1790,X1789,hAPP(c_Map_Omap__of(X1790,X1789),X1788)), inference(variable_rename,[status(thm)],[fact_dom__map__of__conv__image__fst])). 4.05/4.29 fof(c_0_4674, plain, ![X16603, X16604, X16605]:hAPP(c_Set_Oimage(tc_prod(X16605,X16604),X16605,c_Product__Type_Ofst(X16605,X16604)),X16603)=hAPP(c_Relation_ODomain(X16605,X16604),X16603), inference(variable_rename,[status(thm)],[fact_fst__eq__Domain])). 4.05/4.29 fof(c_0_4675, plain, ![X3725, X3726, X3727]:(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3727,X3727),tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3727,X3727),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X3727,X3727),X3726)),c_Transitive__Closure_Ortrancl(X3727,X3726))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3727,X3727)),hAPP(hAPP(c_Product__Type_OPair(X3727,X3727),X3725),X3725)),c_Transitive__Closure_Otrancl(X3727,X3726)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_irrefl__tranclI])])])). 4.05/4.29 fof(c_0_4676, plain, ![X12465, X12466]:((X12465!=X12466|c_Int_OBit0(X12466)=c_Int_OBit0(X12465))&(c_Int_OBit0(X12466)!=c_Int_OBit0(X12465)|X12465=X12466)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J])])). 4.05/4.29 fof(c_0_4677, plain, ![X2359, X2360]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2360))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X2360)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2359)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2360))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__number__of])])). 4.05/4.29 fof(c_0_4678, plain, ![X14777, X14778]:(~class_Int_Onumber__ring(X14778)|~class_Fields_Ofield(X14778)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14778),X14777),hAPP(c_Int_Onumber__class_Onumber__of(X14778),c_Int_OBit1(c_Int_OPls)))=X14777), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__numeral__1])])). 4.05/4.29 fof(c_0_4679, plain, ![X6775, X6776, X6777]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X6777,X6777)),X6776),X6775))|hBOOL(hAPP(hAPP(c_member(tc_prod(X6777,X6777)),X6776),c_Transitive__Closure_Otrancl(X6777,X6775)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__trancl_H])])). 4.05/4.29 fof(c_0_4680, plain, ![X2448, X2449]:((X2449!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|c_Code__Numeral_Onat__of__aux(X2449,X2448)=X2448)&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X2449|c_Code__Numeral_Onat__of__aux(X2449,X2448)=c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X2449),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X2448)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__of__aux__code])])])). 4.05/4.29 fof(c_0_4681, plain, ![X10112, X10113]:c_Code__Numeral_Onat__of__aux(X10113,X10112)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X10113)),X10112), inference(variable_rename,[status(thm)],[fact_nat__of__aux__def])). 4.05/4.29 fof(c_0_4682, plain, ![X11613, X11614]:(~class_Int_Onumber__ring(X11614)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11614),hAPP(c_Int_Onumber__class_Onumber__of(X11614),c_Int_OBit1(c_Int_OPls))),X11613)=X11613), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1])])). 4.05/4.29 fof(c_0_4683, plain, ![X11887, X11888]:(~class_Int_Onumber__ring(X11888)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11888),X11887),hAPP(c_Int_Onumber__class_Onumber__of(X11888),c_Int_OBit1(c_Int_OPls)))=X11887), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1__right])])). 4.05/4.29 fof(c_0_4684, plain, ![X13517, X13518, X13519]:(hBOOL(hAPP(hAPP(c_member(X13519),X13518),hAPP(c_List_Oset(X13519),X13517)))|X13517=hAPP(c_List_OremoveAll(X13519,X13518),X13517)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_removeAll__id])])])). 4.05/4.29 fof(c_0_4685, plain, ![X13520, X13521, X13522]:(~hBOOL(hAPP(c_List_Odistinct(X13522),X13521))|hAPP(c_List_OremoveAll(X13522,X13520),X13521)=c_List_Oremove1(X13522,X13520,X13521)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remove1__removeAll])])). 4.05/4.29 fof(c_0_4686, plain, ![X5967]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5967),c_Int_OPls))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5967)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X5967)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5967),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),X5967)),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])])])). 4.05/4.29 cnf(c_0_4687, 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_4458])). 4.05/4.29 cnf(c_0_4688, 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_4459])). 4.05/4.29 cnf(c_0_4689, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X1))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1)))), inference(split_conjunct,[status(thm)],[c_0_4460])). 4.05/4.29 cnf(c_0_4690, 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_4461])). 4.05/4.29 cnf(c_0_4691, 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_4462])). 4.05/4.29 cnf(c_0_4692, 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_4463])). 4.05/4.29 cnf(c_0_4693, 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_4464])). 4.05/4.29 cnf(c_0_4694, 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_4465])). 4.05/4.29 cnf(c_0_4695, 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_4466])). 4.05/4.29 cnf(c_0_4696, plain, (X1=c_Int_OPls|c_Int_OBit0(X1)!=c_Int_OPls), inference(split_conjunct,[status(thm)],[c_0_4467])). 4.05/4.29 cnf(c_0_4697, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4468])). 4.05/4.29 cnf(c_0_4698, 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_4469])). 4.05/4.29 fof(c_0_4699, plain, ![X4354, X4355]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4355,X4355)),X4354))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4355,X4355)),c_Transitive__Closure_Otrancl(X4355,X4354))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4355,X4355)),c_Transitive__Closure_Otrancl(X4355,X4354)))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4355,X4355)),X4354)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__trancl])])). 4.05/4.29 fof(c_0_4700, plain, ![X15015]:((~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X15015)),c_Int_OMin))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X15015),c_Int_OMin)))&(~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X15015),c_Int_OMin))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X15015)),c_Int_OMin)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I12_J])])). 4.05/4.29 fof(c_0_4701, plain, ![X4656]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X4656)),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4656),c_Int_OMin)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4656),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X4656)),c_Int_OMin)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I13_J])])). 4.05/4.29 fof(c_0_4702, plain, ![X15018]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X15018)),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15018),c_Int_OPls)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15018),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X15018)),c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J])])). 4.05/4.29 fof(c_0_4703, plain, ![X3792]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3792),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X3792)),c_Int_OMin)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X3792)),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3792),c_Int_OMin)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I30_J])])). 4.05/4.29 fof(c_0_4704, plain, ![X395]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X395)),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X395),c_Int_OPls)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X395),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X395)),c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J])])). 4.05/4.29 fof(c_0_4705, plain, ![X12582]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X12582)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X12582)))))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X12582))))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X12582))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit1])])). 4.05/4.29 fof(c_0_4706, plain, ![X2803, X2804]:(~c_Wellfounded_Owf(X2804,hAPP(c_Relation_Oconverse(X2804,X2804),X2803))|c_Wellfounded_Owf(X2804,hAPP(c_Relation_Oconverse(X2804,X2804),c_Transitive__Closure_Otrancl(X2804,X2803)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__converse__trancl])])])). 4.05/4.29 fof(c_0_4707, plain, ![X3235]:((~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X3235))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X3235))))&(~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X3235)))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X3235)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__int__code_I8_J])])). 4.05/4.29 fof(c_0_4708, plain, ![X8493]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X8493)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X8493)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X8493))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X8493))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I9_J])])). 4.05/4.29 fof(c_0_4709, plain, ![X2485]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X2485)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X2485)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X2485))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X2485))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J])])). 4.05/4.29 fof(c_0_4710, plain, ![X17167]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X17167)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X17167)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X17167))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X17167))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I26_J])])). 4.05/4.29 fof(c_0_4711, plain, ![X1370]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1370)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1370)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1370))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1370))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J])])). 4.05/4.29 fof(c_0_4712, plain, ![X9292]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X9292)=X9292, inference(variable_rename,[status(thm)],[fact_add__Pls])). 4.05/4.29 fof(c_0_4713, plain, ![X2683]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2683),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),X2683))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X2683)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2683),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),X2683))=c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__1__add__number__of])])])). 4.05/4.29 fof(c_0_4714, plain, ![X3919]:(~class_Int_Onumber__ring(X3919)|hAPP(c_Int_Onumber__class_Onumber__of(X3919),c_Int_OBit1(c_Int_OPls))=c_Groups_Oone__class_Oone(X3919)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_numeral__1__eq__1])])])). 4.05/4.29 fof(c_0_4715, plain, ![X8988, X8989]:((X8989!=X8988|c_Int_OBit1(X8988)=c_Int_OBit1(X8989))&(c_Int_OBit1(X8988)!=c_Int_OBit1(X8989)|X8989=X8988)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J])])). 4.05/4.29 fof(c_0_4716, plain, ![X7140, X7141]:(~class_Int_Onumber__ring(X7141)|hAPP(c_Int_Onumber__class_Onumber__of(X7141),c_Int_Osucc(X7140))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7141),c_Groups_Oone__class_Oone(X7141)),hAPP(c_Int_Onumber__class_Onumber__of(X7141),X7140))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__succ])])). 4.05/4.29 fof(c_0_4717, plain, ![X13135, X13136]:(~c_Wellfounded_Owf(X13136,X13135)|c_Wellfounded_Owf(X13136,c_Transitive__Closure_Otrancl(X13136,X13135))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__trancl])])])). 4.05/4.29 fof(c_0_4718, plain, ![X6421, X6422]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6422),X6421))|c_List_Oupt(X6422,hAPP(c_Nat_OSuc,X6421))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X6422,X6421)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X6421),c_List_Olist_ONil(tc_Nat_Onat))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6422),X6421))|c_List_Olist_ONil(tc_Nat_Onat)=c_List_Oupt(X6422,hAPP(c_Nat_OSuc,X6421)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upt__Suc])])])). 4.05/4.29 fof(c_0_4719, plain, ![X8634]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8634)))|hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8634))=c_Groups_Oone__class_Oone(tc_Nat_Onat))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X8634)))|hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X8634))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X8634)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of])])])). 4.05/4.29 fof(c_0_4720, plain, ![X14135]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X14135))))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14135))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14135)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X14135)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__pred__iff__0])])). 4.05/4.29 fof(c_0_4721, plain, ![X13648, X13649]:(~class_Int_Onumber__ring(X13649)|~class_Int_Oring__char__0(X13649)|~c_Int_Oiszero(X13649,hAPP(c_Int_Onumber__class_Onumber__of(X13649),c_Int_OBit1(X13648)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_iszero__number__of__Bit1])])])). 4.05/4.29 fof(c_0_4722, plain, ![X16340]:(~class_Int_Onumber__ring(X16340)|~c_Int_Oiszero(X16340,hAPP(c_Int_Onumber__class_Onumber__of(X16340),c_Int_OBit1(c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__iszero__Numeral1])])])). 4.05/4.29 fof(c_0_4723, plain, ![X15154]:((X15154!=c_Int_OMin|c_Int_OMin=c_Int_OBit1(X15154))&(c_Int_OMin!=c_Int_OBit1(X15154)|X15154=c_Int_OMin)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I47_J])])). 4.05/4.29 fof(c_0_4724, plain, ![X15036, X15037]:((c_Code__Numeral_OSuc__code__numeral(X15036)!=c_Code__Numeral_OSuc__code__numeral(X15037)|X15036=X15037)&(X15036!=X15037|c_Code__Numeral_OSuc__code__numeral(X15036)=c_Code__Numeral_OSuc__code__numeral(X15037))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Oinject])])). 4.05/4.29 fof(c_0_4725, plain, ![X4050]:c_Code__Numeral_OSuc__code__numeral(X4050)=hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X4050))), inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__def])). 4.05/4.29 fof(c_0_4726, plain, ![X12281, X12282]:~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X12282)),c_Int_OBit1(X12281))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__int__code_I14_J])])). 4.05/4.29 fof(c_0_4727, plain, ![X12202, X12203]:~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X12203)),c_Int_OBit0(X12202))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__int__code_I15_J])])). 4.05/4.29 cnf(c_0_4728, plain, (c_Int_OBit0(X1)!=c_Int_OBit1(X2)), inference(split_conjunct,[status(thm)],[c_0_4470])). 4.05/4.29 cnf(c_0_4729, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1)))), inference(split_conjunct,[status(thm)],[c_0_4471])). 4.05/4.29 cnf(c_0_4730, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_4472])). 4.05/4.29 cnf(c_0_4731, plain, (c_Int_OMin!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4473, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.29 cnf(c_0_4732, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X1)))), inference(split_conjunct,[status(thm)],[c_0_4476])). 4.05/4.29 cnf(c_0_4733, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4477])). 4.05/4.29 cnf(c_0_4734, plain, (c_Int_OPls!=c_Int_OBit1(X1)), inference(split_conjunct,[status(thm)],[c_0_4478])). 4.05/4.29 fof(c_0_4735, plain, ![X5212]:c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=c_Code__Numeral_OSuc__code__numeral(X5212), inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I2_J])). 4.05/4.29 fof(c_0_4736, plain, ![X14098, X14099, X14100, X14101]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X14101,X14101),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X14101,X14098)),hAPP(c_Set_OCollect(tc_prod(X14101,X14101)),hAPP(c_Product__Type_Oprod_Oprod__case(X14101,X14101,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X14101,tc_fun(X14101,tc_HOL_Obool),tc_fun(X14101,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X14101,tc_HOL_Obool),tc_fun(X14101,tc_HOL_Obool)),X14101),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X14101)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X14101),c_fconj),hAPP(hAPP(c_COMBC(X14101,tc_fun(tc_prod(X14101,X14101),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X14101,X14101),tc_fun(tc_fun(tc_prod(X14101,X14101),tc_HOL_Obool),tc_HOL_Obool),X14101),c_member(tc_prod(X14101,X14101))),hAPP(hAPP(c_COMBC(X14101,X14101,tc_prod(X14101,X14101)),c_Product__Type_OPair(X14101,X14101)),X14100))),c_Transitive__Closure_Ortrancl(X14101,X14098))))),hAPP(hAPP(c_COMBC(X14101,tc_fun(tc_prod(X14101,X14101),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X14101,X14101),tc_fun(tc_fun(tc_prod(X14101,X14101),tc_HOL_Obool),tc_HOL_Obool),X14101),c_member(tc_prod(X14101,X14101))),hAPP(c_Product__Type_OPair(X14101,X14101),X14099))),c_Transitive__Closure_Ortrancl(X14101,X14098))))))=c_Transitive__Closure_Otrancl(X14101,hAPP(hAPP(c_Set_Oinsert(tc_prod(X14101,X14101)),hAPP(hAPP(c_Product__Type_OPair(X14101,X14101),X14100),X14099)),X14098)), inference(variable_rename,[status(thm)],[fact_trancl__insert])). 4.05/4.29 fof(c_0_4737, plain, ![X10457, X10458, X10459, X10460]:hAPP(hAPP(c_List_Omap(tc_prod(X10460,tc_Nat_Onat),X10460),c_Product__Type_Ofst(X10460,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X10460,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X10460,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(X10460,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X10460,tc_Nat_Onat))),X10459)),hAPP(hAPP(c_List_Ozip(X10460,tc_Nat_Onat),X10458),c_List_Oupt(X10457,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10457),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10460)),X10458))))))=hAPP(hAPP(c_List_Omap(tc_prod(X10460,tc_Nat_Onat),X10460),c_Product__Type_Ofst(X10460,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X10460,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X10460,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(X10460,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X10460,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(X10460,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X10460,tc_Nat_Onat))),X10457))),X10459)),hAPP(hAPP(c_List_Ozip(X10460,tc_Nat_Onat),X10458),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10460)),X10458))))), inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma])). 4.05/4.29 fof(c_0_4738, plain, ![X3404, X3405, X3406]: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),X3406)),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))),X3405))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3404)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3404)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3406),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3406),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),X3404),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X3405)))), inference(variable_rename,[status(thm)],[fact_arith__series__int])). 4.05/4.29 fof(c_0_4739, plain, ![X15662, X15663]: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),X15663),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15662)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X15663)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X15662))), inference(variable_rename,[status(thm)],[fact_zmod__number__of__Bit0])). 4.05/4.29 fof(c_0_4740, plain, ![X13380, X13381]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X13381))),hAPP(c_List_Ofilter(tc_List_Olist(X13381),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X13381)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X13381),tc_List_Olist(X13381),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X13381)))),X13380))=c_List_Ofoldr(tc_List_Olist(X13381),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X13381)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X13381))),c_List_Otranspose(X13381,X13380),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_transpose__max__length])). 4.05/4.29 cnf(c_0_4741, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(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))),X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_4479])). 4.05/4.29 cnf(c_0_4742, plain, (c_List_Ofoldr(X1,X2,X3,X4,X5)=hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X5),hAPP(c_List_Orev(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_4480])). 4.05/4.29 fof(c_0_4743, plain, ![X9733, X9734]:c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9734),c_Int_Osucc(X9733)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X9734)),c_Int_OBit1(X9733)), inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit1])). 4.05/4.29 fof(c_0_4744, plain, ![X2236]: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)))),X2236)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2236),X2236), inference(variable_rename,[status(thm)],[fact_nat__mult__2])). 4.05/4.29 fof(c_0_4745, plain, ![X17696]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17696),X17696)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17696),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), inference(variable_rename,[status(thm)],[fact_nat__mult__2__right])). 4.05/4.29 fof(c_0_4746, plain, ![X16690, X16691, X16692, X16693, X16694]:hAPP(hAPP(c_List_Oappend(X16693),hAPP(X16692,X16691)),c_List_Omaps(X16694,X16693,X16692,X16690))=c_List_Omaps(X16694,X16693,X16692,hAPP(hAPP(c_List_Olist_OCons(X16694),X16691),X16690)), inference(variable_rename,[status(thm)],[fact_maps__simps_I1_J])). 4.05/4.29 fof(c_0_4747, plain, ![X15600, X15601, X15602, X15603]:c_List_Oconcat(X15603,hAPP(hAPP(c_List_Omap(X15602,tc_List_Olist(X15603)),X15601),X15600))=c_List_Omaps(X15602,X15603,X15601,X15600), inference(variable_rename,[status(thm)],[fact_concat__map__maps])). 4.05/4.29 fof(c_0_4748, plain, ![X17706, X17707, X17708]:hAPP(hAPP(c_List_Oappend(X17708),X17707),c_List_Oconcat(X17708,X17706))=hAPP(c_List_Ofoldl(tc_List_Olist(X17708),tc_List_Olist(X17708),c_List_Oappend(X17708),X17707),X17706), inference(variable_rename,[status(thm)],[fact_foldl__conv__concat])). 4.05/4.29 fof(c_0_4749, plain, ![X5501, X5502]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5502),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X5501)))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X5502),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5501))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))), inference(variable_rename,[status(thm)],[fact_zpower__number__of__even])). 4.05/4.29 fof(c_0_4750, plain, ![X9273, X9274]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X9274)),c_Int_OBit1(X9273))=c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9274),X9273)), inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit1])). 4.05/4.29 fof(c_0_4751, plain, ![X11436, X11437]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X11437)),c_Int_OBit0(X11436))=c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11437),X11436)), inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit0])). 4.05/4.29 fof(c_0_4752, plain, ![X1726, X1727]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X1727)),X1726)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1727),X1726))),X1726), inference(variable_rename,[status(thm)],[fact_mult__Bit1])). 4.05/4.29 fof(c_0_4753, plain, ![X2372]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X2372))=hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2372)),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))), inference(variable_rename,[status(thm)],[fact_nat__number__of__Bit0])). 4.05/4.29 fof(c_0_4754, plain, ![X10799, X10800]:c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X10800),X10799))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X10800)),X10799), inference(variable_rename,[status(thm)],[fact_mult__Bit0])). 4.05/4.29 fof(c_0_4755, plain, ![X1105]:c_Int_Osucc(c_Int_OBit1(X1105))=c_Int_OBit0(c_Int_Osucc(X1105)), inference(variable_rename,[status(thm)],[fact_succ__Bit1])). 4.05/4.29 fof(c_0_4756, plain, ![X10579, X10580]:hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X10580,X10579))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X10580)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X10579))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_com_Osize_I12_J])). 4.05/4.29 fof(c_0_4757, plain, ![X10464, X10465, X10466]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10466),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10465),X10464))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10466),X10465)),X10464), inference(variable_rename,[status(thm)],[fact_nat__add__assoc])). 4.05/4.29 fof(c_0_4758, plain, ![X4917]:hAPP(c_Nat_OSuc,X4917)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4917),c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1])). 4.05/4.29 cnf(c_0_4759, 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_4481])). 4.05/4.29 cnf(c_0_4760, 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_4482]), ['final']). 4.05/4.29 fof(c_0_4761, plain, ![X6169, X6170]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X6170)),c_Com_Ocom_Ocom__size(X6169))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X6170,X6169)), inference(variable_rename,[status(thm)],[fact_com_Osize_I4_J])). 4.05/4.29 fof(c_0_4762, plain, ![X11717]:c_Divides_Oadjust(X11717)=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)),X11717))))),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)),X11717))))),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))))))), inference(variable_rename,[status(thm)],[fact_adjust__def])). 4.05/4.29 fof(c_0_4763, plain, ![X9914, X9915, X9916]:hAPP(c_Divides_Oadjust(X9916),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X9915),X9914))=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),X9914),X9916)),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)))),X9915)),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)))),X9915)),X9914))), inference(variable_rename,[status(thm)],[fact_adjust__eq])). 4.05/4.29 fof(c_0_4764, plain, ![X3607, X3608, X3609]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X3609),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X3609),X3608),hAPP(c_Nitpick_Odenom(X3609),X3607))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X3609),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X3609),tc_Int_Oint),c_Nitpick_Ofrac(X3609)),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(X3609),X3608))),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(X3609),X3608))))),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(X3609),X3607))),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(X3609),X3607)))))),c_COMBI(tc_Int_Oint)))=c_Nitpick_Oplus__frac(X3609,X3608,X3607), inference(variable_rename,[status(thm)],[fact_Nitpick_Oplus__frac__def])). 4.05/4.29 fof(c_0_4765, plain, ![X10854, X10855, X10856, X10857]:hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10857)),hAPP(hAPP(c_List_Olist_OCons(X10857),X10856),c_List_Oconcat(X10857,hAPP(hAPP(c_List_Omap(tc_List_Olist(X10857),tc_List_Olist(X10857)),c_List_Olist_Olist__case(tc_List_Olist(X10857),X10857,c_List_Olist_ONil(X10857),hAPP(hAPP(c_COMBB(tc_List_Olist(X10857),tc_fun(tc_List_Olist(X10857),tc_List_Olist(X10857)),X10857),c_COMBK(tc_List_Olist(X10857),tc_List_Olist(X10857))),hAPP(hAPP(c_COMBC(X10857,tc_List_Olist(X10857),tc_List_Olist(X10857)),c_List_Olist_OCons(X10857)),c_List_Olist_ONil(X10857))))),X10854)))),c_List_Otranspose(X10857,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10857)),X10855),c_List_Oconcat(tc_List_Olist(X10857),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10857),tc_List_Olist(tc_List_Olist(X10857))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X10857)),X10857,c_List_Olist_ONil(tc_List_Olist(X10857)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X10857),tc_List_Olist(tc_List_Olist(X10857))),X10857),hAPP(hAPP(c_COMBC(tc_List_Olist(X10857),tc_List_Olist(tc_List_Olist(X10857)),tc_List_Olist(tc_List_Olist(X10857))),c_List_Olist_OCons(tc_List_Olist(X10857))),c_List_Olist_ONil(tc_List_Olist(X10857)))))),X10854)))))=c_List_Otranspose(X10857,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10857)),hAPP(hAPP(c_List_Olist_OCons(X10857),X10856),X10855)),X10854)), inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I3_J])). 4.05/4.29 cnf(c_0_4766, 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_4483])). 4.05/4.29 cnf(c_0_4767, 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_Oconcat(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4484])). 4.05/4.29 cnf(c_0_4768, 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_4485])). 4.05/4.29 cnf(c_0_4769, 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_4486])). 4.05/4.29 cnf(c_0_4770, 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_4487])). 4.05/4.29 fof(c_0_4771, plain, ![X3689, X3690, X3691, X3692]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3692)),X3691))),c_List_Ofoldr(tc_List_Olist(X3690),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3690)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3690))),X3689,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3692)),X3691)),c_List_Ofoldr(tc_List_Olist(X3690),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3690)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X3690),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3690)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3690)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X3690),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X3690)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X3690),tc_List_Olist(X3690),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X3690)))),X3689),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(variable_rename,[status(thm)],[fact_transpose__aux__max])). 4.05/4.29 fof(c_0_4772, plain, ![X6130, X6131, X6132, X6133, X6134]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X6134),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X6131))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X6134,X6134),hAPP(hAPP(c_COMBC(tc_Int_Oint,X6134,tc_fun(X6134,X6134)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X6134,tc_fun(X6134,X6134)),tc_Int_Oint),c_If(X6134)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X6134,X6133,X6132),X6130))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X6134,X6134),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X6134,X6134),tc_Int_Oint),X6132),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)),X6130))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X6134,tc_Int_Oint),c_Nat_Onat_Onat__rec(X6134,X6133,X6132)),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)),X6130)))))=hAPP(c_Nat_Onat_Onat__rec(X6134,X6133,X6132),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6131)),X6130)), inference(variable_rename,[status(thm)],[fact_nat__rec__add__eq__if])). 4.05/4.29 fof(c_0_4773, plain, ![X7945, X7946, X7947, X7948, X7949]:c_Nat_Onat_Onat__case(X7949,X7948,X7947,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7946)),X7945))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X7949),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X7946))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X7949,X7949),hAPP(hAPP(c_COMBC(tc_Int_Oint,X7949,tc_fun(X7949,X7949)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7949,tc_fun(X7949,X7949)),tc_Int_Oint),c_If(X7949)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X7949,X7948,X7947,X7945))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7949,tc_Int_Oint),X7947),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)),X7945)))), inference(variable_rename,[status(thm)],[fact_nat__case__add__eq__if])). 4.05/4.29 fof(c_0_4774, plain, ![X2121, X2122]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X2122,tc_HOL_Obool),X2121)=hAPP(c_Set_OCollect(X2122),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2122,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X2122),c_HOL_OAll(tc_fun(X2122,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2122,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X2122,tc_HOL_Obool),tc_HOL_Obool),X2122),hAPP(c_COMBS(tc_fun(X2122,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(X2122,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X2122,tc_HOL_Obool),tc_fun(tc_fun(X2122,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X2122,tc_HOL_Obool))),X2121)))),c_member(X2122)))), inference(variable_rename,[status(thm)],[fact_Inter__eq])). 4.05/4.29 fof(c_0_4775, plain, ![X4678]:hAPP(c_Set_OCollect(tc_prod(X4678,X4678)),hAPP(hAPP(c_COMBB(tc_fun(X4678,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X4678,X4678)),c_HOL_OEx(X4678)),hAPP(hAPP(c_COMBC(tc_prod(X4678,X4678),tc_fun(X4678,tc_prod(X4678,X4678)),tc_fun(X4678,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X4678,X4678),tc_HOL_Obool),tc_fun(tc_fun(X4678,tc_prod(X4678,X4678)),tc_fun(X4678,tc_HOL_Obool)),tc_prod(X4678,X4678)),c_COMBB(tc_prod(X4678,X4678),tc_HOL_Obool,X4678)),c_fequal)),hAPP(hAPP(c_COMBS(X4678,X4678,tc_prod(X4678,X4678)),c_Product__Type_OPair(X4678,X4678)),c_COMBI(X4678)))))=c_Relation_OId(X4678), inference(variable_rename,[status(thm)],[fact_Id__def])). 4.05/4.29 fof(c_0_4776, plain, ![X10456]:c_Relation_OId(X10456)=c_Transitive__Closure_Ortrancl(X10456,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10456,X10456),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_rtrancl__empty])). 4.05/4.29 fof(c_0_4777, plain, ![X4000, X4001]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4001)),hAPP(c_Nat_OSuc,X4000))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X4001))),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,X4000))),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)),X4000)))), inference(variable_rename,[status(thm)],[fact_max__Suc__number__of])). 4.05/4.29 fof(c_0_4778, plain, ![X4540, X4541, X4542, X4543]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X4543),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X4540))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X4543,X4543),hAPP(hAPP(c_COMBC(tc_Int_Oint,X4543,tc_fun(X4543,X4543)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4543,tc_fun(X4543,X4543)),tc_Int_Oint),c_If(X4543)),c_Nat__Numeral_Oneg)),X4542)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X4543,X4543),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X4543,X4543),tc_Int_Oint),X4541),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X4543,tc_Int_Oint),c_Nat_Onat_Onat__rec(X4543,X4542,X4541)),c_Int_Onat))))=hAPP(c_Nat_Onat_Onat__rec(X4543,X4542,X4541),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4540)), inference(variable_rename,[status(thm)],[fact_nat__rec__number__of])). 4.05/4.29 fof(c_0_4779, plain, ![X17146, X17147]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X17147))),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)),X17146))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17147)),hAPP(c_Nat_OSuc,X17146)), inference(variable_rename,[status(thm)],[fact_min__Suc__number__of])). 4.05/4.29 fof(c_0_4780, plain, ![X894, X895, X896]:c_Nitpick_Otimes__frac(X896,X895,X894)=hAPP(hAPP(c_Nitpick_Ofrac(X896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X896),X895)),hAPP(c_Nitpick_Onum(X896),X894))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X896),X895)),hAPP(c_Nitpick_Odenom(X896),X894))), inference(variable_rename,[status(thm)],[fact_Nitpick_Otimes__frac__def])). 4.05/4.29 fof(c_0_4781, plain, ![X6574]:hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X6574),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,X6574))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), inference(variable_rename,[status(thm)],[fact_div2__Suc__Suc])). 4.05/4.29 fof(c_0_4782, plain, ![X8093]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X8093)),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,X8093,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), inference(variable_rename,[status(thm)],[fact_mod2__Suc__Suc])). 4.05/4.29 fof(c_0_4783, plain, ![X17592, X17593]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X17592))),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,X17593))),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),X17593)),c_Int_Onat))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17593)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17592)), inference(variable_rename,[status(thm)],[fact_max__number__of__Suc])). 4.05/4.29 fof(c_0_4784, plain, ![X2446, X2447]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2447)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2446))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2446))),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),X2447)),c_Int_Onat)))), inference(variable_rename,[status(thm)],[fact_min__number__of__Suc])). 4.05/4.29 fof(c_0_4785, plain, ![X4167]:c_Int_Oint__ge__less__than(X4167)=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),X4167)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))), inference(variable_rename,[status(thm)],[fact_int__ge__less__than__def])). 4.05/4.29 fof(c_0_4786, plain, ![X4938, X4939, X4940, X4941]:hAPP(c_Set_OCollect(tc_prod(X4941,X4940)),hAPP(c_Product__Type_Oprod_Oprod__case(X4941,X4940,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X4941,tc_fun(X4940,tc_HOL_Obool),tc_fun(X4940,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X4940,tc_HOL_Obool),tc_fun(X4940,tc_HOL_Obool)),X4941),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4940)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4941),c_fconj),X4939))),X4938)))=hAPP(hAPP(c_Product__Type_OSigma(X4941,X4940),hAPP(c_Set_OCollect(X4941),X4939)),hAPP(hAPP(c_COMBB(tc_fun(X4940,tc_HOL_Obool),tc_fun(X4940,tc_HOL_Obool),X4941),c_Set_OCollect(X4940)),X4938)), inference(variable_rename,[status(thm)],[fact_SetCompr__Sigma__eq])). 4.05/4.29 fof(c_0_4787, plain, ![X7847, X7848, X7849]:c_List_Osublist(X7849,X7848,X7847)=hAPP(hAPP(c_List_Omap(tc_prod(X7849,tc_Nat_Onat),X7849),c_Product__Type_Ofst(X7849,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X7849,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X7849,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(X7849,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X7849,tc_Nat_Onat))),X7847)),hAPP(hAPP(c_List_Ozip(X7849,tc_Nat_Onat),X7848),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7849)),X7848))))), inference(variable_rename,[status(thm)],[fact_sublist__def])). 4.05/4.29 fof(c_0_4788, plain, ![X10040, X10041, X10042, X10043]:c_HOL_OThe(tc_prod(X10043,X10042),hAPP(c_Product__Type_Oprod_Oprod__case(X10043,X10042,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10043,tc_fun(X10042,tc_HOL_Obool),tc_fun(X10042,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X10042,tc_HOL_Obool),tc_fun(X10042,tc_HOL_Obool)),X10043),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10042)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10043),c_fconj),hAPP(c_fequal,X10041)))),hAPP(c_fequal,X10040))))=hAPP(hAPP(c_Product__Type_OPair(X10043,X10042),X10041),X10040), inference(variable_rename,[status(thm)],[fact_The__split__eq])). 4.05/4.29 fof(c_0_4789, plain, ![X15303, X15304, X15305, X15306]:hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X15306),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X15303))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X15306,X15306),hAPP(hAPP(c_COMBC(tc_Int_Oint,X15306,tc_fun(X15306,X15306)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X15306,tc_fun(X15306,X15306)),tc_Int_Oint),c_If(X15306)),c_Nat__Numeral_Oneg)),X15305)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X15306,tc_Int_Oint),X15304),c_Int_Onat)))=c_Nat_Onat_Onat__case(X15306,X15305,X15304,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15303)), inference(variable_rename,[status(thm)],[fact_nat__case__number__of])). 4.05/4.29 fof(c_0_4790, plain, ![X14593, X14594]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X14594)),c_Int_OBit0(X14593))=c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X14594),X14593)), inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit0])). 4.05/4.29 fof(c_0_4791, plain, ![X10190, X10191, X10192, X10193, X10194]:hAPP(c_Fun_Othe__inv__into(X10194,X10193,X10192,X10191),X10190)=c_HOL_OThe(X10194,hAPP(hAPP(c_COMBS(X10194,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10194),c_fconj),hAPP(hAPP(c_COMBC(X10194,tc_fun(X10194,tc_HOL_Obool),tc_HOL_Obool),c_member(X10194)),X10192))),hAPP(hAPP(c_COMBC(X10194,X10193,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X10193,tc_fun(X10193,tc_HOL_Obool),X10194),c_fequal),X10191)),X10190))), inference(variable_rename,[status(thm)],[fact_the__inv__into__def])). 4.05/4.29 fof(c_0_4792, plain, ![X7530, X7531]:c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7531),X7530))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X7531)),c_Int_OBit0(X7530)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I7_J])). 4.05/4.29 cnf(c_0_4793, plain, (c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2))), inference(split_conjunct,[status(thm)],[c_0_4488])). 4.05/4.29 cnf(c_0_4794, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),c_Groups_Oone__class_Oone(tc_Int_Oint))=X1), inference(rw,[status(thm)],[c_0_4489, c_0_4439])). 4.05/4.29 cnf(c_0_4795, 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_4490]), ['final']). 4.05/4.29 fof(c_0_4796, plain, ![X17380, X17381, X17382]:hAPP(c_Set_OCollect(X17382),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X17382),c_fNot),hAPP(hAPP(c_COMBC(X17382,tc_Option_Ooption(X17381),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X17381),tc_fun(tc_Option_Ooption(X17381),tc_HOL_Obool),X17382),c_fequal),X17380)),c_Option_Ooption_ONone(X17381))))=c_Map_Odom(X17382,X17381,X17380), inference(variable_rename,[status(thm)],[fact_dom__def])). 4.05/4.29 fof(c_0_4797, plain, ![X9005, X9006]:c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X9006)),X9005))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X9006)),c_Int_OBit1(X9005)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I8_J])). 4.05/4.29 fof(c_0_4798, plain, ![X6394]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6394),X6394)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=X6394, inference(variable_rename,[status(thm)],[fact_add__self__div__2])). 4.05/4.29 fof(c_0_4799, plain, ![X902, X903]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X903)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X902))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X903))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X902))), inference(variable_rename,[status(thm)],[fact_zdiv__number__of__Bit0])). 4.05/4.29 fof(c_0_4800, plain, ![X10847, X10848]:c_Transitive__Closure_Otrancl(X10848,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10848,X10848),tc_HOL_Obool)),X10847),c_Relation_OId(X10848)))=c_Transitive__Closure_Ortrancl(X10848,X10847), inference(variable_rename,[status(thm)],[fact_trancl__reflcl])). 4.05/4.29 fof(c_0_4801, plain, ![X15741, X15742]:c_Transitive__Closure_Ortrancl(X15742,X15741)=c_Transitive__Closure_Ortrancl(X15742,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15742,X15742),tc_HOL_Obool)),X15741),c_Relation_OId(X15742))), inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl])). 4.05/4.29 fof(c_0_4802, plain, ![X11424]:hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X11424))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11424),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc_H])). 4.05/4.29 fof(c_0_4803, plain, ![X16001, X16002]:hAPP(c_New__DSequence_Opos__not__seq(X16002),X16001)=c_Lazy__Sequence_Ohb__not__seq(hAPP(X16002,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)))),X16001))), inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__not__seq__def])). 4.05/4.29 fof(c_0_4804, plain, ![X5717, X5718]:c_Nitpick_OAbs__Frac(X5718,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(X5718),X5717))),hAPP(c_Nitpick_Odenom(X5718),X5717)))=c_Nitpick_Ouminus__frac(X5718,X5717), inference(variable_rename,[status(thm)],[fact_Nitpick_Ouminus__frac__def])). 4.05/4.29 fof(c_0_4805, plain, ![X7350, X7351]:c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7351),X7350))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X7351)),c_Int_OBit1(X7350)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I10_J])). 4.05/4.29 fof(c_0_4806, plain, ![X3965, X3966]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3966,X3966),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X3966,X3965)),hAPP(hAPP(c_Product__Type_OSigma(X3966,X3966),hAPP(c_Relation_OField(X3966),X3965)),hAPP(c_COMBK(tc_fun(X3966,tc_HOL_Obool),X3966),hAPP(c_Relation_OField(X3966),X3965))))), inference(variable_rename,[status(thm)],[fact_trancl__subset__Field2])). 4.05/4.29 fof(c_0_4807, plain, ![X16898]:c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X16898))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X16898)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I3_J])). 4.05/4.29 fof(c_0_4808, plain, ![X13384, X13385]:c_Nitpick_Oint__lcm(X13385,X13384)=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),X13385)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X13384)))), inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__lcm__def])). 4.05/4.29 fof(c_0_4809, plain, ![X17156, X17157]:c_Nitpick_Onat__lcm(X17157,X17156)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17157),X17156)),c_Nitpick_Onat__gcd(X17157,X17156)), inference(variable_rename,[status(thm)],[fact_Nitpick_Onat__lcm__def])). 4.05/4.29 fof(c_0_4810, plain, ![X4701, X4702]:hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4702),X4701)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X4702))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X4701))), inference(variable_rename,[status(thm)],[fact_nat__abs__mult__distrib])). 4.05/4.29 fof(c_0_4811, plain, ![X14611]:c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X14611)))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X14611)), inference(variable_rename,[status(thm)],[fact_minus__Bit1])). 4.05/4.29 cnf(c_0_4812, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X1))=c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))), inference(split_conjunct,[status(thm)],[c_0_4491])). 4.05/4.29 cnf(c_0_4813, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4492, c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_4814, 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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_4493]), ['final']). 4.05/4.29 cnf(c_0_4815, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4494, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.29 fof(c_0_4816, plain, ![X2143]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X2143))=c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X2143)), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I6_J])). 4.05/4.29 fof(c_0_4817, plain, ![X6401, X6402]:hAPP(c_List_Orev(X6402),c_List_Oconcat(X6402,X6401))=c_List_Oconcat(X6402,hAPP(hAPP(c_List_Omap(tc_List_Olist(X6402),tc_List_Olist(X6402)),c_List_Orev(X6402)),hAPP(c_List_Orev(tc_List_Olist(X6402)),X6401))), inference(variable_rename,[status(thm)],[fact_rev__concat])). 4.05/4.29 fof(c_0_4818, plain, ![X2203]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X2203))=c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2203)), inference(variable_rename,[status(thm)],[fact_minus__Bit0])). 4.05/4.29 fof(c_0_4819, plain, ![X15010, X15011]:c_Transitive__Closure_Otrancl(X15011,X15010)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15011,X15011),tc_HOL_Obool)),X15010),hAPP(hAPP(c_Relation_Orel__comp(X15011,X15011,X15011),c_Transitive__Closure_Otrancl(X15011,X15010)),X15010)), inference(variable_rename,[status(thm)],[fact_trancl__unfold])). 4.05/4.29 fof(c_0_4820, plain, ![X6764, X6765, X6766, X6767]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6767,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6767,tc_HOL_Obool)),X6766),X6765)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6767,tc_HOL_Obool)),X6764),X6765))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6767,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6767,tc_HOL_Obool)),X6766),X6765)),X6764), inference(variable_rename,[status(thm)],[fact_Diff__Int2])). 4.05/4.29 cnf(c_0_4821, 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_4495])). 4.05/4.29 cnf(c_0_4822, 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_4496]), ['final']). 4.05/4.29 fof(c_0_4823, plain, ![X9808, X9809]:c_Transitive__Closure_Ortrancl(X9809,X9808)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X9809,X9809),tc_HOL_Obool)),c_Relation_OId(X9809)),hAPP(hAPP(c_Relation_Orel__comp(X9809,X9809,X9809),c_Transitive__Closure_Ortrancl(X9809,X9808)),X9808)), inference(variable_rename,[status(thm)],[fact_rtrancl__unfold])). 4.05/4.29 fof(c_0_4824, plain, ![X3817]: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)))),X3817))), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J])). 4.05/4.29 fof(c_0_4825, plain, ![X780, X781]:hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X781),X780)=c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(X781)),c_List_Oembed__list(X780))), inference(variable_rename,[status(thm)],[fact_transfer__nat__int__list__functions_I1_J])). 4.05/4.29 fof(c_0_4826, plain, ![X603]:c_List_Oreturn__list(X603)=hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X603), inference(variable_rename,[status(thm)],[fact_return__list__def])). 4.05/4.29 fof(c_0_4827, plain, ![X3758]:c_List_Oembed__list(X3758)=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X3758), inference(variable_rename,[status(thm)],[fact_embed__list__def])). 4.05/4.29 fof(c_0_4828, plain, ![X3787, X3788, X3789, X3790, X3791]:c_List_Ofoldr(X3790,X3791,hAPP(c_COMBC(X3791,X3790,X3791),X3789),hAPP(c_List_Orev(X3790),X3787),X3788)=hAPP(c_List_Ofoldl(X3791,X3790,X3789,X3788),X3787), inference(variable_rename,[status(thm)],[fact_foldl__foldr])). 4.05/4.29 fof(c_0_4829, plain, ![X15565, X15566]:hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X15566,X15565))=c_List_Oupt(hAPP(c_Nat_OSuc,X15566),hAPP(c_Nat_OSuc,X15565)), inference(variable_rename,[status(thm)],[fact_map__Suc__upt])). 4.05/4.29 fof(c_0_4830, plain, ![X12983, X12984]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X12984)),hAPP(c_Nat_OSuc,X12983))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X12984),X12983)), inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastLessThan])). 4.05/4.29 fof(c_0_4831, plain, ![X14146, X14147]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X14147),hAPP(c_Nat_OSuc,X14146))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X14147,X14146), inference(variable_rename,[status(thm)],[fact_atLeastLessThanSuc__atLeastAtMost])). 4.05/4.29 fof(c_0_4832, plain, ![X11095, X11096]:hAPP(c_Relation_ORange(X11096,X11096),c_Transitive__Closure_Otrancl(X11096,X11095))=hAPP(c_Relation_ORange(X11096,X11096),X11095), inference(variable_rename,[status(thm)],[fact_trancl__range])). 4.05/4.29 fof(c_0_4833, plain, ![X16872, X16873]:hAPP(c_Relation_ODomain(X16873,X16873),c_Transitive__Closure_Otrancl(X16873,X16872))=hAPP(c_Relation_ODomain(X16873,X16873),X16872), inference(variable_rename,[status(thm)],[fact_trancl__domain])). 4.05/4.29 fof(c_0_4834, plain, ![X1532, X1533]:c_HOL_OThe(X1533,hAPP(hAPP(c_COMBC(X1533,X1533,tc_HOL_Obool),c_fequal),X1532))=X1532, inference(variable_rename,[status(thm)],[fact_the__eq__trivial])). 4.05/4.29 fof(c_0_4835, plain, ![X10564]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X10564)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X10564)), inference(variable_rename,[status(thm)],[fact_code__numeral_Osize_I4_J])). 4.05/4.29 fof(c_0_4836, plain, ![X15200, X15201]:hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15200),X15201))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X15201,X15200)), inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost__int])). 4.05/4.29 fof(c_0_4837, plain, ![X15189, X15190]:c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X15190,X15189)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15190),c_Groups_Oone__class_Oone(tc_Int_Oint)),X15189), inference(variable_rename,[status(thm)],[fact_atLeastPlusOneAtMost__greaterThanAtMost__int])). 4.05/4.29 fof(c_0_4838, plain, ![X9238, X9239]:hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X9239,X9238))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9238),X9239)),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost__int])). 4.05/4.29 fof(c_0_4839, plain, ![X6125, X6126]:c_Transitive__Closure_Ortrancl(X6126,X6125)=c_Transitive__Closure_Ortrancl(X6126,c_Transitive__Closure_Otrancl(X6126,X6125)), inference(variable_rename,[status(thm)],[fact_trancl__rtrancl__absorb])). 4.05/4.29 fof(c_0_4840, plain, ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)), inference(fof_simplification,[status(thm)],[fact_rel__simps_I2_J])). 4.05/4.29 fof(c_0_4841, plain, ![X6146, X6147, X6148]:((c_List_Olist_ONil(X6148)!=hAPP(c_List_Orotate(X6148,X6147),X6146)|X6146=c_List_Olist_ONil(X6148))&(X6146!=c_List_Olist_ONil(X6148)|c_List_Olist_ONil(X6148)=hAPP(c_List_Orotate(X6148,X6147),X6146))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__is__Nil__conv])])). 4.05/4.29 fof(c_0_4842, plain, ![X4028, X4029]:c_List_Orotate(X4029,X4028)=hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X4029),tc_List_Olist(X4029)),X4028),c_List_Orotate1(X4029)), inference(variable_rename,[status(thm)],[fact_rotate__def])). 4.05/4.29 fof(c_0_4843, plain, ![X11951, X11952]:hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X11952,hAPP(c_Nat_OSuc,X11951)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X11952,X11951), inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upt])). 4.05/4.29 fof(c_0_4844, plain, ![X5168]:hAPP(c_Set_OCollect(X5168),hAPP(c_COMBK(tc_HOL_Obool,X5168),c_fFalse))=c_Orderings_Obot__class_Obot(tc_fun(X5168,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_empty__def])). 4.05/4.29 fof(c_0_4845, plain, ![X13418]:hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X13418),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X13418),hAPP(c_Nat_OSuc,X13418)), inference(variable_rename,[status(thm)],[fact_atLeastLessThan__singleton])). 4.05/4.29 fof(c_0_4846, plain, ![X16718]:c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X16718))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X16718)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_code__numeral_Osize_I2_J])). 4.05/4.29 fof(c_0_4847, plain, ![X4273, X4274, X4275, X4276]:c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X4276,X4275,X4274,c_Code__Numeral_OSuc__code__numeral(X4273))=hAPP(X4274,X4273), inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I5_J])). 4.05/4.29 fof(c_0_4848, plain, ![X7113]:X7113=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X7113)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__minus__one])). 4.05/4.29 fof(c_0_4849, plain, ![X3654, X3655]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3654),X3655)=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X3655,X3654)), inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost])). 4.05/4.29 fof(c_0_4850, plain, ![X14773, X14774]:c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X14774,X14773)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X14774),X14773), inference(variable_rename,[status(thm)],[fact_atLeastSucAtMost__greaterThanAtMost])). 4.05/4.29 fof(c_0_4851, plain, ![X14175]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X14175)),X14175), inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2])). 4.05/4.29 fof(c_0_4852, plain, ![X17140]:hAPP(c_Set_OCollect(X17140),hAPP(c_COMBK(tc_HOL_Obool,X17140),c_fTrue))=c_Orderings_Otop__class_Otop(tc_fun(X17140,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_UNIV__def])). 4.05/4.29 fof(c_0_4853, plain, ![X1294, X1295, X1296, X1297, X1298, X1299, X1300]:(~class_Rings_Osemiring__0(X1300)|(~c_Fun_Oinj__on(tc_prod(X1299,X1298),X1300,hAPP(c_Product__Type_Oprod_Oprod__case(X1299,X1298,X1300),hAPP(hAPP(c_COMBC(X1299,tc_fun(X1298,X1300),tc_fun(X1298,X1300)),hAPP(hAPP(c_COMBB(tc_fun(X1300,X1300),tc_fun(tc_fun(X1298,X1300),tc_fun(X1298,X1300)),X1299),c_COMBB(X1300,X1300,X1298)),hAPP(hAPP(c_COMBB(X1300,tc_fun(X1300,X1300),X1299),c_Groups_Otimes__class_Otimes(X1300)),X1297))),X1296)),hAPP(hAPP(c_Product__Type_OSigma(X1299,X1298),X1295),hAPP(c_COMBK(tc_fun(X1298,tc_HOL_Obool),X1299),X1294)))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1300),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1299,X1300),X1297),X1295)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1298,X1300),X1296),X1294))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1300,X1300),c_Fun_Oid(X1300)),hAPP(c_Set_OCollect(X1300),hAPP(hAPP(c_COMBB(tc_fun(X1299,tc_HOL_Obool),tc_HOL_Obool,X1300),c_HOL_OEx(X1299)),hAPP(hAPP(c_COMBB(tc_fun(X1299,tc_fun(X1298,tc_HOL_Obool)),tc_fun(X1299,tc_HOL_Obool),X1300),hAPP(c_COMBB(tc_fun(X1298,tc_HOL_Obool),tc_HOL_Obool,X1299),c_HOL_OEx(X1298))),hAPP(hAPP(c_COMBC(X1300,tc_fun(X1299,tc_fun(X1298,tc_HOL_Obool)),tc_fun(X1299,tc_fun(X1298,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1299,tc_fun(tc_fun(X1298,tc_HOL_Obool),tc_fun(X1298,tc_HOL_Obool))),tc_fun(tc_fun(X1299,tc_fun(X1298,tc_HOL_Obool)),tc_fun(X1299,tc_fun(X1298,tc_HOL_Obool))),X1300),c_COMBS(X1299,tc_fun(X1298,tc_HOL_Obool),tc_fun(X1298,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1299,tc_fun(X1298,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1299,tc_fun(tc_fun(X1298,tc_HOL_Obool),tc_fun(X1298,tc_HOL_Obool))),X1300),hAPP(c_COMBB(tc_fun(X1298,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1298,tc_HOL_Obool),tc_fun(X1298,tc_HOL_Obool)),X1299),c_COMBS(X1298,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1299,tc_fun(X1298,tc_HOL_Obool)),tc_fun(X1299,tc_fun(X1298,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1300),hAPP(c_COMBB(tc_fun(X1298,tc_HOL_Obool),tc_fun(X1298,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1299),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1298),c_fconj))),hAPP(hAPP(c_COMBC(X1300,tc_fun(X1299,tc_fun(X1298,X1300)),tc_fun(X1299,tc_fun(X1298,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1298,X1300),tc_fun(X1298,tc_HOL_Obool)),tc_fun(tc_fun(X1299,tc_fun(X1298,X1300)),tc_fun(X1299,tc_fun(X1298,tc_HOL_Obool))),X1300),c_COMBB(tc_fun(X1298,X1300),tc_fun(X1298,tc_HOL_Obool),X1299)),hAPP(hAPP(c_COMBB(tc_fun(X1300,tc_HOL_Obool),tc_fun(tc_fun(X1298,X1300),tc_fun(X1298,tc_HOL_Obool)),X1300),c_COMBB(X1300,tc_HOL_Obool,X1298)),c_fequal))),hAPP(hAPP(c_COMBC(X1299,tc_fun(X1298,X1300),tc_fun(X1298,X1300)),hAPP(hAPP(c_COMBB(tc_fun(X1300,X1300),tc_fun(tc_fun(X1298,X1300),tc_fun(X1298,X1300)),X1299),c_COMBB(X1300,X1300,X1298)),hAPP(hAPP(c_COMBB(X1300,tc_fun(X1300,X1300),X1299),c_Groups_Otimes__class_Otimes(X1300)),X1297))),X1296)))))),hAPP(hAPP(c_COMBC(X1299,tc_fun(X1298,tc_HOL_Obool),tc_fun(X1298,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1298,tc_HOL_Obool),tc_fun(X1298,tc_HOL_Obool)),X1299),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1298)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1299),c_fconj),hAPP(hAPP(c_COMBC(X1299,tc_fun(X1299,tc_HOL_Obool),tc_HOL_Obool),c_member(X1299)),X1295)))),hAPP(hAPP(c_COMBC(X1298,tc_fun(X1298,tc_HOL_Obool),tc_HOL_Obool),c_member(X1298)),X1294))))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__mult__setsum__if__inj])])])). 4.05/4.29 fof(c_0_4854, plain, ![X16191, X16192, X16193]:(~class_Orderings_Olinorder(X16193)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16193),X16192))|(X16192=c_Orderings_Obot__class_Obot(tc_fun(X16193,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16193),X16191))|(c_Orderings_Obot__class_Obot(tc_fun(X16193,tc_HOL_Obool))=X16191|c_Big__Operators_Olattice_OInf__fin(X16193,c_Orderings_Oord__class_Omin(X16193),hAPP(c_Set_OCollect(X16193),hAPP(hAPP(c_COMBB(tc_fun(X16193,tc_HOL_Obool),tc_HOL_Obool,X16193),c_HOL_OEx(X16193)),hAPP(hAPP(c_COMBB(tc_fun(X16193,tc_fun(X16193,tc_HOL_Obool)),tc_fun(X16193,tc_HOL_Obool),X16193),hAPP(c_COMBB(tc_fun(X16193,tc_HOL_Obool),tc_HOL_Obool,X16193),c_HOL_OEx(X16193))),hAPP(hAPP(c_COMBC(X16193,tc_fun(X16193,tc_fun(X16193,tc_HOL_Obool)),tc_fun(X16193,tc_fun(X16193,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X16193,tc_fun(tc_fun(X16193,tc_HOL_Obool),tc_fun(X16193,tc_HOL_Obool))),tc_fun(tc_fun(X16193,tc_fun(X16193,tc_HOL_Obool)),tc_fun(X16193,tc_fun(X16193,tc_HOL_Obool))),X16193),c_COMBS(X16193,tc_fun(X16193,tc_HOL_Obool),tc_fun(X16193,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X16193,tc_fun(X16193,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X16193,tc_fun(tc_fun(X16193,tc_HOL_Obool),tc_fun(X16193,tc_HOL_Obool))),X16193),hAPP(c_COMBB(tc_fun(X16193,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X16193,tc_HOL_Obool),tc_fun(X16193,tc_HOL_Obool)),X16193),c_COMBS(X16193,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X16193,tc_fun(X16193,tc_HOL_Obool)),tc_fun(X16193,tc_fun(X16193,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X16193),hAPP(c_COMBB(tc_fun(X16193,tc_HOL_Obool),tc_fun(X16193,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X16193),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X16193),c_fconj))),hAPP(hAPP(c_COMBC(X16193,tc_fun(X16193,tc_fun(X16193,X16193)),tc_fun(X16193,tc_fun(X16193,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X16193,X16193),tc_fun(X16193,tc_HOL_Obool)),tc_fun(tc_fun(X16193,tc_fun(X16193,X16193)),tc_fun(X16193,tc_fun(X16193,tc_HOL_Obool))),X16193),c_COMBB(tc_fun(X16193,X16193),tc_fun(X16193,tc_HOL_Obool),X16193)),hAPP(hAPP(c_COMBB(tc_fun(X16193,tc_HOL_Obool),tc_fun(tc_fun(X16193,X16193),tc_fun(X16193,tc_HOL_Obool)),X16193),c_COMBB(X16193,tc_HOL_Obool,X16193)),c_fequal))),c_Orderings_Oord__class_Omax(X16193)))))),hAPP(hAPP(c_COMBC(X16193,tc_fun(X16193,tc_HOL_Obool),tc_fun(X16193,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X16193,tc_HOL_Obool),tc_fun(X16193,tc_HOL_Obool)),X16193),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X16193)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X16193),c_fconj),hAPP(hAPP(c_COMBC(X16193,tc_fun(X16193,tc_HOL_Obool),tc_HOL_Obool),c_member(X16193)),X16192)))),hAPP(hAPP(c_COMBC(X16193,tc_fun(X16193,tc_HOL_Obool),tc_HOL_Obool),c_member(X16193)),X16191)))))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X16193),c_Big__Operators_Olattice_OInf__fin(X16193,c_Orderings_Oord__class_Omin(X16193),X16192)),c_Big__Operators_Olattice_OInf__fin(X16193,c_Orderings_Oord__class_Omin(X16193),X16191))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__Inf2__distrib])])])). 4.05/4.29 fof(c_0_4855, plain, ![X11194, X11195, X11196]:(~class_Orderings_Olinorder(X11196)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11196),X11195))|(X11195=c_Orderings_Obot__class_Obot(tc_fun(X11196,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11196),X11194))|(X11194=c_Orderings_Obot__class_Obot(tc_fun(X11196,tc_HOL_Obool))|c_Big__Operators_Olattice_OSup__fin(X11196,c_Orderings_Oord__class_Omax(X11196),hAPP(c_Set_OCollect(X11196),hAPP(hAPP(c_COMBB(tc_fun(X11196,tc_HOL_Obool),tc_HOL_Obool,X11196),c_HOL_OEx(X11196)),hAPP(hAPP(c_COMBB(tc_fun(X11196,tc_fun(X11196,tc_HOL_Obool)),tc_fun(X11196,tc_HOL_Obool),X11196),hAPP(c_COMBB(tc_fun(X11196,tc_HOL_Obool),tc_HOL_Obool,X11196),c_HOL_OEx(X11196))),hAPP(hAPP(c_COMBC(X11196,tc_fun(X11196,tc_fun(X11196,tc_HOL_Obool)),tc_fun(X11196,tc_fun(X11196,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X11196,tc_fun(tc_fun(X11196,tc_HOL_Obool),tc_fun(X11196,tc_HOL_Obool))),tc_fun(tc_fun(X11196,tc_fun(X11196,tc_HOL_Obool)),tc_fun(X11196,tc_fun(X11196,tc_HOL_Obool))),X11196),c_COMBS(X11196,tc_fun(X11196,tc_HOL_Obool),tc_fun(X11196,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X11196,tc_fun(X11196,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X11196,tc_fun(tc_fun(X11196,tc_HOL_Obool),tc_fun(X11196,tc_HOL_Obool))),X11196),hAPP(c_COMBB(tc_fun(X11196,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X11196,tc_HOL_Obool),tc_fun(X11196,tc_HOL_Obool)),X11196),c_COMBS(X11196,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X11196,tc_fun(X11196,tc_HOL_Obool)),tc_fun(X11196,tc_fun(X11196,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X11196),hAPP(c_COMBB(tc_fun(X11196,tc_HOL_Obool),tc_fun(X11196,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X11196),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X11196),c_fconj))),hAPP(hAPP(c_COMBC(X11196,tc_fun(X11196,tc_fun(X11196,X11196)),tc_fun(X11196,tc_fun(X11196,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X11196,X11196),tc_fun(X11196,tc_HOL_Obool)),tc_fun(tc_fun(X11196,tc_fun(X11196,X11196)),tc_fun(X11196,tc_fun(X11196,tc_HOL_Obool))),X11196),c_COMBB(tc_fun(X11196,X11196),tc_fun(X11196,tc_HOL_Obool),X11196)),hAPP(hAPP(c_COMBB(tc_fun(X11196,tc_HOL_Obool),tc_fun(tc_fun(X11196,X11196),tc_fun(X11196,tc_HOL_Obool)),X11196),c_COMBB(X11196,tc_HOL_Obool,X11196)),c_fequal))),c_Orderings_Oord__class_Omin(X11196)))))),hAPP(hAPP(c_COMBC(X11196,tc_fun(X11196,tc_HOL_Obool),tc_fun(X11196,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X11196,tc_HOL_Obool),tc_fun(X11196,tc_HOL_Obool)),X11196),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11196)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X11196),c_fconj),hAPP(hAPP(c_COMBC(X11196,tc_fun(X11196,tc_HOL_Obool),tc_HOL_Obool),c_member(X11196)),X11195)))),hAPP(hAPP(c_COMBC(X11196,tc_fun(X11196,tc_HOL_Obool),tc_HOL_Obool),c_member(X11196)),X11194)))))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X11196),c_Big__Operators_Olattice_OSup__fin(X11196,c_Orderings_Oord__class_Omax(X11196),X11195)),c_Big__Operators_Olattice_OSup__fin(X11196,c_Orderings_Oord__class_Omax(X11196),X11194))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__Sup2__distrib])])])). 4.05/4.29 fof(c_0_4856, plain, ![X9814, X9815, X9816]:(~class_Lattices_Odistrib__lattice(X9816)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9816),X9815))|(c_Orderings_Obot__class_Obot(tc_fun(X9816,tc_HOL_Obool))=X9815|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9816),X9814))|(c_Orderings_Obot__class_Obot(tc_fun(X9816,tc_HOL_Obool))=X9814|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9816),c_Big__Operators_Olattice__class_OInf__fin(X9816,X9815)),c_Big__Operators_Olattice__class_OInf__fin(X9816,X9814))=c_Big__Operators_Olattice__class_OInf__fin(X9816,hAPP(c_Set_OCollect(X9816),hAPP(hAPP(c_COMBB(tc_fun(X9816,tc_HOL_Obool),tc_HOL_Obool,X9816),c_HOL_OEx(X9816)),hAPP(hAPP(c_COMBB(tc_fun(X9816,tc_fun(X9816,tc_HOL_Obool)),tc_fun(X9816,tc_HOL_Obool),X9816),hAPP(c_COMBB(tc_fun(X9816,tc_HOL_Obool),tc_HOL_Obool,X9816),c_HOL_OEx(X9816))),hAPP(hAPP(c_COMBC(X9816,tc_fun(X9816,tc_fun(X9816,tc_HOL_Obool)),tc_fun(X9816,tc_fun(X9816,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X9816,tc_fun(tc_fun(X9816,tc_HOL_Obool),tc_fun(X9816,tc_HOL_Obool))),tc_fun(tc_fun(X9816,tc_fun(X9816,tc_HOL_Obool)),tc_fun(X9816,tc_fun(X9816,tc_HOL_Obool))),X9816),c_COMBS(X9816,tc_fun(X9816,tc_HOL_Obool),tc_fun(X9816,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X9816,tc_fun(X9816,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X9816,tc_fun(tc_fun(X9816,tc_HOL_Obool),tc_fun(X9816,tc_HOL_Obool))),X9816),hAPP(c_COMBB(tc_fun(X9816,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X9816,tc_HOL_Obool),tc_fun(X9816,tc_HOL_Obool)),X9816),c_COMBS(X9816,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X9816,tc_fun(X9816,tc_HOL_Obool)),tc_fun(X9816,tc_fun(X9816,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X9816),hAPP(c_COMBB(tc_fun(X9816,tc_HOL_Obool),tc_fun(X9816,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X9816),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X9816),c_fconj))),hAPP(hAPP(c_COMBC(X9816,tc_fun(X9816,tc_fun(X9816,X9816)),tc_fun(X9816,tc_fun(X9816,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X9816,X9816),tc_fun(X9816,tc_HOL_Obool)),tc_fun(tc_fun(X9816,tc_fun(X9816,X9816)),tc_fun(X9816,tc_fun(X9816,tc_HOL_Obool))),X9816),c_COMBB(tc_fun(X9816,X9816),tc_fun(X9816,tc_HOL_Obool),X9816)),hAPP(hAPP(c_COMBB(tc_fun(X9816,tc_HOL_Obool),tc_fun(tc_fun(X9816,X9816),tc_fun(X9816,tc_HOL_Obool)),X9816),c_COMBB(X9816,tc_HOL_Obool,X9816)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X9816)))))),hAPP(hAPP(c_COMBC(X9816,tc_fun(X9816,tc_HOL_Obool),tc_fun(X9816,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X9816,tc_HOL_Obool),tc_fun(X9816,tc_HOL_Obool)),X9816),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X9816)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X9816),c_fconj),hAPP(hAPP(c_COMBC(X9816,tc_fun(X9816,tc_HOL_Obool),tc_HOL_Obool),c_member(X9816)),X9815)))),hAPP(hAPP(c_COMBC(X9816,tc_fun(X9816,tc_HOL_Obool),tc_HOL_Obool),c_member(X9816)),X9814)))))))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__Inf2__distrib])])])). 4.05/4.29 fof(c_0_4857, plain, ![X3808, X3809, X3810]:(~class_Lattices_Odistrib__lattice(X3810)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3810),X3809))|(c_Orderings_Obot__class_Obot(tc_fun(X3810,tc_HOL_Obool))=X3809|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3810),X3808))|(X3808=c_Orderings_Obot__class_Obot(tc_fun(X3810,tc_HOL_Obool))|c_Big__Operators_Olattice__class_OSup__fin(X3810,hAPP(c_Set_OCollect(X3810),hAPP(hAPP(c_COMBB(tc_fun(X3810,tc_HOL_Obool),tc_HOL_Obool,X3810),c_HOL_OEx(X3810)),hAPP(hAPP(c_COMBB(tc_fun(X3810,tc_fun(X3810,tc_HOL_Obool)),tc_fun(X3810,tc_HOL_Obool),X3810),hAPP(c_COMBB(tc_fun(X3810,tc_HOL_Obool),tc_HOL_Obool,X3810),c_HOL_OEx(X3810))),hAPP(hAPP(c_COMBC(X3810,tc_fun(X3810,tc_fun(X3810,tc_HOL_Obool)),tc_fun(X3810,tc_fun(X3810,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X3810,tc_fun(tc_fun(X3810,tc_HOL_Obool),tc_fun(X3810,tc_HOL_Obool))),tc_fun(tc_fun(X3810,tc_fun(X3810,tc_HOL_Obool)),tc_fun(X3810,tc_fun(X3810,tc_HOL_Obool))),X3810),c_COMBS(X3810,tc_fun(X3810,tc_HOL_Obool),tc_fun(X3810,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X3810,tc_fun(X3810,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X3810,tc_fun(tc_fun(X3810,tc_HOL_Obool),tc_fun(X3810,tc_HOL_Obool))),X3810),hAPP(c_COMBB(tc_fun(X3810,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X3810,tc_HOL_Obool),tc_fun(X3810,tc_HOL_Obool)),X3810),c_COMBS(X3810,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X3810,tc_fun(X3810,tc_HOL_Obool)),tc_fun(X3810,tc_fun(X3810,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X3810),hAPP(c_COMBB(tc_fun(X3810,tc_HOL_Obool),tc_fun(X3810,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X3810),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3810),c_fconj))),hAPP(hAPP(c_COMBC(X3810,tc_fun(X3810,tc_fun(X3810,X3810)),tc_fun(X3810,tc_fun(X3810,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3810,X3810),tc_fun(X3810,tc_HOL_Obool)),tc_fun(tc_fun(X3810,tc_fun(X3810,X3810)),tc_fun(X3810,tc_fun(X3810,tc_HOL_Obool))),X3810),c_COMBB(tc_fun(X3810,X3810),tc_fun(X3810,tc_HOL_Obool),X3810)),hAPP(hAPP(c_COMBB(tc_fun(X3810,tc_HOL_Obool),tc_fun(tc_fun(X3810,X3810),tc_fun(X3810,tc_HOL_Obool)),X3810),c_COMBB(X3810,tc_HOL_Obool,X3810)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X3810)))))),hAPP(hAPP(c_COMBC(X3810,tc_fun(X3810,tc_HOL_Obool),tc_fun(X3810,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X3810,tc_HOL_Obool),tc_fun(X3810,tc_HOL_Obool)),X3810),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3810)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3810),c_fconj),hAPP(hAPP(c_COMBC(X3810,tc_fun(X3810,tc_HOL_Obool),tc_HOL_Obool),c_member(X3810)),X3809)))),hAPP(hAPP(c_COMBC(X3810,tc_fun(X3810,tc_HOL_Obool),tc_HOL_Obool),c_member(X3810)),X3808)))))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3810),c_Big__Operators_Olattice__class_OSup__fin(X3810,X3809)),c_Big__Operators_Olattice__class_OSup__fin(X3810,X3808))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__Sup2__distrib])])])). 4.05/4.29 cnf(c_0_4858, 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)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2), inference(split_conjunct,[status(thm)],[c_0_4497])). 4.05/4.29 cnf(c_0_4859, 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_4498])). 4.05/4.29 cnf(c_0_4860, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odivmod__int(X2,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))))|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_4499])). 4.05/4.29 cnf(c_0_4861, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|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)))))=hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~class_Rings_Oring__1(X2)), inference(split_conjunct,[status(thm)],[c_0_4500])). 4.05/4.29 fof(c_0_4862, plain, ![X2913, X2914, X2915, X2916, X2917, X2918, X2919]:(~class_Groups_Ocomm__monoid__add(X2919)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2918),X2917))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2916),X2915))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2916,X2919),hAPP(hAPP(c_COMBS(X2916,tc_fun(X2918,tc_HOL_Obool),X2919),hAPP(hAPP(c_COMBB(tc_fun(X2918,X2919),tc_fun(tc_fun(X2918,tc_HOL_Obool),X2919),X2916),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2918,X2919)),hAPP(c_COMBC(X2918,X2916,X2919),X2914))),hAPP(hAPP(c_COMBB(tc_fun(X2918,tc_HOL_Obool),tc_fun(X2918,tc_HOL_Obool),X2916),c_Set_OCollect(X2918)),hAPP(hAPP(c_COMBB(tc_fun(X2918,tc_HOL_Obool),tc_fun(X2918,tc_HOL_Obool),X2916),hAPP(c_COMBS(X2918,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2918),c_fconj),hAPP(hAPP(c_COMBC(X2918,tc_fun(X2918,tc_HOL_Obool),tc_HOL_Obool),c_member(X2918)),X2917)))),hAPP(c_COMBC(X2918,X2916,tc_HOL_Obool),X2913))))),X2915)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2918,X2919),hAPP(hAPP(c_COMBS(X2918,tc_fun(X2916,tc_HOL_Obool),X2919),hAPP(hAPP(c_COMBB(tc_fun(X2916,X2919),tc_fun(tc_fun(X2916,tc_HOL_Obool),X2919),X2918),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2916,X2919)),X2914)),hAPP(hAPP(c_COMBB(tc_fun(X2916,tc_HOL_Obool),tc_fun(X2916,tc_HOL_Obool),X2918),c_Set_OCollect(X2916)),hAPP(hAPP(c_COMBB(tc_fun(X2916,tc_HOL_Obool),tc_fun(X2916,tc_HOL_Obool),X2918),hAPP(c_COMBS(X2916,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2916),c_fconj),hAPP(hAPP(c_COMBC(X2916,tc_fun(X2916,tc_HOL_Obool),tc_HOL_Obool),c_member(X2916)),X2915)))),X2913)))),X2917)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__setsum__restrict])])])). 4.05/4.29 cnf(c_0_4863, plain, (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))))=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))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4501])). 4.05/4.29 cnf(c_0_4864, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))=hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4502, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_4865, 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_4503, c_0_4427]), ['final']). 4.05/4.29 cnf(c_0_4866, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_4504, c_0_4505]), ['final']). 4.05/4.29 cnf(c_0_4867, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[fact_One__nat__def]), ['final']). 4.05/4.29 cnf(c_0_4868, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),X3))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4506])). 4.05/4.29 fof(c_0_4869, plain, ![X4133, X4134, X4135]:(~class_Orderings_Olinorder(X4135)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4135),X4134))|(c_Orderings_Obot__class_Obot(tc_fun(X4135,tc_HOL_Obool))=X4134|c_Big__Operators_Olattice_OInf__fin(X4135,c_Orderings_Oord__class_Omin(X4135),hAPP(c_Set_OCollect(X4135),hAPP(hAPP(c_COMBB(tc_fun(X4135,tc_HOL_Obool),tc_HOL_Obool,X4135),c_HOL_OEx(X4135)),hAPP(hAPP(c_COMBC(X4135,tc_fun(X4135,tc_HOL_Obool),tc_fun(X4135,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4135,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4135,tc_HOL_Obool),tc_fun(X4135,tc_HOL_Obool)),X4135),c_COMBS(X4135,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4135,tc_HOL_Obool),tc_fun(X4135,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4135),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4135),c_fconj)),hAPP(hAPP(c_COMBC(X4135,tc_fun(X4135,X4135),tc_fun(X4135,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4135,tc_HOL_Obool),tc_fun(tc_fun(X4135,X4135),tc_fun(X4135,tc_HOL_Obool)),X4135),c_COMBB(X4135,tc_HOL_Obool,X4135)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X4135),X4133))))),hAPP(hAPP(c_COMBC(X4135,tc_fun(X4135,tc_HOL_Obool),tc_HOL_Obool),c_member(X4135)),X4134)))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4135),X4133),c_Big__Operators_Olattice_OInf__fin(X4135,c_Orderings_Oord__class_Omin(X4135),X4134))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__Inf1__distrib])])])). 4.05/4.29 fof(c_0_4870, plain, ![X7721, X7722, X7723]:(~class_Orderings_Olinorder(X7723)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7723),X7722))|(X7722=c_Orderings_Obot__class_Obot(tc_fun(X7723,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X7723),X7721),c_Big__Operators_Olattice_OSup__fin(X7723,c_Orderings_Oord__class_Omax(X7723),X7722))=c_Big__Operators_Olattice_OSup__fin(X7723,c_Orderings_Oord__class_Omax(X7723),hAPP(c_Set_OCollect(X7723),hAPP(hAPP(c_COMBB(tc_fun(X7723,tc_HOL_Obool),tc_HOL_Obool,X7723),c_HOL_OEx(X7723)),hAPP(hAPP(c_COMBC(X7723,tc_fun(X7723,tc_HOL_Obool),tc_fun(X7723,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7723,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X7723,tc_HOL_Obool),tc_fun(X7723,tc_HOL_Obool)),X7723),c_COMBS(X7723,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7723,tc_HOL_Obool),tc_fun(X7723,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X7723),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7723),c_fconj)),hAPP(hAPP(c_COMBC(X7723,tc_fun(X7723,X7723),tc_fun(X7723,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7723,tc_HOL_Obool),tc_fun(tc_fun(X7723,X7723),tc_fun(X7723,tc_HOL_Obool)),X7723),c_COMBB(X7723,tc_HOL_Obool,X7723)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X7723),X7721))))),hAPP(hAPP(c_COMBC(X7723,tc_fun(X7723,tc_HOL_Obool),tc_HOL_Obool),c_member(X7723)),X7722)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__Sup1__distrib])])])). 4.05/4.29 fof(c_0_4871, plain, ![X15533, X15534, X15535]:(~class_Groups_Olinordered__ab__semigroup__add(X15535)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15535),X15534))|(c_Orderings_Obot__class_Obot(tc_fun(X15535,tc_HOL_Obool))=X15534|c_Big__Operators_Olinorder__class_OMax(X15535,hAPP(c_Set_OCollect(X15535),hAPP(hAPP(c_COMBB(tc_fun(X15535,tc_HOL_Obool),tc_HOL_Obool,X15535),c_HOL_OEx(X15535)),hAPP(hAPP(c_COMBC(X15535,tc_fun(X15535,tc_HOL_Obool),tc_fun(X15535,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15535,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X15535,tc_HOL_Obool),tc_fun(X15535,tc_HOL_Obool)),X15535),c_COMBS(X15535,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15535,tc_HOL_Obool),tc_fun(X15535,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X15535),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X15535),c_fconj)),hAPP(hAPP(c_COMBC(X15535,tc_fun(X15535,X15535),tc_fun(X15535,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15535,tc_HOL_Obool),tc_fun(tc_fun(X15535,X15535),tc_fun(X15535,tc_HOL_Obool)),X15535),c_COMBB(X15535,tc_HOL_Obool,X15535)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X15535),X15533))))),hAPP(hAPP(c_COMBC(X15535,tc_fun(X15535,tc_HOL_Obool),tc_HOL_Obool),c_member(X15535)),X15534)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15535),X15533),c_Big__Operators_Olinorder__class_OMax(X15535,X15534))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__Max__commute])])). 4.05/4.29 fof(c_0_4872, plain, ![X8139, X8140, X8141]:(~class_Groups_Olinordered__ab__semigroup__add(X8141)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8141),X8140))|(X8140=c_Orderings_Obot__class_Obot(tc_fun(X8141,tc_HOL_Obool))|c_Big__Operators_Olinorder__class_OMin(X8141,hAPP(c_Set_OCollect(X8141),hAPP(hAPP(c_COMBB(tc_fun(X8141,tc_HOL_Obool),tc_HOL_Obool,X8141),c_HOL_OEx(X8141)),hAPP(hAPP(c_COMBC(X8141,tc_fun(X8141,tc_HOL_Obool),tc_fun(X8141,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8141,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X8141,tc_HOL_Obool),tc_fun(X8141,tc_HOL_Obool)),X8141),c_COMBS(X8141,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8141,tc_HOL_Obool),tc_fun(X8141,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X8141),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X8141),c_fconj)),hAPP(hAPP(c_COMBC(X8141,tc_fun(X8141,X8141),tc_fun(X8141,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8141,tc_HOL_Obool),tc_fun(tc_fun(X8141,X8141),tc_fun(X8141,tc_HOL_Obool)),X8141),c_COMBB(X8141,tc_HOL_Obool,X8141)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X8141),X8139))))),hAPP(hAPP(c_COMBC(X8141,tc_fun(X8141,tc_HOL_Obool),tc_HOL_Obool),c_member(X8141)),X8140)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8141),X8139),c_Big__Operators_Olinorder__class_OMin(X8141,X8140))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__Min__commute])])])). 4.05/4.29 cnf(c_0_4873, 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_4507])). 4.05/4.29 fof(c_0_4874, plain, ![X4942, X4943, X4944]:(~class_Lattices_Odistrib__lattice(X4944)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4944),X4943))|(X4943=c_Orderings_Obot__class_Obot(tc_fun(X4944,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4944),X4942),c_Big__Operators_Olattice__class_OSup__fin(X4944,X4943))=c_Big__Operators_Olattice__class_OSup__fin(X4944,hAPP(c_Set_OCollect(X4944),hAPP(hAPP(c_COMBB(tc_fun(X4944,tc_HOL_Obool),tc_HOL_Obool,X4944),c_HOL_OEx(X4944)),hAPP(hAPP(c_COMBC(X4944,tc_fun(X4944,tc_HOL_Obool),tc_fun(X4944,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4944,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X4944,tc_HOL_Obool),tc_fun(X4944,tc_HOL_Obool)),X4944),c_COMBS(X4944,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4944,tc_HOL_Obool),tc_fun(X4944,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X4944),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4944),c_fconj)),hAPP(hAPP(c_COMBC(X4944,tc_fun(X4944,X4944),tc_fun(X4944,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4944,tc_HOL_Obool),tc_fun(tc_fun(X4944,X4944),tc_fun(X4944,tc_HOL_Obool)),X4944),c_COMBB(X4944,tc_HOL_Obool,X4944)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4944),X4942))))),hAPP(hAPP(c_COMBC(X4944,tc_fun(X4944,tc_HOL_Obool),tc_HOL_Obool),c_member(X4944)),X4943)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__Sup1__distrib])])])). 4.05/4.29 fof(c_0_4875, plain, ![X15911, X15912, X15913]:(~class_Lattices_Odistrib__lattice(X15913)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15913),X15912))|(X15912=c_Orderings_Obot__class_Obot(tc_fun(X15913,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15913),X15911),c_Big__Operators_Olattice__class_OInf__fin(X15913,X15912))=c_Big__Operators_Olattice__class_OInf__fin(X15913,hAPP(c_Set_OCollect(X15913),hAPP(hAPP(c_COMBB(tc_fun(X15913,tc_HOL_Obool),tc_HOL_Obool,X15913),c_HOL_OEx(X15913)),hAPP(hAPP(c_COMBC(X15913,tc_fun(X15913,tc_HOL_Obool),tc_fun(X15913,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15913,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X15913,tc_HOL_Obool),tc_fun(X15913,tc_HOL_Obool)),X15913),c_COMBS(X15913,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15913,tc_HOL_Obool),tc_fun(X15913,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X15913),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X15913),c_fconj)),hAPP(hAPP(c_COMBC(X15913,tc_fun(X15913,X15913),tc_fun(X15913,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15913,tc_HOL_Obool),tc_fun(tc_fun(X15913,X15913),tc_fun(X15913,tc_HOL_Obool)),X15913),c_COMBB(X15913,tc_HOL_Obool,X15913)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15913),X15911))))),hAPP(hAPP(c_COMBC(X15913,tc_fun(X15913,tc_HOL_Obool),tc_HOL_Obool),c_member(X15913)),X15912)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__Inf1__distrib])])])). 4.05/4.29 cnf(c_0_4876, 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_4508])). 4.05/4.29 cnf(c_0_4877, plain, (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))))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|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))=hAPP(c_Code__Numeral_Oint__of,X1)|X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[c_0_4509])). 4.05/4.29 fof(c_0_4878, plain, ![X10222, X10223, X10224, X10225]:((~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10225,tc_fun(X10225,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X10225,tc_fun(tc_prod(X10225,X10225),tc_HOL_Obool),tc_fun(X10225,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10225,tc_fun(tc_fun(tc_prod(X10225,X10225),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10225,X10225),tc_HOL_Obool),tc_fun(X10225,tc_HOL_Obool)),X10225),c_COMBC(X10225,tc_fun(tc_prod(X10225,X10225),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10225,tc_prod(X10225,X10225)),tc_fun(X10225,tc_fun(tc_fun(tc_prod(X10225,X10225),tc_HOL_Obool),tc_HOL_Obool)),X10225),hAPP(c_COMBB(tc_prod(X10225,X10225),tc_fun(tc_fun(tc_prod(X10225,X10225),tc_HOL_Obool),tc_HOL_Obool),X10225),c_member(tc_prod(X10225,X10225)))),c_Product__Type_OPair(X10225,X10225)))),X10224)),c_fequal),X10223),X10222))|hBOOL(hAPP(hAPP(c_member(tc_prod(X10225,X10225)),hAPP(hAPP(c_Product__Type_OPair(X10225,X10225),X10223),X10222)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10225,X10225),tc_HOL_Obool)),X10224),c_Relation_OId(X10225)))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10225,X10225)),hAPP(hAPP(c_Product__Type_OPair(X10225,X10225),X10223),X10222)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10225,X10225),tc_HOL_Obool)),X10224),c_Relation_OId(X10225))))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10225,tc_fun(X10225,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X10225,tc_fun(tc_prod(X10225,X10225),tc_HOL_Obool),tc_fun(X10225,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10225,tc_fun(tc_fun(tc_prod(X10225,X10225),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10225,X10225),tc_HOL_Obool),tc_fun(X10225,tc_HOL_Obool)),X10225),c_COMBC(X10225,tc_fun(tc_prod(X10225,X10225),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10225,tc_prod(X10225,X10225)),tc_fun(X10225,tc_fun(tc_fun(tc_prod(X10225,X10225),tc_HOL_Obool),tc_HOL_Obool)),X10225),hAPP(c_COMBB(tc_prod(X10225,X10225),tc_fun(tc_fun(tc_prod(X10225,X10225),tc_HOL_Obool),tc_HOL_Obool),X10225),c_member(tc_prod(X10225,X10225)))),c_Product__Type_OPair(X10225,X10225)))),X10224)),c_fequal),X10223),X10222)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflcl__set__eq])])). 4.05/4.29 fof(c_0_4879, plain, ![X4837, X4838, X4839, X4840, X4841, X4842]:((hBOOL(hAPP(hAPP(c_member(X4840),esk148_6(X4837,X4838,X4839,X4840,X4841,X4842)),X4839))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4840,tc_Nat_Onat),X4837),X4839)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4842,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X4840,tc_HOL_Obool),tc_Nat_Onat,X4842),c_Finite__Set_Ocard(X4840)),hAPP(hAPP(c_COMBB(tc_fun(X4840,tc_HOL_Obool),tc_fun(X4840,tc_HOL_Obool),X4842),c_Set_OCollect(X4840)),hAPP(hAPP(c_COMBB(tc_fun(X4840,tc_HOL_Obool),tc_fun(X4840,tc_HOL_Obool),X4842),hAPP(c_COMBS(X4840,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4840),c_fconj),hAPP(hAPP(c_COMBC(X4840,tc_fun(X4840,tc_HOL_Obool),tc_HOL_Obool),c_member(X4840)),X4839)))),X4838)))),X4841)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4840),X4839))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4842),X4841)))&(hAPP(X4837,esk148_6(X4837,X4838,X4839,X4840,X4841,X4842))!=hAPP(c_Finite__Set_Ocard(X4842),hAPP(c_Set_OCollect(X4842),hAPP(hAPP(c_COMBS(X4842,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4842),c_fconj),hAPP(hAPP(c_COMBC(X4842,tc_fun(X4842,tc_HOL_Obool),tc_HOL_Obool),c_member(X4842)),X4841))),hAPP(hAPP(c_COMBC(X4842,X4840,tc_HOL_Obool),X4838),esk148_6(X4837,X4838,X4839,X4840,X4841,X4842)))))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4840,tc_Nat_Onat),X4837),X4839)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4842,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X4840,tc_HOL_Obool),tc_Nat_Onat,X4842),c_Finite__Set_Ocard(X4840)),hAPP(hAPP(c_COMBB(tc_fun(X4840,tc_HOL_Obool),tc_fun(X4840,tc_HOL_Obool),X4842),c_Set_OCollect(X4840)),hAPP(hAPP(c_COMBB(tc_fun(X4840,tc_HOL_Obool),tc_fun(X4840,tc_HOL_Obool),X4842),hAPP(c_COMBS(X4840,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4840),c_fconj),hAPP(hAPP(c_COMBC(X4840,tc_fun(X4840,tc_HOL_Obool),tc_HOL_Obool),c_member(X4840)),X4839)))),X4838)))),X4841)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4840),X4839))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4842),X4841)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__multicount__gen])])])])])). 4.05/4.29 fof(c_0_4880, plain, ![X5560, X5561, X5562, X5563]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5563),hAPP(c_Set_OCollect(X5563),X5562)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X5561),hAPP(c_Set_OCollect(X5561),hAPP(hAPP(c_COMBB(tc_fun(X5563,tc_HOL_Obool),tc_HOL_Obool,X5561),c_HOL_OEx(X5563)),hAPP(hAPP(c_COMBC(X5561,tc_fun(X5563,tc_HOL_Obool),tc_fun(X5563,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5563,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5563,tc_HOL_Obool),tc_fun(X5563,tc_HOL_Obool)),X5561),c_COMBS(X5563,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5563,tc_HOL_Obool),tc_fun(X5563,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5561),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5563),c_fconj)),hAPP(hAPP(c_COMBC(X5561,tc_fun(X5563,X5561),tc_fun(X5563,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5561,tc_HOL_Obool),tc_fun(tc_fun(X5563,X5561),tc_fun(X5563,tc_HOL_Obool)),X5561),c_COMBB(X5561,tc_HOL_Obool,X5563)),c_fequal)),X5560)))),X5562)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__image__set])])). 4.05/4.29 fof(c_0_4881, plain, ![X12422, X12423, X12424, X12425, X12426, X12427]:((hBOOL(hAPP(hAPP(c_member(X12425),esk379_6(X12422,X12423,X12424,X12425,X12426,X12427)),X12424))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12427,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X12425,tc_HOL_Obool),tc_Nat_Onat,X12427),c_Finite__Set_Ocard(X12425)),hAPP(hAPP(c_COMBB(tc_fun(X12425,tc_HOL_Obool),tc_fun(X12425,tc_HOL_Obool),X12427),c_Set_OCollect(X12425)),hAPP(hAPP(c_COMBB(tc_fun(X12425,tc_HOL_Obool),tc_fun(X12425,tc_HOL_Obool),X12427),hAPP(c_COMBS(X12425,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12425),c_fconj),hAPP(hAPP(c_COMBC(X12425,tc_fun(X12425,tc_HOL_Obool),tc_HOL_Obool),c_member(X12425)),X12424)))),X12423)))),X12426)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12422),hAPP(c_Finite__Set_Ocard(X12425),X12424))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12425),X12424))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12427),X12426)))&(X12422!=hAPP(c_Finite__Set_Ocard(X12427),hAPP(c_Set_OCollect(X12427),hAPP(hAPP(c_COMBS(X12427,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12427),c_fconj),hAPP(hAPP(c_COMBC(X12427,tc_fun(X12427,tc_HOL_Obool),tc_HOL_Obool),c_member(X12427)),X12426))),hAPP(hAPP(c_COMBC(X12427,X12425,tc_HOL_Obool),X12423),esk379_6(X12422,X12423,X12424,X12425,X12426,X12427)))))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12427,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X12425,tc_HOL_Obool),tc_Nat_Onat,X12427),c_Finite__Set_Ocard(X12425)),hAPP(hAPP(c_COMBB(tc_fun(X12425,tc_HOL_Obool),tc_fun(X12425,tc_HOL_Obool),X12427),c_Set_OCollect(X12425)),hAPP(hAPP(c_COMBB(tc_fun(X12425,tc_HOL_Obool),tc_fun(X12425,tc_HOL_Obool),X12427),hAPP(c_COMBS(X12425,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12425),c_fconj),hAPP(hAPP(c_COMBC(X12425,tc_fun(X12425,tc_HOL_Obool),tc_HOL_Obool),c_member(X12425)),X12424)))),X12423)))),X12426)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12422),hAPP(c_Finite__Set_Ocard(X12425),X12424))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12425),X12424))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12427),X12426)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__multicount])])])])])). 4.05/4.29 cnf(c_0_4882, plain, (hAPP(c_Code__Numeral_Oint__of,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)))),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))))))|X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[c_0_4509])). 4.05/4.29 cnf(c_0_4883, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1)))), inference(split_conjunct,[status(thm)],[c_0_4510])). 4.05/4.29 cnf(c_0_4884, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4511])). 4.05/4.29 cnf(c_0_4885, 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_4512])). 4.05/4.29 fof(c_0_4886, plain, ![X17580, X17581]:(~class_Lazy__Sequence_Osmall__lazy(X17581)|c_Lazy__Sequence_Oappend(tc_List_Olist(X17581),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X17581)),c_List_Olist_ONil(X17581)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X17581))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17580)),hAPP(c_Lazy__Sequence_Obind(tc_prod(X17581,tc_List_Olist(X17581)),tc_List_Olist(X17581),c_Lazy__Sequence_Oproduct(X17581,tc_List_Olist(X17581),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X17581,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X17580),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X17581),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X17580),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(X17581,tc_List_Olist(X17581),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X17581))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X17581),tc_List_Olist(X17581)),tc_fun(tc_List_Olist(X17581),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X17581))),X17581),hAPP(c_COMBB(tc_List_Olist(X17581),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X17581)),tc_List_Olist(X17581)),c_Lazy__Sequence_Osingle(tc_List_Olist(X17581)))),c_List_Olist_OCons(X17581))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X17581))))=c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X17581),X17580)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_small__lazy__list_Osimps])])). 4.05/4.29 fof(c_0_4887, plain, ![X14376, X14377, X14378]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X14378,X14378),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X14378,X14378,X14378),X14377),X14376)),X14377))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X14378,tc_HOL_Obool),tc_fun(X14378,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X14378,tc_HOL_Obool),tc_fun(X14378,tc_HOL_Obool),tc_fun(X14378,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X14378,X14377)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X14378,tc_HOL_Obool),tc_fun(X14378,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X14378,X14376)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X14378,tc_HOL_Obool),tc_fun(X14378,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X14378,tc_HOL_Obool),tc_fun(X14378,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X14378,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X14378,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X14378,tc_HOL_Obool),tc_fun(X14378,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X14378,X14377)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ext__compat])])). 4.05/4.29 fof(c_0_4888, plain, ![X4136, X4137, X4138]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4138,X4138),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X4138,X4138,X4138),X4137),X4136)),X4137))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X4138,tc_HOL_Obool),tc_fun(X4138,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X4138,tc_HOL_Obool),tc_fun(X4138,tc_HOL_Obool),tc_fun(X4138,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X4138,X4137)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X4138,tc_HOL_Obool),tc_fun(X4138,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X4138,X4136)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X4138,tc_HOL_Obool),tc_fun(X4138,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4138,tc_HOL_Obool),tc_fun(X4138,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4138,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X4138,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X4138,tc_HOL_Obool),tc_fun(X4138,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X4138,X4137)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__compat])])). 4.05/4.29 cnf(c_0_4889, 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_4513])). 4.05/4.29 cnf(c_0_4890, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_4514])). 4.05/4.29 cnf(c_0_4891, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),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)))))))|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_4514])). 4.05/4.29 cnf(c_0_4892, 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_4510])). 4.05/4.29 fof(c_0_4893, plain, ![X742, X743, X744, X745, X746, X747]:(~class_Groups_Ocomm__monoid__add(X747)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X746),X745))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X746,X747),X744),X745)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X743,X747),hAPP(hAPP(c_COMBB(tc_fun(X746,tc_HOL_Obool),X747,X743),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X746,X747),X744)),hAPP(hAPP(c_COMBB(tc_fun(X746,tc_HOL_Obool),tc_fun(X746,tc_HOL_Obool),X743),c_Set_OCollect(X746)),hAPP(hAPP(c_COMBB(tc_fun(X746,tc_HOL_Obool),tc_fun(X746,tc_HOL_Obool),X743),hAPP(c_COMBS(X746,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X746),c_fconj),hAPP(hAPP(c_COMBC(X746,tc_fun(X746,tc_HOL_Obool),tc_HOL_Obool),c_member(X746)),X745)))),hAPP(c_COMBC(X746,X743,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X743,tc_fun(X743,tc_HOL_Obool),X746),c_fequal),X742)))))),hAPP(c_Set_Oimage(X746,X743,X742),X745)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__image__gen])])])). 4.05/4.29 cnf(c_0_4894, 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_4515])). 4.05/4.29 cnf(c_0_4895, plain, (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_4516])). 4.05/4.29 cnf(c_0_4896, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk391_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))|hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))=c_List_Otranspose(X2,X3)|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_4517])). 4.05/4.29 cnf(c_0_4897, 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_4518, c_0_4519])). 4.05/4.29 cnf(c_0_4898, 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))), inference(split_conjunct,[status(thm)],[c_0_4520]), ['final']). 4.05/4.29 fof(c_0_4899, plain, ![X4422, X4423, X4424]:c_List_Olist_ONil(X4423)=hAPP(hAPP(c_List_Omap(X4424,X4423),X4422),c_List_Olist_ONil(X4424)), inference(variable_rename,[status(thm)],[fact_map_Osimps_I1_J])). 4.05/4.29 fof(c_0_4900, plain, ![X8705, X8706]:(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8706))|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)),X8706))),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,X8705)))))=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)),X8706))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X8705)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__less__Suc])])). 4.05/4.29 cnf(c_0_4901, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),X1),c_member(X2)),X3)),X4))=hAPP(c_Set_Ovimage(X1,X2,X3),X4)), inference(split_conjunct,[status(thm)],[c_0_4521])). 4.05/4.29 cnf(c_0_4902, 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_4522, c_0_4523]), c_0_4523]), ['final']). 4.05/4.29 cnf(c_0_4903, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))=c_List_Otranspose(X2,X3)|X1!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X2)),X3),esk391_3(X1,X2,X3)))|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_4517])). 4.05/4.29 fof(c_0_4904, plain, ![X13226, X13227]:(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13227))|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)),X13227))),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,X13226)))))=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)),X13227))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X13226))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__less__Suc2])])])). 4.05/4.29 fof(c_0_4905, plain, ![X3292, X3293, X3294]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3294),X3293))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X3294)),hAPP(c_Set_OCollect(tc_List_Olist(X3294)),hAPP(hAPP(c_COMBS(tc_List_Olist(X3294),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X3294)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X3294),tc_fun(X3294,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X3294,tc_HOL_Obool),tc_fun(tc_fun(X3294,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X3294)),c_Orderings_Oord__class_Oless__eq(tc_fun(X3294,tc_HOL_Obool))),c_List_Oset(X3294))),X3293))),hAPP(hAPP(c_COMBC(tc_List_Olist(X3294),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X3294)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3294)))),X3292)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__lists__length__le])])). 4.05/4.29 cnf(c_0_4906, plain, (c_List_Olists(X1,X2)=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))), inference(split_conjunct,[status(thm)],[c_0_4524])). 4.05/4.29 cnf(c_0_4907, 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_4525])). 4.05/4.29 cnf(c_0_4908, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk215_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),esk214_3(X1,X2,X3)),esk215_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,esk214_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)))),esk215_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_4526])). 4.05/4.29 fof(c_0_4909, plain, ![X9562, X9563, X9564, X9565, X9566, X9567]:(~class_Groups_Ocomm__monoid__add(X9567)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9566),X9565))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9566,X9567),hAPP(hAPP(c_COMBS(X9566,X9567,X9567),hAPP(hAPP(c_COMBS(X9566,X9567,tc_fun(X9567,X9567)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X9567,tc_fun(X9567,X9567)),X9566),c_If(X9567)),X9564)),X9563)),X9562)),X9565)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9567),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9566,X9567),X9563),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9566,tc_HOL_Obool)),X9565),hAPP(c_Set_OCollect(X9566),X9564)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9566,X9567),X9562),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9566,tc_HOL_Obool)),X9565),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9566,tc_HOL_Obool)),hAPP(c_Set_OCollect(X9566),X9564))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__cases])])])). 4.05/4.29 fof(c_0_4910, plain, ![X11649, X11650, X11651]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11651,tc_HOL_Obool)),X11650),X11649)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11651,tc_HOL_Obool)),X11650),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11651,tc_HOL_Obool)),X11649)), inference(variable_rename,[status(thm)],[fact_Diff__eq])). 4.05/4.29 cnf(c_0_4911, 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_4527])). 4.05/4.29 fof(c_0_4912, plain, ![X16299, X16300, X16301]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16301),X16300))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X16301)),hAPP(c_Set_OCollect(tc_List_Olist(X16301)),hAPP(hAPP(c_COMBS(tc_List_Olist(X16301),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X16301)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X16301),tc_fun(X16301,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X16301,tc_HOL_Obool),tc_fun(tc_fun(X16301,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X16301)),c_Orderings_Oord__class_Oless__eq(tc_fun(X16301,tc_HOL_Obool))),c_List_Oset(X16301))),X16300))),hAPP(hAPP(c_COMBC(tc_List_Olist(X16301),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X16301)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X16301)))),X16299)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__lists__length__eq])])])). 4.05/4.29 fof(c_0_4913, plain, ![X6346, X6347, X6348, X6349]:((hBOOL(hAPP(X6349,esk190_4(X6346,X6347,X6348,X6349)))|c_Wellfounded_Owf(X6346,hAPP(c_Set_OCollect(tc_prod(X6346,X6346)),hAPP(c_Product__Type_Oprod_Oprod__case(X6346,X6346,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X6346,tc_HOL_Obool),tc_fun(X6346,tc_HOL_Obool),X6346),hAPP(c_COMBS(X6346,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6346),c_fconj),X6349))),hAPP(hAPP(c_COMBC(X6346,tc_fun(X6346,X6346),tc_fun(X6346,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6346,tc_HOL_Obool),tc_fun(tc_fun(X6346,X6346),tc_fun(X6346,tc_HOL_Obool)),X6346),c_COMBB(X6346,tc_HOL_Obool,X6346)),c_fequal)),X6347))))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X6348,hAPP(X6347,esk190_4(X6346,X6347,X6348,X6349)))),hAPP(X6348,esk190_4(X6346,X6347,X6348,X6349))))|c_Wellfounded_Owf(X6346,hAPP(c_Set_OCollect(tc_prod(X6346,X6346)),hAPP(c_Product__Type_Oprod_Oprod__case(X6346,X6346,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X6346,tc_HOL_Obool),tc_fun(X6346,tc_HOL_Obool),X6346),hAPP(c_COMBS(X6346,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6346),c_fconj),X6349))),hAPP(hAPP(c_COMBC(X6346,tc_fun(X6346,X6346),tc_fun(X6346,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6346,tc_HOL_Obool),tc_fun(tc_fun(X6346,X6346),tc_fun(X6346,tc_HOL_Obool)),X6346),c_COMBB(X6346,tc_HOL_Obool,X6346)),c_fequal)),X6347))))))), 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__if__measure])])])])])). 4.05/4.29 cnf(c_0_4914, plain, (c_Complete__Lattice_OSup__class_OSup(X1,X2)=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))))))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_4528])). 4.05/4.29 cnf(c_0_4915, 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_4529, c_0_4523]), ['final']). 4.05/4.29 cnf(c_0_4916, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),hAPP(c_COMBC(X2,X1,tc_HOL_Obool),X4)))=hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))),X4)))), inference(split_conjunct,[status(thm)],[c_0_4530])). 4.05/4.29 cnf(c_0_4917, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),c_Orderings_Oord__class_Oless__eq(X1)))))=c_Complete__Lattice_OInf__class_OInf(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_4531])). 4.05/4.29 cnf(c_0_4918, 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_4532])). 4.05/4.29 cnf(c_0_4919, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2))),hAPP(c_Set_OCollect(X1),X3))=hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_4533])). 4.05/4.29 cnf(c_0_4920, 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_4534]), ['final']). 4.05/4.29 fof(c_0_4921, plain, ![X11022, X11023, X11024, X11025]:(~class_Rings_Ocomm__semiring__1(X11025)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11025),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11025),c_Groups_Oone__class_Oone(X11025)),c_Groups_Oone__class_Oone(X11025))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X11025),hAPP(hAPP(c_COMBB(X11025,X11025,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X11025),X11024)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X11025,X11025),hAPP(hAPP(c_COMBB(X11025,tc_fun(X11025,X11025),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X11025)),c_Nat_Osemiring__1__class_Oof__nat(X11025))),X11023))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X11022)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11025),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X11025),X11022)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11025),X11024),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11025),X11024),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11025),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X11025),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11022),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X11023))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_arith__series__general])])])). 4.05/4.29 fof(c_0_4922, plain, ![X5375]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5375)=hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X5375), inference(variable_rename,[status(thm)],[fact_atLeast0LessThan])). 4.05/4.29 cnf(c_0_4923, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk499_3(X1,X2,X3)),esk500_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X1,esk499_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)))),esk500_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_4535])). 4.05/4.29 fof(c_0_4924, plain, ![X12879, X12880, X12881]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X12881,X12881),tc_HOL_Obool)),X12880),hAPP(hAPP(c_Product__Type_OSigma(X12881,X12881),X12879),hAPP(c_COMBK(tc_fun(X12881,tc_HOL_Obool),X12881),X12879))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X12881),tc_List_Olist(X12881)),tc_HOL_Obool)),c_List_Olistrel(X12881,X12880)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X12881),tc_List_Olist(X12881)),c_List_Olists(X12881,X12879)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X12881),tc_HOL_Obool),tc_List_Olist(X12881)),c_List_Olists(X12881,X12879)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__subset])])). 4.05/4.29 cnf(c_0_4925, 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_4536])). 4.05/4.29 cnf(c_0_4926, 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_4537, c_0_4523]), c_0_4523]), c_0_4523]), ['final']). 4.05/4.29 cnf(c_0_4927, 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_4538])). 4.05/4.29 cnf(c_0_4928, 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_4539])). 4.05/4.29 cnf(c_0_4929, 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_4540])). 4.05/4.29 fof(c_0_4930, plain, ![X7806]:hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7806)=hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X7806)), inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw])). 4.05/4.29 fof(c_0_4931, plain, ![X6247, X6248, X6249, X6250]:((~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),X6250),X6249)),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),X6248),X6247)),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),X6250),X6247)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6248),X6249))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6250),X6247)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6248),X6249)))|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),X6250),X6249)),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),X6248),X6247)),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])])). 4.05/4.29 fof(c_0_4932, plain, ![X14733, X14734, X14735, X14736]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14736),X14733)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14734),X14735)))|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),X14736),X14735)),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),X14734),X14733)),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),X14736),X14735)),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),X14734),X14733)),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),X14736),X14733)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14734),X14735))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le])])). 4.05/4.29 fof(c_0_4933, plain, ![X13195, X13196, X13197]:(~hBOOL(hAPP(c_List_Odistinct(X13197),hAPP(hAPP(c_List_Omap(tc_prod(X13197,X13196),X13197),c_Product__Type_Ofst(X13197,X13196)),X13195)))|hAPP(c_List_Oset(tc_prod(X13197,X13196)),X13195)=hAPP(c_Set_OCollect(tc_prod(X13197,X13196)),hAPP(c_Product__Type_Oprod_Oprod__case(X13197,X13196,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X13197,tc_fun(X13196,tc_Option_Ooption(X13196)),tc_fun(X13196,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X13196),tc_HOL_Obool),tc_fun(tc_fun(X13196,tc_Option_Ooption(X13196)),tc_fun(X13196,tc_HOL_Obool)),X13197),c_COMBB(tc_Option_Ooption(X13196),tc_HOL_Obool,X13196)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X13196),tc_fun(tc_Option_Ooption(X13196),tc_HOL_Obool),X13197),c_fequal),hAPP(c_Map_Omap__of(X13197,X13196),X13195)))),c_Option_Ooption_OSome(X13196))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__map__of__compr])])])). 4.05/4.29 cnf(c_0_4934, 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_4541])). 4.05/4.29 cnf(c_0_4935, 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_4542])). 4.05/4.29 cnf(c_0_4936, 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_4543])). 4.05/4.29 fof(c_0_4937, plain, ![X5503, X5504, X5505, X5506]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X5505),X5504))|c_Nitpick_Osetsum_H(X5505,X5506,X5503,X5504)=hAPP(c_List_Omonoid__add__class_Olistsum(X5506),hAPP(hAPP(c_List_Omap(X5505,X5506),X5503),c_Hilbert__Choice_OEps(tc_List_Olist(X5505),hAPP(hAPP(c_COMBS(tc_List_Olist(X5505),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5505)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5505),tc_fun(X5505,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5505,tc_HOL_Obool),tc_fun(tc_fun(X5505,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5505)),c_fequal),c_List_Oset(X5505))),X5504))),c_List_Odistinct(X5505)))))|~class_Groups_Ocomm__monoid__add(X5506))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X5505),X5504))|c_Groups_Ozero__class_Ozero(X5506)=c_Nitpick_Osetsum_H(X5505,X5506,X5503,X5504)|~class_Groups_Ocomm__monoid__add(X5506))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nitpick_Osetsum_H__def])])])])). 4.05/4.29 fof(c_0_4938, plain, ![X16073, X16074, X16075]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16075,tc_HOL_Obool)),X16073),X16074)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16075,tc_HOL_Obool)),X16074),X16073), inference(variable_rename,[status(thm)],[fact_Int__commute])). 4.05/4.29 cnf(c_0_4939, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X3)))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4544])). 4.05/4.29 cnf(c_0_4940, 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_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)), inference(split_conjunct,[status(thm)],[c_0_4545])). 4.05/4.29 cnf(c_0_4941, 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_4513])). 4.05/4.29 cnf(c_0_4942, 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)))))))|X2!=c_Groups_Ozero__class_Ozero(X1)|X3!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4514])). 4.05/4.29 fof(c_0_4943, plain, ![X16787, X16788, X16789]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16789),X16788))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16789,tc_HOL_Obool)),X16787),X16788)=hAPP(hAPP(c_Finite__Set_Ofold(X16789,tc_fun(X16789,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X16789,tc_HOL_Obool),tc_fun(tc_fun(X16789,tc_HOL_Obool),tc_fun(X16789,tc_HOL_Obool)),X16789),hAPP(c_COMBC(tc_fun(X16789,tc_HOL_Obool),tc_fun(X16789,tc_HOL_Obool),tc_fun(X16789,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X16789,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X16789,tc_fun(X16789,tc_HOL_Obool),tc_fun(X16789,tc_HOL_Obool)),c_Set_Oinsert(X16789)),c_Orderings_Obot__class_Obot(tc_fun(X16789,tc_HOL_Obool))))),X16787),X16788)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__fold__remove])])). 4.05/4.29 fof(c_0_4944, plain, ![X10953, X10954, X10955, X10956]:c_Finite__Set_Ofold(X10955,X10956,hAPP(hAPP(c_COMBB(X10956,tc_fun(X10956,X10956),X10955),X10954),X10953))=hAPP(c_Finite__Set_Ofold__image(X10956,X10955,X10954),X10953), inference(variable_rename,[status(thm)],[fact_fold__image__def])). 4.05/4.29 cnf(c_0_4945, 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),esk515_3(X2,X3,X1)),esk515_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))),esk514_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4546])). 4.05/4.29 cnf(c_0_4946, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk515_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))),esk514_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_4546])). 4.05/4.29 fof(c_0_4947, plain, ![X5222, X5223, X5224, X5225]:((hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),esk160_4(X5222,X5223,X5224,X5225)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk161_4(X5222,X5223,X5224,X5225)),esk162_4(X5222,X5223,X5224,X5225)))))|hBOOL(hAPP(hAPP(hAPP(X5222,X5225),X5224),X5223))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X5225),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5224),X5223)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk161_4(X5222,X5223,X5224,X5225)),esk162_4(X5222,X5223,X5224,X5225)))|(hAPP(esk160_4(X5222,X5223,X5224,X5225),esk162_4(X5222,X5223,X5224,X5225))!=c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))|hBOOL(hAPP(hAPP(hAPP(X5222,esk160_4(X5222,X5223,X5224,X5225)),esk161_4(X5222,X5223,X5224,X5225)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk162_4(X5222,X5223,X5224,X5225)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))|hBOOL(hAPP(hAPP(hAPP(X5222,X5225),X5224),X5223))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X5225),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5224),X5223)))))&(~hBOOL(hAPP(hAPP(hAPP(X5222,esk160_4(X5222,X5223,X5224,X5225)),esk161_4(X5222,X5223,X5224,X5225)),esk162_4(X5222,X5223,X5224,X5225)))|hBOOL(hAPP(hAPP(hAPP(X5222,X5225),X5224),X5223))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X5225),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5224),X5223))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_small_H_Opinduct])])])])])). 4.05/4.29 cnf(c_0_4948, 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_4513])). 4.05/4.29 cnf(c_0_4949, 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_4547])). 4.05/4.29 cnf(c_0_4950, 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_4548])). 4.05/4.29 cnf(c_0_4951, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)))|~class_Rings_Osemiring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_4549])). 4.05/4.29 cnf(c_0_4952, 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_4550])). 4.05/4.29 cnf(c_0_4953, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_4516])). 4.05/4.29 cnf(c_0_4954, plain, (X1=c_Groups_Ozero__class_Ozero(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_4516])). 4.05/4.29 fof(c_0_4955, plain, ![X15754, X15755]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X15755),X15754))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Nitpick_Ocard_H(X15755,X15754))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15755),X15754))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15755)),c_Hilbert__Choice_OEps(tc_List_Olist(X15755),hAPP(hAPP(c_COMBS(tc_List_Olist(X15755),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X15755)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X15755),tc_fun(X15755,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X15755,tc_HOL_Obool),tc_fun(tc_fun(X15755,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X15755)),c_fequal),c_List_Oset(X15755))),X15754))),c_List_Odistinct(X15755))))=c_Nitpick_Ocard_H(X15755,X15754))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nitpick_Ocard_H__def])])])). 4.05/4.29 cnf(c_0_4956, 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_4551])). 4.05/4.29 cnf(c_0_4957, 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),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_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4552])). 4.05/4.29 fof(c_0_4958, plain, ![X10939, X10940, X10941, X10942, X10943, X10944]:((~hBOOL(hAPP(hAPP(c_member(X10943),X10941),X10942))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10943,X10944),hAPP(hAPP(c_COMBC(X10943,X10944,X10944),hAPP(hAPP(c_COMBS(X10943,X10944,tc_fun(X10944,X10944)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10944,tc_fun(X10944,X10944)),X10943),c_If(X10944)),hAPP(hAPP(c_COMBC(X10943,X10943,tc_HOL_Obool),c_fequal),X10941))),X10940)),X10939)),X10942)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10944),hAPP(X10940,X10941)),hAPP(hAPP(c_Power_Opower__class_Opower(X10944),X10939),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10943),X10942)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10943),X10942))|~class_Groups_Ocomm__monoid__mult(X10944))&(hBOOL(hAPP(hAPP(c_member(X10943),X10941),X10942))|hAPP(hAPP(c_Power_Opower__class_Opower(X10944),X10939),hAPP(c_Finite__Set_Ocard(X10943),X10942))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10943,X10944),hAPP(hAPP(c_COMBC(X10943,X10944,X10944),hAPP(hAPP(c_COMBS(X10943,X10944,tc_fun(X10944,X10944)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10944,tc_fun(X10944,X10944)),X10943),c_If(X10944)),hAPP(hAPP(c_COMBC(X10943,X10943,tc_HOL_Obool),c_fequal),X10941))),X10940)),X10939)),X10942)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10943),X10942))|~class_Groups_Ocomm__monoid__mult(X10944))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__gen__delta])])])])). 4.05/4.29 cnf(c_0_4959, 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)))|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)))=c_Divides_OnegDivAlg(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_4553])). 4.05/4.29 cnf(c_0_4960, plain, (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)|~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_4545])). 4.05/4.29 fof(c_0_4961, plain, ![X11016, X11017, X11018, X11019, X11020]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X11017),hAPP(c_Set_OCollect(X11017),hAPP(hAPP(c_COMBB(tc_fun(X11019,tc_HOL_Obool),tc_HOL_Obool,X11017),c_HOL_OEx(X11019)),hAPP(hAPP(c_COMBB(tc_fun(X11019,tc_HOL_Obool),tc_fun(X11019,tc_HOL_Obool),X11017),hAPP(c_COMBS(X11019,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X11019),c_fconj),X11018))),X11016)))))|(~hBOOL(hAPP(X11018,X11020))|hBOOL(hAPP(c_Finite__Set_Ofinite(X11017),hAPP(c_Set_OCollect(X11017),hAPP(hAPP(c_COMBC(X11017,X11019,tc_HOL_Obool),X11016),X11020)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11019),hAPP(c_Set_OCollect(X11019),X11018))))&((hBOOL(hAPP(X11018,esk333_4(X11016,X11017,X11018,X11019)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X11017),hAPP(c_Set_OCollect(X11017),hAPP(hAPP(c_COMBB(tc_fun(X11019,tc_HOL_Obool),tc_HOL_Obool,X11017),c_HOL_OEx(X11019)),hAPP(hAPP(c_COMBB(tc_fun(X11019,tc_HOL_Obool),tc_fun(X11019,tc_HOL_Obool),X11017),hAPP(c_COMBS(X11019,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X11019),c_fconj),X11018))),X11016)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11019),hAPP(c_Set_OCollect(X11019),X11018))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11017),hAPP(c_Set_OCollect(X11017),hAPP(hAPP(c_COMBC(X11017,X11019,tc_HOL_Obool),X11016),esk333_4(X11016,X11017,X11018,X11019)))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X11017),hAPP(c_Set_OCollect(X11017),hAPP(hAPP(c_COMBB(tc_fun(X11019,tc_HOL_Obool),tc_HOL_Obool,X11017),c_HOL_OEx(X11019)),hAPP(hAPP(c_COMBB(tc_fun(X11019,tc_HOL_Obool),tc_fun(X11019,tc_HOL_Obool),X11017),hAPP(c_COMBS(X11019,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X11019),c_fconj),X11018))),X11016)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11019),hAPP(c_Set_OCollect(X11019),X11018)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Collect__bounded__ex])])])])])])). 4.05/4.29 cnf(c_0_4962, 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_4554])). 4.05/4.29 cnf(c_0_4963, 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_4555])). 4.05/4.29 fof(c_0_4964, plain, ![X10983, X10984, X10985, X10986, X10987]:(~class_Groups_Ocomm__monoid__add(X10987)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10986),X10985))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10986,X10987),hAPP(hAPP(c_COMBC(X10986,X10987,X10987),hAPP(hAPP(c_COMBS(X10986,X10987,tc_fun(X10987,X10987)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10987,tc_fun(X10987,X10987)),X10986),c_If(X10987)),hAPP(hAPP(c_COMBC(X10986,tc_fun(X10986,tc_HOL_Obool),tc_HOL_Obool),c_member(X10986)),X10983))),X10984)),c_Groups_Ozero__class_Ozero(X10987))),X10985)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10986,X10987),X10984),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10986,tc_HOL_Obool)),X10985),X10983)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__restrict__set])])])). 4.05/4.29 fof(c_0_4965, plain, ![X10585, X10586]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk321_2(X10585,X10586)))|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)))),X10585))=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)))),X10586)))&((~hBOOL(hAPP(X10586,esk321_2(X10585,X10586)))|~hBOOL(hAPP(X10585,esk321_2(X10585,X10586)))|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)))),X10585))=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)))),X10586)))&(hBOOL(hAPP(X10586,esk321_2(X10585,X10586)))|hBOOL(hAPP(X10585,esk321_2(X10585,X10586)))|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)))),X10585))=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)))),X10586))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__nat__int__set__cong])])])])])). 4.05/4.29 fof(c_0_4966, plain, ![X4443, X4444]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4444),c_Int_OPls))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4443)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4444))=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),X4443),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4444)))),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)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4444),c_Int_OPls))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4443)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4444))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4443))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__nat__number__of])])])). 4.05/4.29 cnf(c_0_4967, 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),X2),X1))|c_Divides_OposDivAlg(X2,X1)=hAPP(c_Divides_Oadjust(X1),c_Divides_OposDivAlg(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_4556])). 4.05/4.29 fof(c_0_4968, plain, ![X5988, X5989, X5990, X5991, X5992, X5993]:(((~hBOOL(hAPP(hAPP(c_member(X5993),X5990),X5991))|c_Orderings_Otop__class_Otop(tc_fun(X5989,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X5989,X5993,hAPP(hAPP(c_COMBC(X5989,X5993,X5993),hAPP(hAPP(c_COMBC(X5989,X5993,tc_fun(X5993,X5993)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5993,tc_fun(X5993,X5993)),X5989),c_If(X5993)),hAPP(hAPP(c_COMBC(X5989,tc_fun(X5989,tc_HOL_Obool),tc_HOL_Obool),c_member(X5989)),X5988))),X5992)),X5990)),X5991)|~hBOOL(hAPP(hAPP(c_member(X5993),X5992),X5991)))&(hBOOL(hAPP(hAPP(c_member(X5993),X5990),X5991))|hAPP(c_Set_Ovimage(X5989,X5993,hAPP(hAPP(c_COMBC(X5989,X5993,X5993),hAPP(hAPP(c_COMBC(X5989,X5993,tc_fun(X5993,X5993)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5993,tc_fun(X5993,X5993)),X5989),c_If(X5993)),hAPP(hAPP(c_COMBC(X5989,tc_fun(X5989,tc_HOL_Obool),tc_HOL_Obool),c_member(X5989)),X5988))),X5992)),X5990)),X5991)=X5988|~hBOOL(hAPP(hAPP(c_member(X5993),X5992),X5991))))&((~hBOOL(hAPP(hAPP(c_member(X5993),X5990),X5991))|hAPP(c_Set_Ovimage(X5989,X5993,hAPP(hAPP(c_COMBC(X5989,X5993,X5993),hAPP(hAPP(c_COMBC(X5989,X5993,tc_fun(X5993,X5993)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5993,tc_fun(X5993,X5993)),X5989),c_If(X5993)),hAPP(hAPP(c_COMBC(X5989,tc_fun(X5989,tc_HOL_Obool),tc_HOL_Obool),c_member(X5989)),X5988))),X5992)),X5990)),X5991)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5989,tc_HOL_Obool)),X5988)|hBOOL(hAPP(hAPP(c_member(X5993),X5992),X5991)))&(hBOOL(hAPP(hAPP(c_member(X5993),X5990),X5991))|c_Orderings_Obot__class_Obot(tc_fun(X5989,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X5989,X5993,hAPP(hAPP(c_COMBC(X5989,X5993,X5993),hAPP(hAPP(c_COMBC(X5989,X5993,tc_fun(X5993,X5993)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5993,tc_fun(X5993,X5993)),X5989),c_If(X5993)),hAPP(hAPP(c_COMBC(X5989,tc_fun(X5989,tc_HOL_Obool),tc_HOL_Obool),c_member(X5989)),X5988))),X5992)),X5990)),X5991)|hBOOL(hAPP(hAPP(c_member(X5993),X5992),X5991))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_vimage__if])])])])). 4.05/4.29 fof(c_0_4969, plain, ![X14669, X14670, X14671, X14672]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14671),X14670))|c_Groups_Ozero__class_Ozero(X14672)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X14672),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X14672,X14672),hAPP(hAPP(c_COMBB(X14672,tc_fun(X14672,X14672),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X14672)),X14669)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X14672,tc_Nat_Onat),X14669),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,X14671,X14670))|~class_Groups_Oab__group__add(X14672))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14671),X14670))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X14672),hAPP(X14669,X14671)),hAPP(X14669,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14670),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X14672),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X14672,X14672),hAPP(hAPP(c_COMBB(X14672,tc_fun(X14672,X14672),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X14672)),X14669)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X14672,tc_Nat_Onat),X14669),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,X14671,X14670))|~class_Groups_Oab__group__add(X14672))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__natinterval__difff])])])])). 4.05/4.29 cnf(c_0_4970, 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_4557])). 4.05/4.29 cnf(c_0_4971, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|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)))|~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_4558])). 4.05/4.29 cnf(c_0_4972, 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_4559])). 4.05/4.29 fof(c_0_4973, plain, ![X8539, X8540]:((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)),X8539),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)),X8540),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)),X8540),X8539)),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)),X8540),X8539)),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)),X8539),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)),X8540),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_equiv__intrel__iff])])). 4.05/4.29 cnf(c_0_4974, 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_4560])). 4.05/4.29 fof(c_0_4975, plain, ![X11802, X11803, X11804, X11805]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X11805,X11804),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X11803),X11802)))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11805),X11804),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X11802),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11803)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11803)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X11802),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),X11804),X11802)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zminus1__lemma])])])). 4.05/4.29 cnf(c_0_4976, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4561])). 4.05/4.29 cnf(c_0_4977, 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_4562]), ['final']). 4.05/4.29 cnf(c_0_4978, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)=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)))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4563])). 4.05/4.29 cnf(c_0_4979, 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_4564])). 4.05/4.29 cnf(c_0_4980, plain, (c_Enum_Oenum__the(X1,X2)=c_HOL_OThe(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4565])). 4.05/4.29 fof(c_0_4981, plain, ![X6242, X6243, X6244, X6245, X6246]:((hBOOL(hAPP(hAPP(c_member(X6245),X6243),X6244))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X6245,X6246),hAPP(hAPP(c_COMBC(X6245,X6246,X6246),hAPP(hAPP(c_COMBS(X6245,X6246,tc_fun(X6246,X6246)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X6246,tc_fun(X6246,X6246)),X6245),c_If(X6246)),hAPP(hAPP(c_COMBC(X6245,X6245,tc_HOL_Obool),c_fequal),X6243))),X6242)),c_Groups_Oone__class_Oone(X6246))),X6244)=c_Groups_Oone__class_Oone(X6246)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6245),X6244))|~class_Groups_Ocomm__monoid__mult(X6246))&(~hBOOL(hAPP(hAPP(c_member(X6245),X6243),X6244))|hAPP(X6242,X6243)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X6245,X6246),hAPP(hAPP(c_COMBC(X6245,X6246,X6246),hAPP(hAPP(c_COMBS(X6245,X6246,tc_fun(X6246,X6246)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X6246,tc_fun(X6246,X6246)),X6245),c_If(X6246)),hAPP(hAPP(c_COMBC(X6245,X6245,tc_HOL_Obool),c_fequal),X6243))),X6242)),c_Groups_Oone__class_Oone(X6246))),X6244)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6245),X6244))|~class_Groups_Ocomm__monoid__mult(X6246))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__delta])])])])). 4.05/4.29 fof(c_0_4982, plain, ![X994, X995, X996, X997]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X996),X995))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X996,X997),X994),X995)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X997,X996,c_Groups_Otimes__class_Otimes(X997)),X994),c_Groups_Oone__class_Oone(X997)),X995)|~class_Groups_Ocomm__monoid__mult(X997))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X996),X995))|c_Groups_Oone__class_Oone(X997)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X996,X997),X994),X995)|~class_Groups_Ocomm__monoid__mult(X997))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod_OF__eq])])])])). 4.05/4.29 fof(c_0_4983, plain, ![X9430, X9431, X9432, X9433, X9434]:((hBOOL(hAPP(hAPP(c_member(X9433),X9431),X9432))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9433,X9434),hAPP(hAPP(c_COMBC(X9433,X9434,X9434),hAPP(hAPP(c_COMBS(X9433,X9434,tc_fun(X9434,X9434)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X9434,tc_fun(X9434,X9434)),X9433),c_If(X9434)),hAPP(hAPP(c_COMBC(X9433,X9433,tc_HOL_Obool),c_fequal),X9431))),X9430)),c_Groups_Ozero__class_Ozero(X9434))),X9432)=c_Groups_Ozero__class_Ozero(X9434)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9433),X9432))|~class_Groups_Ocomm__monoid__add(X9434))&(~hBOOL(hAPP(hAPP(c_member(X9433),X9431),X9432))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9433,X9434),hAPP(hAPP(c_COMBC(X9433,X9434,X9434),hAPP(hAPP(c_COMBS(X9433,X9434,tc_fun(X9434,X9434)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X9434,tc_fun(X9434,X9434)),X9433),c_If(X9434)),hAPP(hAPP(c_COMBC(X9433,X9433,tc_HOL_Obool),c_fequal),X9431))),X9430)),c_Groups_Ozero__class_Ozero(X9434))),X9432)=hAPP(X9430,X9431)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9433),X9432))|~class_Groups_Ocomm__monoid__add(X9434))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__delta])])])])). 4.05/4.29 fof(c_0_4984, plain, ![X10902, X10903, X10904, X10905]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X10904),X10903))|c_Groups_Ozero__class_Ozero(X10905)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10904,X10905),X10902),X10903)|~class_Groups_Ocomm__monoid__add(X10905))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10904),X10903))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10904,X10905),X10902),X10903)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10905,X10904,c_Groups_Oplus__class_Oplus(X10905)),X10902),c_Groups_Ozero__class_Ozero(X10905)),X10903)|~class_Groups_Ocomm__monoid__add(X10905))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum_OF__eq])])])])). 4.05/4.29 fof(c_0_4985, plain, ![X3706, X3707, X3708, X3709, X3710, X3711, X3712]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3712,X3711),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3710),X3709)))|(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3708,X3711),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3707),X3706)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3711))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3712),X3708),X3711),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),X3710),X3707)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3709),X3706)),X3711))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3709),X3706),X3711))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__nat__rel__add1__eq])])])). 4.05/4.29 cnf(c_0_4986, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Int_Onumber__ring(X1)|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_4566])). 4.05/4.29 cnf(c_0_4987, 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_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_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4567])). 4.05/4.29 cnf(c_0_4988, 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_4532])). 4.05/4.29 cnf(c_0_4989, 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_4539])). 4.05/4.29 cnf(c_0_4990, 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_4540])). 4.05/4.29 cnf(c_0_4991, plain, (c_List_OtakeWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Orev(X1),hAPP(c_List_Otl(X1),c_List_OdropWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_4568])). 4.05/4.29 cnf(c_0_4992, plain, (hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3))=hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(c_List_Otl(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_4569])). 4.05/4.29 cnf(c_0_4993, 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)), inference(split_conjunct,[status(thm)],[c_0_4570]), ['final']). 4.05/4.29 fof(c_0_4994, plain, ![X5553, X5554, X5555, X5556, X5557, X5558, X5559]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X5559,X5558),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5557),X5556)))|(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X5555,X5558),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5554),X5553)))|(X5558=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),X5559),X5555),X5558),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),X5557),X5554)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5556),X5553)),X5558))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5556),X5553),X5558))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zadd1__lemma])])])). 4.05/4.29 cnf(c_0_4995, 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_4571])). 4.05/4.29 cnf(c_0_4996, 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_4572])). 4.05/4.29 cnf(c_0_4997, 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_4573])). 4.05/4.29 cnf(c_0_4998, 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_4574])). 4.05/4.29 cnf(c_0_4999, 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_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))))))|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_4448])). 4.05/4.29 fof(c_0_5000, plain, ![X8285, X8286, X8287]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X8287,esk262_3(X8285,X8286,X8287))),hAPP(X8286,esk262_3(X8285,X8286,X8287))))|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)),X8286)),X8287)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X8285))=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),X8286),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X8285))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X8287),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X8285)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sum__diff__distrib])])])])). 4.05/4.29 fof(c_0_5001, plain, ![X5132, X5133, X5134, X5135]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5135,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5135,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk158_4(X5132,X5133,X5134,X5135))),X5134)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5135,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),esk158_4(X5132,X5133,X5134,X5135)),X5133))),X5132)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5135,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5135,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X5134)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5135,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X5132)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__finite2__subset])])])])). 4.05/4.29 cnf(c_0_5002, 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_4575])). 4.05/4.29 cnf(c_0_5003, 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_4576])). 4.05/4.29 cnf(c_0_5004, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|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_4447])). 4.05/4.29 fof(c_0_5005, plain, ![X8162, X8163, X8164]:(((X8163!=X8162|c_List_Oconcat(X8164,X8163)=c_List_Oconcat(X8164,X8162)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X8164))),X8163)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X8164))),X8162)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X8164),tc_List_Olist(X8164))),esk257_3(X8162,X8163,X8164)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X8164),tc_List_Olist(X8164))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X8164),tc_List_Olist(X8164)),X8163),X8162)))))&(c_List_Oconcat(X8164,X8163)!=c_List_Oconcat(X8164,X8162)|X8163=X8162|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X8164))),X8163)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X8164))),X8162)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X8164),tc_List_Olist(X8164))),esk257_3(X8162,X8163,X8164)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X8164),tc_List_Olist(X8164))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X8164),tc_List_Olist(X8164)),X8163),X8162))))))&((X8163!=X8162|c_List_Oconcat(X8164,X8163)=c_List_Oconcat(X8164,X8162)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X8164))),X8163)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X8164))),X8162)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X8164),tc_List_Olist(X8164),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X8164),tc_fun(tc_List_Olist(X8164),tc_Nat_Onat),tc_fun(tc_List_Olist(X8164),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X8164),tc_Nat_Onat),tc_fun(tc_List_Olist(X8164),tc_HOL_Obool)),tc_List_Olist(X8164)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X8164))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X8164)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X8164))))),c_Nat_Osize__class_Osize(tc_List_Olist(X8164)))),esk257_3(X8162,X8163,X8164))))&(c_List_Oconcat(X8164,X8163)!=c_List_Oconcat(X8164,X8162)|X8163=X8162|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X8164))),X8163)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X8164))),X8162)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X8164),tc_List_Olist(X8164),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X8164),tc_fun(tc_List_Olist(X8164),tc_Nat_Onat),tc_fun(tc_List_Olist(X8164),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X8164),tc_Nat_Onat),tc_fun(tc_List_Olist(X8164),tc_HOL_Obool)),tc_List_Olist(X8164)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X8164))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X8164)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X8164))))),c_Nat_Osize__class_Osize(tc_List_Olist(X8164)))),esk257_3(X8162,X8163,X8164)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_concat__eq__concat__iff])])])])])). 4.05/4.29 fof(c_0_5006, plain, ![X2096, X2097, X2098]:((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2098),tc_List_Olist(X2098))),esk75_3(X2096,X2097,X2098)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X2098),tc_List_Olist(X2098))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X2098),tc_List_Olist(X2098)),X2097),X2096))))|X2097=X2096|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2098))),X2097)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2098))),X2096)|c_List_Oconcat(X2098,X2096)!=c_List_Oconcat(X2098,X2097))&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X2098),tc_List_Olist(X2098),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X2098),tc_fun(tc_List_Olist(X2098),tc_Nat_Onat),tc_fun(tc_List_Olist(X2098),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X2098),tc_Nat_Onat),tc_fun(tc_List_Olist(X2098),tc_HOL_Obool)),tc_List_Olist(X2098)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X2098))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X2098)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X2098))))),c_Nat_Osize__class_Osize(tc_List_Olist(X2098)))),esk75_3(X2096,X2097,X2098)))|X2097=X2096|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2098))),X2097)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2098))),X2096)|c_List_Oconcat(X2098,X2096)!=c_List_Oconcat(X2098,X2097))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_concat__injective])])])])). 4.05/4.29 cnf(c_0_5007, 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_4577])). 4.05/4.29 cnf(c_0_5008, 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_4578])). 4.05/4.29 fof(c_0_5009, plain, ![X15941, X15942, X15943, X15944, X15945]:((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15943)),hAPP(hAPP(c_List_Otake(X15943),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15945)),X15944)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15943)),X15942))),X15942))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15945)),hAPP(hAPP(c_List_Otake(X15945),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15945)),X15944)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15943)),X15942))),X15944))|hBOOL(hAPP(X15941,hAPP(hAPP(c_List_Ozip(X15945,X15943),X15944),X15942))))&(~hBOOL(hAPP(X15941,hAPP(hAPP(c_List_Ozip(X15945,X15943),hAPP(hAPP(c_List_Otake(X15945),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15945)),X15944)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15943)),X15942))),X15944)),hAPP(hAPP(c_List_Otake(X15943),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15945)),X15944)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15943)),X15942))),X15942))))|hBOOL(hAPP(X15941,hAPP(hAPP(c_List_Ozip(X15945,X15943),X15944),X15942))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__obtain__same__length])])])). 4.05/4.29 cnf(c_0_5010, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Otake(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_4579])). 4.05/4.29 cnf(c_0_5011, plain, (c_Orderings_Oord__class_Omin(tc_Nat_Onat)=c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_inf__nat__def]), ['final']). 4.05/4.29 cnf(c_0_5012, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4580])). 4.05/4.29 cnf(c_0_5013, 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_4581])). 4.05/4.29 cnf(c_0_5014, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),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))))|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_4582])). 4.05/4.29 cnf(c_0_5015, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),X2)|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_4583])). 4.05/4.29 cnf(c_0_5016, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))=hAPP(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)],[c_0_4584, c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_5017, 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_4585])). 4.05/4.29 cnf(c_0_5018, plain, (c_Transitive__Closure_Otrancl(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_4586])). 4.05/4.29 fof(c_0_5019, plain, ![X9141, X9142]:hAPP(hAPP(c_Relation_Orel__comp(X9142,X9142,X9142),X9141),c_Transitive__Closure_Ortrancl(X9142,X9141))=hAPP(hAPP(c_Relation_Orel__comp(X9142,X9142,X9142),c_Transitive__Closure_Ortrancl(X9142,X9141)),X9141), inference(variable_rename,[status(thm)],[fact_r__comp__rtrancl__eq])). 4.05/4.29 fof(c_0_5020, plain, ![X3621, X3622, X3623, X3624]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3624),X3623))|(~hBOOL(hAPP(hAPP(c_member(X3624),X3622),X3623))|(~hBOOL(hAPP(hAPP(c_member(X3624),X3621),X3623))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X3624),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3624,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3624,tc_HOL_Obool)),X3623),hAPP(hAPP(c_Set_Oinsert(X3624),X3622),c_Orderings_Obot__class_Obot(tc_fun(X3624,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X3624),X3621),c_Orderings_Obot__class_Obot(tc_fun(X3624,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X3624),X3623)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff2__less])])])). 4.05/4.29 fof(c_0_5021, plain, ![X15965, X15966, X15967, X15968]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15968,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15968,tc_HOL_Obool)),X15967),hAPP(hAPP(c_Set_Oinsert(X15968),X15966),c_Orderings_Obot__class_Obot(tc_fun(X15968,tc_HOL_Obool))))),X15965)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15968,tc_HOL_Obool)),X15967),hAPP(hAPP(c_Set_Oinsert(X15968),X15966),X15965)), inference(variable_rename,[status(thm)],[fact_Diff__insert2])). 4.05/4.29 fof(c_0_5022, plain, ![X5651, X5652]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,X5652))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X5651)),hAPP(c_Int_Onat,X5652))=hAPP(c_Int_Onat,X5651))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,X5652))|hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X5651),X5652)),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,X5651)),hAPP(c_Int_Onat,X5652)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__nat__eq__if])])])). 4.05/4.29 fof(c_0_5023, plain, ![X17529, X17530, X17531, X17532, X17533]:((hBOOL(hAPP(hAPP(c_member(X17532),X17530),X17531))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17532,X17533),hAPP(hAPP(c_COMBC(X17532,X17533,X17533),hAPP(hAPP(c_COMBS(X17532,X17533,tc_fun(X17533,X17533)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17533,tc_fun(X17533,X17533)),X17532),c_If(X17533)),hAPP(c_fequal,X17530))),X17529)),c_Groups_Ozero__class_Ozero(X17533))),X17531)=c_Groups_Ozero__class_Ozero(X17533)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X17532),X17531))|~class_Groups_Ocomm__monoid__add(X17533))&(~hBOOL(hAPP(hAPP(c_member(X17532),X17530),X17531))|hAPP(X17529,X17530)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17532,X17533),hAPP(hAPP(c_COMBC(X17532,X17533,X17533),hAPP(hAPP(c_COMBS(X17532,X17533,tc_fun(X17533,X17533)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X17533,tc_fun(X17533,X17533)),X17532),c_If(X17533)),hAPP(c_fequal,X17530))),X17529)),c_Groups_Ozero__class_Ozero(X17533))),X17531)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X17532),X17531))|~class_Groups_Ocomm__monoid__add(X17533))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__delta_H])])])])). 4.05/4.29 fof(c_0_5024, plain, ![X4862, X4863, X4864, X4865, X4866]:((~hBOOL(hAPP(hAPP(c_member(X4865),X4863),X4864))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4865,X4866),hAPP(hAPP(c_COMBC(X4865,X4866,X4866),hAPP(hAPP(c_COMBS(X4865,X4866,tc_fun(X4866,X4866)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4866,tc_fun(X4866,X4866)),X4865),c_If(X4866)),hAPP(c_fequal,X4863))),X4862)),c_Groups_Oone__class_Oone(X4866))),X4864)=hAPP(X4862,X4863)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4865),X4864))|~class_Groups_Ocomm__monoid__mult(X4866))&(hBOOL(hAPP(hAPP(c_member(X4865),X4863),X4864))|c_Groups_Oone__class_Oone(X4866)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4865,X4866),hAPP(hAPP(c_COMBC(X4865,X4866,X4866),hAPP(hAPP(c_COMBS(X4865,X4866,tc_fun(X4866,X4866)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4866,tc_fun(X4866,X4866)),X4865),c_If(X4866)),hAPP(c_fequal,X4863))),X4862)),c_Groups_Oone__class_Oone(X4866))),X4864)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4865),X4864))|~class_Groups_Ocomm__monoid__mult(X4866))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__delta_H])])])])). 4.05/4.29 fof(c_0_5025, plain, ![X5294, X5295, X5296, X5297, X5298]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X5298,X5298)),hAPP(hAPP(c_Product__Type_OPair(X5298,X5298),X5295),X5294)),X5296))|hAPP(hAPP(c_Equiv__Relations_Oquotient(X5298),hAPP(hAPP(c_Set_Oinsert(X5298),X5294),c_Orderings_Obot__class_Obot(tc_fun(X5298,tc_HOL_Obool)))),X5296)=hAPP(hAPP(c_Equiv__Relations_Oquotient(X5298),hAPP(hAPP(c_Set_Oinsert(X5298),X5295),c_Orderings_Obot__class_Obot(tc_fun(X5298,tc_HOL_Obool)))),X5296)|~hBOOL(hAPP(hAPP(c_member(X5298),X5294),X5297))|~hBOOL(hAPP(hAPP(c_member(X5298),X5295),X5297))|~c_Equiv__Relations_Oequiv(X5298,X5297,X5296))&(hAPP(hAPP(c_Equiv__Relations_Oquotient(X5298),hAPP(hAPP(c_Set_Oinsert(X5298),X5294),c_Orderings_Obot__class_Obot(tc_fun(X5298,tc_HOL_Obool)))),X5296)!=hAPP(hAPP(c_Equiv__Relations_Oquotient(X5298),hAPP(hAPP(c_Set_Oinsert(X5298),X5295),c_Orderings_Obot__class_Obot(tc_fun(X5298,tc_HOL_Obool)))),X5296)|hBOOL(hAPP(hAPP(c_member(tc_prod(X5298,X5298)),hAPP(hAPP(c_Product__Type_OPair(X5298,X5298),X5295),X5294)),X5296))|~hBOOL(hAPP(hAPP(c_member(X5298),X5294),X5297))|~hBOOL(hAPP(hAPP(c_member(X5298),X5295),X5297))|~c_Equiv__Relations_Oequiv(X5298,X5297,X5296))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__equiv__class__iff2])])])])). 4.05/4.29 fof(c_0_5026, plain, ![X16581, X16582, X16583, X16584, X16585]:((((hBOOL(hAPP(hAPP(c_member(X16585),X16582),X16584))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16585,X16585)),hAPP(hAPP(c_Product__Type_OPair(X16585,X16585),X16582),X16581)),X16583))|~c_Equiv__Relations_Oequiv(X16585,X16584,X16583))&(hBOOL(hAPP(hAPP(c_member(X16585),X16581),X16584))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16585,X16585)),hAPP(hAPP(c_Product__Type_OPair(X16585,X16585),X16582),X16581)),X16583))|~c_Equiv__Relations_Oequiv(X16585,X16584,X16583)))&(hAPP(c_Relation_OImage(X16585,X16585,X16583),hAPP(hAPP(c_Set_Oinsert(X16585),X16581),c_Orderings_Obot__class_Obot(tc_fun(X16585,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X16585,X16585,X16583),hAPP(hAPP(c_Set_Oinsert(X16585),X16582),c_Orderings_Obot__class_Obot(tc_fun(X16585,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16585,X16585)),hAPP(hAPP(c_Product__Type_OPair(X16585,X16585),X16582),X16581)),X16583))|~c_Equiv__Relations_Oequiv(X16585,X16584,X16583)))&(~hBOOL(hAPP(hAPP(c_member(X16585),X16582),X16584))|~hBOOL(hAPP(hAPP(c_member(X16585),X16581),X16584))|hAPP(c_Relation_OImage(X16585,X16585,X16583),hAPP(hAPP(c_Set_Oinsert(X16585),X16581),c_Orderings_Obot__class_Obot(tc_fun(X16585,tc_HOL_Obool))))!=hAPP(c_Relation_OImage(X16585,X16585,X16583),hAPP(hAPP(c_Set_Oinsert(X16585),X16582),c_Orderings_Obot__class_Obot(tc_fun(X16585,tc_HOL_Obool))))|hBOOL(hAPP(hAPP(c_member(tc_prod(X16585,X16585)),hAPP(hAPP(c_Product__Type_OPair(X16585,X16585),X16582),X16581)),X16583))|~c_Equiv__Relations_Oequiv(X16585,X16584,X16583))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__eq__iff])])])). 4.05/4.29 fof(c_0_5027, plain, ![X5603, X5604, X5605, X5606, X5607, X5608, X5609]:((~hBOOL(hAPP(hAPP(c_member(X5609),X5608),hAPP(c_List_Oset(X5609),hAPP(hAPP(c_List_Otake(X5609),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5607)),X5606)),X5605))))|c_Map_Omap__upds(X5609,X5607,X5604,X5605,X5606)=c_Map_Omap__upds(X5609,X5607,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5609,tc_Option_Ooption(X5607)),X5604),X5608),hAPP(c_Option_Ooption_OSome(X5607),X5603)),X5605,X5606))&(hBOOL(hAPP(hAPP(c_member(X5609),X5608),hAPP(c_List_Oset(X5609),hAPP(hAPP(c_List_Otake(X5609),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5607)),X5606)),X5605))))|c_Map_Omap__upds(X5609,X5607,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5609,tc_Option_Ooption(X5607)),X5604),X5608),hAPP(c_Option_Ooption_OSome(X5607),X5603)),X5605,X5606)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5609,tc_Option_Ooption(X5607)),c_Map_Omap__upds(X5609,X5607,X5604,X5605,X5606)),X5608),hAPP(c_Option_Ooption_OSome(X5607),X5603)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__upd__upds__conv__if])])])). 4.05/4.29 fof(c_0_5028, plain, ![X14102, X14103, X14104, X14105, X14106, X14107, X14108]:c_Map_Omap__upds(X14108,X14107,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X14108,tc_Option_Ooption(X14107)),X14106),X14105),hAPP(c_Option_Ooption_OSome(X14107),X14103)),X14104,X14102)=c_Map_Omap__upds(X14108,X14107,X14106,hAPP(hAPP(c_List_Olist_OCons(X14108),X14105),X14104),hAPP(hAPP(c_List_Olist_OCons(X14107),X14103),X14102)), inference(variable_rename,[status(thm)],[fact_map__upds__Cons])). 4.05/4.29 fof(c_0_5029, plain, ![X16928, X16929, X16930, X16931, X16932, X16933, X16934, X16935, X16936]:(((hAPP(hAPP(c_List_Otake(X16931),X16932),X16929)!=hAPP(hAPP(c_List_Otake(X16931),X16932),X16930)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16931,X16931)),hAPP(hAPP(c_Product__Type_OPair(X16931,X16931),hAPP(hAPP(c_List_Onth(X16931),X16930),X16932)),hAPP(hAPP(c_List_Onth(X16931),X16929),X16932))),X16928))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16932),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16931)),X16930)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16931)),X16929))))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16931),tc_List_Olist(X16931))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16931),tc_List_Olist(X16931)),X16930),X16929)),c_List_Olexord(X16931,X16928))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16931)),X16930)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16931)),X16929)))|X16930!=hAPP(hAPP(c_List_Otake(X16931),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16931)),X16930)),X16929)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16931),tc_List_Olist(X16931))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16931),tc_List_Olist(X16931)),X16930),X16929)),c_List_Olexord(X16931,X16928)))))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16936)),X16935)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16936)),X16934)))|hAPP(hAPP(c_List_Otake(X16936),esk508_4(X16933,X16934,X16935,X16936)),X16934)=hAPP(hAPP(c_List_Otake(X16936),esk508_4(X16933,X16934,X16935,X16936)),X16935)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16936),tc_List_Olist(X16936))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16936),tc_List_Olist(X16936)),X16935),X16934)),c_List_Olexord(X16936,X16933))))&(X16935=hAPP(hAPP(c_List_Otake(X16936),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16936)),X16935)),X16934)|hAPP(hAPP(c_List_Otake(X16936),esk508_4(X16933,X16934,X16935,X16936)),X16934)=hAPP(hAPP(c_List_Otake(X16936),esk508_4(X16933,X16934,X16935,X16936)),X16935)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16936),tc_List_Olist(X16936))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16936),tc_List_Olist(X16936)),X16935),X16934)),c_List_Olexord(X16936,X16933)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16936)),X16935)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16936)),X16934)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X16936,X16936)),hAPP(hAPP(c_Product__Type_OPair(X16936,X16936),hAPP(hAPP(c_List_Onth(X16936),X16935),esk508_4(X16933,X16934,X16935,X16936))),hAPP(hAPP(c_List_Onth(X16936),X16934),esk508_4(X16933,X16934,X16935,X16936)))),X16933))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16936),tc_List_Olist(X16936))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16936),tc_List_Olist(X16936)),X16935),X16934)),c_List_Olexord(X16936,X16933))))&(X16935=hAPP(hAPP(c_List_Otake(X16936),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16936)),X16935)),X16934)|hBOOL(hAPP(hAPP(c_member(tc_prod(X16936,X16936)),hAPP(hAPP(c_Product__Type_OPair(X16936,X16936),hAPP(hAPP(c_List_Onth(X16936),X16935),esk508_4(X16933,X16934,X16935,X16936))),hAPP(hAPP(c_List_Onth(X16936),X16934),esk508_4(X16933,X16934,X16935,X16936)))),X16933))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16936),tc_List_Olist(X16936))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16936),tc_List_Olist(X16936)),X16935),X16934)),c_List_Olexord(X16936,X16933))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16936)),X16935)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16936)),X16934)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk508_4(X16933,X16934,X16935,X16936)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16936)),X16935)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16936)),X16934))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16936),tc_List_Olist(X16936))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16936),tc_List_Olist(X16936)),X16935),X16934)),c_List_Olexord(X16936,X16933))))&(X16935=hAPP(hAPP(c_List_Otake(X16936),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16936)),X16935)),X16934)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk508_4(X16933,X16934,X16935,X16936)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16936)),X16935)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16936)),X16934))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16936),tc_List_Olist(X16936))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16936),tc_List_Olist(X16936)),X16935),X16934)),c_List_Olexord(X16936,X16933))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__take__index__conv])])])])])])). 4.05/4.29 fof(c_0_5030, plain, ![X11159, X11160, X11161, X11162, X11163]:(~class_Groups_Ocomm__monoid__add(X11163)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11162),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11161),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X11163),X11160),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X11162,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11161),X11159)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11163),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X11163),X11160),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X11162,X11161))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X11163),X11160),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11161),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11161),X11159)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__ub__add__nat])])])). 4.05/4.29 cnf(c_0_5031, 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_4587])). 4.05/4.29 cnf(c_0_5032, plain, (hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Otimes__class_Otimes(X1)),c_COMBI(X1)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X3)))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4588])). 4.05/4.29 fof(c_0_5033, plain, ![X751, X752]:(((X752!=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)),X751)=c_Divides_Odivmod__nat(X751,X752))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X751),X752))|hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X751)=c_Divides_Odivmod__nat(X751,X752)))&(X752=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X751),X752))|c_Divides_Odivmod__nat(X751,X752)=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),X751),X752),X752)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__nat__if])])])])). 4.05/4.29 cnf(c_0_5034, 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_4589])). 4.05/4.29 cnf(c_0_5035, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X2))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_4572])). 4.05/4.29 cnf(c_0_5036, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_4590])). 4.05/4.29 fof(c_0_5037, plain, ![X12959, X12960, X12961]:(~class_Rings_Oring__1(X12961)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12961),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X12961),X12960)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X12961),X12959))=hAPP(c_Int_Oring__1__class_Oof__int(X12961),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),X12960),X12959)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int])])). 4.05/4.29 cnf(c_0_5038, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|c_Groups_Oone__class_Oone(X1)!=X2|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_4447])). 4.05/4.29 fof(c_0_5039, plain, ![X13897, X13898, X13899, X13900, X13901, X13902, X13903, X13904]:(((X13900=X13902|hBOOL(hAPP(hAPP(c_member(tc_prod(X13904,X13904)),hAPP(hAPP(c_Product__Type_OPair(X13904,X13904),X13902),X13900)),X13898))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X13904,X13903),tc_prod(X13904,X13903))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X13904,X13903),tc_prod(X13904,X13903)),hAPP(hAPP(c_Product__Type_OPair(X13904,X13903),X13902),X13901)),hAPP(hAPP(c_Product__Type_OPair(X13904,X13903),X13900),X13899))),c_Wellfounded_Olex__prod(X13904,X13903,X13898,X13897))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X13903,X13903)),hAPP(hAPP(c_Product__Type_OPair(X13903,X13903),X13901),X13899)),X13897))|hBOOL(hAPP(hAPP(c_member(tc_prod(X13904,X13904)),hAPP(hAPP(c_Product__Type_OPair(X13904,X13904),X13902),X13900)),X13898))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X13904,X13903),tc_prod(X13904,X13903))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X13904,X13903),tc_prod(X13904,X13903)),hAPP(hAPP(c_Product__Type_OPair(X13904,X13903),X13902),X13901)),hAPP(hAPP(c_Product__Type_OPair(X13904,X13903),X13900),X13899))),c_Wellfounded_Olex__prod(X13904,X13903,X13898,X13897)))))&((X13900!=X13902|~hBOOL(hAPP(hAPP(c_member(tc_prod(X13903,X13903)),hAPP(hAPP(c_Product__Type_OPair(X13903,X13903),X13901),X13899)),X13897))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X13904,X13903),tc_prod(X13904,X13903))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X13904,X13903),tc_prod(X13904,X13903)),hAPP(hAPP(c_Product__Type_OPair(X13904,X13903),X13902),X13901)),hAPP(hAPP(c_Product__Type_OPair(X13904,X13903),X13900),X13899))),c_Wellfounded_Olex__prod(X13904,X13903,X13898,X13897))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13904,X13904)),hAPP(hAPP(c_Product__Type_OPair(X13904,X13904),X13902),X13900)),X13898))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X13904,X13903),tc_prod(X13904,X13903))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X13904,X13903),tc_prod(X13904,X13903)),hAPP(hAPP(c_Product__Type_OPair(X13904,X13903),X13902),X13901)),hAPP(hAPP(c_Product__Type_OPair(X13904,X13903),X13900),X13899))),c_Wellfounded_Olex__prod(X13904,X13903,X13898,X13897)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])])). 4.05/4.29 cnf(c_0_5040, 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_4591])). 4.05/4.29 cnf(c_0_5041, 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_4592])). 4.05/4.29 cnf(c_0_5042, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4593])). 4.05/4.29 cnf(c_0_5043, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4594])). 4.05/4.29 cnf(c_0_5044, 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_4595])). 4.05/4.29 cnf(c_0_5045, 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_4596])). 4.05/4.29 cnf(c_0_5046, 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_4597])). 4.05/4.29 cnf(c_0_5047, plain, (hAPP(c_List_OremoveAll(X2,hAPP(X3,X4)),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))=hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_OremoveAll(X1,X4),X5))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_4598])). 4.05/4.29 cnf(c_0_5048, 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_4599])). 4.05/4.29 cnf(c_0_5049, 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_4600])). 4.05/4.29 cnf(c_0_5050, plain, (hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1))=c_Nitpick_Odenom(X1)), inference(split_conjunct,[status(thm)],[c_0_4601])). 4.05/4.29 fof(c_0_5051, plain, ![X9482, X9483, X9484, X9485, X9486, X9487]:hAPP(X9484,hAPP(X9483,X9482))=hAPP(hAPP(c_Fun_Ocomp(X9487,X9486,X9485,X9484),X9483),X9482), inference(variable_rename,[status(thm)],[fact_o__apply])). 4.05/4.29 fof(c_0_5052, plain, ![X13777, X13778, X13779, X13780, X13781, X13782, X13783, X13784]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13784,X13784)),hAPP(hAPP(c_Product__Type_OPair(X13784,X13784),X13783),X13782)),X13781))|(X13780!=hAPP(hAPP(c_List_Oappend(X13784),X13779),hAPP(hAPP(c_List_Olist_OCons(X13784),X13783),X13778))|(X13777!=hAPP(hAPP(c_List_Oappend(X13784),X13779),hAPP(hAPP(c_List_Olist_OCons(X13784),X13782),X13778))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X13784),tc_List_Olist(X13784))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X13784),tc_List_Olist(X13784)),X13780),X13777)),c_List_Olistrel1(X13784,X13781)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel1I])])])). 4.05/4.29 fof(c_0_5053, plain, ![X8808, X8809, X8810, X8811, X8812]:((hBOOL(hAPP(hAPP(c_member(X8812),esk279_5(X8808,X8809,X8810,X8811,X8812)),X8811))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8812,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8812,tc_HOL_Obool)),X8811),hAPP(c_Set_OCollect(X8812),X8809))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8812,tc_HOL_Obool)),X8810),hAPP(c_Set_OCollect(X8812),X8808))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8812,tc_HOL_Obool)),X8811),X8810)))&((hBOOL(hAPP(X8809,esk279_5(X8808,X8809,X8810,X8811,X8812)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8812,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8812,tc_HOL_Obool)),X8811),hAPP(c_Set_OCollect(X8812),X8809))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8812,tc_HOL_Obool)),X8810),hAPP(c_Set_OCollect(X8812),X8808))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8812,tc_HOL_Obool)),X8811),X8810)))&(~hBOOL(hAPP(X8808,esk279_5(X8808,X8809,X8810,X8811,X8812)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8812,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8812,tc_HOL_Obool)),X8811),hAPP(c_Set_OCollect(X8812),X8809))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8812,tc_HOL_Obool)),X8810),hAPP(c_Set_OCollect(X8812),X8808))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8812,tc_HOL_Obool)),X8811),X8810))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__Collect__mono])])])])])). 4.05/4.29 cnf(c_0_5054, 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_4554])). 4.05/4.29 cnf(c_0_5055, 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_4555])). 4.05/4.29 fof(c_0_5056, plain, ![X16914, X16915, X16916, X16917]:(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X16917)),X16916),c_List_Olists(X16917,X16915)))|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X16917)),X16916),c_List_Olists(X16917,X16914)))|hBOOL(hAPP(c_List_Olistsp(X16917,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16917,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X16917,tc_fun(X16917,tc_HOL_Obool),tc_HOL_Obool),c_member(X16917)),X16915)),hAPP(hAPP(c_COMBC(X16917,tc_fun(X16917,tc_HOL_Obool),tc_HOL_Obool),c_member(X16917)),X16914))),X16916)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lists__IntI])])])). 4.05/4.29 cnf(c_0_5057, 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_4602])). 4.05/4.29 fof(c_0_5058, plain, ![X14034, X14035, X14036, X14037, X14038]:(~hBOOL(hAPP(hAPP(c_member(X14038),X14037),hAPP(c_List_Oset(X14038),X14036)))|(hBOOL(hAPP(X14035,X14037))|hAPP(hAPP(c_List_Oappend(X14038),c_List_OdropWhile(X14038,X14035,X14036)),X14034)=c_List_OdropWhile(X14038,X14035,hAPP(hAPP(c_List_Oappend(X14038),X14036),X14034)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dropWhile__append1])])])). 4.05/4.29 fof(c_0_5059, plain, ![X10480, X10481]:(((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10481)),esk318_2(X10480,X10481)),hAPP(c_List_Oset(tc_List_Olist(X10481)),X10480)))|hBOOL(hAPP(c_List_Odistinct(X10481),c_List_Oconcat(X10481,X10480)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10481)),esk317_2(X10480,X10481)),hAPP(c_List_Oset(tc_List_Olist(X10481)),X10480)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X10481)),X10480)))&((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10481)),esk319_2(X10480,X10481)),hAPP(c_List_Oset(tc_List_Olist(X10481)),X10480)))|hBOOL(hAPP(c_List_Odistinct(X10481),c_List_Oconcat(X10481,X10480)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10481)),esk317_2(X10480,X10481)),hAPP(c_List_Oset(tc_List_Olist(X10481)),X10480)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X10481)),X10480)))&((esk318_2(X10480,X10481)!=esk319_2(X10480,X10481)|hBOOL(hAPP(c_List_Odistinct(X10481),c_List_Oconcat(X10481,X10480)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10481)),esk317_2(X10480,X10481)),hAPP(c_List_Oset(tc_List_Olist(X10481)),X10480)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X10481)),X10480)))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10481,tc_HOL_Obool)),hAPP(c_List_Oset(X10481),esk318_2(X10480,X10481))),hAPP(c_List_Oset(X10481),esk319_2(X10480,X10481)))!=c_Orderings_Obot__class_Obot(tc_fun(X10481,tc_HOL_Obool))|hBOOL(hAPP(c_List_Odistinct(X10481),c_List_Oconcat(X10481,X10480)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10481)),esk317_2(X10480,X10481)),hAPP(c_List_Oset(tc_List_Olist(X10481)),X10480)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X10481)),X10480))))))&((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10481)),esk318_2(X10480,X10481)),hAPP(c_List_Oset(tc_List_Olist(X10481)),X10480)))|hBOOL(hAPP(c_List_Odistinct(X10481),c_List_Oconcat(X10481,X10480)))|~hBOOL(hAPP(c_List_Odistinct(X10481),esk317_2(X10480,X10481)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X10481)),X10480)))&((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10481)),esk319_2(X10480,X10481)),hAPP(c_List_Oset(tc_List_Olist(X10481)),X10480)))|hBOOL(hAPP(c_List_Odistinct(X10481),c_List_Oconcat(X10481,X10480)))|~hBOOL(hAPP(c_List_Odistinct(X10481),esk317_2(X10480,X10481)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X10481)),X10480)))&((esk318_2(X10480,X10481)!=esk319_2(X10480,X10481)|hBOOL(hAPP(c_List_Odistinct(X10481),c_List_Oconcat(X10481,X10480)))|~hBOOL(hAPP(c_List_Odistinct(X10481),esk317_2(X10480,X10481)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X10481)),X10480)))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10481,tc_HOL_Obool)),hAPP(c_List_Oset(X10481),esk318_2(X10480,X10481))),hAPP(c_List_Oset(X10481),esk319_2(X10480,X10481)))!=c_Orderings_Obot__class_Obot(tc_fun(X10481,tc_HOL_Obool))|hBOOL(hAPP(c_List_Odistinct(X10481),c_List_Oconcat(X10481,X10480)))|~hBOOL(hAPP(c_List_Odistinct(X10481),esk317_2(X10480,X10481)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X10481)),X10480))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__concat])])])])])). 4.05/4.29 fof(c_0_5060, plain, ![X12031, X12032, X12033, X12034]:(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X12034,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),esk375_4(X12031,X12032,X12033,X12034)),X12032))),X12031)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X12034,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk375_4(X12031,X12032,X12033,X12034))),X12033)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X12034,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X12031)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X12034,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X12033)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__finite2__eq])])])])). 4.05/4.29 cnf(c_0_5061, 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_4603])). 4.05/4.29 fof(c_0_5062, plain, ![X3122, X3123, X3124]:(((hBOOL(hAPP(hAPP(c_member(tc_fun(X3124,tc_HOL_Obool)),esk105_3(X3122,X3123,X3124)),X3123))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3122),hAPP(c_Finite__Set_Ocard(tc_fun(X3124,tc_HOL_Obool)),X3123))=hAPP(c_Finite__Set_Ocard(X3124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3124,tc_HOL_Obool),X3123))|hBOOL(hAPP(hAPP(c_member(tc_fun(X3124,tc_HOL_Obool)),esk104_3(X3122,X3123,X3124)),X3123))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3124,tc_HOL_Obool),X3123)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3124,tc_HOL_Obool)),X3123)))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X3124,tc_HOL_Obool)),esk106_3(X3122,X3123,X3124)),X3123))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3122),hAPP(c_Finite__Set_Ocard(tc_fun(X3124,tc_HOL_Obool)),X3123))=hAPP(c_Finite__Set_Ocard(X3124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3124,tc_HOL_Obool),X3123))|hBOOL(hAPP(hAPP(c_member(tc_fun(X3124,tc_HOL_Obool)),esk104_3(X3122,X3123,X3124)),X3123))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3124,tc_HOL_Obool),X3123)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3124,tc_HOL_Obool)),X3123)))&((esk106_3(X3122,X3123,X3124)!=esk105_3(X3122,X3123,X3124)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3122),hAPP(c_Finite__Set_Ocard(tc_fun(X3124,tc_HOL_Obool)),X3123))=hAPP(c_Finite__Set_Ocard(X3124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3124,tc_HOL_Obool),X3123))|hBOOL(hAPP(hAPP(c_member(tc_fun(X3124,tc_HOL_Obool)),esk104_3(X3122,X3123,X3124)),X3123))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3124,tc_HOL_Obool),X3123)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3124,tc_HOL_Obool)),X3123)))&(c_Orderings_Obot__class_Obot(tc_fun(X3124,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3124,tc_HOL_Obool)),esk105_3(X3122,X3123,X3124)),esk106_3(X3122,X3123,X3124))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3122),hAPP(c_Finite__Set_Ocard(tc_fun(X3124,tc_HOL_Obool)),X3123))=hAPP(c_Finite__Set_Ocard(X3124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3124,tc_HOL_Obool),X3123))|hBOOL(hAPP(hAPP(c_member(tc_fun(X3124,tc_HOL_Obool)),esk104_3(X3122,X3123,X3124)),X3123))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3124,tc_HOL_Obool),X3123)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3124,tc_HOL_Obool)),X3123))))))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X3124,tc_HOL_Obool)),esk105_3(X3122,X3123,X3124)),X3123))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3122),hAPP(c_Finite__Set_Ocard(tc_fun(X3124,tc_HOL_Obool)),X3123))=hAPP(c_Finite__Set_Ocard(X3124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3124,tc_HOL_Obool),X3123))|hAPP(c_Finite__Set_Ocard(X3124),esk104_3(X3122,X3123,X3124))!=X3122|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3124,tc_HOL_Obool),X3123)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3124,tc_HOL_Obool)),X3123)))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X3124,tc_HOL_Obool)),esk106_3(X3122,X3123,X3124)),X3123))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3122),hAPP(c_Finite__Set_Ocard(tc_fun(X3124,tc_HOL_Obool)),X3123))=hAPP(c_Finite__Set_Ocard(X3124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3124,tc_HOL_Obool),X3123))|hAPP(c_Finite__Set_Ocard(X3124),esk104_3(X3122,X3123,X3124))!=X3122|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3124,tc_HOL_Obool),X3123)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3124,tc_HOL_Obool)),X3123)))&((esk106_3(X3122,X3123,X3124)!=esk105_3(X3122,X3123,X3124)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3122),hAPP(c_Finite__Set_Ocard(tc_fun(X3124,tc_HOL_Obool)),X3123))=hAPP(c_Finite__Set_Ocard(X3124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3124,tc_HOL_Obool),X3123))|hAPP(c_Finite__Set_Ocard(X3124),esk104_3(X3122,X3123,X3124))!=X3122|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3124,tc_HOL_Obool),X3123)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3124,tc_HOL_Obool)),X3123)))&(c_Orderings_Obot__class_Obot(tc_fun(X3124,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3124,tc_HOL_Obool)),esk105_3(X3122,X3123,X3124)),esk106_3(X3122,X3123,X3124))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3122),hAPP(c_Finite__Set_Ocard(tc_fun(X3124,tc_HOL_Obool)),X3123))=hAPP(c_Finite__Set_Ocard(X3124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3124,tc_HOL_Obool),X3123))|hAPP(c_Finite__Set_Ocard(X3124),esk104_3(X3122,X3123,X3124))!=X3122|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3124,tc_HOL_Obool),X3123)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3124,tc_HOL_Obool)),X3123))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__partition])])])])])). 4.05/4.29 fof(c_0_5063, plain, ![X3134, X3135]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3135),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3135,tc_HOL_Obool),X3134)))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3135,tc_HOL_Obool)),X3134))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UnionD])])). 4.05/4.29 cnf(c_0_5064, 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_4604])). 4.05/4.29 fof(c_0_5065, plain, ![X5939, X5940, X5941, X5942, X5945, X5946, X5947, X5948, X5949, X5950]:((((hBOOL(hAPP(hAPP(c_member(tc_prod(X5942,X5942)),hAPP(hAPP(c_Product__Type_OPair(X5942,X5942),hAPP(hAPP(c_List_Onth(X5942),X5941),esk184_4(X5939,X5940,X5941,X5942))),esk183_4(X5939,X5940,X5941,X5942))),X5939))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5942),tc_List_Olist(X5942))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5942),tc_List_Olist(X5942)),X5941),X5940)),c_List_Olistrel1(X5942,X5939))))&(hAPP(hAPP(c_List_Olist__update(X5942,X5941),esk184_4(X5939,X5940,X5941,X5942)),esk183_4(X5939,X5940,X5941,X5942))=X5940|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5942),tc_List_Olist(X5942))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5942),tc_List_Olist(X5942)),X5941),X5940)),c_List_Olistrel1(X5942,X5939)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk184_4(X5939,X5940,X5941,X5942)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5942)),X5941)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5942),tc_List_Olist(X5942))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5942),tc_List_Olist(X5942)),X5941),X5940)),c_List_Olistrel1(X5942,X5939)))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5948,X5948)),hAPP(hAPP(c_Product__Type_OPair(X5948,X5948),hAPP(hAPP(c_List_Onth(X5948),X5947),X5950)),X5949)),X5945))|hAPP(hAPP(c_List_Olist__update(X5948,X5947),X5950),X5949)!=X5946|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5950),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5948)),X5947)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5948),tc_List_Olist(X5948))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5948),tc_List_Olist(X5948)),X5947),X5946)),c_List_Olistrel1(X5948,X5945))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__iff__update])])])])])])). 4.05/4.29 cnf(c_0_5066, 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_4605])). 4.05/4.29 cnf(c_0_5067, 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_4606])). 4.05/4.29 fof(c_0_5068, plain, ![X8301, X8302, X8303, X8304, X8305, X8306]:((hBOOL(hAPP(hAPP(c_member(X8306),X8305),X8304))|c_Map_Orestrict__map(X8306,X8303,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X8306,tc_Option_Ooption(X8303)),X8302),X8305),X8301),X8304)=c_Map_Orestrict__map(X8306,X8303,X8302,X8304))&(~hBOOL(hAPP(hAPP(c_member(X8306),X8305),X8304))|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X8306,tc_Option_Ooption(X8303)),c_Map_Orestrict__map(X8306,X8303,X8302,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8306,tc_HOL_Obool)),X8304),hAPP(hAPP(c_Set_Oinsert(X8306),X8305),c_Orderings_Obot__class_Obot(tc_fun(X8306,tc_HOL_Obool)))))),X8305),X8301)=c_Map_Orestrict__map(X8306,X8303,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X8306,tc_Option_Ooption(X8303)),X8302),X8305),X8301),X8304))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_restrict__fun__upd])])])). 4.05/4.29 fof(c_0_5069, plain, ![X586, X587, X588, X589, X590, X591]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X591,tc_Option_Ooption(X590)),c_Map_Orestrict__map(X591,X590,X589,X588)),X587),X586)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X591,tc_Option_Ooption(X590)),c_Map_Orestrict__map(X591,X590,X589,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X591,tc_HOL_Obool)),X588),hAPP(hAPP(c_Set_Oinsert(X591),X587),c_Orderings_Obot__class_Obot(tc_fun(X591,tc_HOL_Obool)))))),X587),X586), inference(variable_rename,[status(thm)],[fact_fun__upd__restrict])). 4.05/4.29 cnf(c_0_5070, plain, (c_Groups_Oone__class_Oone(X1)=X2|hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))=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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4607, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_5071, plain, (X2!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4608, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_5072, 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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4609, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_5073, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),c_Groups_Ozero__class_Ozero(X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4610, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 fof(c_0_5074, plain, ![X2532, X2533, X2534]:((~c_Wellfounded_Owf(X2534,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2534,X2534),tc_HOL_Obool)),X2533),X2532))|c_Wellfounded_Owf(X2534,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2534,X2534),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2534,X2534),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X2534,X2534,X2534),X2533),X2533)),hAPP(hAPP(c_Relation_Orel__comp(X2534,X2534,X2534),X2532),X2533))),X2532)))&(~c_Wellfounded_Owf(X2534,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2534,X2534),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2534,X2534),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X2534,X2534,X2534),X2533),X2533)),hAPP(hAPP(c_Relation_Orel__comp(X2534,X2534,X2534),X2532),X2533))),X2532))|c_Wellfounded_Owf(X2534,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2534,X2534),tc_HOL_Obool)),X2533),X2532)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__union__merge])])). 4.05/4.29 fof(c_0_5075, plain, ![X10008, X10009, X10010, X10011]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10011,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10011,tc_HOL_Obool)),X10010),X10009)),X10008)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10011,tc_HOL_Obool)),X10010),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10011,tc_HOL_Obool)),X10009),X10008)), inference(variable_rename,[status(thm)],[fact_Un__assoc])). 4.05/4.29 fof(c_0_5076, plain, ![X3215, X3216, X3217]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3217,tc_HOL_Obool)),X3215),X3216)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3217,tc_HOL_Obool)),X3216),X3215), inference(variable_rename,[status(thm)],[fact_Un__commute])). 4.05/4.29 fof(c_0_5077, plain, ![X11850, X11851, X11852, X11853, X11854, X11855]:((X11851!=X11850|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X11855),tc_List_Olist(X11855))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X11855),tc_List_Olist(X11855)),X11854),X11853)),c_List_Olistrel1(X11855,X11852)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X11855),tc_List_Olist(X11855))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X11855),tc_List_Olist(X11855)),hAPP(hAPP(c_List_Oappend(X11855),X11854),X11851)),hAPP(hAPP(c_List_Oappend(X11855),X11853),X11850))),c_List_Olistrel1(X11855,X11852))))&(X11853!=X11854|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X11855),tc_List_Olist(X11855))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X11855),tc_List_Olist(X11855)),X11851),X11850)),c_List_Olistrel1(X11855,X11852)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X11855),tc_List_Olist(X11855))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X11855),tc_List_Olist(X11855)),hAPP(hAPP(c_List_Oappend(X11855),X11854),X11851)),hAPP(hAPP(c_List_Oappend(X11855),X11853),X11850))),c_List_Olistrel1(X11855,X11852))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__listrel1I])])])). 4.05/4.29 fof(c_0_5078, plain, ![X17412, X17413, X17414, X17415, X17416, X17417, X17418]:((X17415!=X17414|hBOOL(hAPP(hAPP(c_member(tc_prod(X17418,X17418)),hAPP(hAPP(c_Product__Type_OPair(X17418,X17418),X17413),X17412)),X17416))|~hBOOL(hAPP(hAPP(c_member(X17418),X17412),X17414))|~hBOOL(hAPP(hAPP(c_member(X17418),X17413),X17415))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X17418,tc_HOL_Obool)),X17414),hAPP(hAPP(c_Equiv__Relations_Oquotient(X17418),X17417),X17416)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X17418,tc_HOL_Obool)),X17415),hAPP(hAPP(c_Equiv__Relations_Oquotient(X17418),X17417),X17416)))|~c_Equiv__Relations_Oequiv(X17418,X17417,X17416))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X17418,X17418)),hAPP(hAPP(c_Product__Type_OPair(X17418,X17418),X17413),X17412)),X17416))|X17415=X17414|~hBOOL(hAPP(hAPP(c_member(X17418),X17412),X17414))|~hBOOL(hAPP(hAPP(c_member(X17418),X17413),X17415))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X17418,tc_HOL_Obool)),X17414),hAPP(hAPP(c_Equiv__Relations_Oquotient(X17418),X17417),X17416)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X17418,tc_HOL_Obool)),X17415),hAPP(hAPP(c_Equiv__Relations_Oquotient(X17418),X17417),X17416)))|~c_Equiv__Relations_Oequiv(X17418,X17417,X17416))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_quotient__eq__iff])])])])). 4.05/4.29 fof(c_0_5079, plain, ![X2288, X2289, X2290, X2291, X2292, X2293]:(((X2292!=X2290|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2293),tc_List_Olist(X2293))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2293),tc_List_Olist(X2293)),X2291),X2289)),c_List_Olex(X2293,X2288)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2293),tc_List_Olist(X2293))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2293),tc_List_Olist(X2293)),hAPP(hAPP(c_List_Olist_OCons(X2293),X2292),X2291)),hAPP(hAPP(c_List_Olist_OCons(X2293),X2290),X2289))),c_List_Olex(X2293,X2288))))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2293)),X2289)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2293)),X2291)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2293,X2293)),hAPP(hAPP(c_Product__Type_OPair(X2293,X2293),X2292),X2290)),X2288))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2293),tc_List_Olist(X2293))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2293),tc_List_Olist(X2293)),hAPP(hAPP(c_List_Olist_OCons(X2293),X2292),X2291)),hAPP(hAPP(c_List_Olist_OCons(X2293),X2290),X2289))),c_List_Olex(X2293,X2288)))))&(((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2293)),X2289)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2293)),X2291)|X2292=X2290|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2293),tc_List_Olist(X2293))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2293),tc_List_Olist(X2293)),hAPP(hAPP(c_List_Olist_OCons(X2293),X2292),X2291)),hAPP(hAPP(c_List_Olist_OCons(X2293),X2290),X2289))),c_List_Olex(X2293,X2288))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X2293,X2293)),hAPP(hAPP(c_Product__Type_OPair(X2293,X2293),X2292),X2290)),X2288))|X2292=X2290|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2293),tc_List_Olist(X2293))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2293),tc_List_Olist(X2293)),hAPP(hAPP(c_List_Olist_OCons(X2293),X2292),X2291)),hAPP(hAPP(c_List_Olist_OCons(X2293),X2290),X2289))),c_List_Olex(X2293,X2288)))))&((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2293)),X2289)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2293)),X2291)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2293),tc_List_Olist(X2293))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2293),tc_List_Olist(X2293)),X2291),X2289)),c_List_Olex(X2293,X2288)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2293),tc_List_Olist(X2293))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2293),tc_List_Olist(X2293)),hAPP(hAPP(c_List_Olist_OCons(X2293),X2292),X2291)),hAPP(hAPP(c_List_Olist_OCons(X2293),X2290),X2289))),c_List_Olex(X2293,X2288))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X2293,X2293)),hAPP(hAPP(c_Product__Type_OPair(X2293,X2293),X2292),X2290)),X2288))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2293),tc_List_Olist(X2293))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2293),tc_List_Olist(X2293)),X2291),X2289)),c_List_Olex(X2293,X2288)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2293),tc_List_Olist(X2293))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2293),tc_List_Olist(X2293)),hAPP(hAPP(c_List_Olist_OCons(X2293),X2292),X2291)),hAPP(hAPP(c_List_Olist_OCons(X2293),X2290),X2289))),c_List_Olex(X2293,X2288))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lex])])])). 4.05/4.29 fof(c_0_5080, plain, ![X1581, X1582, X1583, X1584, X1585, X1586]:(((X1585!=X1583|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1586),tc_List_Olist(X1586))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1586),tc_List_Olist(X1586)),X1584),X1582)),c_List_Olexord(X1586,X1581)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1586),tc_List_Olist(X1586))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1586),tc_List_Olist(X1586)),hAPP(hAPP(c_List_Olist_OCons(X1586),X1585),X1584)),hAPP(hAPP(c_List_Olist_OCons(X1586),X1583),X1582))),c_List_Olexord(X1586,X1581))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X1586,X1586)),hAPP(hAPP(c_Product__Type_OPair(X1586,X1586),X1585),X1583)),X1581))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1586),tc_List_Olist(X1586))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1586),tc_List_Olist(X1586)),hAPP(hAPP(c_List_Olist_OCons(X1586),X1585),X1584)),hAPP(hAPP(c_List_Olist_OCons(X1586),X1583),X1582))),c_List_Olexord(X1586,X1581)))))&((X1585=X1583|hBOOL(hAPP(hAPP(c_member(tc_prod(X1586,X1586)),hAPP(hAPP(c_Product__Type_OPair(X1586,X1586),X1585),X1583)),X1581))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1586),tc_List_Olist(X1586))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1586),tc_List_Olist(X1586)),hAPP(hAPP(c_List_Olist_OCons(X1586),X1585),X1584)),hAPP(hAPP(c_List_Olist_OCons(X1586),X1583),X1582))),c_List_Olexord(X1586,X1581))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1586),tc_List_Olist(X1586))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1586),tc_List_Olist(X1586)),X1584),X1582)),c_List_Olexord(X1586,X1581)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1586,X1586)),hAPP(hAPP(c_Product__Type_OPair(X1586,X1586),X1585),X1583)),X1581))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1586),tc_List_Olist(X1586))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1586),tc_List_Olist(X1586)),hAPP(hAPP(c_List_Olist_OCons(X1586),X1585),X1584)),hAPP(hAPP(c_List_Olist_OCons(X1586),X1583),X1582))),c_List_Olexord(X1586,X1581)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__cons__cons])])])). 4.05/4.29 cnf(c_0_5081, 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_4611])). 4.05/4.29 fof(c_0_5082, plain, ![X7345, X7346, X7347, X7348]:((hBOOL(hAPP(hAPP(c_member(X7348),esk230_4(X7345,X7346,X7347,X7348)),hAPP(c_List_Oset(X7348),X7347)))|c_List_OdropWhile(X7348,X7346,X7345)=c_List_OdropWhile(X7348,X7346,hAPP(hAPP(c_List_Oappend(X7348),X7347),X7345)))&(~hBOOL(hAPP(X7346,esk230_4(X7345,X7346,X7347,X7348)))|c_List_OdropWhile(X7348,X7346,X7345)=c_List_OdropWhile(X7348,X7346,hAPP(hAPP(c_List_Oappend(X7348),X7347),X7345)))), 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])])])])])). 4.05/4.29 fof(c_0_5083, plain, ![X10535, X10536]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10536))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10536),X10535))|c_Divides_Odivmod__nat(X10535,X10536)=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),X10535),X10536)),X10536))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10535),X10536),X10536)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__nat__step])])])). 4.05/4.29 fof(c_0_5084, plain, ![X13600, X13601, X13602]:((((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),X13600)),X13601)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600))=X13602|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X13602,X13601),X13600)))&(X13601!=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),X13600)|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X13602,X13601),X13600))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13601),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13601))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X13601|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X13602,X13601),X13600)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600)),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)),X13601))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X13601|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X13602,X13601),X13600))))&((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),X13600)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13601))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X13601|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X13602,X13601),X13600)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600)),X13601))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13601))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X13601|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X13602,X13601),X13600))))))&(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X13601|(X13601=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),X13600)),X13601)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600))!=X13602)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X13602,X13601),X13600)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13601))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13601))|(X13601=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),X13600)),X13601)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600))!=X13602)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X13602,X13601),X13600)))&(~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),X13600)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600)),X13601))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13601))|(X13601=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),X13600)),X13601)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600))!=X13602)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X13602,X13601),X13600))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13601))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13601),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|(X13601=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),X13600)),X13601)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600))!=X13602)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X13602,X13601),X13600)))&(~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),X13600)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600)),X13601))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13601),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|(X13601=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),X13600)),X13601)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600))!=X13602)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X13602,X13601),X13600))))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X13601|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X13600)|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),X13600)),X13601)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600))!=X13602)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X13602,X13601),X13600)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13601))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13601))|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X13600)|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),X13600)),X13601)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600))!=X13602)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X13602,X13601),X13600)))&(~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),X13600)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600)),X13601))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13601))|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X13600)|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),X13600)),X13601)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600))!=X13602)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X13602,X13601),X13600))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13601))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13601),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600)),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),X13600)|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),X13600)),X13601)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600))!=X13602)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X13602,X13601),X13600)))&(~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),X13600)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600)),X13601))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13601),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600)),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),X13600)|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),X13600)),X13601)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X13600))!=X13602)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X13602,X13601),X13600)))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__nat__rel__def])])])])). 4.05/4.29 fof(c_0_5085, plain, ![X2164]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2164)), inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J])). 4.05/4.29 fof(c_0_5086, plain, ![X6121, X6122, X6123, X6124]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6124),tc_List_Olist(X6124))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6124),tc_List_Olist(X6124)),X6123),X6122)),c_List_Olexord(X6124,X6121)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6124)),X6123)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6124)),X6122)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6124),tc_List_Olist(X6124))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6124),tc_List_Olist(X6124)),X6123),X6122)),c_List_Olex(X6124,X6121))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6124),tc_List_Olist(X6124))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6124),tc_List_Olist(X6124)),X6123),X6122)),c_List_Olexord(X6124,X6121)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6124),tc_List_Olist(X6124))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6124),tc_List_Olist(X6124)),X6123),X6122)),c_List_Olex(X6124,X6121))))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6124)),X6123)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6124)),X6122)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6124),tc_List_Olist(X6124))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6124),tc_List_Olist(X6124)),X6123),X6122)),c_List_Olex(X6124,X6121)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__lex])])])). 4.05/4.29 fof(c_0_5087, plain, ![X9439, X9440, X9441, X9442, X9443]:((((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9442)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9440)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9442)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9440)))|hAPP(hAPP(c_List_Oappend(X9443),X9440),X9439)=hAPP(hAPP(c_List_Oappend(X9443),X9442),X9441))&(hAPP(hAPP(c_List_Oappend(X9443),hAPP(hAPP(c_List_Odrop(X9443),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9440)),X9442)),X9441)!=X9439|X9440!=hAPP(hAPP(c_List_Otake(X9443),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9440)),X9442)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9442)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9440)))|hAPP(hAPP(c_List_Oappend(X9443),X9440),X9439)=hAPP(hAPP(c_List_Oappend(X9443),X9442),X9441)))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9442)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9440)))|(X9441!=hAPP(hAPP(c_List_Oappend(X9443),hAPP(hAPP(c_List_Odrop(X9443),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9442)),X9440)),X9439)|hAPP(hAPP(c_List_Otake(X9443),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9442)),X9440)!=X9442)|hAPP(hAPP(c_List_Oappend(X9443),X9440),X9439)=hAPP(hAPP(c_List_Oappend(X9443),X9442),X9441))&(hAPP(hAPP(c_List_Oappend(X9443),hAPP(hAPP(c_List_Odrop(X9443),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9440)),X9442)),X9441)!=X9439|X9440!=hAPP(hAPP(c_List_Otake(X9443),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9440)),X9442)|(X9441!=hAPP(hAPP(c_List_Oappend(X9443),hAPP(hAPP(c_List_Odrop(X9443),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9442)),X9440)),X9439)|hAPP(hAPP(c_List_Otake(X9443),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9442)),X9440)!=X9442)|hAPP(hAPP(c_List_Oappend(X9443),X9440),X9439)=hAPP(hAPP(c_List_Oappend(X9443),X9442),X9441))))&(((X9441=hAPP(hAPP(c_List_Oappend(X9443),hAPP(hAPP(c_List_Odrop(X9443),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9442)),X9440)),X9439)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9442)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9440)))|hAPP(hAPP(c_List_Oappend(X9443),X9440),X9439)!=hAPP(hAPP(c_List_Oappend(X9443),X9442),X9441))&(hAPP(hAPP(c_List_Otake(X9443),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9442)),X9440)=X9442|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9442)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9440)))|hAPP(hAPP(c_List_Oappend(X9443),X9440),X9439)!=hAPP(hAPP(c_List_Oappend(X9443),X9442),X9441)))&((hAPP(hAPP(c_List_Oappend(X9443),hAPP(hAPP(c_List_Odrop(X9443),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9440)),X9442)),X9441)=X9439|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9442)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9440)))|hAPP(hAPP(c_List_Oappend(X9443),X9440),X9439)!=hAPP(hAPP(c_List_Oappend(X9443),X9442),X9441))&(X9440=hAPP(hAPP(c_List_Otake(X9443),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9440)),X9442)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9442)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9443)),X9440)))|hAPP(hAPP(c_List_Oappend(X9443),X9440),X9439)!=hAPP(hAPP(c_List_Oappend(X9443),X9442),X9441))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_append__eq__append__conv__if])])])])). 4.05/4.29 cnf(c_0_5088, 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_4566])). 4.05/4.29 fof(c_0_5089, plain, ![X15593, X15594, X15595, X15596, X15597, X15598, X15599]:(~c_Fun_Oinj__on(X15599,X15598,X15597,hAPP(c_Set_Oimage(X15596,X15599,X15595),X15594))|(~c_Fun_Oinj__on(X15596,X15599,X15595,X15594)|(~hBOOL(hAPP(hAPP(c_member(X15598),X15593),hAPP(c_Set_Oimage(X15599,X15598,X15597),hAPP(c_Set_Oimage(X15596,X15599,X15595),X15594))))|hAPP(c_Fun_Othe__inv__into(X15596,X15598,X15594,hAPP(c_Fun_Ocomp(X15599,X15598,X15596,X15597),X15595)),X15593)=hAPP(hAPP(c_Fun_Ocomp(X15599,X15596,X15598,c_Fun_Othe__inv__into(X15596,X15599,X15594,X15595)),c_Fun_Othe__inv__into(X15599,X15598,hAPP(c_Set_Oimage(X15596,X15599,X15595),X15594),X15597)),X15593)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_the__inv__into__comp])])])). 4.05/4.29 fof(c_0_5090, plain, ![X5480, X5481, X5482, X5483]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X5483),hAPP(c_Set_OCollect(X5483),hAPP(hAPP(c_COMBS(X5483,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5483),c_fconj),hAPP(hAPP(c_COMBC(X5483,tc_fun(X5483,tc_HOL_Obool),tc_HOL_Obool),c_member(X5483)),X5482))),hAPP(hAPP(c_COMBC(X5483,X5481,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5481,tc_fun(X5481,tc_HOL_Obool),X5483),c_fequal),X5480)),hAPP(X5480,esk172_4(X5480,X5481,X5482,X5483)))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5481),hAPP(c_Set_Oimage(X5483,X5481,X5480),X5482)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X5483),X5482)))&(hBOOL(hAPP(hAPP(c_member(X5483),esk172_4(X5480,X5481,X5482,X5483)),X5482))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5481),hAPP(c_Set_Oimage(X5483,X5481,X5480),X5482)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X5483),X5482)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pigeonhole__infinite])])])])])). 4.05/4.29 cnf(c_0_5091, plain, (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))))=hAPP(hAPP(c_List_Onth(X2),c_List_OdropWhile(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)),c_List_OdropWhile(X2,X3,X4))))), inference(split_conjunct,[status(thm)],[c_0_4612])). 4.05/4.29 fof(c_0_5092, plain, ![X9901, X9902, X9903]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9903)),X9901)),X9902)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9903)),hAPP(hAPP(c_List_Odrop(X9903),X9902),X9901)), inference(variable_rename,[status(thm)],[fact_length__drop])). 4.05/4.29 fof(c_0_5093, plain, ![X11739, X11740, X11741, X11742, X11743, X11744, X11745, X11746, X11747, X11748]:((((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11739),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(X11740!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11739),X11742)),X11743)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11743),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11739),X11743))|hBOOL(hAPP(X11741,X11742)))|~hBOOL(hAPP(X11741,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11740),X11739))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11739))|(X11740!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11739),X11744)),X11745)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11745),X11739))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11745))|hBOOL(hAPP(X11741,X11744)))|~hBOOL(hAPP(X11741,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11740),X11739)))))&(X11739!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(X11741,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X11741,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11740),X11739)))))&((((X11746=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)),X11746))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,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)),X11746))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746)))))&(((((X11746=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk363_3(X11746,X11747,X11748))),esk364_3(X11746,X11747,X11748))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk363_3(X11746,X11747,X11748))),esk364_3(X11746,X11747,X11748))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746)))))&((X11746=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X11746,X11747,X11748)),X11746))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X11746,X11747,X11748)),X11746))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))))&((X11746=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)),esk364_3(X11746,X11747,X11748)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,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)),esk364_3(X11746,X11747,X11748)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))))&((X11746=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(~hBOOL(hAPP(X11748,esk363_3(X11746,X11747,X11748)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X11748,esk363_3(X11746,X11747,X11748)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746)))))))&((((((X11746=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)),X11746))|X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk361_3(X11746,X11747,X11748))),esk362_3(X11746,X11747,X11748)))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,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)),X11746))|X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk361_3(X11746,X11747,X11748))),esk362_3(X11746,X11747,X11748)))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746)))))&(((((X11746=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk363_3(X11746,X11747,X11748))),esk364_3(X11746,X11747,X11748))|X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk361_3(X11746,X11747,X11748))),esk362_3(X11746,X11747,X11748)))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk363_3(X11746,X11747,X11748))),esk364_3(X11746,X11747,X11748))|X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk361_3(X11746,X11747,X11748))),esk362_3(X11746,X11747,X11748)))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746)))))&((X11746=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X11746,X11747,X11748)),X11746))|X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk361_3(X11746,X11747,X11748))),esk362_3(X11746,X11747,X11748)))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X11746,X11747,X11748)),X11746))|X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk361_3(X11746,X11747,X11748))),esk362_3(X11746,X11747,X11748)))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))))&((X11746=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)),esk364_3(X11746,X11747,X11748)))|X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk361_3(X11746,X11747,X11748))),esk362_3(X11746,X11747,X11748)))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,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)),esk364_3(X11746,X11747,X11748)))|X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk361_3(X11746,X11747,X11748))),esk362_3(X11746,X11747,X11748)))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))))&((X11746=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(~hBOOL(hAPP(X11748,esk363_3(X11746,X11747,X11748)))|X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk361_3(X11746,X11747,X11748))),esk362_3(X11746,X11747,X11748)))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X11748,esk363_3(X11746,X11747,X11748)))|X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk361_3(X11746,X11747,X11748))),esk362_3(X11746,X11747,X11748)))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746)))))))&(((X11746=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)),X11746))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_3(X11746,X11747,X11748)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,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)),X11746))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_3(X11746,X11747,X11748)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746)))))&(((((X11746=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk363_3(X11746,X11747,X11748))),esk364_3(X11746,X11747,X11748))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_3(X11746,X11747,X11748)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk363_3(X11746,X11747,X11748))),esk364_3(X11746,X11747,X11748))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_3(X11746,X11747,X11748)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746)))))&((X11746=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X11746,X11747,X11748)),X11746))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_3(X11746,X11747,X11748)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X11746,X11747,X11748)),X11746))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_3(X11746,X11747,X11748)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))))&((X11746=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)),esk364_3(X11746,X11747,X11748)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_3(X11746,X11747,X11748)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,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)),esk364_3(X11746,X11747,X11748)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_3(X11746,X11747,X11748)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))))&((X11746=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(~hBOOL(hAPP(X11748,esk363_3(X11746,X11747,X11748)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_3(X11746,X11747,X11748)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X11748,esk363_3(X11746,X11747,X11748)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_3(X11746,X11747,X11748)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))))))&(((X11746=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)),X11746))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),esk362_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,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)),X11746))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),esk362_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746)))))&(((((X11746=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk363_3(X11746,X11747,X11748))),esk364_3(X11746,X11747,X11748))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),esk362_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk363_3(X11746,X11747,X11748))),esk364_3(X11746,X11747,X11748))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),esk362_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746)))))&((X11746=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X11746,X11747,X11748)),X11746))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),esk362_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X11746,X11747,X11748)),X11746))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),esk362_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))))&((X11746=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)),esk364_3(X11746,X11747,X11748)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),esk362_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,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)),esk364_3(X11746,X11747,X11748)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),esk362_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))))&((X11746=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(~hBOOL(hAPP(X11748,esk363_3(X11746,X11747,X11748)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),esk362_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X11748,esk363_3(X11746,X11747,X11748)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11746),esk362_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))))))&(((X11746=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)),X11746))|~hBOOL(hAPP(X11748,esk361_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,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)),X11746))|~hBOOL(hAPP(X11748,esk361_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746)))))&(((((X11746=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk363_3(X11746,X11747,X11748))),esk364_3(X11746,X11747,X11748))|~hBOOL(hAPP(X11748,esk361_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(X11747=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11746),esk363_3(X11746,X11747,X11748))),esk364_3(X11746,X11747,X11748))|~hBOOL(hAPP(X11748,esk361_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746)))))&((X11746=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X11746,X11747,X11748)),X11746))|~hBOOL(hAPP(X11748,esk361_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X11746,X11747,X11748)),X11746))|~hBOOL(hAPP(X11748,esk361_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))))&((X11746=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)),esk364_3(X11746,X11747,X11748)))|~hBOOL(hAPP(X11748,esk361_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,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)),esk364_3(X11746,X11747,X11748)))|~hBOOL(hAPP(X11748,esk361_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))))&((X11746=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|(~hBOOL(hAPP(X11748,esk363_3(X11746,X11747,X11748)))|~hBOOL(hAPP(X11748,esk361_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746))))&(~hBOOL(hAPP(X11748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(X11748,esk363_3(X11746,X11747,X11748)))|~hBOOL(hAPP(X11748,esk361_3(X11746,X11747,X11748))))|hBOOL(hAPP(X11748,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11747),X11746)))))))))), 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])])])])])])])). 4.05/4.29 cnf(c_0_5094, 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_4613])). 4.05/4.29 cnf(c_0_5095, 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_4614])). 4.05/4.29 fof(c_0_5096, plain, ![X11470, X11471, X11472, X11473, X11474, X11475, X11476, X11477, X11478, X11479]:((((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X11470|hBOOL(hAPP(X11472,X11471))|~hBOOL(hAPP(X11472,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11471,X11470))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11470),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11470),X11474))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11474),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),X11470),X11473)),X11474)!=X11471|hBOOL(hAPP(X11472,X11474)))|~hBOOL(hAPP(X11472,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11471,X11470)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11470))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11476),X11470))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11470),X11475)),X11476)!=X11471|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11476))|hBOOL(hAPP(X11472,X11476)))|~hBOOL(hAPP(X11472,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11471,X11470)))))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11477))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X11477,X11478,X11479)),X11477))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk354_3(X11477,X11478,X11479))),esk355_3(X11477,X11478,X11479))=X11478|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X11477,X11478,X11479)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(~hBOOL(hAPP(X11479,esk355_3(X11477,X11478,X11479)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))))&(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11477))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),esk353_3(X11477,X11478,X11479)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X11477,X11478,X11479)),X11477))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),esk353_3(X11477,X11478,X11479)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk354_3(X11477,X11478,X11479))),esk355_3(X11477,X11478,X11479))=X11478|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),esk353_3(X11477,X11478,X11479)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X11477,X11478,X11479)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),esk353_3(X11477,X11478,X11479)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(~hBOOL(hAPP(X11479,esk355_3(X11477,X11478,X11479)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),esk353_3(X11477,X11478,X11479)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11477))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_3(X11477,X11478,X11479)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X11477,X11478,X11479)),X11477))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_3(X11477,X11478,X11479)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk354_3(X11477,X11478,X11479))),esk355_3(X11477,X11478,X11479))=X11478|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_3(X11477,X11478,X11479)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X11477,X11478,X11479)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_3(X11477,X11478,X11479)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(~hBOOL(hAPP(X11479,esk355_3(X11477,X11478,X11479)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_3(X11477,X11478,X11479)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11477))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk352_3(X11477,X11478,X11479))),esk353_3(X11477,X11478,X11479))=X11478|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X11477,X11478,X11479)),X11477))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk352_3(X11477,X11478,X11479))),esk353_3(X11477,X11478,X11479))=X11478|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk354_3(X11477,X11478,X11479))),esk355_3(X11477,X11478,X11479))=X11478|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk352_3(X11477,X11478,X11479))),esk353_3(X11477,X11478,X11479))=X11478|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X11477,X11478,X11479)))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk352_3(X11477,X11478,X11479))),esk353_3(X11477,X11478,X11479))=X11478|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(~hBOOL(hAPP(X11479,esk355_3(X11477,X11478,X11479)))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk352_3(X11477,X11478,X11479))),esk353_3(X11477,X11478,X11479))=X11478|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11477))|(~hBOOL(hAPP(X11479,esk353_3(X11477,X11478,X11479)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X11477,X11478,X11479)),X11477))|(~hBOOL(hAPP(X11479,esk353_3(X11477,X11478,X11479)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk354_3(X11477,X11478,X11479))),esk355_3(X11477,X11478,X11479))=X11478|(~hBOOL(hAPP(X11479,esk353_3(X11477,X11478,X11479)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X11477,X11478,X11479)))|(~hBOOL(hAPP(X11479,esk353_3(X11477,X11478,X11479)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(~hBOOL(hAPP(X11479,esk355_3(X11477,X11478,X11479)))|(~hBOOL(hAPP(X11479,esk353_3(X11477,X11478,X11479)))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X11477)|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11477))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X11477,X11478,X11479)),X11477))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk354_3(X11477,X11478,X11479))),esk355_3(X11477,X11478,X11479))=X11478|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X11477,X11478,X11479)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(~hBOOL(hAPP(X11479,esk355_3(X11477,X11478,X11479)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))))&(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11477))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),esk353_3(X11477,X11478,X11479)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X11477,X11478,X11479)),X11477))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),esk353_3(X11477,X11478,X11479)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk354_3(X11477,X11478,X11479))),esk355_3(X11477,X11478,X11479))=X11478|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),esk353_3(X11477,X11478,X11479)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X11477,X11478,X11479)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),esk353_3(X11477,X11478,X11479)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(~hBOOL(hAPP(X11479,esk355_3(X11477,X11478,X11479)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11477),esk353_3(X11477,X11478,X11479)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11477))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_3(X11477,X11478,X11479)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X11477,X11478,X11479)),X11477))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_3(X11477,X11478,X11479)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk354_3(X11477,X11478,X11479))),esk355_3(X11477,X11478,X11479))=X11478|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_3(X11477,X11478,X11479)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X11477,X11478,X11479)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_3(X11477,X11478,X11479)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(~hBOOL(hAPP(X11479,esk355_3(X11477,X11478,X11479)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_3(X11477,X11478,X11479)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11477))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk352_3(X11477,X11478,X11479))),esk353_3(X11477,X11478,X11479))=X11478|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X11477,X11478,X11479)),X11477))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk352_3(X11477,X11478,X11479))),esk353_3(X11477,X11478,X11479))=X11478|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk354_3(X11477,X11478,X11479))),esk355_3(X11477,X11478,X11479))=X11478|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk352_3(X11477,X11478,X11479))),esk353_3(X11477,X11478,X11479))=X11478|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X11477,X11478,X11479)))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk352_3(X11477,X11478,X11479))),esk353_3(X11477,X11478,X11479))=X11478|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(~hBOOL(hAPP(X11479,esk355_3(X11477,X11478,X11479)))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk352_3(X11477,X11478,X11479))),esk353_3(X11477,X11478,X11479))=X11478|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11477))|(~hBOOL(hAPP(X11479,esk353_3(X11477,X11478,X11479)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X11477,X11478,X11479)),X11477))|(~hBOOL(hAPP(X11479,esk353_3(X11477,X11478,X11479)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477))))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11477),esk354_3(X11477,X11478,X11479))),esk355_3(X11477,X11478,X11479))=X11478|(~hBOOL(hAPP(X11479,esk353_3(X11477,X11478,X11479)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X11477,X11478,X11479)))|(~hBOOL(hAPP(X11479,esk353_3(X11477,X11478,X11479)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))&(~hBOOL(hAPP(X11479,esk355_3(X11477,X11478,X11479)))|(~hBOOL(hAPP(X11479,esk353_3(X11477,X11478,X11479)))|~hBOOL(hAPP(X11479,X11478)))|hBOOL(hAPP(X11479,c_Divides_Odiv__class_Omod(tc_Int_Oint,X11478,X11477)))))))))), 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])])])])])])])). 4.05/4.29 fof(c_0_5097, plain, ![X1950, X1951, X1954, X1956]:(((~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1954),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1951)))|~hBOOL(hAPP(X1950,X1954))|hBOOL(hAPP(X1950,esk72_2(X1950,X1951)))|(~hBOOL(hAPP(X1950,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1950,X1951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk71_2(X1950,X1951)),X1951))))|~hBOOL(hAPP(X1950,esk70_2(X1950,X1951))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1951)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk73_2(X1950,X1951)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1951)))|~hBOOL(hAPP(X1950,X1956))|(~hBOOL(hAPP(X1950,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1950,X1951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk71_2(X1950,X1951)),X1951))))|~hBOOL(hAPP(X1950,esk70_2(X1950,X1951))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1951)))&(hBOOL(hAPP(X1950,esk73_2(X1950,X1951)))|~hBOOL(hAPP(X1950,X1956))|(~hBOOL(hAPP(X1950,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1950,X1951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk71_2(X1950,X1951)),X1951))))|~hBOOL(hAPP(X1950,esk70_2(X1950,X1951))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1951)))))&((~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1954),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1951)))|~hBOOL(hAPP(X1950,X1954))|hBOOL(hAPP(X1950,esk72_2(X1950,X1951)))|(hBOOL(hAPP(X1950,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1950,X1951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk71_2(X1950,X1951)),X1951))))|hBOOL(hAPP(X1950,esk70_2(X1950,X1951))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1951)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk73_2(X1950,X1951)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1951)))|~hBOOL(hAPP(X1950,X1956))|(hBOOL(hAPP(X1950,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1950,X1951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk71_2(X1950,X1951)),X1951))))|hBOOL(hAPP(X1950,esk70_2(X1950,X1951))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1951)))&(hBOOL(hAPP(X1950,esk73_2(X1950,X1951)))|~hBOOL(hAPP(X1950,X1956))|(hBOOL(hAPP(X1950,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1950,X1951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk71_2(X1950,X1951)),X1951))))|hBOOL(hAPP(X1950,esk70_2(X1950,X1951))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1951)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_periodic__finite__ex])])])])])). 4.05/4.29 fof(c_0_5098, plain, ![X14712, X14713]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14713),X14712)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14712),X14713), inference(variable_rename,[status(thm)],[fact_zmult__commute])). 4.05/4.29 cnf(c_0_5099, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4615])). 4.05/4.29 cnf(c_0_5100, 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_4616])). 4.05/4.29 cnf(c_0_5101, 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_4617])). 4.05/4.29 fof(c_0_5102, plain, ![X1358, X1359, X1360]:((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),esk38_3(X1358,X1359,X1360)),esk39_3(X1358,X1359,X1360))))|hBOOL(hAPP(hAPP(X1358,X1360),X1359))|~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),X1360),X1359))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk38_3(X1358,X1359,X1360)),esk39_3(X1358,X1359,X1360)))|hBOOL(hAPP(hAPP(X1358,esk38_3(X1358,X1359,X1360)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk39_3(X1358,X1359,X1360)),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(hAPP(X1358,X1360),X1359))|~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),X1360),X1359))))&(~hBOOL(hAPP(hAPP(X1358,esk38_3(X1358,X1359,X1360)),esk39_3(X1358,X1359,X1360)))|hBOOL(hAPP(hAPP(X1358,X1360),X1359))|~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),X1360),X1359)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_small__lazy_H_Opinduct])])])])])). 4.05/4.29 fof(c_0_5103, plain, ![X13574, X13575, X13576, X13577, X13578, X13579, X13580, X13581]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13580),X13578),esk419_8(X13574,X13575,X13576,X13577,X13578,X13579,X13580,X13581)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13580,X13581),X13574),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13580,X13578),X13576))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13580,X13581),X13575),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13580,X13579),X13577))|X13577!=X13576|X13579!=X13578|(~class_Orderings_Oord(X13580)|~class_Groups_Ocomm__monoid__add(X13581)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13580),esk419_8(X13574,X13575,X13576,X13577,X13578,X13579,X13580,X13581)),X13576))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13580,X13581),X13574),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13580,X13578),X13576))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13580,X13581),X13575),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13580,X13579),X13577))|X13577!=X13576|X13579!=X13578|(~class_Orderings_Oord(X13580)|~class_Groups_Ocomm__monoid__add(X13581)))&(hAPP(X13575,esk419_8(X13574,X13575,X13576,X13577,X13578,X13579,X13580,X13581))!=hAPP(X13574,esk419_8(X13574,X13575,X13576,X13577,X13578,X13579,X13580,X13581))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13580,X13581),X13574),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13580,X13578),X13576))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13580,X13581),X13575),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13580,X13579),X13577))|X13577!=X13576|X13579!=X13578|(~class_Orderings_Oord(X13580)|~class_Groups_Ocomm__monoid__add(X13581))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__ivl__cong])])])])])). 4.05/4.29 fof(c_0_5104, plain, ![X7360, X7361, X7362, X7363]:(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7363),esk232_4(X7360,X7361,X7362,X7363)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7360),hAPP(X7361,X7362)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X7361,X7363)),X7360))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7363),X7362))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk231_4(X7360,X7361,X7362,X7363)),X7362)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk232_4(X7360,X7361,X7362,X7363)),X7362))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7360),hAPP(X7361,X7362)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X7361,X7363)),X7360))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7363),X7362))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk231_4(X7360,X7361,X7362,X7363)),X7362))))&(X7360=hAPP(X7361,esk232_4(X7360,X7361,X7362,X7363))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7360),hAPP(X7361,X7362)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X7361,X7363)),X7360))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7363),X7362))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk231_4(X7360,X7361,X7362,X7363)),X7362))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7363),esk232_4(X7360,X7361,X7362,X7363)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7360),hAPP(X7361,X7362)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X7361,X7363)),X7360))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7363),X7362))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7363),esk231_4(X7360,X7361,X7362,X7363))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk232_4(X7360,X7361,X7362,X7363)),X7362))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7360),hAPP(X7361,X7362)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X7361,X7363)),X7360))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7363),X7362))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7363),esk231_4(X7360,X7361,X7362,X7363)))))&(X7360=hAPP(X7361,esk232_4(X7360,X7361,X7362,X7363))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7360),hAPP(X7361,X7362)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X7361,X7363)),X7360))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7363),X7362))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7363),esk231_4(X7360,X7361,X7362,X7363))))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7363),esk232_4(X7360,X7361,X7362,X7363)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7360),hAPP(X7361,X7362)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X7361,X7363)),X7360))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7363),X7362))|~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(X7361,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk231_4(X7360,X7361,X7362,X7363)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X7361,esk231_4(X7360,X7361,X7362,X7363))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk232_4(X7360,X7361,X7362,X7363)),X7362))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7360),hAPP(X7361,X7362)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X7361,X7363)),X7360))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7363),X7362))|~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(X7361,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk231_4(X7360,X7361,X7362,X7363)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X7361,esk231_4(X7360,X7361,X7362,X7363))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))))&(X7360=hAPP(X7361,esk232_4(X7360,X7361,X7362,X7363))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7360),hAPP(X7361,X7362)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X7361,X7363)),X7360))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7363),X7362))|~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(X7361,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk231_4(X7360,X7361,X7362,X7363)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X7361,esk231_4(X7360,X7361,X7362,X7363))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__intermed__int__val])])])])])). 4.05/4.29 cnf(c_0_5105, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(X2))=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))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4618])). 4.05/4.29 cnf(c_0_5106, 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_fdisj),X2)),X3))=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))), inference(split_conjunct,[status(thm)],[c_0_4619])). 4.05/4.29 fof(c_0_5107, plain, ![X5269, X5270, X5271, X5272, X5273, X5276, X5277, X5278, X5279, X5280, X5281, X5282, X5283]:(((((X5271=hAPP(hAPP(c_List_Oappend(X5273),esk163_5(X5269,X5270,X5271,X5272,X5273)),hAPP(hAPP(c_List_Olist_OCons(X5273),X5270),esk164_5(X5269,X5270,X5271,X5272,X5273)))|hAPP(c_List_Ofilter(X5273,X5272),X5271)!=hAPP(hAPP(c_List_Olist_OCons(X5273),X5270),X5269))&(hBOOL(hAPP(X5272,X5270))|hAPP(c_List_Ofilter(X5273,X5272),X5271)!=hAPP(hAPP(c_List_Olist_OCons(X5273),X5270),X5269)))&(hAPP(c_List_Ofilter(X5273,X5272),esk164_5(X5269,X5270,X5271,X5272,X5273))=X5269|hAPP(c_List_Ofilter(X5273,X5272),X5271)!=hAPP(hAPP(c_List_Olist_OCons(X5273),X5270),X5269)))&(~hBOOL(hAPP(hAPP(c_member(X5273),X5276),hAPP(c_List_Oset(X5273),esk163_5(X5269,X5270,X5271,X5272,X5273))))|~hBOOL(hAPP(X5272,X5276))|hAPP(c_List_Ofilter(X5273,X5272),X5271)!=hAPP(hAPP(c_List_Olist_OCons(X5273),X5270),X5269)))&((hBOOL(hAPP(hAPP(c_member(X5281),esk165_6(X5277,X5278,X5279,X5280,X5281,X5282)),hAPP(c_List_Oset(X5281),X5282)))|(X5279!=hAPP(hAPP(c_List_Oappend(X5281),X5282),hAPP(hAPP(c_List_Olist_OCons(X5281),X5278),X5283))|~hBOOL(hAPP(X5280,X5278))|hAPP(c_List_Ofilter(X5281,X5280),X5283)!=X5277)|hAPP(c_List_Ofilter(X5281,X5280),X5279)=hAPP(hAPP(c_List_Olist_OCons(X5281),X5278),X5277))&(hBOOL(hAPP(X5280,esk165_6(X5277,X5278,X5279,X5280,X5281,X5282)))|(X5279!=hAPP(hAPP(c_List_Oappend(X5281),X5282),hAPP(hAPP(c_List_Olist_OCons(X5281),X5278),X5283))|~hBOOL(hAPP(X5280,X5278))|hAPP(c_List_Ofilter(X5281,X5280),X5283)!=X5277)|hAPP(c_List_Ofilter(X5281,X5280),X5279)=hAPP(hAPP(c_List_Olist_OCons(X5281),X5278),X5277)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__eq__Cons__iff])])])])])])])). 4.05/4.29 fof(c_0_5108, plain, ![X9333, X9334, X9335, X9336, X9337, X9338, X9339]:(hBOOL(hAPP(hAPP(c_member(X9339),X9338),hAPP(c_List_Oset(X9339),X9337)))|c_Map_Omap__upds(X9339,X9336,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X9339,tc_Option_Ooption(X9336)),X9335),X9338),hAPP(c_Option_Ooption_OSome(X9336),X9334)),X9337,X9333)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X9339,tc_Option_Ooption(X9336)),c_Map_Omap__upds(X9339,X9336,X9335,X9337,X9333)),X9338),hAPP(c_Option_Ooption_OSome(X9336),X9334))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__upds__twist])])])). 4.05/4.29 fof(c_0_5109, plain, ![X6440, X6441, X6442]:((hBOOL(hAPP(X6442,X6441))|hAPP(c_Set_OCollect(X6440),hAPP(hAPP(c_COMBS(X6440,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6440),c_fconj),hAPP(hAPP(c_COMBC(X6440,X6440,tc_HOL_Obool),c_fequal),X6441))),X6442))=c_Orderings_Obot__class_Obot(tc_fun(X6440,tc_HOL_Obool)))&(~hBOOL(hAPP(X6442,X6441))|hAPP(hAPP(c_Set_Oinsert(X6440),X6441),c_Orderings_Obot__class_Obot(tc_fun(X6440,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X6440),hAPP(hAPP(c_COMBS(X6440,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6440),c_fconj),hAPP(hAPP(c_COMBC(X6440,X6440,tc_HOL_Obool),c_fequal),X6441))),X6442)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Collect__conv__if])])])). 4.05/4.29 fof(c_0_5110, plain, ![X3837, X3838]:(~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X3838),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X3838))),X3837)))|c_List_OtakeWhile(tc_List_Olist(X3838),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X3838)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X3838),tc_List_Olist(X3838),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X3838))),X3837)=c_List_Otranspose(X3838,c_List_Otranspose(X3838,X3837))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__transpose])])). 4.05/4.29 cnf(c_0_5111, 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_4620])). 4.05/4.29 fof(c_0_5112, plain, ![X7544, X7545, X7546, X7547]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk239_4(X7544,X7545,X7546,X7547)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X7546)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7545),X7547))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7545),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7547),X7546))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7545),c_Groups_Oone__class_Oone(tc_Int_Oint))),X7544))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7546)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk240_4(X7544,X7545,X7546,X7547)),X7544))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7545),X7547))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7545),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7547),X7546))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7545),c_Groups_Oone__class_Oone(tc_Int_Oint))),X7544))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7546)))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk240_4(X7544,X7545,X7546,X7547)),esk239_4(X7544,X7545,X7546,X7547))=X7547|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7545),X7547))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7545),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7547),X7546))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7545),c_Groups_Oone__class_Oone(tc_Int_Oint))),X7544))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7546))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bset_I8_J])])])])])])). 4.05/4.29 fof(c_0_5113, plain, ![X11633, X11634, X11635, X11636]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11636),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11635)),X11634)))|hAPP(c_List_Orev(X11635),hAPP(hAPP(c_List_Olist__update(X11635,X11634),X11636),X11633))=hAPP(hAPP(c_List_Olist__update(X11635,hAPP(c_List_Orev(X11635),X11634)),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(X11635)),X11634)),X11636)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X11633)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__update])])). 4.05/4.29 fof(c_0_5114, plain, ![X9556, X9557, X9558]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9558),X9557)),X9556)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9558),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9557),X9556)), inference(variable_rename,[status(thm)],[fact_diff__diff__left])). 4.05/4.29 fof(c_0_5115, plain, ![X12662, X12663, X12664, X12665]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X12664),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12664),c_fNot),hAPP(hAPP(c_COMBS(X12664,X12665,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X12665,tc_fun(X12665,tc_HOL_Obool),X12664),c_fequal),X12663)),X12662))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12664,X12665)),X12663),X12662))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12664,X12665)),X12663),X12662))|(~class_Orderings_Oorder(X12665)|~class_Enum_Oenum(X12664)))&((hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X12664),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12664),c_fNot),hAPP(hAPP(c_COMBS(X12664,X12665,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X12665,tc_fun(X12665,tc_HOL_Obool),X12664),c_fequal),X12663)),X12662))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12664,X12665)),X12663),X12662))|(~class_Orderings_Oorder(X12665)|~class_Enum_Oenum(X12664)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12664,X12665)),X12663),X12662))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12664,X12665)),X12663),X12662))|(~class_Orderings_Oorder(X12665)|~class_Enum_Oenum(X12664))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__fun_I2_J])])])])). 4.05/4.29 fof(c_0_5116, plain, ![X3450, X3451, X3452]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3452),X3451))|c_List_Oupt(X3452,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3451),X3450))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X3452,X3451)),c_List_Oupt(X3451,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3451),X3450)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upt__add__eq__append])])])). 4.05/4.29 cnf(c_0_5117, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk187_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_4621])). 4.05/4.29 cnf(c_0_5118, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk185_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_4622])). 4.05/4.29 cnf(c_0_5119, 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_4623])). 4.05/4.29 fof(c_0_5120, plain, ![X14926, X14927, X14928, X14929, X14930]:((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X14930|hAPP(c_New__DSequence_Oneg__decr__bind(X14929,X14928,X14927,X14926),X14930)=c_Lazy__Sequence_Ohit__bound(X14928))&(X14930=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hAPP(c_New__DSequence_Oneg__decr__bind(X14929,X14928,X14927,X14926),X14930)=c_Lazy__Sequence_Ohb__bind(X14929,X14928,hAPP(X14927,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X14930),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X14929,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X14928))),X14926),X14930)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_New__DSequence_Oneg__decr__bind__def])])])). 4.05/4.29 fof(c_0_5121, plain, ![X6481, X6482, X6483, X6484]:c_Lazy__Sequence_Ohb__bind(X6484,X6483,X6482,X6481)=c_Lazy__Sequence_Ohb__flat(X6483,c_Lazy__Sequence_Ohb__map(X6484,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X6483)),X6481,X6482)), inference(variable_rename,[status(thm)],[fact_hb__bind__def])). 4.05/4.29 fof(c_0_5122, plain, ![X7446, X7447, X7448]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7446),X7447))|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)),X7448)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X7446),X7447))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7448),X7447)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7446),X7447))|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)),X7448)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X7446),X7447))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7448),X7447))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7448),X7447))|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7446),X7448)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7447),X7448))=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)),X7448)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X7446),X7447)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__minus__const__atLeastLessThan__nat])])])])). 4.05/4.29 fof(c_0_5123, plain, ![X17187, X17188, X17189]:((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),esk516_3(X17187,X17188,X17189)),esk517_3(X17187,X17188,X17189))))|hBOOL(hAPP(hAPP(X17187,X17189),X17188))|~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),X17189),X17188))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk516_3(X17187,X17188,X17189)),esk517_3(X17187,X17188,X17189)))|hBOOL(hAPP(hAPP(X17187,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk516_3(X17187,X17188,X17189)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk517_3(X17187,X17188,X17189)))|hBOOL(hAPP(hAPP(X17187,X17189),X17188))|~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),X17189),X17188))))&(~hBOOL(hAPP(hAPP(X17187,esk516_3(X17187,X17188,X17189)),esk517_3(X17187,X17188,X17189)))|hBOOL(hAPP(hAPP(X17187,X17189),X17188))|~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),X17189),X17188)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upto_Opinduct])])])])])). 4.05/4.29 fof(c_0_5124, plain, ![X15774, X15775]:(~c_Nat__Transfer_Onat__set(X15775)|(~c_Nat__Transfer_Onat__set(X15774)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X15775),X15774)=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),X15775)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X15774))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J])])])). 4.05/4.29 fof(c_0_5125, plain, ![X4965, X4966, X4967, X4968, X4969]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4968,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4969,X4968,X4967),X4966)),hAPP(c_Set_Oimage(X4969,X4968,X4967),X4965))=hAPP(c_Set_Oimage(X4969,X4968,X4967),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4969,tc_HOL_Obool)),X4966),X4965)), inference(variable_rename,[status(thm)],[fact_image__Un])). 4.05/4.29 fof(c_0_5126, plain, ![X998, X999, X1000, X1001, X1002, X1003]:hAPP(c_Set_Oimage(X1003,X1002,X1001),hAPP(c_Set_Oimage(X1000,X1003,X999),X998))=hAPP(c_Set_Oimage(X1000,X1002,hAPP(hAPP(c_COMBB(X1003,X1002,X1000),X1001),X999)),X998), inference(variable_rename,[status(thm)],[fact_image__image])). 4.05/4.29 fof(c_0_5127, plain, ![X1615, X1616, X1617, X1618, X1619]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1618),X1617)),X1615)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1619),X1617)),X1616)|X1616=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),X1618),X1619)),X1617)),X1615)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1619),X1618)))&(X1616!=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),X1618),X1619)),X1617)),X1615)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1618),X1617)),X1615)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1619),X1617)),X1616)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1619),X1618)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2])])])). 4.05/4.29 fof(c_0_5128, plain, ![X3932, X3933, X3934, X3935]: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),X3935),X3933)),X3934)),X3932)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3935),X3934)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3933),X3934)),X3932)), inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib])). 4.05/4.29 cnf(c_0_5129, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X2)), inference(split_conjunct,[status(thm)],[c_0_4624])). 4.05/4.29 cnf(c_0_5130, plain, (c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)=c_Orderings_Oord__class_Omax(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_sup__nat__def]), ['final']). 4.05/4.29 cnf(c_0_5131, 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_4625]), ['final']). 4.05/4.29 fof(c_0_5132, plain, ![X12940, X12941, X12942, X12943]:((hBOOL(hAPP(X12943,X12942))|c_List_OdropWhile(X12941,X12943,hAPP(hAPP(c_List_Olist_OCons(X12941),X12942),X12940))=hAPP(hAPP(c_List_Olist_OCons(X12941),X12942),X12940))&(~hBOOL(hAPP(X12943,X12942))|c_List_OdropWhile(X12941,X12943,X12940)=c_List_OdropWhile(X12941,X12943,hAPP(hAPP(c_List_Olist_OCons(X12941),X12942),X12940)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dropWhile_Osimps_I2_J])])])). 4.05/4.29 cnf(c_0_5133, 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_4626])). 4.05/4.29 cnf(c_0_5134, 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_4627])). 4.05/4.29 fof(c_0_5135, plain, ![X7065]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X7065|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7065)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7065))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X7065)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])])). 4.05/4.29 cnf(c_0_5136, 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_4628])). 4.05/4.29 cnf(c_0_5137, 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_4629])). 4.05/4.29 fof(c_0_5138, plain, ![X13632, X13633, X13634, X13635, X13636, X13637, X13638, X13640, X13641, X13642, X13643, X13644, X13647]:(((hBOOL(hAPP(hAPP(c_member(X13636),esk421_7(X13632,X13633,X13634,X13635,X13636,X13637,X13638)),hAPP(c_List_Oset(X13636),X13637)))|X13632!=hAPP(hAPP(c_List_Oappend(X13636),X13637),hAPP(hAPP(c_List_Olist_OCons(X13636),X13635),X13638))|~hBOOL(hAPP(X13633,X13635))|hAPP(c_List_Ofilter(X13636,X13633),X13638)!=X13634|hAPP(c_List_Ofilter(X13636,X13633),X13632)=hAPP(hAPP(c_List_Olist_OCons(X13636),X13635),X13634))&(hBOOL(hAPP(X13633,esk421_7(X13632,X13633,X13634,X13635,X13636,X13637,X13638)))|X13632!=hAPP(hAPP(c_List_Oappend(X13636),X13637),hAPP(hAPP(c_List_Olist_OCons(X13636),X13635),X13638))|~hBOOL(hAPP(X13633,X13635))|hAPP(c_List_Ofilter(X13636,X13633),X13638)!=X13634|hAPP(c_List_Ofilter(X13636,X13633),X13632)=hAPP(hAPP(c_List_Olist_OCons(X13636),X13635),X13634)))&((((X13640=hAPP(hAPP(c_List_Oappend(X13644),esk422_5(X13640,X13641,X13642,X13643,X13644)),hAPP(hAPP(c_List_Olist_OCons(X13644),X13643),esk423_5(X13640,X13641,X13642,X13643,X13644)))|hAPP(c_List_Ofilter(X13644,X13641),X13640)!=hAPP(hAPP(c_List_Olist_OCons(X13644),X13643),X13642))&(~hBOOL(hAPP(hAPP(c_member(X13644),X13647),hAPP(c_List_Oset(X13644),esk422_5(X13640,X13641,X13642,X13643,X13644))))|~hBOOL(hAPP(X13641,X13647))|hAPP(c_List_Ofilter(X13644,X13641),X13640)!=hAPP(hAPP(c_List_Olist_OCons(X13644),X13643),X13642)))&(hBOOL(hAPP(X13641,X13643))|hAPP(c_List_Ofilter(X13644,X13641),X13640)!=hAPP(hAPP(c_List_Olist_OCons(X13644),X13643),X13642)))&(hAPP(c_List_Ofilter(X13644,X13641),esk423_5(X13640,X13641,X13642,X13643,X13644))=X13642|hAPP(c_List_Ofilter(X13644,X13641),X13640)!=hAPP(hAPP(c_List_Olist_OCons(X13644),X13643),X13642)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Cons__eq__filter__iff])])])])])])])). 4.05/4.29 cnf(c_0_5139, 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_4630])). 4.05/4.29 cnf(c_0_5140, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(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)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4631])). 4.05/4.29 fof(c_0_5141, plain, ![X9707, X9708, X9709]:(((hAPP(X9708,esk296_3(X9707,X9708,X9709))=X9707|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9707),hAPP(X9708,X9709)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X9708,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X9707))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk295_3(X9707,X9708,X9709)),X9709)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk296_3(X9707,X9708,X9709)),X9709))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9707),hAPP(X9708,X9709)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X9708,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X9707))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk295_3(X9707,X9708,X9709)),X9709))))&((hAPP(X9708,esk296_3(X9707,X9708,X9709))=X9707|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9707),hAPP(X9708,X9709)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X9708,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X9707))|~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(X9708,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk295_3(X9707,X9708,X9709)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X9708,esk295_3(X9707,X9708,X9709))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk296_3(X9707,X9708,X9709)),X9709))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9707),hAPP(X9708,X9709)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X9708,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X9707))|~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(X9708,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk295_3(X9707,X9708,X9709)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X9708,esk295_3(X9707,X9708,X9709))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat0__intermed__int__val])])])])])). 4.05/4.29 fof(c_0_5142, plain, ![X2845, X2846, X2847]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk97_3(X2845,X2846,X2847)),X2847))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2845),hAPP(X2846,X2847)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2846,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2845))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk96_3(X2845,X2846,X2847)),X2847)))&(hAPP(X2846,esk97_3(X2845,X2846,X2847))=X2845|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2845),hAPP(X2846,X2847)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2846,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2845))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk96_3(X2845,X2846,X2847)),X2847))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk97_3(X2845,X2846,X2847)),X2847))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2845),hAPP(X2846,X2847)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2846,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2845))|~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(X2846,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk96_3(X2845,X2846,X2847)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2846,esk96_3(X2845,X2846,X2847))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))&(hAPP(X2846,esk97_3(X2845,X2846,X2847))=X2845|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2845),hAPP(X2846,X2847)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2846,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2845))|~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(X2846,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk96_3(X2845,X2846,X2847)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2846,esk96_3(X2845,X2846,X2847))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__val__lemma])])])])])). 4.05/4.29 fof(c_0_5143, plain, ![X5261, X5262, X5263, X5264, X5265, X5266]:((X5261!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5266),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5266),X5265),X5262)),X5264)),X5263)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5266),X5265),X5264)),X5263)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5266),X5262),X5264)),X5261)|~class_Rings_Oring(X5266))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5266),X5265),X5264)),X5263)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5266),X5262),X5264)),X5261)|X5261=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5266),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5266),X5265),X5262)),X5264)),X5263)|~class_Rings_Oring(X5266))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])])). 4.05/4.29 fof(c_0_5144, plain, ![X11844, X11845, X11846]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11846))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11844),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11845),X11844),X11846))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11845,X11844))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X11845,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11844),X11846))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zmult2__eq])])). 4.05/4.29 fof(c_0_5145, plain, ![X15475, X15476, X15477, X15478, X15479]:hAPP(hAPP(c_List_Otake(tc_prod(X15479,X15478)),X15477),hAPP(hAPP(c_List_Ozip(X15479,X15478),X15476),X15475))=hAPP(hAPP(c_List_Ozip(X15479,X15478),hAPP(hAPP(c_List_Otake(X15479),X15477),X15476)),hAPP(hAPP(c_List_Otake(X15478),X15477),X15475)), inference(variable_rename,[status(thm)],[fact_take__zip])). 4.05/4.29 cnf(c_0_5146, 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_4632])). 4.05/4.29 cnf(c_0_5147, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X1))), inference(split_conjunct,[status(thm)],[c_0_4633])). 4.05/4.29 cnf(c_0_5148, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I2_J])). 4.05/4.29 cnf(c_0_5149, plain, (hAPP(c_Int_Onat,X1)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)), inference(rw,[status(thm)],[c_0_4634, c_0_4635]), ['final']). 4.05/4.29 cnf(c_0_5150, 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_nat__number__of__Pls])). 4.05/4.29 fof(c_0_5151, plain, ![X14450, X14451, X14452, X14453]:(~class_Int_Onumber__ring(X14453)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14453),hAPP(c_Int_Onumber__class_Onumber__of(X14453),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X14452),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X14450)))),X14451)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14453),hAPP(c_Int_Onumber__class_Onumber__of(X14453),X14452)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X14453),X14451),hAPP(c_Int_Onumber__class_Onumber__of(X14453),X14450)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__number__of__diff2])])])). 4.05/4.29 cnf(c_0_5152, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk185_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_4622])). 4.05/4.29 cnf(c_0_5153, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk187_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_4621])). 4.05/4.29 fof(c_0_5154, plain, ![X7204, X7205, X7206, X7207]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7206),X7205))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7207),X7204),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X7205),hAPP(c_Nat_OSuc,X7206)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7207),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7207),X7204),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X7205),X7206))),hAPP(X7204,X7206))|~class_Groups_Ocomm__monoid__add(X7207))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7206),X7205))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7207),X7204),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X7205),hAPP(c_Nat_OSuc,X7206)))=c_Groups_Ozero__class_Ozero(X7207)|~class_Groups_Ocomm__monoid__add(X7207))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__op__ivl__Suc])])])])). 4.05/4.29 fof(c_0_5155, plain, ![X6510, X6511, X6512, X6515, X6516]:(((((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6512),esk197_3(X6510,X6511,X6512))),esk198_3(X6510,X6511,X6512))=X6510|hBOOL(hAPP(hAPP(X6511,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6510),X6512)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6510,X6512)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6512)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk198_3(X6510,X6511,X6512)),X6512))|hBOOL(hAPP(hAPP(X6511,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6510),X6512)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6510,X6512)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6512))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk198_3(X6510,X6511,X6512)))|hBOOL(hAPP(hAPP(X6511,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6510),X6512)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6510,X6512)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6512))))&(~hBOOL(hAPP(hAPP(X6511,esk197_3(X6510,X6511,X6512)),esk198_3(X6510,X6511,X6512)))|hBOOL(hAPP(hAPP(X6511,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6510),X6512)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6510,X6512)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6512))))&(~hBOOL(hAPP(hAPP(X6511,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6510),X6512)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6510,X6512)))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6512),X6515)),X6516)!=X6510|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6516),X6512))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6516))|hBOOL(hAPP(hAPP(X6511,X6515),X6516)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6512)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__pos__lemma])])])])])). 4.05/4.29 fof(c_0_5156, plain, ![X12043, X12044, X12045, X12046, X12047]:((~hBOOL(hAPP(hAPP(X12044,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12043),X12045)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12043,X12045)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12047),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X12043!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12045),X12046)),X12047)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12045),X12047))|hBOOL(hAPP(hAPP(X12044,X12046),X12047)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12045),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk377_3(X12043,X12044,X12045)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X12044,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12043),X12045)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12043,X12045)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12045),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&(X12043=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12045),esk376_3(X12043,X12044,X12045))),esk377_3(X12043,X12044,X12045))|hBOOL(hAPP(hAPP(X12044,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12043),X12045)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12043,X12045)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12045),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12045),esk377_3(X12043,X12044,X12045)))|hBOOL(hAPP(hAPP(X12044,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12043),X12045)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12043,X12045)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12045),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))&(~hBOOL(hAPP(hAPP(X12044,esk376_3(X12043,X12044,X12045)),esk377_3(X12043,X12044,X12045)))|hBOOL(hAPP(hAPP(X12044,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12043),X12045)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X12043,X12045)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12045),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])])])])])])). 4.05/4.29 fof(c_0_5157, plain, ![X16224, X16225, X16226]:(~hBOOL(hAPP(c_List_Odistinct(X16226),hAPP(hAPP(c_List_Omap(tc_prod(X16226,X16225),X16226),c_Product__Type_Ofst(X16226,X16225)),X16224)))|c_Map_Oran(X16226,X16225,hAPP(c_Map_Omap__of(X16226,X16225),X16224))=hAPP(c_Set_Oimage(tc_prod(X16226,X16225),X16225,c_Product__Type_Osnd(X16226,X16225)),hAPP(c_List_Oset(tc_prod(X16226,X16225)),X16224))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ran__distinct])])). 4.05/4.29 fof(c_0_5158, plain, ![X3686, X3687, X3688]:hAPP(c_Set_Oimage(tc_prod(X3688,X3687),X3687,c_Product__Type_Osnd(X3688,X3687)),X3686)=hAPP(c_Relation_ORange(X3688,X3687),X3686), inference(variable_rename,[status(thm)],[fact_snd__eq__Range])). 4.05/4.29 fof(c_0_5159, plain, ![X15792, X15793, X15794]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15794,X15794),tc_HOL_Obool)),c_Relation_OId(X15794)),X15793))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15794,X15794),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X15794,X15794,X15794),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X15794,X15794),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X15794,X15792)),X15793)),X15792)),X15793))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15794,X15794),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X15794,X15792)),X15793)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__Int__subset])])])). 4.05/4.29 fof(c_0_5160, plain, ![X13663, X13664, X13665, X13666, X13667]:(~class_Orderings_Olinorder(X13667)|(~c_Fun_Oinj__on(X13666,X13667,X13665,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13666,tc_HOL_Obool)),hAPP(c_List_Oset(X13666),X13664)),hAPP(c_List_Oset(X13666),X13663)))|(~c_List_Olinorder__class_Osorted(X13667,hAPP(hAPP(c_List_Omap(X13666,X13667),X13665),X13664))|(~hBOOL(hAPP(c_List_Odistinct(X13667),hAPP(hAPP(c_List_Omap(X13666,X13667),X13665),X13664)))|(~c_List_Olinorder__class_Osorted(X13667,hAPP(hAPP(c_List_Omap(X13666,X13667),X13665),X13663))|(~hBOOL(hAPP(c_List_Odistinct(X13667),hAPP(hAPP(c_List_Omap(X13666,X13667),X13665),X13663)))|(hAPP(c_List_Oset(X13666),X13663)!=hAPP(c_List_Oset(X13666),X13664)|X13664=X13663))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__sorted__distinct__set__unique])])])). 4.05/4.29 fof(c_0_5161, plain, ![X3467, X3468, X3469]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3469,tc_HOL_Obool)),hAPP(c_List_Oset(X3469),X3468)),hAPP(c_List_Oset(X3469),X3467))=hAPP(c_List_Oset(X3469),hAPP(hAPP(c_List_Oappend(X3469),X3468),X3467)), inference(variable_rename,[status(thm)],[fact_set__append])). 4.05/4.29 fof(c_0_5162, plain, ![X12870, X12871, X12872]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X12872)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12872)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12871)),X12870))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12871)),X12870))&((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X12871)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12872)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12871)),X12870))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12872)),X12870)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X12872))))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X12871)))|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),X12872),X12871))),X12870)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12872)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X12871)),X12870))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X12872)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__number__of__add__left])])])])). 4.05/4.29 fof(c_0_5163, plain, ![X12700]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X12700)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X12700)))))=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),X12700))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__neg__1__number__of])])). 4.05/4.29 cnf(c_0_5164, 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_4636])). 4.05/4.29 cnf(c_0_5165, 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_4637, c_0_4434]), ['final']). 4.05/4.29 fof(c_0_5166, plain, ![X1122, X1123]:hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1123),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1122))=hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1123),X1122)), inference(variable_rename,[status(thm)],[fact_negateSnd__eq])). 4.05/4.29 cnf(c_0_5167, 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_4638])). 4.05/4.29 fof(c_0_5168, plain, ![X9859, X9860, X9861]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9861))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9860),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),X9860),X9859))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X9861))),X9859))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_decr__lemma])])])). 4.05/4.29 fof(c_0_5169, plain, ![X7392, X7393, X7394, X7395, X7396]:(((X7394=hAPP(hAPP(c_List_Oappend(X7396),c_List_OtakeWhile(X7396,X7395,X7394)),hAPP(hAPP(c_List_Olist_OCons(X7396),X7393),X7392))|c_List_OdropWhile(X7396,X7395,X7394)!=hAPP(hAPP(c_List_Olist_OCons(X7396),X7393),X7392))&(~hBOOL(hAPP(X7395,X7393))|c_List_OdropWhile(X7396,X7395,X7394)!=hAPP(hAPP(c_List_Olist_OCons(X7396),X7393),X7392)))&(X7394!=hAPP(hAPP(c_List_Oappend(X7396),c_List_OtakeWhile(X7396,X7395,X7394)),hAPP(hAPP(c_List_Olist_OCons(X7396),X7393),X7392))|hBOOL(hAPP(X7395,X7393))|c_List_OdropWhile(X7396,X7395,X7394)=hAPP(hAPP(c_List_Olist_OCons(X7396),X7393),X7392))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dropWhile__eq__Cons__conv])])])])). 4.05/4.29 cnf(c_0_5170, 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_4639])). 4.05/4.29 fof(c_0_5171, plain, ![X1278, X1279, X1280]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1280))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1279),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1278),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),X1278),X1279))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1280))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incr__lemma])])). 4.05/4.29 fof(c_0_5172, plain, ![X7941, X7942, X7943, X7944]:((X7943!=X7942|~hBOOL(hAPP(hAPP(c_member(X7944),X7943),hAPP(c_List_Oset(X7944),X7941)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X7944,X7944)),hAPP(hAPP(c_Product__Type_OPair(X7944,X7944),X7943),X7942)),hAPP(c_List_Oset(tc_prod(X7944,X7944)),hAPP(hAPP(c_List_Ozip(X7944,X7944),X7941),X7941)))))&((X7943=X7942|~hBOOL(hAPP(hAPP(c_member(tc_prod(X7944,X7944)),hAPP(hAPP(c_Product__Type_OPair(X7944,X7944),X7943),X7942)),hAPP(c_List_Oset(tc_prod(X7944,X7944)),hAPP(hAPP(c_List_Ozip(X7944,X7944),X7941),X7941)))))&(hBOOL(hAPP(hAPP(c_member(X7944),X7943),hAPP(c_List_Oset(X7944),X7941)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X7944,X7944)),hAPP(hAPP(c_Product__Type_OPair(X7944,X7944),X7943),X7942)),hAPP(c_List_Oset(tc_prod(X7944,X7944)),hAPP(hAPP(c_List_Ozip(X7944,X7944),X7941),X7941))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__same])])])). 4.05/4.29 cnf(c_0_5173, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk125_2(X2,X1)),esk125_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))|c_Wellfounded_Oacyclic(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4640])). 4.05/4.29 cnf(c_0_5174, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk124_2(X2,X1)),esk124_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))|c_Wellfounded_Oacyclic(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4641])). 4.05/4.29 fof(c_0_5175, plain, ![X3703]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X3703)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X3703))=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),X3703)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__1__number__of])])). 4.05/4.29 cnf(c_0_5176, plain, (X1=X5|X1!=hAPP(c_Product__Type_Osnd(X2,X3),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_4642])). 4.05/4.29 cnf(c_0_5177, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk23_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_4639])). 4.05/4.29 fof(c_0_5178, plain, ![X547, X548]:(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X548))|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)),X548))),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,X547)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__less])])])). 4.05/4.29 cnf(c_0_5179, 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_4643])). 4.05/4.29 cnf(c_0_5180, 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_4644])). 4.05/4.29 fof(c_0_5181, plain, ![X5917, X5918]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5918),X5917))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5918,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X5918,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X5918,tc_HOL_Obool),tc_fun(X5918,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X5918,tc_HOL_Obool))),X5917))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__subsets])])). 4.05/4.29 fof(c_0_5182, plain, ![X13674, X13675, X13676]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13676),X13675)),X13674))|c_List_Oupt(X13676,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13676),X13675))=hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X13675),c_List_Oupt(X13676,X13674))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_take__upt])])])). 4.05/4.29 cnf(c_0_5183, 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)),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_4645])). 4.05/4.29 fof(c_0_5184, plain, ![X16327, X16328, X16329]:((hBOOL(hAPP(hAPP(c_member(X16329),esk488_3(X16327,X16328,X16329)),hAPP(c_List_Oset(X16329),c_List_OdropWhile(X16329,X16328,X16327))))|c_List_OtakeWhile(X16329,X16328,X16327)=hAPP(c_List_Ofilter(X16329,X16328),X16327))&(hBOOL(hAPP(X16328,esk488_3(X16327,X16328,X16329)))|c_List_OtakeWhile(X16329,X16328,X16327)=hAPP(c_List_Ofilter(X16329,X16328),X16327))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile__eq__filter])])])])])). 4.05/4.29 cnf(c_0_5185, 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_4646])). 4.05/4.29 fof(c_0_5186, plain, ![X662, X663, X664]:(X664=c_List_Olist_ONil(X663)|hAPP(hAPP(c_List_Onth(X663),X664),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X662,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X663)),X664)))=hAPP(c_List_Ohd(X663),hAPP(c_List_Orotate(X663,X662),X664))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__rotate__conv__nth])])). 4.05/4.29 cnf(c_0_5187, 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_4647])). 4.05/4.29 cnf(c_0_5188, 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_4648]), ['final']). 4.05/4.29 fof(c_0_5189, plain, ![X6426, X6427, X6428, X6429]:(hAPP(c_Map_Omap__of(X6429,X6428),X6426)!=hAPP(c_Map_Omap__of(X6429,X6428),X6427)|hAPP(c_Set_Oimage(tc_prod(X6429,X6428),X6429,c_Product__Type_Ofst(X6429,X6428)),hAPP(c_List_Oset(tc_prod(X6429,X6428)),X6427))=hAPP(c_Set_Oimage(tc_prod(X6429,X6428),X6429,c_Product__Type_Ofst(X6429,X6428)),hAPP(c_List_Oset(tc_prod(X6429,X6428)),X6426))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__eq__dom])])). 4.05/4.29 fof(c_0_5190, plain, ![X2920, X2921]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2921))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2920))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2920),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2921),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2920),X2921)),X2920))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__power__div__base])])])). 4.05/4.29 fof(c_0_5191, plain, ![X7640, X7641, X7642, X7643, X7644, X7645, X7646, X7647]:((hBOOL(hAPP(hAPP(c_member(X7646),esk245_8(X7640,X7641,X7642,X7643,X7644,X7645,X7646,X7647)),X7643))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7646,X7647),X7641),X7643)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7645,X7647),X7640),X7642)|hAPP(c_Set_Oimage(X7646,X7645,X7644),X7643)!=X7642|~c_Fun_Oinj__on(X7646,X7645,X7644,X7643)|~class_Groups_Ocomm__monoid__add(X7647))&(hAPP(X7641,esk245_8(X7640,X7641,X7642,X7643,X7644,X7645,X7646,X7647))!=hAPP(X7640,hAPP(X7644,esk245_8(X7640,X7641,X7642,X7643,X7644,X7645,X7646,X7647)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7646,X7647),X7641),X7643)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7645,X7647),X7640),X7642)|hAPP(c_Set_Oimage(X7646,X7645,X7644),X7643)!=X7642|~c_Fun_Oinj__on(X7646,X7645,X7644,X7643)|~class_Groups_Ocomm__monoid__add(X7647))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__reindex__cong])])])])])). 4.05/4.29 fof(c_0_5192, plain, ![X6004, X6005, X6006]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6006),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6005)),X6004)))|hAPP(c_Random_Opick(X6005,hAPP(hAPP(c_List_Omap(X6005,tc_prod(tc_Code__Numeral_Ocode__numeral,X6005)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X6005),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X6004)),hAPP(c_Code__Numeral_Oof__nat,X6006))=hAPP(hAPP(c_List_Onth(X6005),X6004),X6006)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pick__same])])])). 4.05/4.29 fof(c_0_5193, plain, ![X9212, X9213, X9214, X9215, X9216, X9217, X9218, X9219]:((hBOOL(hAPP(hAPP(c_member(X9218),esk286_8(X9212,X9213,X9214,X9215,X9216,X9217,X9218,X9219)),X9215))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9217,X9219),X9212),X9214)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9218,X9219),X9213),X9215)|X9214!=hAPP(c_Set_Oimage(X9218,X9217,X9216),X9215)|~c_Fun_Oinj__on(X9218,X9217,X9216,X9215)|~class_Groups_Ocomm__monoid__mult(X9219))&(hAPP(hAPP(c_Fun_Ocomp(X9217,X9219,X9218,X9212),X9216),esk286_8(X9212,X9213,X9214,X9215,X9216,X9217,X9218,X9219))!=hAPP(X9213,esk286_8(X9212,X9213,X9214,X9215,X9216,X9217,X9218,X9219))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9217,X9219),X9212),X9214)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9218,X9219),X9213),X9215)|X9214!=hAPP(c_Set_Oimage(X9218,X9217,X9216),X9215)|~c_Fun_Oinj__on(X9218,X9217,X9216,X9215)|~class_Groups_Ocomm__monoid__mult(X9219))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_strong__setprod__reindex__cong])])])])])). 4.05/4.29 fof(c_0_5194, plain, ![X16540, X16541, X16542, X16543]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16542))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16542))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X16542|X16541=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16543),X16542))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16542),X16541)),X16540)!=X16543)&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16540),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16542),X16540))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16542))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X16542|X16541=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16543),X16542))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16542),X16541)),X16540)!=X16543))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16542))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16540),X16542))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16540)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X16542|X16541=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16543),X16542))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16542),X16541)),X16540)!=X16543)&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16540),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16542),X16540))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16540),X16542))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16540)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X16542|X16541=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16543),X16542))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16542),X16541)),X16540)!=X16543))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__div__eq])])])])). 4.05/4.29 cnf(c_0_5195, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4649])). 4.05/4.29 cnf(c_0_5196, 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_4650])). 4.05/4.29 cnf(c_0_5197, 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_4651])). 4.05/4.29 cnf(c_0_5198, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1)))=c_Groups_Oone__class_Oone(X2)|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_4573])). 4.05/4.29 fof(c_0_5199, plain, ![X13806, X13807, X13808]:((X13807=c_List_Olist_ONil(X13808)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X13808),hAPP(hAPP(c_List_Onth(X13808),X13807),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X13806)=c_List_Ofoldr(X13808,X13808,c_Orderings_Oord__class_Omax(X13808),X13807,X13806)|~c_List_Olinorder__class_Osorted(X13808,hAPP(c_List_Orev(X13808),X13807))|~class_Orderings_Olinorder(X13808))&(X13807!=c_List_Olist_ONil(X13808)|X13806=c_List_Ofoldr(X13808,X13808,c_Orderings_Oord__class_Omax(X13808),X13807,X13806)|~c_List_Olinorder__class_Osorted(X13808,hAPP(c_List_Orev(X13808),X13807))|~class_Orderings_Olinorder(X13808))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_foldr__max__sorted])])])])). 4.05/4.29 cnf(c_0_5200, 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_4652])). 4.05/4.29 cnf(c_0_5201, 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_4653, c_0_4523]), c_0_4523]), ['final']). 4.05/4.29 cnf(c_0_5202, 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_4652])). 4.05/4.29 cnf(c_0_5203, 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_4654, c_0_4655])). 4.05/4.29 cnf(c_0_5204, plain, (hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2)),X3)),X4)=hAPP(c_List_Ofilter(X1,X3),hAPP(c_List_Ofilter(X1,X2),X4))), inference(split_conjunct,[status(thm)],[c_0_4656])). 4.05/4.29 cnf(c_0_5205, 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_4657, c_0_4523]), c_0_4523]), c_0_4523]), ['final']). 4.05/4.29 cnf(c_0_5206, 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_4658])). 4.05/4.29 fof(c_0_5207, plain, ![X15678, X15679, X15680, X15681]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15680))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15680))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X15681,X15680),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X15679),X15678)))|X15681!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15680),X15679)),X15678))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15678),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15680),X15678))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15680))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X15681,X15680),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X15679),X15678)))|X15681!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15680),X15679)),X15678)))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15680))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15678))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15678),X15680)))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X15681,X15680),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X15679),X15678)))|X15681!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15680),X15679)),X15678))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15678),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15680),X15678))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15678))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15678),X15680)))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X15681,X15680),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X15679),X15678)))|X15681!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15680),X15679)),X15678)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__relI])])])])). 4.05/4.29 fof(c_0_5208, plain, ![X8592, X8593, X8594, X8595]:(((hBOOL(hAPP(c_List_Olistsp(X8595,X8594),X8592))|~hBOOL(hAPP(c_List_Olistsp(X8595,hAPP(hAPP(c_COMBS(X8595,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X8595),c_fconj),X8594)),X8593)),X8592)))&(hBOOL(hAPP(c_List_Olistsp(X8595,X8593),X8592))|~hBOOL(hAPP(c_List_Olistsp(X8595,hAPP(hAPP(c_COMBS(X8595,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X8595),c_fconj),X8594)),X8593)),X8592))))&(~hBOOL(hAPP(c_List_Olistsp(X8595,X8594),X8592))|~hBOOL(hAPP(c_List_Olistsp(X8595,X8593),X8592))|hBOOL(hAPP(c_List_Olistsp(X8595,hAPP(hAPP(c_COMBS(X8595,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X8595),c_fconj),X8594)),X8593)),X8592)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__conj__eq])])])). 4.05/4.29 fof(c_0_5209, plain, ![X5311, X5312, X5313]:(~class_Groups_Omonoid__add(X5313)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5313),X5312),c_List_Ofoldr(X5313,X5313,c_Groups_Oplus__class_Oplus(X5313),X5311,c_Groups_Ozero__class_Ozero(X5313)))=hAPP(c_List_Ofoldl(X5313,X5313,c_Groups_Oplus__class_Oplus(X5313),X5312),X5311)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1__lemma])])). 4.05/4.29 fof(c_0_5210, plain, ![X11930, X11931, X11932, X11933, X11934]:(((X11933!=X11932|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11934),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11934),X11933),X11931)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11934),X11932),X11930))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11934),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11934),X11933),X11930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11934),X11932),X11931))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X11934))&(X11931!=X11930|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11934),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11934),X11933),X11931)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11934),X11932),X11930))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11934),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11934),X11933),X11930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11934),X11932),X11931))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X11934)))&(X11933=X11932|X11931=X11930|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11934),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11934),X11933),X11931)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11934),X11932),X11930))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11934),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11934),X11933),X11930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11934),X11932),X11931))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X11934))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])])). 4.05/4.29 fof(c_0_5211, plain, ![X13867, X13868, X13869]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13869),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),X13869)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13868)),X13867)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13869),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),X13869),X13868))),X13867)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13869)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X13868)),X13867)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__number__of__mult__left])])])). 4.05/4.29 fof(c_0_5212, plain, ![X7755, X7756, X7757]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk247_3(X7755,X7756,X7757)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X7757)))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7756),X7757)=X7756|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7756),c_Groups_Oone__class_Oone(tc_Int_Oint))),X7755))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7757)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk248_3(X7755,X7756,X7757)),X7755))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7756),X7757)=X7756|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7756),c_Groups_Oone__class_Oone(tc_Int_Oint))),X7755))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7757)))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk248_3(X7755,X7756,X7757)),esk247_3(X7755,X7756,X7757))=X7756|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7756),X7757)=X7756|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X7756),c_Groups_Oone__class_Oone(tc_Int_Oint))),X7755))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7757))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bset_I3_J])])])])])). 4.05/4.29 fof(c_0_5213, plain, ![X367, X368, X369, X370]:(~class_Groups_Ocomm__monoid__add(X370)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X370),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X370,tc_Nat_Onat),X369),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X368),X367))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X370),X369),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X368)),hAPP(c_Nat_OSuc,X367)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__shift__bounds__Suc__ivl])])])). 4.05/4.29 fof(c_0_5214, plain, ![X14441, X14442, X14443]:(~class_Groups_Ocomm__monoid__add(X14443)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X14443),X14442),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14441)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14443),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X14443),X14442),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X14441))),hAPP(X14442,X14441))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__lessThan__Suc])])])). 4.05/4.29 cnf(c_0_5215, 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_4659])). 4.05/4.29 cnf(c_0_5216, 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_4660])). 4.05/4.29 fof(c_0_5217, plain, ![X7649, X7650, X7651]:(~class_Orderings_Olinorder(X7651)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7651),X7650),X7649))|c_SetInterval_Oord__class_OatLeastAtMost(X7651,X7650,X7649)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7651,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7651,X7650),X7649)),hAPP(hAPP(c_Set_Oinsert(X7651),X7649),c_Orderings_Obot__class_Obot(tc_fun(X7651,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I6_J])])])). 4.05/4.29 fof(c_0_5218, plain, ![X13603, X13604, X13605, X13606]:hAPP(hAPP(c_Set_Oinsert(X13606),X13604),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13606,tc_HOL_Obool)),X13605),X13603))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13606,tc_HOL_Obool)),X13605),hAPP(hAPP(c_Set_Oinsert(X13606),X13604),X13603)), inference(variable_rename,[status(thm)],[fact_Un__insert__right])). 4.05/4.29 fof(c_0_5219, plain, ![X6572, X6573]:X6572=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6573,tc_HOL_Obool)),X6572),c_Orderings_Obot__class_Obot(tc_fun(X6573,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Un__empty__right])). 4.05/4.29 fof(c_0_5220, plain, ![X11667, X11668, X11669, X11670, X11671]:(~class_Complete__Lattice_Ocomplete__lattice(X11671)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11670),X11669))|hAPP(hAPP(c_Finite__Set_Ofold(X11670,X11671,hAPP(hAPP(c_COMBB(X11671,tc_fun(X11671,X11671),X11670),c_Lattices_Osemilattice__inf__class_Oinf(X11671)),X11667)),X11668),X11669)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X11671),X11668),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11670,X11671),X11669),X11667)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__INFI__fold__inf])])])). 4.05/4.29 fof(c_0_5221, plain, ![X4032, X4033, X4034, X4035, X4036]:(~class_Complete__Lattice_Ocomplete__lattice(X4036)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4035),X4034))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4036),X4033),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4035,X4036),X4034),X4032))=hAPP(hAPP(c_Finite__Set_Ofold(X4035,X4036,hAPP(hAPP(c_COMBB(X4036,tc_fun(X4036,X4036),X4035),c_Lattices_Osemilattice__sup__class_Osup(X4036)),X4032)),X4033),X4034))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__SUPR__fold__sup])])])). 4.05/4.29 fof(c_0_5222, plain, ![X17196, X17197]:(X17197=c_List_Olist_ONil(X17196)|(~hBOOL(hAPP(c_List_Odistinct(X17196),X17197))|c_List_Obutlast(X17196,X17197)=c_List_OtakeWhile(X17196,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X17196),c_fNot),hAPP(hAPP(c_COMBC(X17196,X17196,tc_HOL_Obool),c_fequal),c_List_Olast(X17196,X17197))),X17197))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile__not__last])])])). 4.05/4.29 fof(c_0_5223, plain, ![X11123, X11124, X11125, X11126]:(~class_Groups_Ocomm__monoid__add(X11126)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11125),X11124))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11126),hAPP(X11123,X11125)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X11126),X11123),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X11125,X11124)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X11126),X11123),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X11125,X11124)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__head])])])). 4.05/4.29 cnf(c_0_5224, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4661])). 4.05/4.29 cnf(c_0_5225, 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_4662])). 4.05/4.29 cnf(c_0_5226, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)=hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_4663])). 4.05/4.29 fof(c_0_5227, plain, ![X13880, X13881, X13882, X13883]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13882))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13882))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X13882|c_Divides_Odiv__class_Omod(tc_Int_Oint,X13883,X13882)=X13880)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13882),X13881)),X13880)!=X13883)&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13880),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13882),X13880))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13882))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X13882|c_Divides_Odiv__class_Omod(tc_Int_Oint,X13883,X13882)=X13880)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13882),X13881)),X13880)!=X13883))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13882))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13880),X13882))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13880)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X13882|c_Divides_Odiv__class_Omod(tc_Int_Oint,X13883,X13882)=X13880)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13882),X13881)),X13880)!=X13883)&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13880),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13882),X13880))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13880),X13882))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13880)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X13882|c_Divides_Odiv__class_Omod(tc_Int_Oint,X13883,X13882)=X13880)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13882),X13881)),X13880)!=X13883))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__mod__eq])])])])). 4.05/4.29 fof(c_0_5228, plain, ![X6218, X6219, X6220, X6221, X6222]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6222),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6221),X6220)))|hAPP(hAPP(c_List_Onth(X6219),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X6219),X6218),c_List_Oupt(X6220,X6221))),X6222)=hAPP(X6218,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6220),X6222))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__map__upt])])])). 4.05/4.29 fof(c_0_5229, plain, ![X15814, X15815, X15816, X15817, X15818]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk474_5(X15814,X15815,X15816,X15817,X15818)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X15818),X15814),X15816)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X15818),X15815),X15817)|~c_Nat__Transfer_Onat__set(X15816)|X15816!=X15817|(~class_Groups_Ocomm__monoid__add(X15818)|~class_Groups_Ocomm__monoid__mult(X15818)))&(hAPP(X15815,esk474_5(X15814,X15815,X15816,X15817,X15818))!=hAPP(X15814,esk474_5(X15814,X15815,X15816,X15817,X15818))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X15818),X15814),X15816)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X15818),X15815),X15817)|~c_Nat__Transfer_Onat__set(X15816)|X15816!=X15817|(~class_Groups_Ocomm__monoid__add(X15818)|~class_Groups_Ocomm__monoid__mult(X15818)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I2_J])])])])])). 4.05/4.29 fof(c_0_5230, plain, ![X4478, X4479, X4480, X4481, X4482]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk139_5(X4478,X4479,X4480,X4481,X4482)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X4482),X4478),X4480)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X4482),X4479),X4481)|~c_Nat__Transfer_Onat__set(X4480)|X4480!=X4481|(~class_Groups_Ocomm__monoid__mult(X4482)|~class_Groups_Ocomm__monoid__add(X4482)))&(hAPP(X4479,esk139_5(X4478,X4479,X4480,X4481,X4482))!=hAPP(X4478,esk139_5(X4478,X4479,X4480,X4481,X4482))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X4482),X4478),X4480)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X4482),X4479),X4481)|~c_Nat__Transfer_Onat__set(X4480)|X4480!=X4481|(~class_Groups_Ocomm__monoid__mult(X4482)|~class_Groups_Ocomm__monoid__add(X4482)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I1_J])])])])])). 4.05/4.29 fof(c_0_5231, plain, ![X6548, X6549, X6550, X6551, X6552, X6553]:((hBOOL(hAPP(hAPP(c_member(X6552),esk199_6(X6548,X6549,X6550,X6551,X6552,X6553)),X6551))|(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6552,X6553),X6550),X6551)!=X6549|(~hBOOL(hAPP(hAPP(c_member(X6552),X6548),X6551))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6553),hAPP(X6550,X6548)),X6549))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6552),X6551))|~class_Groups_Oordered__ab__group__add(X6553))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6553),c_Groups_Ozero__class_Ozero(X6553)),hAPP(X6550,esk199_6(X6548,X6549,X6550,X6551,X6552,X6553))))|(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6552,X6553),X6550),X6551)!=X6549|(~hBOOL(hAPP(hAPP(c_member(X6552),X6548),X6551))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6553),hAPP(X6550,X6548)),X6549))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6552),X6551))|~class_Groups_Oordered__ab__group__add(X6553))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__nonneg__leq__bound])])])])])). 4.05/4.29 cnf(c_0_5232, 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_4664])). 4.05/4.29 fof(c_0_5233, plain, ![X9745, X9746, X9747, X9748, X9749, X9750]:((hAPP(c_Product__Type_Oapsnd(X9750,X9749,X9748,X9745),X9746)!=hAPP(c_Product__Type_Oapsnd(X9750,X9749,X9748,X9747),X9746)|hAPP(X9747,hAPP(c_Product__Type_Osnd(X9748,X9750),X9746))=hAPP(X9745,hAPP(c_Product__Type_Osnd(X9748,X9750),X9746)))&(hAPP(X9747,hAPP(c_Product__Type_Osnd(X9748,X9750),X9746))!=hAPP(X9745,hAPP(c_Product__Type_Osnd(X9748,X9750),X9746))|hAPP(c_Product__Type_Oapsnd(X9750,X9749,X9748,X9745),X9746)=hAPP(c_Product__Type_Oapsnd(X9750,X9749,X9748,X9747),X9746))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apsnd__eq__conv])])). 4.05/4.29 fof(c_0_5234, plain, ![X3286, X3287, X3288, X3289, X3290, X3291]:((hAPP(c_Product__Type_Oapfst(X3291,X3290,X3289,X3288),X3287)!=hAPP(c_Product__Type_Oapfst(X3291,X3290,X3289,X3286),X3287)|hAPP(X3288,hAPP(c_Product__Type_Ofst(X3291,X3289),X3287))=hAPP(X3286,hAPP(c_Product__Type_Ofst(X3291,X3289),X3287)))&(hAPP(X3288,hAPP(c_Product__Type_Ofst(X3291,X3289),X3287))!=hAPP(X3286,hAPP(c_Product__Type_Ofst(X3291,X3289),X3287))|hAPP(c_Product__Type_Oapfst(X3291,X3290,X3289,X3288),X3287)=hAPP(c_Product__Type_Oapfst(X3291,X3290,X3289,X3286),X3287))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apfst__eq__conv])])). 4.05/4.29 fof(c_0_5235, plain, ![X5860, X5861, X5862, X5863]:c_Product__Type_Oapfst(X5863,X5862,X5861,X5860)=c_Product__Type_Omap__pair(X5863,X5862,X5861,X5861,X5860,c_Fun_Oid(X5861)), inference(variable_rename,[status(thm)],[fact_apfst__def])). 4.05/4.29 fof(c_0_5236, plain, ![X16034, X16035, X16036]:(~class_Orderings_Olinorder(X16036)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16036),X16035),X16034))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16036,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X16036),X16035),c_Orderings_Obot__class_Obot(tc_fun(X16036,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X16036,X16035,X16034))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X16036,X16035),X16034))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I3_J])])])). 4.05/4.29 fof(c_0_5237, plain, ![X1479, X1480, X1481, X1482]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1482,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1482),X1481),X1480)),X1479)=hAPP(hAPP(c_Set_Oinsert(X1482),X1481),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1482,tc_HOL_Obool)),X1480),X1479)), inference(variable_rename,[status(thm)],[fact_Un__insert__left])). 4.05/4.29 fof(c_0_5238, plain, ![X2871, X2872]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2872,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2872,tc_HOL_Obool))),X2871)=X2871, inference(variable_rename,[status(thm)],[fact_Un__empty__left])). 4.05/4.29 fof(c_0_5239, plain, ![X3775, X3776, X3778, X3779, X3780]:(((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3776)),esk117_2(X3775,X3776)),hAPP(c_List_Oset(tc_List_Olist(X3776)),X3775)))|c_List_Oconcat(X3776,X3775)=c_List_Olist_ONil(X3776))&(esk117_2(X3775,X3776)!=c_List_Olist_ONil(X3776)|c_List_Oconcat(X3776,X3775)=c_List_Olist_ONil(X3776)))&(c_List_Oconcat(X3779,X3778)!=c_List_Olist_ONil(X3779)|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3779)),X3780),hAPP(c_List_Oset(tc_List_Olist(X3779)),X3778)))|X3780=c_List_Olist_ONil(X3779)))), 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_Nil__eq__concat__conv])])])])])])). 4.05/4.29 fof(c_0_5240, plain, ![X15795, X15796, X15797, X15799]:((hBOOL(hAPP(X15796,esk473_3(X15795,X15796,X15797)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15795))|(~hBOOL(hAPP(X15796,X15799))|hBOOL(hAPP(X15796,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15795),X15797))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15797)))&(~hBOOL(hAPP(X15796,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk473_3(X15795,X15796,X15797)),X15797)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15795))|(~hBOOL(hAPP(X15796,X15799))|hBOOL(hAPP(X15796,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15795),X15797))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15797)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_incr__mult__lemma])])])])])])). 4.05/4.29 fof(c_0_5241, plain, ![X3715, X3716, X3718, X3719, X3720]:(((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3716)),esk116_2(X3715,X3716)),hAPP(c_List_Oset(tc_List_Olist(X3716)),X3715)))|c_List_Oconcat(X3716,X3715)=c_List_Olist_ONil(X3716))&(c_List_Olist_ONil(X3716)!=esk116_2(X3715,X3716)|c_List_Oconcat(X3716,X3715)=c_List_Olist_ONil(X3716)))&(c_List_Oconcat(X3719,X3718)!=c_List_Olist_ONil(X3719)|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3719)),X3720),hAPP(c_List_Oset(tc_List_Olist(X3719)),X3718)))|c_List_Olist_ONil(X3719)=X3720))), 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])])])])])])). 4.05/4.29 cnf(c_0_5242, 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_4576])). 4.05/4.29 cnf(c_0_5243, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)))), inference(split_conjunct,[status(thm)],[c_0_4615])). 4.05/4.29 cnf(c_0_5244, 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_4616])). 4.05/4.29 fof(c_0_5245, plain, ![X15095, X15096, X15097, X15098]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk453_4(X15095,X15096,X15097,X15098)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X15097)))|(X15098=X15096|X15096!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15098),X15097))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X15096),X15095))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15097)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk454_4(X15095,X15096,X15097,X15098)),X15095))|(X15098=X15096|X15096!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15098),X15097))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X15096),X15095))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15097)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk454_4(X15095,X15096,X15097,X15098)),esk453_4(X15095,X15096,X15097,X15098))=X15098|(X15098=X15096|X15096!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15098),X15097))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X15096),X15095))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15097))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_aset_I4_J])])])])])])). 4.05/4.29 cnf(c_0_5246, 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_4617])). 4.05/4.29 cnf(c_0_5247, 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_4665])). 4.05/4.29 fof(c_0_5248, plain, ![X9598, X9599, X9600]:(~hBOOL(hAPP(c_List_Odistinct(X9600),X9599))|c_List_Osublist(X9600,X9599,X9598)=hAPP(c_List_Ofilter(X9600,hAPP(hAPP(c_COMBC(X9600,tc_fun(X9600,tc_HOL_Obool),tc_HOL_Obool),c_member(X9600)),hAPP(c_List_Oset(X9600),c_List_Osublist(X9600,X9599,X9598)))),X9599)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__in__sublist])])])). 4.05/4.29 fof(c_0_5249, plain, ![X5192, X5193, X5194, X5195]:((c_Orderings_Obot__class_Obot(tc_fun(X5194,tc_HOL_Obool))=X5195|X5192=hAPP(c_Set_Oimage(tc_prod(X5194,X5193),X5193,c_Product__Type_Osnd(X5194,X5193)),hAPP(hAPP(c_Product__Type_OSigma(X5194,X5193),X5195),hAPP(c_COMBK(tc_fun(X5193,tc_HOL_Obool),X5194),X5192))))&(X5195!=c_Orderings_Obot__class_Obot(tc_fun(X5194,tc_HOL_Obool))|hAPP(c_Set_Oimage(tc_prod(X5194,X5193),X5193,c_Product__Type_Osnd(X5194,X5193)),hAPP(hAPP(c_Product__Type_OSigma(X5194,X5193),X5195),hAPP(c_COMBK(tc_fun(X5193,tc_HOL_Obool),X5194),X5192)))=c_Orderings_Obot__class_Obot(tc_fun(X5193,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_snd__image__times])])])). 4.05/4.29 fof(c_0_5250, plain, ![X1938, X1939, X1940, X1941]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk68_4(X1938,X1939,X1940,X1941)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1940)))|(X1941=X1939|X1939!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1941),X1940))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1939),X1938))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1940)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk69_4(X1938,X1939,X1940,X1941)),X1938))|(X1941=X1939|X1939!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1941),X1940))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1939),X1938))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1940)))&(X1941=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk69_4(X1938,X1939,X1940,X1941)),esk68_4(X1938,X1939,X1940,X1941))|(X1941=X1939|X1939!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1941),X1940))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1939),X1938))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1940))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bset_I4_J])])])])])])). 4.05/4.29 fof(c_0_5251, plain, ![X3880, X3881, X3882, X3883]:((X3883=c_Orderings_Obot__class_Obot(tc_fun(X3882,tc_HOL_Obool))|X3880=hAPP(c_Set_Oimage(tc_prod(X3881,X3882),X3881,c_Product__Type_Ofst(X3881,X3882)),hAPP(hAPP(c_Product__Type_OSigma(X3881,X3882),X3880),hAPP(c_COMBK(tc_fun(X3882,tc_HOL_Obool),X3881),X3883))))&(c_Orderings_Obot__class_Obot(tc_fun(X3882,tc_HOL_Obool))!=X3883|c_Orderings_Obot__class_Obot(tc_fun(X3881,tc_HOL_Obool))=hAPP(c_Set_Oimage(tc_prod(X3881,X3882),X3881,c_Product__Type_Ofst(X3881,X3882)),hAPP(hAPP(c_Product__Type_OSigma(X3881,X3882),X3880),hAPP(c_COMBK(tc_fun(X3882,tc_HOL_Obool),X3881),X3883))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fst__image__times])])])). 4.05/4.29 fof(c_0_5252, plain, ![X8653, X8654, X8655, X8656, X8657]:(c_Orderings_Otop__class_Otop(tc_fun(X8656,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X8657,X8656,X8655),c_Orderings_Otop__class_Otop(tc_fun(X8657,tc_HOL_Obool)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8657,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X8657,X8656,X8655),X8654)),X8653))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8656,tc_HOL_Obool)),X8654),hAPP(c_Set_Oimage(X8657,X8656,X8655),X8653))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__subsetD])])). 4.05/4.29 fof(c_0_5253, plain, ![X8698, X8699, X8700, X8701, X8702]:(((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8702),X8699),X8701))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8702),X8701),X8700))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X8702,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X8702,X8701,X8700)),c_SetInterval_Oord__class_OatLeastAtMost(X8702,X8699,X8698)))|~class_Orderings_Oorder(X8702))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8702),X8699),X8701))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8702),X8700),X8698))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8702),X8701),X8700))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X8702,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X8702,X8701,X8700)),c_SetInterval_Oord__class_OatLeastAtMost(X8702,X8699,X8698)))|~class_Orderings_Oorder(X8702)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8702),X8700),X8698))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8702),X8701),X8700))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X8702,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X8702,X8701,X8700)),c_SetInterval_Oord__class_OatLeastAtMost(X8702,X8699,X8698)))|~class_Orderings_Oorder(X8702)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8702),X8699),X8698))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X8702,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X8702,X8701,X8700)),c_SetInterval_Oord__class_OatLeastAtMost(X8702,X8699,X8698)))|~class_Orderings_Oorder(X8702)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8702),X8701),X8700))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8702),X8699),X8698))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X8702,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X8702,X8701,X8700)),c_SetInterval_Oord__class_OatLeastAtMost(X8702,X8699,X8698)))|~class_Orderings_Oorder(X8702))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8702),X8699),X8701))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8702),X8699),X8701))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8702),X8700),X8698))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8702),X8699),X8698))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X8702,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X8702,X8701,X8700)),c_SetInterval_Oord__class_OatLeastAtMost(X8702,X8699,X8698)))|~class_Orderings_Oorder(X8702))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8702),X8700),X8698))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8702),X8699),X8701))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8702),X8700),X8698))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8702),X8699),X8698))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X8702,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X8702,X8701,X8700)),c_SetInterval_Oord__class_OatLeastAtMost(X8702,X8699,X8698)))|~class_Orderings_Oorder(X8702))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastatMost__psubset__iff])])])])). 4.05/4.29 fof(c_0_5254, plain, ![X5142, X5143, X5144]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5144),X5143),X5142))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5144),X5143),X5142))|X5142=X5143)|~class_Orderings_Oorder(X5144))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5144),X5143),X5142))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5144),X5143),X5142))|~class_Orderings_Oorder(X5144))&(X5142!=X5143|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5144),X5143),X5142))|~class_Orderings_Oorder(X5144)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__le__less])])])])). 4.05/4.29 fof(c_0_5255, plain, ![X15645, X15646, X15647, X15648]:((c_Option_Ooption_ONone(X15647)!=hAPP(hAPP(c_Map_Omap__of(X15648,X15647),X15646),X15645)|~hBOOL(hAPP(hAPP(c_member(X15648),X15645),hAPP(c_Set_Oimage(tc_prod(X15648,X15647),X15648,c_Product__Type_Ofst(X15648,X15647)),hAPP(c_List_Oset(tc_prod(X15648,X15647)),X15646)))))&(hBOOL(hAPP(hAPP(c_member(X15648),X15645),hAPP(c_Set_Oimage(tc_prod(X15648,X15647),X15648,c_Product__Type_Ofst(X15648,X15647)),hAPP(c_List_Oset(tc_prod(X15648,X15647)),X15646))))|c_Option_Ooption_ONone(X15647)=hAPP(hAPP(c_Map_Omap__of(X15648,X15647),X15646),X15645))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__eq__None__iff])])])). 4.05/4.29 fof(c_0_5256, plain, ![X12954, X12955, X12956]:(~class_Orderings_Olinorder(X12956)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12956),X12955),X12954))|c_SetInterval_Oord__class_OatLeastAtMost(X12956,X12955,X12954)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12956,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X12956),X12955),c_Orderings_Obot__class_Obot(tc_fun(X12956,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X12956,X12955,X12954)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I5_J])])])). 4.05/4.29 fof(c_0_5257, plain, ![X17251, X17252, X17253]:(~class_Orderings_Olinorder(X17253)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17253),X17252),X17251))|c_SetInterval_Oord__class_OgreaterThanAtMost(X17253,X17252,X17251)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17253,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X17253,X17252,X17251)),hAPP(hAPP(c_Set_Oinsert(X17253),X17251),c_Orderings_Obot__class_Obot(tc_fun(X17253,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I4_J])])])). 4.05/4.29 fof(c_0_5258, plain, ![X6846, X6847, X6848, X6849, X6850, X6852]:(((c_Fun_Oinj__on(X6848,X6847,esk212_4(X6846,X6847,X6848,X6849),X6849)|X6849!=hAPP(c_Set_Oimage(X6847,X6848,X6850),X6846)|c_Orderings_Obot__class_Obot(tc_fun(X6848,tc_HOL_Obool))=X6849)&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6847,tc_HOL_Obool)),hAPP(c_Set_Oimage(X6848,X6847,esk212_4(X6846,X6847,X6848,X6849)),X6849)),X6846))|X6849!=hAPP(c_Set_Oimage(X6847,X6848,X6850),X6846)|c_Orderings_Obot__class_Obot(tc_fun(X6848,tc_HOL_Obool))=X6849))&(~c_Fun_Oinj__on(X6848,X6847,X6852,X6849)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6847,tc_HOL_Obool)),hAPP(c_Set_Oimage(X6848,X6847,X6852),X6849)),X6846))|X6849=hAPP(c_Set_Oimage(X6847,X6848,esk213_4(X6846,X6847,X6848,X6849)),X6846)|c_Orderings_Obot__class_Obot(tc_fun(X6848,tc_HOL_Obool))=X6849)), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__surj])])])])])). 4.05/4.29 fof(c_0_5259, plain, ![X14379, X14380, X14381, X14382]:(~class_Complete__Lattice_Ocomplete__lattice(X14382)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14381),X14380))|hAPP(hAPP(c_Finite__Set_Ofold(X14381,X14382,hAPP(hAPP(c_COMBB(X14382,tc_fun(X14382,X14382),X14381),c_Lattices_Osemilattice__sup__class_Osup(X14382)),X14379)),c_Orderings_Obot__class_Obot(X14382)),X14380)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14381,X14382),X14380),X14379))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUPR__fold__sup])])])). 4.05/4.29 fof(c_0_5260, plain, ![X14367, X14368, X14369, X14370]:(~class_Complete__Lattice_Ocomplete__lattice(X14370)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14369),X14368))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14369,X14370),X14368),X14367)=hAPP(hAPP(c_Finite__Set_Ofold(X14369,X14370,hAPP(hAPP(c_COMBB(X14370,tc_fun(X14370,X14370),X14369),c_Lattices_Osemilattice__inf__class_Oinf(X14370)),X14367)),c_Orderings_Otop__class_Otop(X14370)),X14368))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__fold__inf])])). 4.05/4.29 fof(c_0_5261, plain, ![X17607, X17608, X17609]:(~class_Groups_Ocomm__monoid__add(X17609)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17609),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X17609),X17608),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X17607))),hAPP(X17608,hAPP(c_Nat_OSuc,X17607)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X17609),X17608),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17607)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__atMost__Suc])])). 4.05/4.29 fof(c_0_5262, plain, ![X12042]:hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X12042)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12042), inference(variable_rename,[status(thm)],[fact_atLeast0AtMost])). 4.05/4.29 fof(c_0_5263, plain, ![X3800, X3801, X3802, X3803]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X3803,X3803)),hAPP(hAPP(c_Product__Type_OPair(X3803,X3803),X3802),X3801)),hAPP(c_Wellfounded_Omeasure(X3803),X3800)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X3800,X3802)),hAPP(X3800,X3801))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X3800,X3802)),hAPP(X3800,X3801)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X3803,X3803)),hAPP(hAPP(c_Product__Type_OPair(X3803,X3803),X3802),X3801)),hAPP(c_Wellfounded_Omeasure(X3803),X3800))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])])). 4.05/4.29 fof(c_0_5264, plain, ![X12555]:c_Wellfounded_Omeasure(X12555)=hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X12555),c_Wellfounded_Oless__than), inference(variable_rename,[status(thm)],[fact_measure__def])). 4.05/4.29 fof(c_0_5265, plain, ![X5739, X5740, X5741, X5742, X5743, X5744, X5745, X5746]:(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X5739|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5743),X5739))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5739),X5742)),X5743)!=X5740|hBOOL(hAPP(X5741,X5742))))|~hBOOL(hAPP(X5741,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X5740),X5739))))&(X5739!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X5741,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X5741,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X5740),X5739)))))&(((X5744=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X5744|hBOOL(hAPP(X5746,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X5745),X5744))))&(~hBOOL(hAPP(X5746,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X5744|hBOOL(hAPP(X5746,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X5745),X5744)))))&(((X5744=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk181_3(X5744,X5745,X5746)),X5744))|hBOOL(hAPP(X5746,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X5745),X5744))))&(~hBOOL(hAPP(X5746,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk181_3(X5744,X5745,X5746)),X5744))|hBOOL(hAPP(X5746,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X5745),X5744)))))&(((X5744=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),X5744),esk180_3(X5744,X5745,X5746))),esk181_3(X5744,X5745,X5746))=X5745|hBOOL(hAPP(X5746,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X5745),X5744))))&(~hBOOL(hAPP(X5746,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),X5744),esk180_3(X5744,X5745,X5746))),esk181_3(X5744,X5745,X5746))=X5745|hBOOL(hAPP(X5746,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X5745),X5744)))))&((X5744=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(X5746,esk180_3(X5744,X5745,X5746)))|hBOOL(hAPP(X5746,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X5745),X5744))))&(~hBOOL(hAPP(X5746,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X5746,esk180_3(X5744,X5745,X5746)))|hBOOL(hAPP(X5746,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X5745),X5744))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_split__div])])])])])])])). 4.05/4.29 fof(c_0_5266, plain, ![X10229, X10230, X10231]:(((X10230=c_Groups_Ozero__class_Ozero(X10231)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10231),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10231),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10231),X10230),X10230)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10231),X10229),X10229))),c_Groups_Ozero__class_Ozero(X10231)))|~class_Rings_Olinordered__ring__strict(X10231))&(c_Groups_Ozero__class_Ozero(X10231)=X10229|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10231),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10231),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10231),X10230),X10230)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10231),X10229),X10229))),c_Groups_Ozero__class_Ozero(X10231)))|~class_Rings_Olinordered__ring__strict(X10231)))&(X10230!=c_Groups_Ozero__class_Ozero(X10231)|c_Groups_Ozero__class_Ozero(X10231)!=X10229|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10231),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10231),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10231),X10230),X10230)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10231),X10229),X10229))),c_Groups_Ozero__class_Ozero(X10231)))|~class_Rings_Olinordered__ring__strict(X10231))), 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])])])])). 4.05/4.29 cnf(c_0_5267, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4666])). 4.05/4.29 cnf(c_0_5268, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4667])). 4.05/4.29 cnf(c_0_5269, 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_4668])). 4.05/4.29 cnf(c_0_5270, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_4669])). 4.05/4.29 fof(c_0_5271, plain, ![X5169, X5170, X5171, X5172, X5173, X5174, X5175, X5176]:(~class_Groups_Ocomm__monoid__mult(X5176)|(~c_Fun_Oinj__on(X5175,X5174,X5173,X5172)|(X5171!=hAPP(c_Set_Oimage(X5175,X5174,X5173),X5172)|(hAPP(c_Fun_Ocomp(X5174,X5176,X5175,X5169),X5173)!=X5170|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5174,X5176),X5169),X5171)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5175,X5176),X5170),X5172))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__reindex__cong])])])). 4.05/4.29 fof(c_0_5272, plain, ![X13178, X13179, X13180, X13181]:(~class_Groups_Oab__group__add(X13181)|hAPP(c_Groups_Ouminus__class_Ouminus(X13181),hAPP(c_List_Omonoid__add__class_Olistsum(X13181),hAPP(hAPP(c_List_Omap(X13180,X13181),X13179),X13178)))=hAPP(c_List_Omonoid__add__class_Olistsum(X13181),hAPP(hAPP(c_List_Omap(X13180,X13181),hAPP(c_Fun_Ocomp(X13181,X13181,X13180,c_Groups_Ouminus__class_Ouminus(X13181)),X13179)),X13178))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_uminus__listsum__map])])])). 4.05/4.29 fof(c_0_5273, plain, ![X5684, X5685, X5686, X5687, X5688, X5689]:hAPP(hAPP(c_List_Omap(X5686,X5688),hAPP(c_Fun_Ocomp(X5689,X5688,X5686,X5687),X5685)),X5684)=hAPP(hAPP(c_List_Omap(X5689,X5688),X5687),hAPP(hAPP(c_List_Omap(X5686,X5689),X5685),X5684)), inference(variable_rename,[status(thm)],[fact_List_Omap_Ocompositionality])). 4.05/4.29 fof(c_0_5274, plain, ![X11400, X11401]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk349_2(X11400,X11401)),hAPP(X11401,esk349_2(X11400,X11401))))|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)),X11401)),X11400))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__less__ub])])])). 4.05/4.29 fof(c_0_5275, plain, ![X1040, X1041, X1042, X1043, X1046]:(((hBOOL(hAPP(hAPP(c_member(X1042),esk24_4(X1040,X1041,X1042,X1043)),X1041))|(~hBOOL(hAPP(hAPP(c_member(X1042),X1043),X1041))|hAPP(X1040,X1043)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1042,tc_Nat_Onat),X1040),X1041)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1042),X1041)))&((X1043!=esk24_4(X1040,X1041,X1042,X1043)|(~hBOOL(hAPP(hAPP(c_member(X1042),X1043),X1041))|hAPP(X1040,X1043)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1042,tc_Nat_Onat),X1040),X1041)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1042),X1041)))&(hAPP(X1040,esk24_4(X1040,X1041,X1042,X1043))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(~hBOOL(hAPP(hAPP(c_member(X1042),X1043),X1041))|hAPP(X1040,X1043)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1042,tc_Nat_Onat),X1040),X1041)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1042),X1041)))))&(((hBOOL(hAPP(hAPP(c_member(X1042),esk25_3(X1040,X1041,X1042)),X1041))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1042,tc_Nat_Onat),X1040),X1041)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1042),X1041)))&(hAPP(X1040,esk25_3(X1040,X1041,X1042))=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1042,tc_Nat_Onat),X1040),X1041)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1042),X1041))))&(~hBOOL(hAPP(hAPP(c_member(X1042),X1046),X1041))|(esk25_3(X1040,X1041,X1042)=X1046|hAPP(X1040,X1046)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1042,tc_Nat_Onat),X1040),X1041)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1042),X1041))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__eq__Suc0__iff])])])])])])). 4.05/4.29 cnf(c_0_5276, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|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(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X1))),X2)), inference(split_conjunct,[status(thm)],[c_0_4670])). 4.05/4.29 fof(c_0_5277, plain, ![X2577, X2578, X2579, X2580, X2581]:(~c_Fun_Oinj__on(X2581,X2580,X2579,c_Orderings_Otop__class_Otop(tc_fun(X2581,tc_HOL_Obool)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2580,tc_HOL_Obool)),X2578),hAPP(c_Set_Oimage(X2581,X2580,X2579),X2577)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2581,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X2581,X2580,X2579),X2578)),X2577)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_vimage__subsetI])])])). 4.05/4.29 fof(c_0_5278, plain, ![X7281, X7282, X7283, X7284, X7285, X7286]:((hAPP(c_Set_Oimage(tc_Nat_Onat,X7282,X7284),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)),X7283)))!=X7281|hBOOL(hAPP(c_Finite__Set_Ofinite(X7282),X7281)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7286),X7285))|hAPP(c_Set_Oimage(tc_Nat_Onat,X7286,esk228_2(X7285,X7286)),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)),esk227_2(X7285,X7286))))=X7285)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__conv__nat__seg__image])])])])])). 4.05/4.29 fof(c_0_5279, plain, ![X17093, X17094]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X17093,X17094)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X17093),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X17094))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X17093),X17094))|X17094=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X17093,X17094)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X17093),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X17094))=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),X17093),X17094))),c_Groups_Oone__class_Oone(tc_Int_Oint))|X17094=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])])])])). 4.05/4.29 fof(c_0_5280, plain, ![X1819, X1820, X1821, X1822]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1822,tc_HOL_Obool)),X1821),X1820))|(~hBOOL(hAPP(hAPP(c_member(X1822),X1819),X1821))|hBOOL(hAPP(hAPP(c_member(X1822),X1819),X1820)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subsetD])])])). 4.05/4.29 fof(c_0_5281, plain, ![X15463, X15464, X15465, X15466, X15467]:(c_List_Opartition(X15467,X15466,X15465)!=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X15467),tc_List_Olist(X15467)),X15464),X15463)|hAPP(c_List_Oset(X15467),X15465)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15467,tc_HOL_Obool)),hAPP(c_List_Oset(X15467),X15464)),hAPP(c_List_Oset(X15467),X15463))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_partition__set])])])). 4.05/4.29 cnf(c_0_5282, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)))), inference(split_conjunct,[status(thm)],[c_0_4626])). 4.05/4.29 cnf(c_0_5283, 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_4627])). 4.05/4.29 cnf(c_0_5284, 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_4628])). 4.05/4.29 cnf(c_0_5285, 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_4671])). 4.05/4.29 cnf(c_0_5286, 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_4629])). 4.05/4.29 cnf(c_0_5287, 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_4672])). 4.05/4.29 fof(c_0_5288, plain, ![X5521, X5522, X5523, X5526, X5527, X5528, X5529, X5530]:((((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X5521|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X5521|hBOOL(hAPP(X5523,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5522,X5521))))&(~hBOOL(hAPP(X5523,X5522))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X5521|hBOOL(hAPP(X5523,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5522,X5521)))))&(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X5521|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk174_3(X5521,X5522,X5523)),X5521))|hBOOL(hAPP(X5523,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5522,X5521))))&(~hBOOL(hAPP(X5523,X5522))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk174_3(X5521,X5522,X5523)),X5521))|hBOOL(hAPP(X5523,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5522,X5521)))))&(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X5521|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5521),esk173_3(X5521,X5522,X5523))),esk174_3(X5521,X5522,X5523))=X5522|hBOOL(hAPP(X5523,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5522,X5521))))&(~hBOOL(hAPP(X5523,X5522))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5521),esk173_3(X5521,X5522,X5523))),esk174_3(X5521,X5522,X5523))=X5522|hBOOL(hAPP(X5523,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5522,X5521)))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X5521|~hBOOL(hAPP(X5523,esk174_3(X5521,X5522,X5523)))|hBOOL(hAPP(X5523,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5522,X5521))))&(~hBOOL(hAPP(X5523,X5522))|~hBOOL(hAPP(X5523,esk174_3(X5521,X5522,X5523)))|hBOOL(hAPP(X5523,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5522,X5521))))))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X5526|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5530),X5526))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5526),X5529)),X5530)!=X5527|hBOOL(hAPP(X5528,X5530))))|~hBOOL(hAPP(X5528,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5527,X5526))))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X5526|hBOOL(hAPP(X5528,X5527))|~hBOOL(hAPP(X5528,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5527,X5526)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_split__mod])])])])])])])). 4.05/4.29 fof(c_0_5289, plain, ![X2530, X2531]:(~class_Orderings_Olinorder(X2531)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2531,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X2531),X2530)),hAPP(hAPP(c_Set_Oinsert(X2531),X2530),c_Orderings_Obot__class_Obot(tc_fun(X2531,tc_HOL_Obool))))=hAPP(c_SetInterval_Oord__class_OatMost(X2531),X2530)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I2_J])])). 4.05/4.29 fof(c_0_5290, plain, ![X17386, X17387]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17387)))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17387),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17386))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17386)))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17387),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17386))=hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17387),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17386)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17387))))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17386)))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17387),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17386))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X17387)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X17387)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__nat__number__of])])])])). 4.05/4.29 cnf(c_0_5291, 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_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_4666])). 4.05/4.29 cnf(c_0_5292, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_4667])). 4.05/4.29 cnf(c_0_5293, 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_4668])). 4.05/4.29 cnf(c_0_5294, 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_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_4669])). 4.05/4.29 fof(c_0_5295, plain, ![X17388]:(~c_Nat__Transfer_Onat__set(X17388)|X17388=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),X17388))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__return__embed])])). 4.05/4.29 fof(c_0_5296, plain, ![X8128, X8129]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X8129,X8128)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X8129,X8128),tc_HOL_Obool))))|(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Finite__Set_Ocard(X8128),c_Orderings_Otop__class_Otop(tc_fun(X8128,tc_HOL_Obool)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X8129),c_Orderings_Otop__class_Otop(tc_fun(X8129,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__fun__UNIVD1])])])). 4.05/4.29 fof(c_0_5297, plain, ![X15865, X15866, X15867, X15868, X15869, X15870, X15871, X15873, X15874, X15875, X15876, X15877, X15878, X15879, X15880]:(((hAPP(c_Option_Ooption_OSome(X15871),esk477_7(X15865,X15866,X15867,X15868,X15869,X15870,X15871))=hAPP(X15867,X15866)|c_Map_Omap__comp(X15871,X15870,X15869,X15868,X15867,X15866)!=hAPP(c_Option_Ooption_OSome(X15870),X15865))&(hAPP(c_Option_Ooption_OSome(X15870),X15865)=hAPP(X15868,esk477_7(X15865,X15866,X15867,X15868,X15869,X15870,X15871))|c_Map_Omap__comp(X15871,X15870,X15869,X15868,X15867,X15866)!=hAPP(c_Option_Ooption_OSome(X15870),X15865)))&(hAPP(c_Option_Ooption_OSome(X15879),X15880)!=hAPP(X15875,X15874)|hAPP(c_Option_Ooption_OSome(X15878),X15873)!=hAPP(X15876,X15880)|c_Map_Omap__comp(X15879,X15878,X15877,X15876,X15875,X15874)=hAPP(c_Option_Ooption_OSome(X15878),X15873))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__comp__Some__iff])])])])])])). 4.05/4.29 fof(c_0_5298, plain, ![X5780, X5781, X5782, X5783, X5784, X5785]:c_Map_Omap__comp(X5785,X5784,X5783,X5782,X5781,X5780)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X5784),X5785,c_Option_Ooption_ONone(X5784),X5782),hAPP(X5781,X5780)), inference(variable_rename,[status(thm)],[fact_map__comp__def])). 4.05/4.29 fof(c_0_5299, plain, ![X12012, X12013, X12014]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12014),X12013))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12014),X12012))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12013),X12012)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12013),X12014)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12012),X12014)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat_Odiff__diff__eq])])])). 4.05/4.29 fof(c_0_5300, plain, ![X4131, X4132]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4132)))|hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4132)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4131)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4132)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4131)))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4132)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4132)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4131)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__nat__number__of])])])). 4.05/4.29 fof(c_0_5301, plain, ![X2517, X2518]:(~class_Groups_Omonoid__add(X2518)|hAPP(c_List_Ofoldl(X2518,X2518,c_Groups_Oplus__class_Oplus(X2518),c_Groups_Ozero__class_Ozero(X2518)),X2517)=c_List_Ofoldr(X2518,X2518,c_Groups_Oplus__class_Oplus(X2518),X2517,c_Groups_Ozero__class_Ozero(X2518))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1])])). 4.05/4.29 fof(c_0_5302, plain, ![X3509, X3510, X3511, X3512]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3510)),X3509)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3512)),X3511)|(~hBOOL(hAPP(c_List_Odistinct(X3512),X3511))|hAPP(c_List_Oset(X3512),X3511)=c_Map_Odom(X3512,X3510,hAPP(c_Map_Omap__of(X3512,X3510),hAPP(hAPP(c_List_Ozip(X3512,X3510),X3511),X3509))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dom__map__of__zip])])])). 4.05/4.29 cnf(c_0_5303, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))=c_Map_Odom(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4673])). 4.05/4.29 cnf(c_0_5304, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),X3)=hAPP(c_Relation_ODomain(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_4674]), ['final']). 4.05/4.29 fof(c_0_5305, plain, ![X17324, X17325, X17326, X17327, X17328]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17328,tc_HOL_Obool)),X17327),X17326))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17325,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X17325,X17328,X17324),X17327)),hAPP(c_Set_Ovimage(X17325,X17328,X17324),X17326)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_vimage__mono])])])). 4.05/4.29 fof(c_0_5306, plain, ![X9850, X9851, X9852]:(~class_Groups_Ocomm__monoid__add(X9852)|(c_Groups_Ozero__class_Ozero(X9852)!=hAPP(X9851,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X9852),X9851),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9850))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X9852),X9851),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X9850)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__shift__lb__Suc0__0__upt])])])). 4.05/4.29 cnf(c_0_5307, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4468])). 4.05/4.29 cnf(c_0_5308, 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_4466])). 4.05/4.29 cnf(c_0_5309, 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_4462])). 4.05/4.29 fof(c_0_5310, plain, ![X14886]:(~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),X14886)))|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),X14886)))=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),X14886))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos__1__number__of])])). 4.05/4.29 cnf(c_0_5311, 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_4465])). 4.05/4.29 cnf(c_0_5312, 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_4461])). 4.05/4.29 cnf(c_0_5313, 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_4469])). 4.05/4.29 cnf(c_0_5314, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X1))), inference(split_conjunct,[status(thm)],[c_0_4460])). 4.05/4.29 cnf(c_0_5315, 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_4464])). 4.05/4.29 cnf(c_0_5316, 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_4459])). 4.05/4.29 cnf(c_0_5317, 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_4463])). 4.05/4.29 cnf(c_0_5318, 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_4458])). 4.05/4.29 fof(c_0_5319, plain, ![X3804]:(~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),X3804)))|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),X3804))=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),X3804)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__pos__pos__1__number__of])])])). 4.05/4.29 cnf(c_0_5320, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))!=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))|~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_4675])). 4.05/4.29 fof(c_0_5321, plain, ![X15889, X15890]:(hAPP(X15890,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(tc_Nat_Onat,tc_Nat_Onat),X15890),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15889))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X15890),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15889))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__shift__lb__Suc0__0])])])). 4.05/4.29 fof(c_0_5322, plain, ![X9670, X9671]:(~class_Orderings_Olinorder(X9671)|hAPP(c_SetInterval_Oord__class_OatLeast(X9671),X9670)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9671,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X9671),X9670),c_Orderings_Obot__class_Obot(tc_fun(X9671,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X9671),X9670))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I1_J])])). 4.05/4.29 fof(c_0_5323, plain, ![X3767, X3768, X3769]:((~c_Relation_Ototal__on(X3769,X3768,X3767)|c_Relation_Ototal__on(X3769,X3768,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X3769,X3769),tc_HOL_Obool)),X3767),c_Relation_OId(X3769))))&(~c_Relation_Ototal__on(X3769,X3768,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X3769,X3769),tc_HOL_Obool)),X3767),c_Relation_OId(X3769)))|c_Relation_Ototal__on(X3769,X3768,X3767))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__diff__Id])])). 4.05/4.29 fof(c_0_5324, plain, ![X3266, X3267]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3267),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),X3267))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3266)))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3267),X3266))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib__neg])])). 4.05/4.29 fof(c_0_5325, plain, ![X6144, X6145]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6144),c_Int_OPls))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6145)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6144))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6145)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6145),c_Int_OPls)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6144),c_Int_OPls))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6145)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6144))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6145),X6144))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6145),c_Int_OPls))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6145),c_Int_OPls))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6145)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6144))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6144))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__nat__number__of])])])])). 4.05/4.29 fof(c_0_5326, plain, ![X11097, X11098]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11098),X11097))|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(X11098),X11097))=hAPP(c_Finite__Set_Ocard(tc_fun(X11098,tc_HOL_Obool)),hAPP(c_Set_OPow(X11098),X11097))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Pow])])). 4.05/4.29 fof(c_0_5327, plain, ![X5111, X5112]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5112),X5111))|c_List_Oupt(X5112,X5111)=hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X5112),c_List_Oupt(hAPP(c_Nat_OSuc,X5112),X5111))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__conv__Cons])])). 4.05/4.29 cnf(c_0_5328, plain, (X2=X1|c_Int_OBit0(X1)!=c_Int_OBit0(X2)), inference(split_conjunct,[status(thm)],[c_0_4676])). 4.05/4.29 cnf(c_0_5329, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))), inference(split_conjunct,[status(thm)],[c_0_4677])). 4.05/4.29 fof(c_0_5330, plain, ![X16786]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16786),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_mult__0__right])). 4.05/4.29 fof(c_0_5331, plain, ![X9590]:X9590=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9590),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right])). 4.05/4.29 fof(c_0_5332, plain, ![X1350, X1351, X1352, X1353, X1354, X1355, X1356]:((c_List_Olist_ONil(X1352)!=c_List_OdropWhile(X1352,X1351,X1350)|(~hBOOL(hAPP(hAPP(c_member(X1352),X1353),hAPP(c_List_Oset(X1352),X1350)))|hBOOL(hAPP(X1351,X1353))))&((hBOOL(hAPP(hAPP(c_member(X1356),esk37_3(X1354,X1355,X1356)),hAPP(c_List_Oset(X1356),X1354)))|c_List_Olist_ONil(X1356)=c_List_OdropWhile(X1356,X1355,X1354))&(~hBOOL(hAPP(X1355,esk37_3(X1354,X1355,X1356)))|c_List_Olist_ONil(X1356)=c_List_OdropWhile(X1356,X1355,X1354)))), 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])])])])])])])). 4.05/4.29 cnf(c_0_5333, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls)))=X2|~class_Int_Onumber__ring(X1)|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_4678])). 4.05/4.29 fof(c_0_5334, plain, ![X13955, X13956]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X13956))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X13955))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13956),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13956),X13955))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_n__less__n__mult__m])])])). 4.05/4.29 fof(c_0_5335, plain, ![X13773, X13774]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X13774))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X13773))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13774),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13773),X13774))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_n__less__m__mult__n])])])). 4.05/4.29 fof(c_0_5336, plain, ![X7992, X7993, X7994]:((~hBOOL(hAPP(c_Predicate_OPowp(X7994,hAPP(hAPP(c_COMBC(X7994,tc_fun(X7994,tc_HOL_Obool),tc_HOL_Obool),c_member(X7994)),X7993)),X7992))|hBOOL(hAPP(hAPP(c_member(tc_fun(X7994,tc_HOL_Obool)),X7992),hAPP(c_Set_OPow(X7994),X7993))))&(~hBOOL(hAPP(hAPP(c_member(tc_fun(X7994,tc_HOL_Obool)),X7992),hAPP(c_Set_OPow(X7994),X7993)))|hBOOL(hAPP(c_Predicate_OPowp(X7994,hAPP(hAPP(c_COMBC(X7994,tc_fun(X7994,tc_HOL_Obool),tc_HOL_Obool),c_member(X7994)),X7993)),X7992)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Powp__Pow__eq])])). 4.05/4.29 cnf(c_0_5337, 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_4679])). 4.05/4.29 fof(c_0_5338, plain, ![X6735, X6736, X6737, X6738, X6739, X6740, X6742, X6743, X6744, X6745, X6746, X6747, X6748]:(((hAPP(X6736,X6735)=hAPP(c_Option_Ooption_OSome(X6740),esk208_6(X6735,X6736,X6737,X6738,X6739,X6740))|hAPP(X6736,X6735)=c_Option_Ooption_ONone(X6740)|c_Option_Ooption_ONone(X6739)!=c_Map_Omap__comp(X6740,X6739,X6738,X6737,X6736,X6735))&(c_Option_Ooption_ONone(X6739)=hAPP(X6737,esk208_6(X6735,X6736,X6737,X6738,X6739,X6740))|hAPP(X6736,X6735)=c_Option_Ooption_ONone(X6740)|c_Option_Ooption_ONone(X6739)!=c_Map_Omap__comp(X6740,X6739,X6738,X6737,X6736,X6735)))&((hAPP(X6743,X6742)!=hAPP(c_Option_Ooption_OSome(X6747),X6748)|c_Option_Ooption_ONone(X6746)!=hAPP(X6744,X6748)|c_Option_Ooption_ONone(X6746)=c_Map_Omap__comp(X6747,X6746,X6745,X6744,X6743,X6742))&(hAPP(X6743,X6742)!=c_Option_Ooption_ONone(X6747)|c_Option_Ooption_ONone(X6746)=c_Map_Omap__comp(X6747,X6746,X6745,X6744,X6743,X6742)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__comp__None__iff])])])])])])). 4.05/4.29 cnf(c_0_5339, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk23_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_4639])). 4.05/4.29 cnf(c_0_5340, 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_4680])). 4.05/4.29 cnf(c_0_5341, 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_4681])). 4.05/4.29 fof(c_0_5342, plain, ![X7090, X7091, X7092]:(~class_Groups_Oab__semigroup__add(X7092)|c_List_Ofoldr(X7092,X7092,c_Groups_Oplus__class_Oplus(X7092),X7091,X7090)=hAPP(c_List_Ofoldl(X7092,X7092,c_Groups_Oplus__class_Oplus(X7092),X7090),X7091)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_foldr__conv__foldl])])])). 4.05/4.29 cnf(c_0_5343, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2)))), inference(split_conjunct,[status(thm)],[c_0_4649])). 4.05/4.29 cnf(c_0_5344, 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_4650])). 4.05/4.29 cnf(c_0_5345, 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_4651])). 4.05/4.29 fof(c_0_5346, plain, ![X14306, X14307, X14308]:((X14307!=c_Groups_Ozero__class_Ozero(X14308)|X14306!=c_Groups_Ozero__class_Ozero(X14308)|c_Groups_Ozero__class_Ozero(X14308)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14308),X14307),X14307)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14308),X14306),X14306))|~class_Rings_Olinordered__ring__strict(X14308))&((X14307=c_Groups_Ozero__class_Ozero(X14308)|c_Groups_Ozero__class_Ozero(X14308)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14308),X14307),X14307)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14308),X14306),X14306))|~class_Rings_Olinordered__ring__strict(X14308))&(X14306=c_Groups_Ozero__class_Ozero(X14308)|c_Groups_Ozero__class_Ozero(X14308)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14308),X14307),X14307)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14308),X14306),X14306))|~class_Rings_Olinordered__ring__strict(X14308)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff])])])). 4.05/4.29 fof(c_0_5347, plain, ![X17661, X17662]:((~c_Wellfounded_Oacyclic(X17662,hAPP(c_Set_OCollect(tc_prod(X17662,X17662)),hAPP(c_Product__Type_Oprod_Oprod__case(X17662,X17662,tc_HOL_Obool),X17661)))|c_Wellfounded_Oacyclic(X17662,hAPP(c_Set_OCollect(tc_prod(X17662,X17662)),hAPP(c_Product__Type_Oprod_Oprod__case(X17662,X17662,tc_HOL_Obool),c_Predicate_Oconversep(X17662,X17662,X17661)))))&(~c_Wellfounded_Oacyclic(X17662,hAPP(c_Set_OCollect(tc_prod(X17662,X17662)),hAPP(c_Product__Type_Oprod_Oprod__case(X17662,X17662,tc_HOL_Obool),c_Predicate_Oconversep(X17662,X17662,X17661))))|c_Wellfounded_Oacyclic(X17662,hAPP(c_Set_OCollect(tc_prod(X17662,X17662)),hAPP(c_Product__Type_Oprod_Oprod__case(X17662,X17662,tc_HOL_Obool),X17661))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclicP__converse])])). 4.05/4.29 fof(c_0_5348, plain, ![X7162, X7163, X7164]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7164),X7163)),X7162))|hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X7164,X7162)),X7163)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7164),X7163)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__upt])])). 4.05/4.29 fof(c_0_5349, plain, ![X4494, X4495, X4496]:((~hBOOL(hAPP(c_List_Olistsp(X4496,hAPP(hAPP(c_COMBC(X4496,tc_fun(X4496,tc_HOL_Obool),tc_HOL_Obool),c_member(X4496)),X4495)),X4494))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4496)),X4494),c_List_Olists(X4496,X4495))))&(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4496)),X4494),c_List_Olists(X4496,X4495)))|hBOOL(hAPP(c_List_Olistsp(X4496,hAPP(hAPP(c_COMBC(X4496,tc_fun(X4496,tc_HOL_Obool),tc_HOL_Obool),c_member(X4496)),X4495)),X4494)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__lists__eq])])). 4.05/4.29 fof(c_0_5350, plain, ![X5734, X5735]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X5735))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X5734))|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),X5734),X5735))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_one__less__mult])])])). 4.05/4.29 fof(c_0_5351, plain, ![X8251, X8252]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X8251))|~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),X8252),X8251))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X8252))|~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),X8252),X8251)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X8251))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X8252))|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),X8252),X8251))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff])])])). 4.05/4.29 fof(c_0_5352, plain, ![X2434, X2435]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X2435,X2435)),X2434),c_Relation_OId(X2435)))|hAPP(hAPP(c_Product__Type_OPair(X2435,X2435),esk87_2(X2434,X2435)),esk87_2(X2434,X2435))=X2434), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IdE])])])). 4.05/4.29 fof(c_0_5353, plain, ![X8720, X8721, X8722, X8723]:(X8723!=X8722|(~hBOOL(hAPP(hAPP(c_member(X8721),X8723),X8720))|hBOOL(hAPP(hAPP(c_member(tc_prod(X8721,X8721)),hAPP(hAPP(c_Product__Type_OPair(X8721,X8721),X8723),X8722)),c_Relation_OId__on(X8721,X8720))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Id__on__eqI])])])). 4.05/4.29 fof(c_0_5354, plain, ![X16108]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X16108)))|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),X16108))=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X16108)))|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),X16108)))=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),X16108)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_one__mod__nat__number__of])])])). 4.05/4.29 fof(c_0_5355, plain, ![X16519, X16520, X16521, X16522]:((hAPP(hAPP(c_List_Olist_OCons(X16522),X16520),X16519)!=hAPP(c_List_Orev(X16522),X16521)|X16521=hAPP(hAPP(c_List_Oappend(X16522),hAPP(c_List_Orev(X16522),X16519)),hAPP(hAPP(c_List_Olist_OCons(X16522),X16520),c_List_Olist_ONil(X16522))))&(X16521!=hAPP(hAPP(c_List_Oappend(X16522),hAPP(c_List_Orev(X16522),X16519)),hAPP(hAPP(c_List_Olist_OCons(X16522),X16520),c_List_Olist_ONil(X16522)))|hAPP(hAPP(c_List_Olist_OCons(X16522),X16520),X16519)=hAPP(c_List_Orev(X16522),X16521))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__eq__Cons__iff])])). 4.05/4.29 fof(c_0_5356, plain, ![X16434, X16435, X16436]:hAPP(hAPP(c_List_Oappend(X16436),hAPP(c_List_Orev(X16436),X16434)),hAPP(hAPP(c_List_Olist_OCons(X16436),X16435),c_List_Olist_ONil(X16436)))=hAPP(c_List_Orev(X16436),hAPP(hAPP(c_List_Olist_OCons(X16436),X16435),X16434)), inference(variable_rename,[status(thm)],[fact_rev_Osimps_I2_J])). 4.05/4.29 cnf(c_0_5357, 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_4682])). 4.05/4.29 fof(c_0_5358, plain, ![X7374, X7375]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7375),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),X7375)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7374)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7375),c_Int_OPls))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7375),X7374))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7375)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7374)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__nat__number__of])])])). 4.05/4.29 cnf(c_0_5359, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls)))=X2|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4683])). 4.05/4.29 fof(c_0_5360, plain, ![X16264]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16264))|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,X16264)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16264)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__atLeastZeroLessThan__int])])). 4.05/4.29 fof(c_0_5361, plain, ![X8527, X8528, X8529, X8530]:(~class_Groups_Ocomm__monoid__add(X8530)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X8530),X8529),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X8528,X8527)))=hAPP(c_List_Omonoid__add__class_Olistsum(X8530),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X8530),X8529),c_List_Oupto(X8528,X8527)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_interv__listsum__conv__setsum__set__int])])])). 4.05/4.29 fof(c_0_5362, plain, ![X1708, X1709]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1709,X1708)=hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1709,X1708)), inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upto])). 4.05/4.29 fof(c_0_5363, plain, ![X2248, X2249, X2250, X2251, X2252]:(((hAPP(hAPP(c_List_Omap(tc_prod(X2252,X2250),X2252),c_Product__Type_Ofst(X2252,X2250)),X2248)=X2251|X2248!=hAPP(hAPP(c_List_Ozip(X2252,X2250),X2251),X2249)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2252)),X2251)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2250)),X2249))&(hAPP(hAPP(c_List_Omap(tc_prod(X2252,X2250),X2250),c_Product__Type_Osnd(X2252,X2250)),X2248)=X2249|X2248!=hAPP(hAPP(c_List_Ozip(X2252,X2250),X2251),X2249)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2252)),X2251)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2250)),X2249)))&(hAPP(hAPP(c_List_Omap(tc_prod(X2252,X2250),X2252),c_Product__Type_Ofst(X2252,X2250)),X2248)!=X2251|hAPP(hAPP(c_List_Omap(tc_prod(X2252,X2250),X2250),c_Product__Type_Osnd(X2252,X2250)),X2248)!=X2249|X2248=hAPP(hAPP(c_List_Ozip(X2252,X2250),X2251),X2249)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2252)),X2251)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2250)),X2249))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__eq__conv])])])). 4.05/4.29 fof(c_0_5364, plain, ![X3763, X3764, X3765, X3766]:(~c_Fun_Oinj__on(X3766,X3765,X3764,c_Complete__Lattice_OSup__class_OSup(tc_fun(X3766,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X3766),tc_fun(X3766,tc_HOL_Obool),c_List_Oset(X3766)),X3763)))|c_Fun_Oinj__on(tc_List_Olist(X3766),tc_List_Olist(X3765),hAPP(c_List_Omap(X3766,X3765),X3764),X3763)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__mapI])])). 4.05/4.29 fof(c_0_5365, plain, ![X10438, X10439, X10440, X10441]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10440,tc_fun(X10441,tc_HOL_Obool)),X10438),X10439)=c_Complete__Lattice_OSup__class_OSup(tc_fun(X10441,tc_HOL_Obool),hAPP(c_Set_Oimage(X10440,tc_fun(X10441,tc_HOL_Obool),X10439),X10438)), inference(variable_rename,[status(thm)],[fact_Union__image__eq])). 4.05/4.29 fof(c_0_5366, plain, ![X13074, X13075, X13076, X13077, X13081]:(((c_List_Olist_ONil(X13075)!=X13074|c_List_Olinorder__class_Osorted(X13075,X13074)|~class_Orderings_Olinorder(X13075))&((hBOOL(hAPP(hAPP(c_member(X13075),esk400_4(X13074,X13075,X13076,X13077)),hAPP(c_List_Oset(X13075),X13076)))|X13074!=hAPP(hAPP(c_List_Olist_OCons(X13075),X13077),X13076)|~c_List_Olinorder__class_Osorted(X13075,X13076)|c_List_Olinorder__class_Osorted(X13075,X13074)|~class_Orderings_Olinorder(X13075))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13075),X13077),esk400_4(X13074,X13075,X13076,X13077)))|X13074!=hAPP(hAPP(c_List_Olist_OCons(X13075),X13077),X13076)|~c_List_Olinorder__class_Osorted(X13075,X13076)|c_List_Olinorder__class_Osorted(X13075,X13074)|~class_Orderings_Olinorder(X13075))))&(((X13074=hAPP(hAPP(c_List_Olist_OCons(X13075),esk402_2(X13074,X13075)),esk401_2(X13074,X13075))|c_List_Olist_ONil(X13075)=X13074|~c_List_Olinorder__class_Osorted(X13075,X13074)|~class_Orderings_Olinorder(X13075))&(~hBOOL(hAPP(hAPP(c_member(X13075),X13081),hAPP(c_List_Oset(X13075),esk401_2(X13074,X13075))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13075),esk402_2(X13074,X13075)),X13081))|c_List_Olist_ONil(X13075)=X13074|~c_List_Olinorder__class_Osorted(X13075,X13074)|~class_Orderings_Olinorder(X13075)))&(c_List_Olinorder__class_Osorted(X13075,esk401_2(X13074,X13075))|c_List_Olist_ONil(X13075)=X13074|~c_List_Olinorder__class_Osorted(X13075,X13074)|~class_Orderings_Olinorder(X13075)))), 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_sorted_Osimps])])])])])])])). 4.05/4.29 cnf(c_0_5367, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_4602])). 4.05/4.29 fof(c_0_5368, plain, ![X4610, X4611, X4612]:(c_List_Olist_ONil(X4612)=c_List_OdropWhile(X4612,X4611,X4610)|~hBOOL(hAPP(X4611,hAPP(c_List_Ohd(X4612),c_List_OdropWhile(X4612,X4611,X4610))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__dropWhile])])])). 4.05/4.29 fof(c_0_5369, plain, ![X5089, X5090]:(~c_Nat__Transfer_Ois__nat(X5090)|(~c_Nat__Transfer_Ois__nat(X5089)|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,X5090),hAPP(c_Int_Onat,X5089)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X5090,X5089))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__functions])])])). 4.05/4.29 cnf(c_0_5370, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|X3=hAPP(c_List_OremoveAll(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_4684])). 4.05/4.29 fof(c_0_5371, plain, ![X17211, X17212, X17213, X17214]:(((c_Groups_Ozero__class_Ozero(X17214)=X17212|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17214),hAPP(c_Int_Onumber__class_Onumber__of(X17214),X17211)),X17212)=X17213|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17214),X17213),X17212)!=hAPP(c_Int_Onumber__class_Onumber__of(X17214),X17211)|(~class_Int_Onumber(X17214)|~class_Fields_Ofield__inverse__zero(X17214)))&(X17212!=c_Groups_Ozero__class_Ozero(X17214)|c_Groups_Ozero__class_Ozero(X17214)=hAPP(c_Int_Onumber__class_Onumber__of(X17214),X17211)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17214),X17213),X17212)!=hAPP(c_Int_Onumber__class_Onumber__of(X17214),X17211)|(~class_Int_Onumber(X17214)|~class_Fields_Ofield__inverse__zero(X17214))))&(((X17212=c_Groups_Ozero__class_Ozero(X17214)|c_Groups_Ozero__class_Ozero(X17214)!=X17212|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17214),X17213),X17212)=hAPP(c_Int_Onumber__class_Onumber__of(X17214),X17211)|(~class_Int_Onumber(X17214)|~class_Fields_Ofield__inverse__zero(X17214)))&(c_Groups_Ozero__class_Ozero(X17214)!=hAPP(c_Int_Onumber__class_Onumber__of(X17214),X17211)|c_Groups_Ozero__class_Ozero(X17214)!=X17212|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17214),X17213),X17212)=hAPP(c_Int_Onumber__class_Onumber__of(X17214),X17211)|(~class_Int_Onumber(X17214)|~class_Fields_Ofield__inverse__zero(X17214))))&((X17212=c_Groups_Ozero__class_Ozero(X17214)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17214),hAPP(c_Int_Onumber__class_Onumber__of(X17214),X17211)),X17212)!=X17213|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17214),X17213),X17212)=hAPP(c_Int_Onumber__class_Onumber__of(X17214),X17211)|(~class_Int_Onumber(X17214)|~class_Fields_Ofield__inverse__zero(X17214)))&(c_Groups_Ozero__class_Ozero(X17214)!=hAPP(c_Int_Onumber__class_Onumber__of(X17214),X17211)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17214),hAPP(c_Int_Onumber__class_Onumber__of(X17214),X17211)),X17212)!=X17213|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17214),X17213),X17212)=hAPP(c_Int_Onumber__class_Onumber__of(X17214),X17211)|(~class_Int_Onumber(X17214)|~class_Fields_Ofield__inverse__zero(X17214)))))), 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])])])])). 4.05/4.29 fof(c_0_5372, plain, ![X1782, X1783, X1784, X1785, X1786]:(((~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1784),hAPP(c_List_Oset(tc_Nat_Onat),X1782)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1784|hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1783),X1782)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1783|hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1783),X1782)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk60_2(X1785,X1786)),hAPP(c_List_Oset(tc_Nat_Onat),X1785)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1786|hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1786),X1785)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=esk60_2(X1785,X1786)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1786|hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1786),X1785)=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_sum__eq__0__conv])])])])])])). 4.05/4.29 fof(c_0_5373, plain, ![X2562, X2563]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2563))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2562))|hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2563),X2562))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X2563)),hAPP(c_Int_Onat,X2562)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__add__distrib])])])). 4.05/4.29 fof(c_0_5374, plain, ![X1947, X1948, X1949]:(((c_Groups_Ozero__class_Ozero(X1949)=X1948|c_Groups_Ozero__class_Ozero(X1949)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1949),X1948),X1947)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1949),c_Groups_Ozero__class_Ozero(X1949)),X1947))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1949),c_Groups_Ozero__class_Ozero(X1949)),X1948))|~class_Groups_Oordered__comm__monoid__add(X1949))&(c_Groups_Ozero__class_Ozero(X1949)=X1947|c_Groups_Ozero__class_Ozero(X1949)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1949),X1948),X1947)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1949),c_Groups_Ozero__class_Ozero(X1949)),X1947))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1949),c_Groups_Ozero__class_Ozero(X1949)),X1948))|~class_Groups_Oordered__comm__monoid__add(X1949)))&(c_Groups_Ozero__class_Ozero(X1949)!=X1948|c_Groups_Ozero__class_Ozero(X1949)!=X1947|c_Groups_Ozero__class_Ozero(X1949)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1949),X1948),X1947)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1949),c_Groups_Ozero__class_Ozero(X1949)),X1947))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1949),c_Groups_Ozero__class_Ozero(X1949)),X1948))|~class_Groups_Oordered__comm__monoid__add(X1949))), 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])])])])). 4.05/4.29 fof(c_0_5375, plain, ![X11466, X11467, X11468, X11469]:((c_Groups_Ozero__class_Ozero(X11469)=X11468|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11469),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11469),X11468),X11467)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11469),X11468),X11466))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11469),X11467),X11466)|~class_Divides_Osemiring__div(X11469))&(X11468!=c_Groups_Ozero__class_Ozero(X11469)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11469),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11469),X11468),X11467)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11469),X11468),X11466))=c_Groups_Ozero__class_Ozero(X11469)|~class_Divides_Osemiring__div(X11469))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__mult1__if])])])])). 4.05/4.29 fof(c_0_5376, plain, ![X4057, X4058, X4059, X4060]:((~hBOOL(hAPP(X4057,X4059))|~hBOOL(hAPP(hAPP(c_member(X4060),X4059),X4058))|hBOOL(hAPP(hAPP(c_member(X4060),X4059),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4060,tc_HOL_Obool)),X4058),hAPP(c_Set_OCollect(X4060),X4057)))))&((hBOOL(hAPP(X4057,X4059))|~hBOOL(hAPP(hAPP(c_member(X4060),X4059),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4060,tc_HOL_Obool)),X4058),hAPP(c_Set_OCollect(X4060),X4057)))))&(hBOOL(hAPP(hAPP(c_member(X4060),X4059),X4058))|~hBOOL(hAPP(hAPP(c_member(X4060),X4059),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4060,tc_HOL_Obool)),X4058),hAPP(c_Set_OCollect(X4060),X4057))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__Collect])])])). 4.05/4.29 fof(c_0_5377, plain, ![X13032]:(hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X13032|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,X13032)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X13032)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral__decr])])). 4.05/4.29 cnf(c_0_5378, 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])). 4.05/4.29 cnf(c_0_5379, plain, (c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral)=c_Code__Numeral_Oof__nat), inference(split_conjunct,[status(thm)],[fact_Code__Numeral_Oof__nat__code]), ['final']). 4.05/4.29 fof(c_0_5380, plain, ![X15271, X15272]:(((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15272)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15271)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15271)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15272))&((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15271)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15272)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15272)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15271)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15272))&(hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15271)))|X15272=X15271|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15272)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15271)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15272))))&(((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15272)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15272)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15271)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15272))&(((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15271)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15271)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15272)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15271)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15272))&(X15272!=X15271|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15271)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15272)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15271)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15272)))&((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15271)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15272)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15272)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15271)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15272))&(X15272!=X15271|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15272)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15272)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15271)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15272)))))&((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15272)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15271)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15271)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15272))&(((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15271)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15271)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15271)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15271)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15272))&(X15272!=X15271|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15271)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15271)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15271)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15272)))&((~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15271)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15272)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15271)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15271)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15272))&(X15272!=X15271|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15272)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X15271)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15271)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X15272))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__nat__number__of])])])])). 4.05/4.29 fof(c_0_5381, plain, ![X5124, X5125]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5125)))|hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5125)),X5124))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5125)),X5124))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5125)))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5124)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5125)),X5124))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__nat__number__of])])])). 4.05/4.29 fof(c_0_5382, plain, ![X6725, X6726, X6727, X6728]:(~c_Fun_Oinj__on(X6728,X6727,X6726,c_Orderings_Otop__class_Otop(tc_fun(X6728,tc_HOL_Obool)))|hAPP(c_Set_Ovimage(X6728,X6727,X6726),hAPP(c_Set_Oimage(X6728,X6727,X6726),X6725))=X6725), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__vimage__image__eq])])])). 4.05/4.29 fof(c_0_5383, plain, ![X17200, X17201, X17202, X17203]:(hAPP(c_Set_Oimage(X17203,X17202,X17201),c_Orderings_Otop__class_Otop(tc_fun(X17203,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X17202,tc_HOL_Obool))|X17200=hAPP(c_Set_Oimage(X17203,X17202,X17201),hAPP(c_Set_Ovimage(X17203,X17202,X17201),X17200))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__image__vimage__eq])])). 4.05/4.29 fof(c_0_5384, plain, ![X13626, X13627, X13628, X13629]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13629),X13628))|(~c_Fun_Oinj__on(X13627,X13629,X13626,c_Orderings_Otop__class_Otop(tc_fun(X13627,tc_HOL_Obool)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X13627),hAPP(c_Set_Ovimage(X13627,X13629,X13626),X13628))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimageI])])). 4.05/4.29 fof(c_0_5385, plain, ![X16262, X16263]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16263))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16263),X16262))|hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X16262),X16263))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X16262)),hAPP(c_Int_Onat,X16263)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__diff__distrib])])])). 4.05/4.29 fof(c_0_5386, plain, ![X14241, X14242, X14243, X14244]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14244),hAPP(c_Set_Ovimage(X14244,X14243,X14242),X14241)))|(hAPP(c_Set_Oimage(X14244,X14243,X14242),c_Orderings_Otop__class_Otop(tc_fun(X14244,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X14243,tc_HOL_Obool))|hBOOL(hAPP(c_Finite__Set_Ofinite(X14243),X14241)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimageD])])). 4.05/4.29 cnf(c_0_5387, plain, (hAPP(c_List_OremoveAll(X1,X3),X2)=c_List_Oremove1(X1,X3,X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4685])). 4.05/4.29 fof(c_0_5388, plain, ![X9625, X9626, X9627, X9628]:((hBOOL(hAPP(hAPP(c_member(X9628),X9627),X9626))|c_Orderings_Obot__class_Obot(tc_fun(X9625,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X9625,X9628,hAPP(c_COMBK(X9628,X9625),X9627)),X9626))&(~hBOOL(hAPP(hAPP(c_member(X9628),X9627),X9626))|hAPP(c_Set_Ovimage(X9625,X9628,hAPP(c_COMBK(X9628,X9625),X9627)),X9626)=c_Orderings_Otop__class_Otop(tc_fun(X9625,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_vimage__const])])])). 4.05/4.29 fof(c_0_5389, plain, ![X10340, X10341, X10342, X10343, X10344]:((~hBOOL(hAPP(hAPP(c_member(X10344),X10343),hAPP(c_Set_Ovimage(X10344,X10342,X10341),hAPP(hAPP(c_Set_Oinsert(X10342),X10340),c_Orderings_Obot__class_Obot(tc_fun(X10342,tc_HOL_Obool))))))|hAPP(X10341,X10343)=X10340)&(hAPP(X10341,X10343)!=X10340|hBOOL(hAPP(hAPP(c_member(X10344),X10343),hAPP(c_Set_Ovimage(X10344,X10342,X10341),hAPP(hAPP(c_Set_Oinsert(X10342),X10340),c_Orderings_Obot__class_Obot(tc_fun(X10342,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__singleton__eq])])). 4.05/4.29 fof(c_0_5390, plain, ![X14939, X14940, X14941, X14942, X14943]:(~hBOOL(hAPP(hAPP(c_member(X14943),hAPP(X14942,X14941)),X14940))|hBOOL(hAPP(hAPP(c_member(X14939),X14941),hAPP(c_Set_Ovimage(X14939,X14943,X14942),X14940)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_vimageI2])])])). 4.05/4.29 fof(c_0_5391, plain, ![X5213, X5214, X5215, X5216, X5217]:(~hBOOL(hAPP(hAPP(c_member(X5217),X5216),hAPP(c_Set_Ovimage(X5217,X5215,X5214),X5213)))|hBOOL(hAPP(hAPP(c_member(X5215),hAPP(X5214,X5216)),X5213))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageD])])). 4.05/4.29 cnf(c_0_5392, 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_4660])). 4.05/4.29 cnf(c_0_5393, 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_4659])). 4.05/4.29 fof(c_0_5394, plain, ![X3257, X3258]:(~class_Int_Onumber__ring(X3258)|hAPP(c_Int_Onumber__class_Onumber__of(X3258),c_Int_Opred(X3257))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3258),hAPP(c_Groups_Ouminus__class_Ouminus(X3258),c_Groups_Oone__class_Oone(X3258))),hAPP(c_Int_Onumber__class_Onumber__of(X3258),X3257))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__pred])])). 4.05/4.29 fof(c_0_5395, plain, ![X5339, X5340]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5340))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5339))|hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5340,X5339))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X5340),hAPP(c_Int_Onat,X5339)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__mod__distrib])])])). 4.05/4.29 fof(c_0_5396, plain, ![X15820, X15821, X15822]:((hAPP(c_Int_Onumber__class_Onumber__of(X15822),X15820)!=hAPP(c_Int_Onumber__class_Onumber__of(X15822),X15821)|c_Int_Oiszero(X15822,hAPP(c_Int_Onumber__class_Onumber__of(X15822),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15821),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X15820))))|~class_Int_Onumber__ring(X15822))&(~c_Int_Oiszero(X15822,hAPP(c_Int_Onumber__class_Onumber__of(X15822),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15821),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X15820))))|hAPP(c_Int_Onumber__class_Onumber__of(X15822),X15820)=hAPP(c_Int_Onumber__class_Onumber__of(X15822),X15821)|~class_Int_Onumber__ring(X15822))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__number__of__eq])])])])). 4.05/4.29 cnf(c_0_5397, 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_4686])). 4.05/4.29 cnf(c_0_5398, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4687, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.29 cnf(c_0_5399, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4688, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.29 cnf(c_0_5400, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X1))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4689, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.29 cnf(c_0_5401, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OPls))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4690, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.29 cnf(c_0_5402, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OPls))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4691, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.29 cnf(c_0_5403, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4692, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.29 cnf(c_0_5404, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4693, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.29 cnf(c_0_5405, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4694, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.29 cnf(c_0_5406, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4695, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.29 cnf(c_0_5407, plain, (X1=c_Int_OPls|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)!=c_Int_OPls), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4696, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.29 cnf(c_0_5408, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OPls))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4697, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.29 cnf(c_0_5409, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4698, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.29 fof(c_0_5410, plain, ![X12645, X12646]:((~c_Relation_Orefl__on(X12646,c_Orderings_Otop__class_Otop(tc_fun(X12646,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X12646,X12646)),hAPP(c_Product__Type_Oprod_Oprod__case(X12646,X12646,tc_HOL_Obool),X12645)))|c_Predicate_Oreflp(X12646,X12645))&(~c_Predicate_Oreflp(X12646,X12645)|c_Relation_Orefl__on(X12646,c_Orderings_Otop__class_Otop(tc_fun(X12646,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X12646,X12646)),hAPP(c_Product__Type_Oprod_Oprod__case(X12646,X12646,tc_HOL_Obool),X12645))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflp__def])])). 4.05/4.29 cnf(c_0_5411, 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_4699])). 4.05/4.29 fof(c_0_5412, plain, ![X3341, X3342, X3343, X3344, X3346, X3347]:(((hAPP(X3342,esk109_4(X3341,X3342,X3343,X3344))=X3341|~hBOOL(hAPP(hAPP(c_member(X3343),X3341),hAPP(c_Set_Oimage(X3344,X3343,X3342),c_Orderings_Otop__class_Otop(tc_fun(X3344,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X3344,X3343,X3342,c_Orderings_Otop__class_Otop(tc_fun(X3344,tc_HOL_Obool))))&(X3341!=hAPP(X3342,X3346)|X3346=esk109_4(X3341,X3342,X3343,X3344)|~hBOOL(hAPP(hAPP(c_member(X3343),X3341),hAPP(c_Set_Oimage(X3344,X3343,X3342),c_Orderings_Otop__class_Otop(tc_fun(X3344,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X3344,X3343,X3342,c_Orderings_Otop__class_Otop(tc_fun(X3344,tc_HOL_Obool)))))&((X3341=hAPP(X3342,esk110_5(X3341,X3342,X3343,X3344,X3347))|hAPP(X3342,X3347)!=X3341|hBOOL(hAPP(hAPP(c_member(X3343),X3341),hAPP(c_Set_Oimage(X3344,X3343,X3342),c_Orderings_Otop__class_Otop(tc_fun(X3344,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X3344,X3343,X3342,c_Orderings_Otop__class_Otop(tc_fun(X3344,tc_HOL_Obool))))&(esk110_5(X3341,X3342,X3343,X3344,X3347)!=X3347|hAPP(X3342,X3347)!=X3341|hBOOL(hAPP(hAPP(c_member(X3343),X3341),hAPP(c_Set_Oimage(X3344,X3343,X3342),c_Orderings_Otop__class_Otop(tc_fun(X3344,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X3344,X3343,X3342,c_Orderings_Otop__class_Otop(tc_fun(X3344,tc_HOL_Obool)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_range__ex1__eq])])])])])])). 4.05/4.29 fof(c_0_5413, plain, ![X6943, X6944, X6945, X6946]:hBOOL(hAPP(hAPP(c_member(X6946),hAPP(X6945,X6944)),hAPP(c_Set_Oimage(X6943,X6946,X6945),c_Orderings_Otop__class_Otop(tc_fun(X6943,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_rangeI])). 4.05/4.29 fof(c_0_5414, plain, ![X13994, X13995, X13996, X13997, X13998]:((X13995!=X13994|hAPP(hAPP(c_List_Omap(X13998,X13997),X13996),X13994)=hAPP(hAPP(c_List_Omap(X13998,X13997),X13996),X13995)|~c_Fun_Oinj__on(X13998,X13997,X13996,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13998,tc_HOL_Obool)),hAPP(c_List_Oset(X13998),X13995)),hAPP(c_List_Oset(X13998),X13994))))&(hAPP(hAPP(c_List_Omap(X13998,X13997),X13996),X13994)!=hAPP(hAPP(c_List_Omap(X13998,X13997),X13996),X13995)|X13995=X13994|~c_Fun_Oinj__on(X13998,X13997,X13996,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13998,tc_HOL_Obool)),hAPP(c_List_Oset(X13998),X13995)),hAPP(c_List_Oset(X13998),X13994))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__map__eq__map])])])). 4.05/4.29 fof(c_0_5415, plain, ![X12429, X12430, X12431, X12432, X12433]:((~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X12431,X12432)),X12430),X12429))|(~hBOOL(hAPP(hAPP(c_member(X12431),X12433),hAPP(c_List_Oset(X12431),c_Enum_Oenum__class_Oenum(X12431))))|hAPP(X12430,X12433)=hAPP(X12429,X12433))|(~class_Enum_Oenum(X12431)|~class_HOL_Oequal(X12432)))&((hBOOL(hAPP(hAPP(c_member(X12431),esk380_4(X12429,X12430,X12431,X12432)),hAPP(c_List_Oset(X12431),c_Enum_Oenum__class_Oenum(X12431))))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X12431,X12432)),X12430),X12429))|(~class_Enum_Oenum(X12431)|~class_HOL_Oequal(X12432)))&(hAPP(X12430,esk380_4(X12429,X12430,X12431,X12432))!=hAPP(X12429,esk380_4(X12429,X12430,X12431,X12432))|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X12431,X12432)),X12430),X12429))|(~class_Enum_Oenum(X12431)|~class_HOL_Oequal(X12432))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equal__fun__def])])])])])])). 4.05/4.29 fof(c_0_5416, plain, ![X7953, X7954]:(~class_Enum_Oenum(X7954)|hBOOL(hAPP(hAPP(c_member(X7954),X7953),hAPP(c_List_Oset(X7954),c_Enum_Oenum__class_Oenum(X7954))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__enum])])). 4.05/4.29 fof(c_0_5417, plain, ![X9267, X9268, X9269]:(~class_Orderings_Olinorder(X9269)|c_Big__Operators_Olattice_OInf__fin(X9269,c_Orderings_Oord__class_Omin(X9269),hAPP(c_List_Oset(X9269),hAPP(hAPP(c_List_Olist_OCons(X9269),X9268),X9267)))=hAPP(c_List_Ofoldl(X9269,X9269,c_Orderings_Oord__class_Omin(X9269),X9268),X9267)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin__set__fold])])])). 4.05/4.29 fof(c_0_5418, plain, ![X458, X459, X460]:hAPP(c_List_Oset(X460),hAPP(hAPP(c_List_Olist_OCons(X460),X459),X458))=hAPP(hAPP(c_Set_Oinsert(X460),X459),hAPP(c_List_Oset(X460),X458)), inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I2_J])). 4.05/4.29 fof(c_0_5419, plain, ![X14494, X14495, X14496]:(~class_Orderings_Olinorder(X14496)|hAPP(c_List_Ofoldl(X14496,X14496,c_Orderings_Oord__class_Omax(X14496),X14495),X14494)=c_Big__Operators_Olattice_OSup__fin(X14496,c_Orderings_Oord__class_Omax(X14496),hAPP(c_List_Oset(X14496),hAPP(hAPP(c_List_Olist_OCons(X14496),X14495),X14494)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin__set__fold])])). 4.05/4.29 fof(c_0_5420, plain, ![X2225]:hAPP(c_Nat_OSuc,X2225)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2225), inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left])). 4.05/4.29 fof(c_0_5421, plain, ![X5353, X5354]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5353),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Oring__1__class_Oof__int(X5354),X5353)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5354),hAPP(c_Int_Onat,X5353))|~class_Rings_Oring__1(X5354))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5353),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Oring__1__class_Oof__int(X5354),X5353)=hAPP(c_Groups_Ouminus__class_Ouminus(X5354),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5354),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5353))))|~class_Rings_Oring__1(X5354))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__of__nat])])])])). 4.05/4.29 fof(c_0_5422, plain, ![X7438, X7439, X7440]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7440)),X7439)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|hAPP(c_List_Orotate(X7440,X7438),X7439)=X7439), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__length01])])). 4.05/4.29 fof(c_0_5423, plain, ![X5531, X5532, X5533, X5534, X5535, X5536, X5537]:(hAPP(X5537,X5536)!=hAPP(c_Option_Ooption_OSome(X5535),X5534)|hAPP(X5531,X5534)=c_Map_Omap__comp(X5535,X5533,X5532,X5531,X5537,X5536)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__comp__simps_I2_J])])). 4.05/4.29 cnf(c_0_5424, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_4700])). 4.05/4.29 cnf(c_0_5425, 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_4701])). 4.05/4.29 cnf(c_0_5426, 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_4702])). 4.05/4.29 cnf(c_0_5427, 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_4703])). 4.05/4.29 cnf(c_0_5428, 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_4704])). 4.05/4.29 cnf(c_0_5429, 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_4705])). 4.05/4.29 cnf(c_0_5430, 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_4706])). 4.05/4.29 cnf(c_0_5431, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1))), inference(split_conjunct,[status(thm)],[c_0_4707])). 4.05/4.29 cnf(c_0_5432, 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_4708])). 4.05/4.29 cnf(c_0_5433, 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_4709])). 4.05/4.29 cnf(c_0_5434, 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_4710])). 4.05/4.29 cnf(c_0_5435, 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_4711])). 4.05/4.29 cnf(c_0_5436, 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_4665])). 4.05/4.29 fof(c_0_5437, plain, ![X13621, X13622]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13622))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13622),X13621)),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),X13622),X13621))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__neg__trivial])])). 4.05/4.29 fof(c_0_5438, plain, ![X16237, X16238, X16239]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16237),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16239),hAPP(c_Nat_OSuc,X16238))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16239),X16238)),X16237))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16237),X16239)=X16238|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16239)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16237),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16239),hAPP(c_Nat_OSuc,X16238))))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16237),X16239)!=X16238|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16239)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16239),X16238)),X16237))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16237),X16239)!=X16238|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X16239))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__div__lemma])])])). 4.05/4.29 fof(c_0_5439, plain, ![X11834, X11835]:((hAPP(c_Int_Onumber__class_Onumber__of(X11835),X11834)!=c_Groups_Ozero__class_Ozero(X11835)|c_Int_Oiszero(X11835,hAPP(c_Int_Onumber__class_Onumber__of(X11835),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11834))))|~class_Int_Onumber__ring(X11835))&(~c_Int_Oiszero(X11835,hAPP(c_Int_Onumber__class_Onumber__of(X11835),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11834))))|hAPP(c_Int_Onumber__class_Onumber__of(X11835),X11834)=c_Groups_Ozero__class_Ozero(X11835)|~class_Int_Onumber__ring(X11835))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__special_I1_J])])])])). 4.05/4.29 cnf(c_0_5440, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X1)=X1), inference(split_conjunct,[status(thm)],[c_0_4712])). 4.05/4.29 fof(c_0_5441, plain, ![X2186, X2187]:((c_Groups_Ozero__class_Ozero(X2187)!=hAPP(c_Int_Onumber__class_Onumber__of(X2187),X2186)|c_Int_Oiszero(X2187,hAPP(c_Int_Onumber__class_Onumber__of(X2187),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2186),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))|~class_Int_Onumber__ring(X2187))&(~c_Int_Oiszero(X2187,hAPP(c_Int_Onumber__class_Onumber__of(X2187),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2186),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))|c_Groups_Ozero__class_Ozero(X2187)=hAPP(c_Int_Onumber__class_Onumber__of(X2187),X2186)|~class_Int_Onumber__ring(X2187))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I3_J])])])). 4.05/4.29 cnf(c_0_5442, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)=c_Int_OPls), inference(split_conjunct,[status(thm)],[fact_minus__Pls])). 4.05/4.29 fof(c_0_5443, plain, ![X2556, X2557]:((~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X2557)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2556)))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2557),X2556))|~c_Nat__Transfer_Onat__set(X2556)|~c_Nat__Transfer_Ois__nat(X2557))&(~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2557),X2556))|hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X2557)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2556)))|~c_Nat__Transfer_Onat__set(X2556)|~c_Nat__Transfer_Ois__nat(X2557))), 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_I2_J])])])])). 4.05/4.29 fof(c_0_5444, plain, ![X4240, X4241]:(~c_Nat__Transfer_Onat__set(X4241)|(~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X4240),X4241))|c_Nat__Transfer_Ois__nat(X4240))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J])])). 4.05/4.29 cnf(c_0_5445, 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),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_Int_Osucc(X1))), inference(split_conjunct,[status(thm)],[c_0_4713])). 4.05/4.29 fof(c_0_5446, plain, ![X16963, X16964, X16965, X16967, X16968, X16969, X16970]:(((hBOOL(hAPP(hAPP(c_member(tc_fun(X16965,tc_HOL_Obool)),esk509_3(X16963,X16964,X16965)),X16964))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16965,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X16965,tc_HOL_Obool),X16964)),X16963)=c_Orderings_Obot__class_Obot(tc_fun(X16965,tc_HOL_Obool)))&(c_Orderings_Obot__class_Obot(tc_fun(X16965,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16965,tc_HOL_Obool)),esk509_3(X16963,X16964,X16965)),X16963)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16965,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X16965,tc_HOL_Obool),X16964)),X16963)=c_Orderings_Obot__class_Obot(tc_fun(X16965,tc_HOL_Obool))))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16969,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X16969,tc_HOL_Obool),X16968)),X16967)!=c_Orderings_Obot__class_Obot(tc_fun(X16969,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_member(tc_fun(X16969,tc_HOL_Obool)),X16970),X16968))|c_Orderings_Obot__class_Obot(tc_fun(X16969,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16969,tc_HOL_Obool)),X16970),X16967)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__disjoint])])])])])])). 4.05/4.29 fof(c_0_5447, plain, ![X6685, X6686, X6687, X6689, X6690, X6691, X6692]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X6685,X6685)),esk206_3(X6685,X6686,X6687)),hAPP(c_List_Oset(tc_prod(X6685,X6685)),hAPP(hAPP(c_List_Ozip(X6685,X6685),X6687),X6686))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6685)),X6686)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6685)),X6687)|X6686=X6687)&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6685,X6685,tc_HOL_Obool),c_fequal),esk206_3(X6685,X6686,X6687)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6685)),X6686)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6685)),X6687)|X6686=X6687))&((~hBOOL(hAPP(hAPP(c_member(tc_prod(X6689,X6689)),X6692),hAPP(c_List_Oset(tc_prod(X6689,X6689)),hAPP(hAPP(c_List_Ozip(X6689,X6689),X6691),X6690))))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6689,X6689,tc_HOL_Obool),c_fequal),X6692))|X6690!=X6691)&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6689)),X6690)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6689)),X6691)|X6690!=X6691))), 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__zip__eq])])])])])])])). 4.05/4.29 fof(c_0_5448, plain, ![X16103, X16104, X16105, X16106]:((hBOOL(hAPP(hAPP(c_member(X16106),esk482_4(X16103,X16104,X16105,X16106)),c_Option_Oset(X16106,X16105)))|(X16105!=hAPP(c_Option_Ooption_OSome(X16106),X16103)|hBOOL(hAPP(X16104,X16103))))&(~hBOOL(hAPP(X16104,esk482_4(X16103,X16104,X16105,X16106)))|(X16105!=hAPP(c_Option_Ooption_OSome(X16106),X16103)|hBOOL(hAPP(X16104,X16103))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ospec])])])])])). 4.05/4.29 fof(c_0_5449, plain, ![X2286, X2287]:c_Option_Oset(X2287,hAPP(c_Option_Ooption_OSome(X2287),X2286))=hAPP(hAPP(c_Set_Oinsert(X2287),X2286),c_Orderings_Obot__class_Obot(tc_fun(X2287,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Option_Oset_Osimps_I2_J])). 4.05/4.29 fof(c_0_5450, plain, ![X8051, X8052]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8052))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8051))|hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X8052,X8051))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X8052)),hAPP(c_Int_Onat,X8051)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J])])). 4.05/4.29 fof(c_0_5451, plain, ![X5049]:((~c_Com_OWT__bodies|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),X5049),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),X5049))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),esk155_0),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))|c_Com_OWT__bodies)&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),esk155_0))|c_Com_OWT__bodies))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_WT__bodies__def])])])])])])). 4.05/4.29 fof(c_0_5452, plain, ![X6667, X6668, X6669]:((~hBOOL(hAPP(c_List_Odistinct(X6669),hAPP(c_List_Orotate(X6669,X6668),X6667)))|hBOOL(hAPP(c_List_Odistinct(X6669),X6667)))&(~hBOOL(hAPP(c_List_Odistinct(X6669),X6667))|hBOOL(hAPP(c_List_Odistinct(X6669),hAPP(c_List_Orotate(X6669,X6668),X6667))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__rotate])])). 4.05/4.29 fof(c_0_5453, plain, ![X1563, X1564, X1565, X1566]:((X1565!=hAPP(hAPP(c_List_Otake(X1566),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1566)),X1565)),X1563)|X1564!=hAPP(hAPP(c_List_Odrop(X1566),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1566)),X1565)),X1563)|X1563=hAPP(hAPP(c_List_Oappend(X1566),X1565),X1564))&((X1565=hAPP(hAPP(c_List_Otake(X1566),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1566)),X1565)),X1563)|X1563!=hAPP(hAPP(c_List_Oappend(X1566),X1565),X1564))&(X1564=hAPP(hAPP(c_List_Odrop(X1566),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1566)),X1565)),X1563)|X1563!=hAPP(hAPP(c_List_Oappend(X1566),X1565),X1564)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__conv__conj])])])). 4.05/4.29 fof(c_0_5454, plain, ![X10960, X10961]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10961),X10960))|c_List_Olast(tc_Nat_Onat,c_List_Oupt(X10961,X10960))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10960),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__upt])])). 4.05/4.29 fof(c_0_5455, plain, ![X8959, X8960, X8961, X8962, X8963, X8964]:(~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8964)|(c_Groups_Ozero__class_Ozero(X8964)=X8963|(X8961!=X8962|X8960=X8959|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8964),X8961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8964),X8963),X8959))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8964),X8962),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8964),X8963),X8960))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__scale__eq__noteq])])])). 4.05/4.29 fof(c_0_5456, plain, ![X440, X441, X442]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X440),X442)),X441))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X440),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X441),X442)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X442),X441)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X440),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X441),X442)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X440),X442)),X441))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X442),X441)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__diff__conv2])])])])). 4.05/4.29 fof(c_0_5457, plain, ![X3019, X3020, X3021]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3021),X3020)),X3019))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3020),X3019))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__leD2])])])). 4.05/4.29 fof(c_0_5458, plain, ![X2036, X2037, X2038]:(~class_Orderings_Olinorder(X2038)|c_List_Olinorder__class_Osorted(X2038,hAPP(c_List_Ofilter(X2038,hAPP(hAPP(c_COMBC(X2038,X2038,tc_HOL_Obool),c_fequal),hAPP(X2037,X2036))),X2036))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__same])])). 4.05/4.29 cnf(c_0_5459, 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_4644])). 4.05/4.29 cnf(c_0_5460, 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_4643])). 4.05/4.29 fof(c_0_5461, plain, ![X17631, X17632, X17633]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17633,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17632)),X17631))|X17631=hAPP(c_List_Orotate(X17632,X17633),X17631)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__id])])). 4.05/4.29 fof(c_0_5462, plain, ![X9056, X9057, X9058, X9059]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9058)),X9059)),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X9057|X9056=c_List_Olast(X9058,hAPP(hAPP(c_List_Olist__update(X9058,X9059),X9057),X9056))|c_List_Olist_ONil(X9058)=X9059)&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9058)),X9059)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X9057|c_List_Olast(X9058,X9059)=c_List_Olast(X9058,hAPP(hAPP(c_List_Olist__update(X9058,X9059),X9057),X9056))|c_List_Olist_ONil(X9058)=X9059)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__list__update])])])). 4.05/4.29 fof(c_0_5463, plain, ![X2676, X2677]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2677),X2676))|hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X2676),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2677),X2676))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2677),hAPP(c_Nat_OSuc,X2676)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2677),X2676))|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2677),hAPP(c_Nat_OSuc,X2676))=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_atLeastLessThanSuc])])])). 4.05/4.29 fof(c_0_5464, plain, ![X16203, X16204]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X16204))|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),X16204),X16203)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__one__le__power])])). 4.05/4.29 cnf(c_0_5465, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(c_Int_OPls))=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_4714])). 4.05/4.29 fof(c_0_5466, plain, ![X1571, X1572, X1573, X1576, X1577, X1578, X1579, X1580]:(((((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1571|c_Orderings_Obot__class_Obot(tc_fun(X1573,tc_HOL_Obool))=esk49_3(X1571,X1572,X1573)|hAPP(c_Nat_OSuc,X1571)!=hAPP(c_Finite__Set_Ocard(X1573),X1572))&(hAPP(c_Finite__Set_Ocard(X1573),esk49_3(X1571,X1572,X1573))=X1571|hAPP(c_Nat_OSuc,X1571)!=hAPP(c_Finite__Set_Ocard(X1573),X1572)))&(~hBOOL(hAPP(hAPP(c_member(X1573),esk48_3(X1571,X1572,X1573)),esk49_3(X1571,X1572,X1573)))|hAPP(c_Nat_OSuc,X1571)!=hAPP(c_Finite__Set_Ocard(X1573),X1572)))&(X1572=hAPP(hAPP(c_Set_Oinsert(X1573),esk48_3(X1571,X1572,X1573)),esk49_3(X1571,X1572,X1573))|hAPP(c_Nat_OSuc,X1571)!=hAPP(c_Finite__Set_Ocard(X1573),X1572)))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1576|hAPP(c_Finite__Set_Ocard(X1578),X1580)!=X1576|hBOOL(hAPP(hAPP(c_member(X1578),X1579),X1580))|X1577!=hAPP(hAPP(c_Set_Oinsert(X1578),X1579),X1580)|hAPP(c_Nat_OSuc,X1576)=hAPP(c_Finite__Set_Ocard(X1578),X1577))&(c_Orderings_Obot__class_Obot(tc_fun(X1578,tc_HOL_Obool))!=X1580|hAPP(c_Finite__Set_Ocard(X1578),X1580)!=X1576|hBOOL(hAPP(hAPP(c_member(X1578),X1579),X1580))|X1577!=hAPP(hAPP(c_Set_Oinsert(X1578),X1579),X1580)|hAPP(c_Nat_OSuc,X1576)=hAPP(c_Finite__Set_Ocard(X1578),X1577)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Suc__eq])])])])])])])). 4.05/4.29 fof(c_0_5467, plain, ![X16477, X16478, X16479]:(~class_Lattices_Olattice(X16479)|c_Big__Operators_Olattice__class_OInf__fin(X16479,hAPP(c_List_Oset(X16479),hAPP(hAPP(c_List_Olist_OCons(X16479),X16478),X16477)))=hAPP(c_List_Ofoldl(X16479,X16479,c_Lattices_Osemilattice__inf__class_Oinf(X16479),X16478),X16477)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin__set__fold])])])). 4.05/4.29 fof(c_0_5468, plain, ![X16859, X16860, X16861]:(~class_Lattices_Olattice(X16861)|c_Big__Operators_Olattice__class_OSup__fin(X16861,hAPP(c_List_Oset(X16861),hAPP(hAPP(c_List_Olist_OCons(X16861),X16860),X16859)))=hAPP(c_List_Ofoldl(X16861,X16861,c_Lattices_Osemilattice__sup__class_Osup(X16861),X16860),X16859)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin__set__fold])])). 4.05/4.29 fof(c_0_5469, plain, ![X15330, X15331, X15332]:(~class_Orderings_Olinorder(X15332)|hAPP(c_List_Ofoldl(X15332,X15332,c_Orderings_Oord__class_Omin(X15332),X15331),X15330)=c_Big__Operators_Olinorder__class_OMin(X15332,hAPP(c_List_Oset(X15332),hAPP(hAPP(c_List_Olist_OCons(X15332),X15331),X15330)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min__fin__set__fold])])])). 4.05/4.29 fof(c_0_5470, plain, ![X17684, X17685, X17686]:(~class_Orderings_Olinorder(X17686)|hAPP(c_List_Ofoldl(X17686,X17686,c_Orderings_Oord__class_Omax(X17686),X17685),X17684)=c_Big__Operators_Olinorder__class_OMax(X17686,hAPP(c_List_Oset(X17686),hAPP(hAPP(c_List_Olist_OCons(X17686),X17685),X17684)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__fin__set__fold])])). 4.05/4.29 fof(c_0_5471, plain, ![X6670, X6671]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6671))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X6671)),hAPP(c_Int_Onat,X6670))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6671),X6670))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__mult__distrib])])])). 4.05/4.29 fof(c_0_5472, plain, ![X8841, X8842]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8842))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X8842)),hAPP(c_Int_Onat,X8841))=hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8842),X8841))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__div__distrib])])])). 4.05/4.29 fof(c_0_5473, plain, ![X3255, X3256]:((~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),X3255)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3256),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3255))=hAPP(c_Int_Onumber__class_Onumber__of(X3256),X3255)|~class_Int_Onumber__ring(X3256))&(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),X3255)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3256),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3255))=c_Groups_Ozero__class_Ozero(X3256)|~class_Int_Onumber__ring(X3256))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__lemma])])])])). 4.05/4.29 fof(c_0_5474, plain, ![X6995, X6996, X6997, X6998]:(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X6996|~hBOOL(hAPP(hAPP(c_member(X6998),X6997),hAPP(c_List_Oset(X6998),c_List_Oreplicate(X6998,X6996,X6995)))))&(X6997=X6995|~hBOOL(hAPP(hAPP(c_member(X6998),X6997),hAPP(c_List_Oset(X6998),c_List_Oreplicate(X6998,X6996,X6995))))))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X6996|X6997!=X6995|hBOOL(hAPP(hAPP(c_member(X6998),X6997),hAPP(c_List_Oset(X6998),c_List_Oreplicate(X6998,X6996,X6995)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__replicate])])])). 4.05/4.29 fof(c_0_5475, plain, ![X14668]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14668))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X14668),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_OMin),X14668)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmod__minus1])])])). 4.05/4.29 cnf(c_0_5476, plain, (X2=X1|c_Int_OBit1(X1)!=c_Int_OBit1(X2)), inference(split_conjunct,[status(thm)],[c_0_4715])). 4.05/4.29 fof(c_0_5477, plain, ![X13109, X13110, X13111, X13112]:((X13109=c_List_Olist_ONil(X13112)|X13110!=c_List_Olast(X13112,X13109)|c_List_Obutlast(X13112,X13109)!=X13111|X13109=hAPP(hAPP(c_List_Oappend(X13112),X13111),hAPP(hAPP(c_List_Olist_OCons(X13112),X13110),c_List_Olist_ONil(X13112))))&(((X13109!=c_List_Olist_ONil(X13112)|X13109!=hAPP(hAPP(c_List_Oappend(X13112),X13111),hAPP(hAPP(c_List_Olist_OCons(X13112),X13110),c_List_Olist_ONil(X13112))))&(X13110=c_List_Olast(X13112,X13109)|X13109!=hAPP(hAPP(c_List_Oappend(X13112),X13111),hAPP(hAPP(c_List_Olist_OCons(X13112),X13110),c_List_Olist_ONil(X13112)))))&(c_List_Obutlast(X13112,X13109)=X13111|X13109!=hAPP(hAPP(c_List_Oappend(X13112),X13111),hAPP(hAPP(c_List_Olist_OCons(X13112),X13110),c_List_Olist_ONil(X13112)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__eq__iff__butlast])])])). 4.05/4.29 fof(c_0_5478, plain, ![X15823, X15824]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15824),X15823))|c_Divides_Odivmod__nat(X15824,X15823)=hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15824)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__nat__base])])])). 4.05/4.29 fof(c_0_5479, plain, ![X9031, X9032, X9033]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9033),c_Groups_Ozero__class_Ozero(X9033)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9033),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9033),X9032),X9032)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9033),X9031),X9031))))|(c_Groups_Ozero__class_Ozero(X9033)!=X9031|X9032!=c_Groups_Ozero__class_Ozero(X9033))|~class_Rings_Olinordered__ring__strict(X9033))&((c_Groups_Ozero__class_Ozero(X9033)=X9031|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9033),c_Groups_Ozero__class_Ozero(X9033)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9033),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9033),X9032),X9032)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9033),X9031),X9031))))|~class_Rings_Olinordered__ring__strict(X9033))&(X9032=c_Groups_Ozero__class_Ozero(X9033)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9033),c_Groups_Ozero__class_Ozero(X9033)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9033),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9033),X9032),X9032)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9033),X9031),X9031))))|~class_Rings_Olinordered__ring__strict(X9033)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sum__squares__gt__zero__iff])])])])). 4.05/4.29 fof(c_0_5480, plain, ![X2853]:(~c_List_Onat__list(X2853)|X2853=c_List_Oembed__list(c_List_Oreturn__list(X2853))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__list__return__embed])])). 4.05/4.29 fof(c_0_5481, plain, ![X5610, X5611]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5610),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5611),hAPP(c_Int_Onumber__class_Onumber__of(X5611),X5610)),c_Groups_Ozero__class_Ozero(X5611)))|(~class_Rings_Olinordered__idom(X5611)|~class_Int_Onumber__ring(X5611)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5611),hAPP(c_Int_Onumber__class_Onumber__of(X5611),X5610)),c_Groups_Ozero__class_Ozero(X5611)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5610),c_Int_OPls))|(~class_Rings_Olinordered__idom(X5611)|~class_Int_Onumber__ring(X5611)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__special_I3_J])])])])). 4.05/4.29 fof(c_0_5482, plain, ![X7590, X7591]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7590),c_Int_OPls))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7591),hAPP(c_Int_Onumber__class_Onumber__of(X7591),X7590)),c_Groups_Ozero__class_Ozero(X7591)))|(~class_Int_Onumber__ring(X7591)|~class_Rings_Olinordered__idom(X7591)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7591),hAPP(c_Int_Onumber__class_Onumber__of(X7591),X7590)),c_Groups_Ozero__class_Ozero(X7591)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7590),c_Int_OPls))|(~class_Int_Onumber__ring(X7591)|~class_Rings_Olinordered__idom(X7591)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__special_I3_J])])])])). 4.05/4.29 fof(c_0_5483, plain, ![X9602, X9603]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X9602))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9603),c_Groups_Ozero__class_Ozero(X9603)),hAPP(c_Int_Onumber__class_Onumber__of(X9603),X9602)))|(~class_Int_Onumber__ring(X9603)|~class_Rings_Olinordered__idom(X9603)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9603),c_Groups_Ozero__class_Ozero(X9603)),hAPP(c_Int_Onumber__class_Onumber__of(X9603),X9602)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X9602))|(~class_Int_Onumber__ring(X9603)|~class_Rings_Olinordered__idom(X9603)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__special_I1_J])])])])). 4.05/4.29 fof(c_0_5484, plain, ![X14294, X14295]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14295),c_Groups_Ozero__class_Ozero(X14295)),hAPP(c_Int_Onumber__class_Onumber__of(X14295),X14294)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X14294))|(~class_Rings_Olinordered__idom(X14295)|~class_Int_Onumber__ring(X14295)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X14294))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14295),c_Groups_Ozero__class_Ozero(X14295)),hAPP(c_Int_Onumber__class_Onumber__of(X14295),X14294)))|(~class_Rings_Olinordered__idom(X14295)|~class_Int_Onumber__ring(X14295)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__special_I1_J])])])])). 4.05/4.29 fof(c_0_5485, plain, ![X1590, X1591, X1593]:(((hBOOL(hAPP(X1591,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk50_2(X1590,X1591)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~hBOOL(hAPP(X1591,X1590))|hBOOL(hAPP(X1591,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1593),esk50_2(X1590,X1591)))|~hBOOL(hAPP(X1591,X1593))|~hBOOL(hAPP(X1591,X1590))|hBOOL(hAPP(X1591,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk50_2(X1590,X1591)),X1590))|~hBOOL(hAPP(X1591,X1590))|hBOOL(hAPP(X1591,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less])])])])])])). 4.05/4.29 fof(c_0_5486, plain, ![X11198]:(~class_Orderings_Owellorder(X11198)|c_Wellfounded_Owf(X11198,hAPP(c_Set_OCollect(tc_prod(X11198,X11198)),hAPP(c_Product__Type_Oprod_Oprod__case(X11198,X11198,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X11198))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf])])). 4.05/4.29 cnf(c_0_5487, 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_4716])). 4.05/4.29 cnf(c_0_5488, plain, (c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X2))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4717])). 4.05/4.29 cnf(c_0_5489, 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_4699])). 4.05/4.29 cnf(c_0_5490, 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_4641])). 4.05/4.29 fof(c_0_5491, plain, ![X10262, X10263]:(((X10263=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X10262=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X10262),X10263)),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),X10262))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X10263)))=c_Nitpick_Onorm__frac(X10262,X10263)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10263),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X10262|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(X10262,X10263)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10263),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&(X10263!=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))=c_Nitpick_Onorm__frac(X10262,X10263)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10263),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10263),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Nitpick_Onorm__frac(X10262,X10263)=c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X10262),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X10263)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_norm__frac_Osimps])])])])). 4.05/4.29 fof(c_0_5492, plain, ![X6413, X6414]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6414),X6413))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6414)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6413))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6414),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),X6414)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6413)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6414)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X6413)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6414),X6413))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6414),c_Int_OPls))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__nat__number__of])])])])). 4.05/4.29 fof(c_0_5493, plain, ![X7925, X7926, X7928, X7929, X7930]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7925),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk254_2(X7925,X7926))=X7925|hBOOL(hAPP(X7926,hAPP(c_Int_Onat,X7925))))&(~hBOOL(hAPP(X7926,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk254_2(X7925,X7926))=X7925|hBOOL(hAPP(X7926,hAPP(c_Int_Onat,X7925)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7925),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X7926,esk254_2(X7925,X7926)))|hBOOL(hAPP(X7926,hAPP(c_Int_Onat,X7925))))&(~hBOOL(hAPP(X7926,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X7926,esk254_2(X7925,X7926)))|hBOOL(hAPP(X7926,hAPP(c_Int_Onat,X7925))))))&((hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7930)!=X7928|hBOOL(hAPP(X7929,X7930))|~hBOOL(hAPP(X7929,hAPP(c_Int_Onat,X7928))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7928),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X7929,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X7929,hAPP(c_Int_Onat,X7928)))))), 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])])])])])])])). 4.05/4.29 fof(c_0_5494, plain, ![X14301, X14302]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X14301)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X14302),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14301))=hAPP(c_Int_Onumber__class_Onumber__of(X14302),X14301)|~class_Int_Onumber__ring(X14302))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X14301)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X14302),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14301))=c_Groups_Ozero__class_Ozero(X14302)|~class_Int_Onumber__ring(X14302))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__eq])])])])). 4.05/4.29 fof(c_0_5495, plain, ![X10656, X10657]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10657))|hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X10657),X10656))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X10657)),X10656)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J])])])). 4.05/4.29 fof(c_0_5496, plain, ![X10602, X10603]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10603),X10602))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10602))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X10603)),hAPP(c_Int_Onat,X10602))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10603),X10602))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X10603)),hAPP(c_Int_Onat,X10602))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10602))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X10603)),hAPP(c_Int_Onat,X10602)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__conj])])])). 4.05/4.29 fof(c_0_5497, plain, ![X2339, X2340]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2340),X2339))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X2340)),hAPP(c_Int_Onat,X2339)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2340)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X2340)),hAPP(c_Int_Onat,X2339)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2340),X2339))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2340)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__eq__zless])])])). 4.05/4.29 fof(c_0_5498, plain, ![X1446, X1447]:(~c_Wellfounded_OwfP(X1447,X1446)|c_Wellfounded_Oacyclic(X1447,hAPP(c_Set_OCollect(tc_prod(X1447,X1447)),hAPP(c_Product__Type_Oprod_Oprod__case(X1447,X1447,tc_HOL_Obool),X1446)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wfP__acyclicP])])])). 4.05/4.29 fof(c_0_5499, plain, ![X16971, X16972]:((~c_Wellfounded_Owf(X16972,hAPP(c_Set_OCollect(tc_prod(X16972,X16972)),hAPP(c_Product__Type_Oprod_Oprod__case(X16972,X16972,tc_HOL_Obool),X16971)))|c_Wellfounded_OwfP(X16972,X16971))&(~c_Wellfounded_OwfP(X16972,X16971)|c_Wellfounded_Owf(X16972,hAPP(c_Set_OCollect(tc_prod(X16972,X16972)),hAPP(c_Product__Type_Oprod_Oprod__case(X16972,X16972,tc_HOL_Obool),X16971))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__def])])). 4.05/4.29 fof(c_0_5500, plain, ![X6157]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6157))|hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X6157))=hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X6157))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__nat__eq__nat__zadd1])])])). 4.05/4.29 fof(c_0_5501, plain, ![X9352, X9353]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9353),X9352))|X9353=hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X9353,X9352))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__upt])])])). 4.05/4.29 fof(c_0_5502, plain, ![X6417, X6418]:((hBOOL(hAPP(hAPP(c_member(X6418),esk191_2(X6417,X6418)),X6417))|hAPP(c_Finite__Set_Ocard(X6418),X6417)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6418),X6417)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(c_Finite__Set_Ocard(X6418),X6417)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6418),X6417)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card_Oneutral])])])])])). 4.05/4.29 fof(c_0_5503, plain, ![X5595, X5596]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X5596),X5595))|hAPP(c_Finite__Set_Ocard(X5596),X5595)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X5596,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X5596),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5595))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X5596),X5595))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X5596),X5595))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__def])])])). 4.05/4.29 cnf(c_0_5504, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_4700])). 4.05/4.29 cnf(c_0_5505, 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_4701])). 4.05/4.29 cnf(c_0_5506, 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_4702])). 4.05/4.29 cnf(c_0_5507, 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_4704])). 4.05/4.29 cnf(c_0_5508, 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_4703])). 4.05/4.29 cnf(c_0_5509, 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_4705])). 4.05/4.29 cnf(c_0_5510, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1)))), inference(split_conjunct,[status(thm)],[c_0_4707])). 4.05/4.29 cnf(c_0_5511, 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_4708])). 4.05/4.29 cnf(c_0_5512, 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_4718])). 4.05/4.29 fof(c_0_5513, plain, ![X17351, X17352, X17353, X17356, X17357, X17358, X17359, X17360]:(((hBOOL(hAPP(hAPP(c_member(X17353),esk520_3(X17351,X17352,X17353)),X17352))|c_Orderings_Obot__class_Obot(tc_fun(X17353,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17353,tc_HOL_Obool)),X17352),X17351))&((hBOOL(hAPP(hAPP(c_member(X17353),esk521_3(X17351,X17352,X17353)),X17351))|c_Orderings_Obot__class_Obot(tc_fun(X17353,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17353,tc_HOL_Obool)),X17352),X17351))&(esk520_3(X17351,X17352,X17353)=esk521_3(X17351,X17352,X17353)|c_Orderings_Obot__class_Obot(tc_fun(X17353,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17353,tc_HOL_Obool)),X17352),X17351))))&(c_Orderings_Obot__class_Obot(tc_fun(X17358,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17358,tc_HOL_Obool)),X17357),X17356)|(~hBOOL(hAPP(hAPP(c_member(X17358),X17359),X17357))|(~hBOOL(hAPP(hAPP(c_member(X17358),X17360),X17356))|X17359!=X17360)))), 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_disjoint__iff__not__equal])])])])])])). 4.05/4.29 fof(c_0_5514, plain, ![X4601, X4602, X4603, X4604]:((((c_Groups_Ozero__class_Ozero(X4604)=X4602|X4602!=c_Groups_Ozero__class_Ozero(X4604)|X4601=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4604),X4603),X4602)|~class_Fields_Ofield__inverse__zero(X4604))&(X4601!=c_Groups_Ozero__class_Ozero(X4604)|X4602!=c_Groups_Ozero__class_Ozero(X4604)|X4601=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4604),X4603),X4602)|~class_Fields_Ofield__inverse__zero(X4604)))&((c_Groups_Ozero__class_Ozero(X4604)=X4602|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4604),X4601),X4602)!=X4603|X4601=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4604),X4603),X4602)|~class_Fields_Ofield__inverse__zero(X4604))&(X4601!=c_Groups_Ozero__class_Ozero(X4604)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4604),X4601),X4602)!=X4603|X4601=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4604),X4603),X4602)|~class_Fields_Ofield__inverse__zero(X4604))))&((X4602=c_Groups_Ozero__class_Ozero(X4604)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4604),X4601),X4602)=X4603|X4601!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4604),X4603),X4602)|~class_Fields_Ofield__inverse__zero(X4604))&(c_Groups_Ozero__class_Ozero(X4604)!=X4602|X4601=c_Groups_Ozero__class_Ozero(X4604)|X4601!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4604),X4603),X4602)|~class_Fields_Ofield__inverse__zero(X4604)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__eq__eq])])])])). 4.05/4.29 cnf(c_0_5515, 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_4710])). 4.05/4.29 cnf(c_0_5516, 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_4709])). 4.05/4.29 cnf(c_0_5517, 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_4711])). 4.05/4.29 fof(c_0_5518, plain, ![X496]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X496))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X496)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__eq__minus1])])])). 4.05/4.29 fof(c_0_5519, plain, ![X6237, X6238]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X6238)),X6237))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6238),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6237)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6238)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6238),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6237)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X6238)),X6237))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6238)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__iff])])])). 4.05/4.29 fof(c_0_5520, plain, ![X11319, X11320]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11320),X11319),X11319)!=c_Groups_Ozero__class_Ozero(X11320)|X11319=c_Groups_Ozero__class_Ozero(X11320)|~hBOOL(hAPP(hAPP(c_member(X11320),X11319),c_Int_Oring__1__class_OInts(X11320)))|~class_Int_Oring__char__0(X11320))&(X11319!=c_Groups_Ozero__class_Ozero(X11320)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11320),X11319),X11319)=c_Groups_Ozero__class_Ozero(X11320)|~hBOOL(hAPP(hAPP(c_member(X11320),X11319),c_Int_Oring__1__class_OInts(X11320)))|~class_Int_Oring__char__0(X11320))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__double__eq__0__iff])])])])). 4.05/4.29 fof(c_0_5521, plain, ![X13447, X13448, X13449, X13450]:((X13448!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13450),X13447),X13449)|X13447=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13450),X13448),X13449)|c_Groups_Ozero__class_Ozero(X13450)=X13449|~class_Rings_Odivision__ring(X13450))&(X13447!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13450),X13448),X13449)|X13448=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13450),X13447),X13449)|c_Groups_Ozero__class_Ozero(X13450)=X13449|~class_Rings_Odivision__ring(X13450))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonzero__eq__divide__eq])])])])). 4.05/4.29 fof(c_0_5522, plain, ![X10338, X10339]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10339),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10338),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10339),X10338)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10339),X10338))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10339),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10338),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq])])). 4.05/4.29 fof(c_0_5523, plain, ![X16256, X16257, X16258, X16259]:(~class_Rings_Odivision__ring(X16259)|(X16258=c_Groups_Ozero__class_Ozero(X16259)|(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16259),X16256),X16258)!=X16257|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16259),X16257),X16258)=X16256))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__eq__imp])])])). 4.05/4.29 cnf(c_0_5524, 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_4719])). 4.05/4.29 fof(c_0_5525, plain, ![X9977, X9978, X9979, X9980]:(hBOOL(hAPP(X9980,X9979))|hAPP(c_List_Ofilter(X9978,X9980),X9977)=c_List_Oremove1(X9978,X9979,hAPP(c_List_Ofilter(X9978,X9980),X9977))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remove1__filter__not])])])). 4.05/4.29 fof(c_0_5526, plain, ![X12769, X12770, X12771, X12772]:hAPP(c_List_Ofilter(X12772,X12771),c_List_Oremove1(X12772,X12770,X12769))=c_List_Oremove1(X12772,X12770,hAPP(c_List_Ofilter(X12772,X12771),X12769)), inference(variable_rename,[status(thm)],[fact_filter__remove1])). 4.05/4.29 fof(c_0_5527, plain, ![X1304, X1305]:(~class_Int_Onumber__ring(X1305)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1304))|hBOOL(hAPP(hAPP(c_member(X1305),hAPP(c_Int_Onumber__class_Onumber__of(X1305),X1304)),c_Nat_Osemiring__1__class_ONats(X1305))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nats__number__of])])])). 4.05/4.29 fof(c_0_5528, plain, ![X12124, X12125]:((~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),X12125)),X12124)))|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X12124|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X12125))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X12124|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),X12125)),X12124))))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X12125|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),X12125)),X12124)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff])])])). 4.05/4.29 fof(c_0_5529, plain, ![X15132, X15133, X15134]:(X15133!=hAPP(hAPP(c_Relation_Orel__comp(X15134,X15134,X15134),hAPP(c_Relation_Oconverse(X15134,X15134),X15133)),X15133)|(hAPP(c_Relation_ODomain(X15134,X15134),X15133)!=X15132|c_Equiv__Relations_Oequiv(X15134,X15132,X15133))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comp__equivI])])])). 4.05/4.29 fof(c_0_5530, plain, ![X12895, X12896]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12896),hAPP(c_Groups_Oabs__class_Oabs(X12896),X12895)),c_Groups_Ozero__class_Ozero(X12896)))|c_Groups_Ozero__class_Ozero(X12896)=X12895|~class_Groups_Oordered__ab__group__add__abs(X12896))&(c_Groups_Ozero__class_Ozero(X12896)!=X12895|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12896),hAPP(c_Groups_Oabs__class_Oabs(X12896),X12895)),c_Groups_Ozero__class_Ozero(X12896)))|~class_Groups_Oordered__ab__group__add__abs(X12896))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__le__zero__iff])])])])). 4.05/4.29 fof(c_0_5531, plain, ![X15998, X15999, X16000]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X16000,X16000)),hAPP(hAPP(c_Product__Type_OPair(X16000,X16000),X15999),X15998)),c_Relation_OId(X16000)))|X15999=X15998)&(X15999!=X15998|hBOOL(hAPP(hAPP(c_member(tc_prod(X16000,X16000)),hAPP(hAPP(c_Product__Type_OPair(X16000,X16000),X15999),X15998)),c_Relation_OId(X16000))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__in__Id__conv])])). 4.05/4.29 fof(c_0_5532, plain, ![X10226, X10227, X10228]:(((hAPP(c_Groups_Ouminus__class_Ouminus(X10228),X10226)!=X10227|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10228),X10227),X10227)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10228),X10226),X10226)|~class_Rings_Oidom(X10228))&(X10227!=X10226|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10228),X10227),X10227)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10228),X10226),X10226)|~class_Rings_Oidom(X10228)))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10228),X10227),X10227)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10228),X10226),X10226)|(hAPP(c_Groups_Ouminus__class_Ouminus(X10228),X10226)=X10227|X10227=X10226)|~class_Rings_Oidom(X10228))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])])). 4.05/4.29 fof(c_0_5533, plain, ![X11582]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X11582))|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,X11582))))&(~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,X11582)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X11582)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__nat__eq])])). 4.05/4.29 fof(c_0_5534, plain, ![X4666]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X4666|c_Groups_Osgn__class_Osgn(tc_Int_Oint,X4666)=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)),X4666))|c_Groups_Osgn__class_Osgn(tc_Int_Oint,X4666)=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)=X4666)&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4666))|c_Groups_Oone__class_Oone(tc_Int_Oint)=c_Groups_Osgn__class_Osgn(tc_Int_Oint,X4666)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X4666))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zsgn__def])])])])). 4.05/4.29 fof(c_0_5535, plain, ![X12204, X12205]:((((hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X12204|X12205=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),X12205),X12204))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X12205|X12205=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),X12205),X12204)))&((hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X12204|X12204=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),X12205),X12204))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X12205|X12204=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),X12205),X12204))))&((X12205!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X12204!=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),X12205),X12204))&(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X12204|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X12205|hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12205),X12204)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__1])])])). 4.05/4.29 fof(c_0_5536, plain, ![X1247, X1248]:((~hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1248),X1247))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1248)),X1247)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1248)),X1247))|hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1248),X1247)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J])])). 4.05/4.29 fof(c_0_5537, plain, ![X12950, X12951, X12953]:((((hAPP(c_List_Oset(X12951),esk396_2(X12950,X12951))=X12950|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12951),X12950))|~class_Orderings_Olinorder(X12951))&(c_List_Olinorder__class_Osorted(X12951,esk396_2(X12950,X12951))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12951),X12950))|~class_Orderings_Olinorder(X12951)))&(hBOOL(hAPP(c_List_Odistinct(X12951),esk396_2(X12950,X12951)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12951),X12950))|~class_Orderings_Olinorder(X12951)))&(X12950!=hAPP(c_List_Oset(X12951),X12953)|~hBOOL(hAPP(c_List_Odistinct(X12951),X12953))|~c_List_Olinorder__class_Osorted(X12951,X12953)|esk396_2(X12950,X12951)=X12953|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12951),X12950))|~class_Orderings_Olinorder(X12951))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__sorted__distinct__unique])])])])])])). 4.05/4.29 fof(c_0_5538, plain, ![X9638, X9639]:hBOOL(hAPP(c_Finite__Set_Ofinite(X9639),hAPP(c_List_Oset(X9639),X9638))), inference(variable_rename,[status(thm)],[fact_finite__set])). 4.05/4.29 fof(c_0_5539, plain, ![X1936, X1937]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1937)),hAPP(c_Int_Onat,X1936)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1937),X1936))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1937)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1937),X1936))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1937)),hAPP(c_Int_Onat,X1936)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1937))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1937)),hAPP(c_Int_Onat,X1936)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1937),X1936))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1936)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1937),X1936))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1937)),hAPP(c_Int_Onat,X1936)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1936))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__eq__zle])])])). 4.05/4.29 fof(c_0_5540, plain, ![X1774, X1775]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1774),X1775))|c_List_Oupt(X1775,X1774)=c_List_Olist_ONil(tc_Nat_Onat))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1774|c_List_Oupt(X1775,X1774)=c_List_Olist_ONil(tc_Nat_Onat)))&(c_List_Oupt(X1775,X1774)!=c_List_Olist_ONil(tc_Nat_Onat)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1774),X1775))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1774))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__eq__Nil__conv])])])). 4.05/4.29 cnf(c_0_5541, 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_4720])). 4.05/4.29 fof(c_0_5542, plain, ![X8053, X8054]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X8054)),X8053))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8054),X8053)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8054),X8053))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X8054)),X8053)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__pred__less])])). 4.05/4.29 fof(c_0_5543, plain, ![X17383, X17384, X17385]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X17385,X17384),X17383))|X17383=c_Divides_Odivmod__nat(X17385,X17384)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__eq])])). 4.05/4.29 fof(c_0_5544, plain, ![X10408, X10409]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10409),X10408))|c_List_Oupt(X10409,X10408)=c_List_Olist_ONil(tc_Nat_Onat))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10409),X10408))|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X10409),c_List_Oupt(hAPP(c_Nat_OSuc,X10409),X10408))=c_List_Oupt(X10409,X10408))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upt__rec])])])). 4.05/4.29 fof(c_0_5545, plain, ![X17564, X17565]:(~class_Rings_Oring__1(X17565)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17564))|hAPP(c_Int_Oring__1__class_Oof__int(X17565),X17564)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X17565),hAPP(c_Int_Onat,X17564)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__nat])])). 4.05/4.29 fof(c_0_5546, plain, ![X6286, X6287]:(((X6286!=hAPP(c_Groups_Ouminus__class_Ouminus(X6287),c_Groups_Oone__class_Oone(X6287))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6287),X6286),X6286)=c_Groups_Oone__class_Oone(X6287)|~class_Rings_Oring__1__no__zero__divisors(X6287))&(c_Groups_Oone__class_Oone(X6287)!=X6286|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6287),X6286),X6286)=c_Groups_Oone__class_Oone(X6287)|~class_Rings_Oring__1__no__zero__divisors(X6287)))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6287),X6286),X6286)!=c_Groups_Oone__class_Oone(X6287)|(X6286=hAPP(c_Groups_Ouminus__class_Ouminus(X6287),c_Groups_Oone__class_Oone(X6287))|c_Groups_Oone__class_Oone(X6287)=X6286)|~class_Rings_Oring__1__no__zero__divisors(X6287))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_square__eq__1__iff])])])])). 4.05/4.29 fof(c_0_5547, plain, ![X9357]:((X9357=hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X9357)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X9357))|X9357!=hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral__not__eq__zero])])). 4.05/4.29 fof(c_0_5548, plain, ![X8914, X8915]:(~class_Fields_Ofield__inverse__zero(X8915)|~class_Int_Onumber__ring(X8915)|c_Groups_Ozero__class_Ozero(X8915)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8915),X8914),hAPP(c_Int_Onumber__class_Onumber__of(X8915),c_Int_OPls))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral0])])). 4.05/4.29 fof(c_0_5549, plain, ![X14699, X14700, X14701]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X14699|c_Groups_Ozero__class_Ozero(X14701)!=X14700|hAPP(hAPP(c_Power_Opower__class_Opower(X14701),X14700),X14699)=c_Groups_Ozero__class_Ozero(X14701)|(~class_Rings_Omult__zero(X14701)|~class_Rings_Ono__zero__divisors(X14701)|~class_Rings_Ozero__neq__one(X14701)|~class_Power_Opower(X14701)))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X14699|hAPP(hAPP(c_Power_Opower__class_Opower(X14701),X14700),X14699)!=c_Groups_Ozero__class_Ozero(X14701)|(~class_Rings_Omult__zero(X14701)|~class_Rings_Ono__zero__divisors(X14701)|~class_Rings_Ozero__neq__one(X14701)|~class_Power_Opower(X14701)))&(c_Groups_Ozero__class_Ozero(X14701)=X14700|hAPP(hAPP(c_Power_Opower__class_Opower(X14701),X14700),X14699)!=c_Groups_Ozero__class_Ozero(X14701)|(~class_Rings_Omult__zero(X14701)|~class_Rings_Ono__zero__divisors(X14701)|~class_Rings_Ozero__neq__one(X14701)|~class_Power_Opower(X14701))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])])). 4.05/4.29 fof(c_0_5550, plain, ![X12480, X12481]:((((X12480=c_Groups_Oone__class_Oone(tc_Int_Oint)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X12481|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12481),X12480))&(X12481=c_Groups_Oone__class_Oone(tc_Int_Oint)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X12481|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12481),X12480)))&((X12480=c_Groups_Oone__class_Oone(tc_Int_Oint)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X12480|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12481),X12480))&(X12481=c_Groups_Oone__class_Oone(tc_Int_Oint)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X12480|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12481),X12480))))&((hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)!=X12481|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)!=X12480|c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12481),X12480))&(X12480!=c_Groups_Oone__class_Oone(tc_Int_Oint)|X12481!=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12481),X12480)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__eq__1__iff])])])). 4.05/4.29 fof(c_0_5551, plain, ![X7804, X7805]:(((hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=X7805|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X7805),X7804)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(X7804!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X7805),X7804)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))&(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X7805),X7804)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X7805|X7804=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__eq__Suc__0__iff])])])). 4.05/4.29 fof(c_0_5552, plain, ![X437, X438, X439]:((c_Groups_Ozero__class_Ozero(X439)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X439),X438),X437)|X438=hAPP(c_Groups_Ouminus__class_Ouminus(X439),X437)|~class_Groups_Ogroup__add(X439))&(X438!=hAPP(c_Groups_Ouminus__class_Ouminus(X439),X437)|c_Groups_Ozero__class_Ozero(X439)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X439),X438),X437)|~class_Groups_Ogroup__add(X439))), 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])])])])). 4.05/4.29 fof(c_0_5553, plain, ![X6460]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X6460)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6460)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6460))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X6460))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__nat__eq])])). 4.05/4.29 fof(c_0_5554, plain, ![X1773]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1773))|X1773=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1773)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1773))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1773))=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])])])). 4.05/4.29 fof(c_0_5555, plain, ![X5778, X5779]:((X5778!=X5779|hAPP(c_Int_Onat,X5779)=hAPP(c_Int_Onat,X5778)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5778))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5779)))&(hAPP(c_Int_Onat,X5779)!=hAPP(c_Int_Onat,X5778)|X5778=X5779|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5778))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5779)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__nat__int__relations_I1_J])])])])). 4.05/4.29 fof(c_0_5556, plain, ![X4037, X4038, X4039, X4040]:(((c_Groups_Ozero__class_Ozero(X4040)=hAPP(c_Int_Onumber__class_Onumber__of(X4040),X4037)|X4038=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4040),X4039),hAPP(c_Int_Onumber__class_Onumber__of(X4040),X4037))|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4040),X4038),hAPP(c_Int_Onumber__class_Onumber__of(X4040),X4037))!=X4039|(~class_Fields_Ofield__inverse__zero(X4040)|~class_Int_Onumber(X4040)))&(hAPP(c_Int_Onumber__class_Onumber__of(X4040),X4037)!=c_Groups_Ozero__class_Ozero(X4040)|X4039=c_Groups_Ozero__class_Ozero(X4040)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4040),X4038),hAPP(c_Int_Onumber__class_Onumber__of(X4040),X4037))!=X4039|(~class_Fields_Ofield__inverse__zero(X4040)|~class_Int_Onumber(X4040))))&(((hAPP(c_Int_Onumber__class_Onumber__of(X4040),X4037)=c_Groups_Ozero__class_Ozero(X4040)|c_Groups_Ozero__class_Ozero(X4040)!=hAPP(c_Int_Onumber__class_Onumber__of(X4040),X4037)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4040),X4038),hAPP(c_Int_Onumber__class_Onumber__of(X4040),X4037))=X4039|(~class_Fields_Ofield__inverse__zero(X4040)|~class_Int_Onumber(X4040)))&(X4039!=c_Groups_Ozero__class_Ozero(X4040)|c_Groups_Ozero__class_Ozero(X4040)!=hAPP(c_Int_Onumber__class_Onumber__of(X4040),X4037)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4040),X4038),hAPP(c_Int_Onumber__class_Onumber__of(X4040),X4037))=X4039|(~class_Fields_Ofield__inverse__zero(X4040)|~class_Int_Onumber(X4040))))&((hAPP(c_Int_Onumber__class_Onumber__of(X4040),X4037)=c_Groups_Ozero__class_Ozero(X4040)|X4038!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4040),X4039),hAPP(c_Int_Onumber__class_Onumber__of(X4040),X4037))|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4040),X4038),hAPP(c_Int_Onumber__class_Onumber__of(X4040),X4037))=X4039|(~class_Fields_Ofield__inverse__zero(X4040)|~class_Int_Onumber(X4040)))&(X4039!=c_Groups_Ozero__class_Ozero(X4040)|X4038!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4040),X4039),hAPP(c_Int_Onumber__class_Onumber__of(X4040),X4037))|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4040),X4038),hAPP(c_Int_Onumber__class_Onumber__of(X4040),X4037))=X4039|(~class_Fields_Ofield__inverse__zero(X4040)|~class_Int_Onumber(X4040)))))), 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])])])])). 4.05/4.29 cnf(c_0_5557, 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_4721])). 4.05/4.29 fof(c_0_5558, plain, ![X1530, X1531]:((c_List_Oremdups(X1531,X1530)!=X1530|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1531)),X1530)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1531)),c_List_Oremdups(X1531,X1530)))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1531)),X1530)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1531)),c_List_Oremdups(X1531,X1530))|c_List_Oremdups(X1531,X1530)=X1530)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__remdups__eq])])). 4.05/4.29 fof(c_0_5559, plain, ![X16076, X16077]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16077)),c_List_Oremdups(X16077,X16076))=hAPP(c_Finite__Set_Ocard(X16077),hAPP(c_List_Oset(X16077),X16076)), inference(variable_rename,[status(thm)],[fact_length__remdups__card__conv])). 4.05/4.29 fof(c_0_5560, plain, ![X8109, X8110]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8110),X8109))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X8110)),hAPP(c_Code__Numeral_Oof__nat,X8109))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X8110)),hAPP(c_Code__Numeral_Oof__nat,X8109)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8110),X8109)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__code])])). 4.05/4.29 fof(c_0_5561, plain, ![X9869, X9870]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X9870)),hAPP(c_Code__Numeral_Oof__nat,X9869)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9870),X9869)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9870),X9869))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X9870)),hAPP(c_Code__Numeral_Oof__nat,X9869))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__code])])). 4.05/4.29 fof(c_0_5562, plain, ![X9572, X9573, X9574, X9575, X9577]:((hAPP(c_Set_OCollect(X9573),X9572)!=c_Orderings_Obot__class_Obot(tc_fun(X9573,tc_HOL_Obool))|~hBOOL(hAPP(X9572,X9574)))&(hBOOL(hAPP(X9575,esk292_1(X9575)))|hAPP(c_Set_OCollect(X9577),X9575)=c_Orderings_Obot__class_Obot(tc_fun(X9577,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_Collect__empty__eq])])])])])])). 4.05/4.29 fof(c_0_5563, plain, ![X1752, X1754, X1755, X1756, X1757]:((hBOOL(hAPP(X1752,esk58_1(X1752)))|hAPP(c_Set_OCollect(X1754),X1752)=c_Orderings_Obot__class_Obot(tc_fun(X1754,tc_HOL_Obool)))&(hAPP(c_Set_OCollect(X1756),X1755)!=c_Orderings_Obot__class_Obot(tc_fun(X1756,tc_HOL_Obool))|~hBOOL(hAPP(X1755,X1757)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_empty__Collect__eq])])])])])])). 4.05/4.29 cnf(c_0_5564, 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_4722])). 4.05/4.29 fof(c_0_5565, plain, ![X5855, X5856]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X5855)),X5856))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5856),X5855)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5856),X5855))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X5855)),X5856)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq])])])). 4.05/4.29 fof(c_0_5566, plain, ![X14052, X14053]:(~class_Int_Onumber__ring(X14053)|X14052=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14053),hAPP(c_Int_Onumber__class_Onumber__of(X14053),c_Int_OPls)),X14052)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0])])). 4.05/4.29 fof(c_0_5567, plain, ![X5351, X5352]:(~class_Int_Onumber__ring(X5352)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5352),X5351),hAPP(c_Int_Onumber__class_Onumber__of(X5352),c_Int_OPls))=X5351), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__numeral__0__right])])])). 4.05/4.29 fof(c_0_5568, plain, ![X6909, X6910]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6910),hAPP(c_Int_Onat,X6909)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6910)),X6909)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6910)),X6909))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6910),hAPP(c_Int_Onat,X6909))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__eq__int__zless])])). 4.05/4.29 fof(c_0_5569, plain, ![X16457, X16458, X16459, X16460, X16461, X16462, X16463]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16457),hAPP(c_Nat_OSuc,X16460))))|~hBOOL(hAPP(X16459,X16460))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16457),X16460)),X16458))|hBOOL(hAPP(X16459,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16458),X16457))))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X16457|~hBOOL(hAPP(X16459,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(X16459,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16458),X16457)))))&((((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X16461|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16461),hAPP(c_Nat_OSuc,esk494_3(X16461,X16462,X16463)))))|~hBOOL(hAPP(X16463,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16462),X16461))))&(hBOOL(hAPP(X16463,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16461),hAPP(c_Nat_OSuc,esk494_3(X16461,X16462,X16463)))))|~hBOOL(hAPP(X16463,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16462),X16461)))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X16461|hBOOL(hAPP(X16463,esk494_3(X16461,X16462,X16463)))|~hBOOL(hAPP(X16463,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16462),X16461))))&(hBOOL(hAPP(X16463,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(X16463,esk494_3(X16461,X16462,X16463)))|~hBOOL(hAPP(X16463,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16462),X16461))))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X16461|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16461),esk494_3(X16461,X16462,X16463))),X16462))|~hBOOL(hAPP(X16463,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16462),X16461))))&(hBOOL(hAPP(X16463,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),X16461),esk494_3(X16461,X16462,X16463))),X16462))|~hBOOL(hAPP(X16463,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X16462),X16461))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__div_H])])])])])])). 4.05/4.29 cnf(c_0_5570, plain, (X1=c_Int_OMin|c_Int_OMin!=c_Int_OBit1(X1)), inference(split_conjunct,[status(thm)],[c_0_4723])). 4.05/4.29 cnf(c_0_5571, 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_4720])). 4.05/4.29 fof(c_0_5572, plain, ![X5126, X5128, X5129, X5131]:((~hBOOL(hAPP(X5126,esk156_1(X5126)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5128))|hBOOL(hAPP(X5126,hAPP(c_Int_Onat,X5128)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk157_1(X5129)))|hBOOL(hAPP(X5129,X5131)))&(~hBOOL(hAPP(X5129,hAPP(c_Int_Onat,esk157_1(X5129))))|hBOOL(hAPP(X5129,X5131))))), 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])])])])])])])). 4.05/4.29 fof(c_0_5573, plain, ![X10975, X10976, X10978, X10979]:(((hBOOL(hAPP(X10975,hAPP(c_Int_Onat,esk331_1(X10975))))|~hBOOL(hAPP(X10975,X10976)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk331_1(X10975)))|~hBOOL(hAPP(X10975,X10976))))&(~hBOOL(hAPP(X10978,hAPP(c_Int_Onat,X10979)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10979))|hBOOL(hAPP(X10978,esk332_1(X10978))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__nat])])])])])])). 4.05/4.29 fof(c_0_5574, plain, ![X5818, X5819, X5820]:((c_Groups_Ozero__class_Ozero(X5820)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5820),X5819),X5818)|(X5818=c_Groups_Ozero__class_Ozero(X5820)|c_Groups_Ozero__class_Ozero(X5820)=X5819)|~class_Rings_Oring__no__zero__divisors(X5820))&((X5818!=c_Groups_Ozero__class_Ozero(X5820)|c_Groups_Ozero__class_Ozero(X5820)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5820),X5819),X5818)|~class_Rings_Oring__no__zero__divisors(X5820))&(c_Groups_Ozero__class_Ozero(X5820)!=X5819|c_Groups_Ozero__class_Ozero(X5820)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5820),X5819),X5818)|~class_Rings_Oring__no__zero__divisors(X5820)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__eq__0__iff])])])])). 4.05/4.29 fof(c_0_5575, plain, ![X15993, X15994, X15995, X15996, X15997]:((X15994!=X15993|X15996=X15995|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15997),X15996),X15995)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15997),X15994),X15993)|~class_Groups_Oab__group__add(X15997))&(X15996!=X15995|X15994=X15993|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15997),X15996),X15995)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15997),X15994),X15993)|~class_Groups_Oab__group__add(X15997))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq])])])). 4.05/4.29 fof(c_0_5576, plain, ![X6403, X6404]:((c_Groups_Ozero__class_Ozero(X6404)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6404),X6403),X6403)|c_Groups_Ozero__class_Ozero(X6404)=X6403|~class_Groups_Olinordered__ab__group__add(X6404))&(c_Groups_Ozero__class_Ozero(X6404)!=X6403|c_Groups_Ozero__class_Ozero(X6404)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6404),X6403),X6403)|~class_Groups_Olinordered__ab__group__add(X6404))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_double__zero__sym])])])])). 4.05/4.29 fof(c_0_5577, plain, ![X4016, X4017]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4016))|X4017=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Int_Onat,X4016)!=X4017)&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4016))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4017)=X4016|hAPP(c_Int_Onat,X4016)!=X4017))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4016))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4016))|hAPP(c_Int_Onat,X4016)=X4017)&(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4017)!=X4016|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4016))|hAPP(c_Int_Onat,X4016)=X4017))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4016))|X4017!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Int_Onat,X4016)=X4017)&(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4017)!=X4016|X4017!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Int_Onat,X4016)=X4017)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__eq__iff2])])])])). 4.05/4.29 fof(c_0_5578, plain, ![X6992, X6993, X6994]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6994),X6993),X6992)!=X6993|X6992=c_Groups_Ozero__class_Ozero(X6994)|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6994))&(X6992!=c_Groups_Ozero__class_Ozero(X6994)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6994),X6993),X6992)=X6993|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6994))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])])). 4.05/4.29 fof(c_0_5579, plain, ![X10153]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X10153)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X10153))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X10153))&(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X10153)))|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),X10153)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__nat__number__of])])])). 4.05/4.29 fof(c_0_5580, plain, ![X12519, X12520, X12521]:((X12520!=X12519|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12521),X12520),X12519)=c_Groups_Ozero__class_Ozero(X12521)|~class_Groups_Oab__group__add(X12521))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12521),X12520),X12519)!=c_Groups_Ozero__class_Ozero(X12521)|X12520=X12519|~class_Groups_Oab__group__add(X12521))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__iff__diff__eq__0])])])])). 4.05/4.29 fof(c_0_5581, plain, ![X5058, X5059, X5060]:((X5058!=hAPP(c_Groups_Ouminus__class_Ouminus(X5060),X5059)|X5059=hAPP(c_Groups_Ouminus__class_Ouminus(X5060),X5058)|~class_Groups_Ogroup__add(X5060))&(X5059!=hAPP(c_Groups_Ouminus__class_Ouminus(X5060),X5058)|X5058=hAPP(c_Groups_Ouminus__class_Ouminus(X5060),X5059)|~class_Groups_Ogroup__add(X5060))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__equation__iff])])])). 4.05/4.29 cnf(c_0_5582, plain, (X1=X2|c_Code__Numeral_OSuc__code__numeral(X1)!=c_Code__Numeral_OSuc__code__numeral(X2)), inference(split_conjunct,[status(thm)],[c_0_4724])). 4.05/4.29 cnf(c_0_5583, plain, (c_Code__Numeral_OSuc__code__numeral(X1)=hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))), inference(split_conjunct,[status(thm)],[c_0_4725])). 4.05/4.29 fof(c_0_5584, plain, ![X3172, X3173]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3173),c_Groups_Ozero__class_Ozero(X3173)),hAPP(c_Groups_Oabs__class_Oabs(X3173),X3172)))|c_Groups_Ozero__class_Ozero(X3173)!=X3172|~class_Groups_Oordered__ab__group__add__abs(X3173))&(c_Groups_Ozero__class_Ozero(X3173)=X3172|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3173),c_Groups_Ozero__class_Ozero(X3173)),hAPP(c_Groups_Oabs__class_Oabs(X3173),X3172)))|~class_Groups_Oordered__ab__group__add__abs(X3173))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__abs__iff])])])])). 4.05/4.29 fof(c_0_5585, plain, ![X2200]:(hBOOL(hAPP(c_Nat__Numeral_Oneg,X2200))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X2200))=X2200), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__neg__nat])])])). 4.05/4.29 fof(c_0_5586, plain, ![X8316]:((X8316!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8316),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8316),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|X8316=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc0])])). 4.05/4.29 fof(c_0_5587, plain, ![X13268]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13268),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onat,X13268)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(hAPP(c_Int_Onat,X13268)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13268),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__iff])])). 4.05/4.29 fof(c_0_5588, plain, ![X12390]:(~class_Int_Onumber__ring(X12390)|c_Int_Oiszero(X12390,hAPP(c_Int_Onumber__class_Onumber__of(X12390),c_Int_OPls))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_iszero__Numeral0])])])). 4.05/4.29 fof(c_0_5589, plain, ![X14901]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14901),c_Int_OPls))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14901)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X14901)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14901),c_Int_OPls)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__0])])). 4.05/4.29 fof(c_0_5590, plain, ![X4178]:(~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X4178)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4178)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__imp__number__of__eq__0])])])). 4.05/4.29 fof(c_0_5591, plain, ![X17091, X17092]:((X17091!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Ozero__class_Ozero(X17092)=hAPP(c_Int_Oring__1__class_Oof__int(X17092),X17091)|~class_Int_Oring__char__0(X17092))&(c_Groups_Ozero__class_Ozero(X17092)!=hAPP(c_Int_Oring__1__class_Oof__int(X17092),X17091)|X17091=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~class_Int_Oring__char__0(X17092))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__eq__0__iff])])])). 4.05/4.29 fof(c_0_5592, plain, ![X1107, X1108]:((X1107!=hAPP(c_Groups_Ouminus__class_Ouminus(X1108),X1107)|c_Groups_Ozero__class_Ozero(X1108)=X1107|~class_Groups_Olinordered__ab__group__add(X1108))&(c_Groups_Ozero__class_Ozero(X1108)!=X1107|X1107=hAPP(c_Groups_Ouminus__class_Ouminus(X1108),X1107)|~class_Groups_Olinordered__ab__group__add(X1108))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__zero])])])). 4.05/4.29 fof(c_0_5593, plain, ![X660, X661]:((X660!=c_Groups_Ozero__class_Ozero(X661)|c_Groups_Osgn__class_Osgn(X661,X660)=c_Groups_Ozero__class_Ozero(X661)|~class_Rings_Olinordered__idom(X661))&(c_Groups_Osgn__class_Osgn(X661,X660)!=c_Groups_Ozero__class_Ozero(X661)|X660=c_Groups_Ozero__class_Ozero(X661)|~class_Rings_Olinordered__idom(X661))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__0__0])])])). 4.05/4.29 fof(c_0_5594, plain, ![X1363, X1364, X1365]:(~class_Orderings_Oorder(X1365)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1365),X1364),X1363))|X1363!=X1364)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])])). 4.05/4.29 fof(c_0_5595, plain, ![X4361, X4362, X4363]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4363),X4361),X4362))|X4362!=X4361|~class_Orderings_Olinorder(X4363))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4363),X4362),X4361))|X4362!=X4361|~class_Orderings_Olinorder(X4363)))&(X4362=X4361|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4363),X4361),X4362))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4363),X4362),X4361)))|~class_Orderings_Olinorder(X4363))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__neq__iff])])])])). 4.05/4.29 fof(c_0_5596, plain, ![X12475]:(~class_Int_Onumber__ring(X12475)|c_Groups_Ozero__class_Ozero(X12475)=hAPP(c_Int_Onumber__class_Onumber__of(X12475),c_Int_OPls)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J])])). 4.05/4.29 fof(c_0_5597, plain, ![X7028, X7029]:((c_Groups_Ozero__class_Ozero(X7029)!=X7028|c_Int_Oiszero(X7029,X7028)|~class_Rings_Osemiring__1(X7029))&(~c_Int_Oiszero(X7029,X7028)|c_Groups_Ozero__class_Ozero(X7029)=X7028|~class_Rings_Osemiring__1(X7029))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_iszero__def])])])])). 4.05/4.29 fof(c_0_5598, plain, ![X10436, X10437]:((hAPP(c_Code__Numeral_Oof__nat,X10436)!=hAPP(c_Code__Numeral_Oof__nat,X10437)|X10437=X10436)&(X10437!=X10436|hAPP(c_Code__Numeral_Oof__nat,X10436)=hAPP(c_Code__Numeral_Oof__nat,X10437))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Oof__nat__inject])])). 4.05/4.29 fof(c_0_5599, plain, ![X8855, X8856]:(~c_Com_OWT__bodies|(hAPP(c_Com_Obody,X8856)!=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X8855)|hBOOL(hAPP(c_Com_OWT,X8855)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT__bodiesD])])). 4.05/4.29 cnf(c_0_5600, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2)))), inference(split_conjunct,[status(thm)],[c_0_4726])). 4.05/4.29 cnf(c_0_5601, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2)))), inference(split_conjunct,[status(thm)],[c_0_4727])). 4.05/4.29 cnf(c_0_5602, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4728, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_5603, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4729, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.29 cnf(c_0_5604, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4730, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.29 cnf(c_0_5605, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))!=c_Int_OMin), inference(rw,[status(thm)],[c_0_4731, c_0_4505])). 4.05/4.29 fof(c_0_5606, plain, ![X11445, X11446, X11447, X11448, X11449, X11451, X11452, X11453, X11454, X11456]:((((((hBOOL(hAPP(hAPP(c_member(tc_prod(X11448,X11448)),hAPP(hAPP(c_Product__Type_OPair(X11448,X11448),X11449),esk350_5(X11445,X11446,X11447,X11448,X11449))),X11445))|~hBOOL(hAPP(hAPP(c_member(X11448),X11449),X11447))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X11448,tc_HOL_Obool),tc_fun(X11448,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X11448,tc_HOL_Obool),tc_fun(X11448,tc_HOL_Obool)),X11447),X11446)),c_Wellfounded_Omax__ext(X11448,X11445))))&(hBOOL(hAPP(hAPP(c_member(X11448),esk350_5(X11445,X11446,X11447,X11448,X11449)),X11446))|~hBOOL(hAPP(hAPP(c_member(X11448),X11449),X11447))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X11448,tc_HOL_Obool),tc_fun(X11448,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X11448,tc_HOL_Obool),tc_fun(X11448,tc_HOL_Obool)),X11447),X11446)),c_Wellfounded_Omax__ext(X11448,X11445)))))&(X11446!=c_Orderings_Obot__class_Obot(tc_fun(X11448,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X11448,tc_HOL_Obool),tc_fun(X11448,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X11448,tc_HOL_Obool),tc_fun(X11448,tc_HOL_Obool)),X11447),X11446)),c_Wellfounded_Omax__ext(X11448,X11445)))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X11448),X11446))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X11448,tc_HOL_Obool),tc_fun(X11448,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X11448,tc_HOL_Obool),tc_fun(X11448,tc_HOL_Obool)),X11447),X11446)),c_Wellfounded_Omax__ext(X11448,X11445)))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X11448),X11447))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X11448,tc_HOL_Obool),tc_fun(X11448,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X11448,tc_HOL_Obool),tc_fun(X11448,tc_HOL_Obool)),X11447),X11446)),c_Wellfounded_Omax__ext(X11448,X11445)))))&((hBOOL(hAPP(hAPP(c_member(X11454),esk351_4(X11451,X11452,X11453,X11454)),X11453))|X11452=c_Orderings_Obot__class_Obot(tc_fun(X11454,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11454),X11452))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11454),X11453))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X11454,tc_HOL_Obool),tc_fun(X11454,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X11454,tc_HOL_Obool),tc_fun(X11454,tc_HOL_Obool)),X11453),X11452)),c_Wellfounded_Omax__ext(X11454,X11451))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X11454,X11454)),hAPP(hAPP(c_Product__Type_OPair(X11454,X11454),esk351_4(X11451,X11452,X11453,X11454)),X11456)),X11451))|~hBOOL(hAPP(hAPP(c_member(X11454),X11456),X11452))|X11452=c_Orderings_Obot__class_Obot(tc_fun(X11454,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11454),X11452))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11454),X11453))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X11454,tc_HOL_Obool),tc_fun(X11454,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X11454,tc_HOL_Obool),tc_fun(X11454,tc_HOL_Obool)),X11453),X11452)),c_Wellfounded_Omax__ext(X11454,X11451)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_max__ext_Osimps])])])])])])])). 4.05/4.29 fof(c_0_5607, plain, ![X9587, X9588, X9589]:((~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X9589,X9589,hAPP(hAPP(c_COMBB(tc_fun(X9589,tc_HOL_Obool),tc_fun(X9589,tc_HOL_Obool),X9589),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X9589),c_fNot)),c_fequal)),X9588),X9587))|X9588!=X9587)&(X9588=X9587|hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X9589,X9589,hAPP(hAPP(c_COMBB(tc_fun(X9589,tc_HOL_Obool),tc_fun(X9589,tc_HOL_Obool),X9589),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X9589),c_fNot)),c_fequal)),X9588),X9587)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__noteq])])). 4.05/4.29 cnf(c_0_5608, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))), inference(rw,[status(thm)],[c_0_4732, c_0_4475])). 4.05/4.29 cnf(c_0_5609, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OPls))), inference(rw,[status(thm)],[c_0_4733, c_0_4475])). 4.05/4.29 cnf(c_0_5610, plain, (c_Int_OPls!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)), inference(rw,[status(thm)],[c_0_4734, c_0_4475])). 4.05/4.29 fof(c_0_5611, plain, ![X8376, X8377, X8378, X8379, X8381, X8382, X8383, X8384, X8385, X8386]:(((hBOOL(hAPP(hAPP(c_member(X8379),esk265_4(X8376,X8377,X8378,X8379)),X8377))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8379),X8376))|X8376=c_Orderings_Obot__class_Obot(tc_fun(X8379,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8379),X8377))|c_Wellfounded_Omax__extp(X8379,X8378,X8377,X8376))&(~hBOOL(hAPP(hAPP(c_member(X8379),X8381),X8376))|~hBOOL(hAPP(hAPP(X8378,esk265_4(X8376,X8377,X8378,X8379)),X8381))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8379),X8376))|X8376=c_Orderings_Obot__class_Obot(tc_fun(X8379,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8379),X8377))|c_Wellfounded_Omax__extp(X8379,X8378,X8377,X8376)))&((((hBOOL(hAPP(c_Finite__Set_Ofinite(X8385),X8382))|~c_Wellfounded_Omax__extp(X8385,X8384,X8383,X8382))&((hBOOL(hAPP(hAPP(c_member(X8385),esk266_5(X8382,X8383,X8384,X8385,X8386)),X8382))|~hBOOL(hAPP(hAPP(c_member(X8385),X8386),X8383))|~c_Wellfounded_Omax__extp(X8385,X8384,X8383,X8382))&(hBOOL(hAPP(hAPP(X8384,X8386),esk266_5(X8382,X8383,X8384,X8385,X8386)))|~hBOOL(hAPP(hAPP(c_member(X8385),X8386),X8383))|~c_Wellfounded_Omax__extp(X8385,X8384,X8383,X8382))))&(X8382!=c_Orderings_Obot__class_Obot(tc_fun(X8385,tc_HOL_Obool))|~c_Wellfounded_Omax__extp(X8385,X8384,X8383,X8382)))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X8385),X8383))|~c_Wellfounded_Omax__extp(X8385,X8384,X8383,X8382)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_max__extp_Oequations])])])])])])])). 4.05/4.29 fof(c_0_5612, plain, ![X16049, X16050]:(((X16050!=X16049|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16050),X16049)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16050),X16049))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16050),X16049))))&(X16050=X16049|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16050),X16049))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16050),X16049)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])])). 4.05/4.29 cnf(c_0_5613, 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_4735])). 4.05/4.29 fof(c_0_5614, plain, ~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)), inference(fof_simplification,[status(thm)],[fact_eq__int__code_I5_J])). 4.05/4.29 fof(c_0_5615, plain, ~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)), inference(fof_simplification,[status(thm)],[fact_eq__int__code_I2_J])). 4.05/4.29 fof(c_0_5616, plain, ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)), inference(fof_simplification,[status(thm)],[fact_rel__simps_I3_J])). 4.05/4.29 fof(c_0_5617, plain, ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)), inference(fof_simplification,[status(thm)],[fact_rel__simps_I20_J])). 4.05/4.29 fof(c_0_5618, plain, ![X8557]:(~c_Hoare__Mirabelle_Ostate__not__singleton|esk274_1(X8557)!=X8557), 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_single__stateE])])])])])). 4.05/4.29 fof(c_0_5619, plain, ![X4381, X4382]:((X4382=X4381|c_Hoare__Mirabelle_Ostate__not__singleton)&(~c_Hoare__Mirabelle_Ostate__not__singleton|esk137_0!=esk136_0)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_state__not__singleton__def])])])])). 4.05/4.29 fof(c_0_5620, negated_conjecture, ~(hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))))), inference(assume_negation,[status(cth)],[conj_4])). 4.05/4.29 cnf(c_0_5621, 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_4736])). 4.05/4.29 cnf(c_0_5622, 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_4737])). 4.05/4.29 cnf(c_0_5623, 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_4738])). 4.05/4.29 fof(c_0_5624, plain, ![X4550, X4551, X4552, X4553]: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),X4553),X4551)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4552),X4550))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4553),X4550)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4552),X4551)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X4553),X4552)),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),X4551),X4550)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[fact_mult])). 4.05/4.29 cnf(c_0_5625, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X2)))), inference(split_conjunct,[status(thm)],[c_0_4739])). 4.05/4.29 fof(c_0_5626, plain, ![X6408, X6409, X6410, X6411, X6412]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6412,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6412,tc_HOL_Obool)),c_Map_Odom(X6412,X6411,X6409)),hAPP(c_Set_OCollect(X6412),X6410))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6412,tc_HOL_Obool)),c_Map_Odom(X6412,X6411,X6408)),hAPP(c_Set_OCollect(X6412),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X6412),c_fNot),X6410))))=c_Map_Odom(X6412,X6411,hAPP(hAPP(c_COMBS(X6412,tc_Option_Ooption(X6411),tc_Option_Ooption(X6411)),hAPP(hAPP(c_COMBS(X6412,tc_Option_Ooption(X6411),tc_fun(tc_Option_Ooption(X6411),tc_Option_Ooption(X6411))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X6411),tc_fun(tc_Option_Ooption(X6411),tc_Option_Ooption(X6411))),X6412),c_If(tc_Option_Ooption(X6411))),X6410)),X6409)),X6408)), inference(variable_rename,[status(thm)],[fact_dom__if])). 4.05/4.29 fof(c_0_5627, plain, ![X14530, X14531, X14532, X14533, X14534, X14535]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14534,tc_HOL_Obool)),hAPP(c_Set_Oimage(X14535,X14534,X14532),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14535,tc_HOL_Obool)),X14530),hAPP(c_Set_OCollect(X14535),X14533)))),hAPP(c_Set_Oimage(X14535,X14534,X14531),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14535,tc_HOL_Obool)),X14530),hAPP(c_Set_OCollect(X14535),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X14535),c_fNot),X14533)))))=hAPP(c_Set_Oimage(X14535,X14534,hAPP(hAPP(c_COMBS(X14535,X14534,X14534),hAPP(hAPP(c_COMBS(X14535,X14534,tc_fun(X14534,X14534)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X14534,tc_fun(X14534,X14534)),X14535),c_If(X14534)),X14533)),X14532)),X14531)),X14530), inference(variable_rename,[status(thm)],[fact_if__image__distrib])). 4.05/4.29 fof(c_0_5628, plain, ![X2854, X2855, X2856]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2854),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2856),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2856),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2854),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2855))))=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),X2856)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X2855))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X2854))), inference(variable_rename,[status(thm)],[fact_arith__series__nat])). 4.05/4.29 cnf(c_0_5629, 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_4740])). 4.05/4.29 cnf(c_0_5630, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(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)),X2))), inference(rw,[status(thm)],[c_0_4741, c_0_4742])). 4.05/4.29 fof(c_0_5631, plain, ![X9319, X9320, X9321]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9321)),c_List_Osublist(X9321,X9320,X9319))=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(X9321)),X9320)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X9319)))), inference(variable_rename,[status(thm)],[fact_length__sublist])). 4.05/4.29 cnf(c_0_5632, plain, (c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_Osucc(X2)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit1(X2))), inference(split_conjunct,[status(thm)],[c_0_4743])). 4.05/4.29 fof(c_0_5633, plain, ![X1284, X1285, X1286, X1287, X1288, X1289, X1290, X1291, X1292, X1293]:(hAPP(c_Set_Oimage(X1293,X1292,X1291),X1290)!=X1289|(X1284!=hAPP(c_Set_Oimage(X1288,X1287,X1286),X1285)|hAPP(c_Set_Oimage(tc_prod(X1293,X1288),tc_prod(X1292,X1287),c_Product__Type_Omap__pair(X1293,X1292,X1288,X1287,X1291,X1286)),hAPP(hAPP(c_Product__Type_OSigma(X1293,X1288),X1290),hAPP(c_COMBK(tc_fun(X1288,tc_HOL_Obool),X1293),X1285)))=hAPP(hAPP(c_Product__Type_OSigma(X1292,X1287),X1289),hAPP(c_COMBK(tc_fun(X1287,tc_HOL_Obool),X1292),X1284)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__pair__surj__on])])])). 4.05/4.29 fof(c_0_5634, plain, ![X5402, X5403, X5404, X5405, X5406]:hAPP(hAPP(c_List_Omap(X5404,X5406),X5403),c_List_OdropWhile(X5404,hAPP(c_Fun_Ocomp(X5406,tc_HOL_Obool,X5404,X5405),X5403),X5402))=c_List_OdropWhile(X5406,X5405,hAPP(hAPP(c_List_Omap(X5404,X5406),X5403),X5402)), inference(variable_rename,[status(thm)],[fact_dropWhile__map])). 4.05/4.29 cnf(c_0_5635, 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_4744])). 4.05/4.29 cnf(c_0_5636, 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_4745])). 4.05/4.29 fof(c_0_5637, plain, ![X11769, X11770, X11771, X11772]:hAPP(c_Relation_OImage(X11772,X11771,X11770),hAPP(hAPP(c_Set_Oinsert(X11772),X11769),c_Orderings_Obot__class_Obot(tc_fun(X11772,tc_HOL_Obool))))=hAPP(c_Set_OCollect(X11771),hAPP(hAPP(c_COMBC(X11771,tc_fun(tc_prod(X11772,X11771),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X11772,X11771),tc_fun(tc_fun(tc_prod(X11772,X11771),tc_HOL_Obool),tc_HOL_Obool),X11771),c_member(tc_prod(X11772,X11771))),hAPP(c_Product__Type_OPair(X11772,X11771),X11769))),X11770)), inference(variable_rename,[status(thm)],[fact_Image__singleton])). 4.05/4.29 cnf(c_0_5638, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(X2,X3)),c_List_Omaps(X4,X1,X2,X5))=c_List_Omaps(X4,X1,X2,hAPP(hAPP(c_List_Olist_OCons(X4),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_4746])). 4.05/4.29 cnf(c_0_5639, 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_4747])). 4.05/4.29 cnf(c_0_5640, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Oconcat(X1,X3))=hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_4748])). 4.05/4.29 cnf(c_0_5641, 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_4749])). 4.05/4.29 fof(c_0_5642, plain, ![X5197, X5198, X5199, X5200]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5200,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X5199)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X5200,tc_HOL_Obool),tc_Nat_Onat),X5198),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X5197)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5200,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X5197,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5199),X5197))),X5198), inference(variable_rename,[status(thm)],[fact_UN__le__add__shift])). 4.05/4.29 fof(c_0_5643, plain, ![X9048, X9049, X9050, X9051, X9052, X9053, X9054]:c_List_Ofoldr(X9051,X9053,hAPP(c_Fun_Ocomp(X9054,tc_fun(X9053,X9053),X9051,X9052),X9050),X9049,X9048)=c_List_Ofoldr(X9054,X9053,X9052,hAPP(hAPP(c_List_Omap(X9051,X9054),X9050),X9049),X9048), inference(variable_rename,[status(thm)],[fact_foldr__map])). 4.05/4.29 cnf(c_0_5644, 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_4750])). 4.05/4.29 cnf(c_0_5645, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X2))=c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4751])). 4.05/4.29 fof(c_0_5646, plain, ![X8433, X8434, X8435, X8436]:hAPP(hAPP(c_List_Omap(X8436,X8435),X8434),c_List_Oconcat(X8436,X8433))=c_List_Oconcat(X8435,hAPP(hAPP(c_List_Omap(tc_List_Olist(X8436),tc_List_Olist(X8435)),hAPP(c_List_Omap(X8436,X8435),X8434)),X8433)), inference(variable_rename,[status(thm)],[fact_map__concat])). 4.05/4.29 fof(c_0_5647, plain, ![X3615, X3616, X3617, X3618, X3619, X3620]:c_List_Ofoldr(X3620,X3619,X3618,hAPP(hAPP(c_List_Olist_OCons(X3620),X3617),X3616),X3615)=hAPP(hAPP(X3618,X3617),c_List_Ofoldr(X3620,X3619,X3618,X3616,X3615)), inference(variable_rename,[status(thm)],[fact_foldr_Osimps_I2_J])). 4.05/4.29 cnf(c_0_5648, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X1)),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),X2)), inference(split_conjunct,[status(thm)],[c_0_4752])). 4.05/4.29 fof(c_0_5649, plain, ![X8597, X8598, X8599]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8599),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8598),X8597))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8599),X8598)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8599),X8597)), inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2])). 4.05/4.29 fof(c_0_5650, plain, ![X15747, X15748, X15749, X15750, X15751, X15752, X15753]:hAPP(c_Product__Type_Oapsnd(X15753,X15752,X15751,X15750),hAPP(c_Product__Type_Oapfst(X15749,X15751,X15753,X15748),X15747))=hAPP(hAPP(c_Product__Type_OPair(X15751,X15752),hAPP(X15748,hAPP(c_Product__Type_Ofst(X15749,X15753),X15747))),hAPP(X15750,hAPP(c_Product__Type_Osnd(X15749,X15753),X15747))), inference(variable_rename,[status(thm)],[fact_apsnd__apfst])). 4.05/4.29 fof(c_0_5651, plain, ![X14827, X14828, X14829, X14830, X14831, X14832, X14833]:hAPP(c_Product__Type_Oapfst(X14833,X14832,X14831,X14830),hAPP(c_Product__Type_Oapsnd(X14829,X14831,X14833,X14828),X14827))=hAPP(hAPP(c_Product__Type_OPair(X14832,X14831),hAPP(X14830,hAPP(c_Product__Type_Ofst(X14833,X14829),X14827))),hAPP(X14828,hAPP(c_Product__Type_Osnd(X14833,X14829),X14827))), inference(variable_rename,[status(thm)],[fact_apfst__apsnd])). 4.05/4.29 cnf(c_0_5652, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(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_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_4753])). 4.05/4.29 fof(c_0_5653, plain, ![X5540, X5541, X5542, X5543, X5544, X5545, X5546]:hAPP(c_Product__Type_Oapfst(X5542,X5544,X5545,X5541),hAPP(c_Product__Type_Oapsnd(X5546,X5545,X5542,X5543),X5540))=hAPP(c_Product__Type_Oapsnd(X5546,X5545,X5544,X5543),hAPP(c_Product__Type_Oapfst(X5542,X5544,X5546,X5541),X5540)), inference(variable_rename,[status(thm)],[fact_apsnd__apfst__commute])). 4.05/4.29 cnf(c_0_5654, 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_4754])). 4.05/4.29 fof(c_0_5655, plain, ![X12919, X12920]:hAPP(c_Set_Oimage(X12920,tc_List_Olist(X12920),hAPP(hAPP(c_COMBC(X12920,tc_List_Olist(X12920),tc_List_Olist(X12920)),c_List_Olist_OCons(X12920)),c_List_Olist_ONil(X12920))),X12919)=c_List_Oset__Cons(X12920,X12919,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X12920)),c_List_Olist_ONil(X12920)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X12920),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_set__Cons__sing__Nil])). 4.05/4.29 cnf(c_0_5656, plain, (c_Int_Osucc(c_Int_OBit1(X1))=c_Int_OBit0(c_Int_Osucc(X1))), inference(split_conjunct,[status(thm)],[c_0_4755])). 4.05/4.29 fof(c_0_5657, plain, ![X9387, X9388, X9389, X9390, X9391, X9392, X9393]:hAPP(c_Product__Type_Oapsnd(X9393,X9392,X9391,X9390),hAPP(c_Product__Type_Oapsnd(X9389,X9393,X9391,X9388),X9387))=hAPP(c_Product__Type_Oapsnd(X9389,X9392,X9391,hAPP(c_Fun_Ocomp(X9393,X9392,X9389,X9390),X9388)),X9387), inference(variable_rename,[status(thm)],[fact_apsnd__compose])). 4.05/4.29 fof(c_0_5658, plain, ![X1851, X1852, X1853, X1854, X1855, X1856, X1857]:hAPP(c_Product__Type_Oapfst(X1857,X1856,X1855,X1854),hAPP(c_Product__Type_Oapfst(X1853,X1857,X1855,X1852),X1851))=hAPP(c_Product__Type_Oapfst(X1853,X1856,X1855,hAPP(c_Fun_Ocomp(X1857,X1856,X1853,X1854),X1852)),X1851), inference(variable_rename,[status(thm)],[fact_apfst__compose])). 4.05/4.29 fof(c_0_5659, plain, ![X5507, X5508, X5509, X5510, X5511]:hAPP(c_List_Orotate(X5511,X5510),hAPP(hAPP(c_List_Omap(X5509,X5511),X5508),X5507))=hAPP(hAPP(c_List_Omap(X5509,X5511),X5508),hAPP(c_List_Orotate(X5509,X5510),X5507)), inference(variable_rename,[status(thm)],[fact_rotate__map])). 4.05/4.29 fof(c_0_5660, plain, ![X12323, X12324, X12325, X12326, X12327]:((c_Option_Ooption_ONone(X12326)!=X12327|c_Map_Odom(X12325,X12326,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X12325,tc_Option_Ooption(X12326)),X12324),X12323),X12327))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12325,tc_HOL_Obool)),c_Map_Odom(X12325,X12326,X12324)),hAPP(hAPP(c_Set_Oinsert(X12325),X12323),c_Orderings_Obot__class_Obot(tc_fun(X12325,tc_HOL_Obool)))))&(X12327=c_Option_Ooption_ONone(X12326)|c_Map_Odom(X12325,X12326,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X12325,tc_Option_Ooption(X12326)),X12324),X12323),X12327))=hAPP(hAPP(c_Set_Oinsert(X12325),X12323),c_Map_Odom(X12325,X12326,X12324)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__fun__upd])])). 4.05/4.29 fof(c_0_5661, plain, ![X16527, X16528]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16528)),c_List_Oconcat(X16528,X16527))=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X16528),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X16528))),X16527)), inference(variable_rename,[status(thm)],[fact_length__concat])). 4.05/4.29 fof(c_0_5662, plain, ![X5994, X5995, X5996, X5997]:c_List_Olist_Olist__size(X5997,X5996,hAPP(hAPP(c_List_Olist_OCons(X5997),X5995),X5994))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X5996,X5995)),c_List_Olist_Olist__size(X5997,X5996,X5994))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_list_Osize_I2_J])). 4.05/4.29 fof(c_0_5663, plain, ![X10004, X10005, X10006, X10007]:hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X10007,X10006),c_Lazy__Sequence_Olazy__sequence_OInsert(X10007,X10005,X10004))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X10006,X10005)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X10007,X10006),X10004))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I2_J])). 4.05/4.29 fof(c_0_5664, plain, ![X17181, X17182, X17183]:hAPP(c_Relation_ORange(X17183,X17182),hAPP(c_Set_OCollect(tc_prod(X17183,X17182)),hAPP(c_Product__Type_Oprod_Oprod__case(X17183,X17182,tc_HOL_Obool),X17181)))=hAPP(c_Set_OCollect(X17182),hAPP(hAPP(c_COMBB(tc_fun(X17183,tc_HOL_Obool),tc_HOL_Obool,X17182),c_HOL_OEx(X17183)),hAPP(c_COMBC(X17183,X17182,tc_HOL_Obool),X17181))), inference(variable_rename,[status(thm)],[fact_Range__Collect__split])). 4.05/4.29 fof(c_0_5665, plain, ![X446, X447]:hAPP(c_Relation_OField(X447),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X447,X447),tc_HOL_Obool),X446))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X447,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X447,X447),tc_HOL_Obool),tc_fun(X447,tc_HOL_Obool),c_Relation_OField(X447)),X446)), inference(variable_rename,[status(thm)],[fact_Field__Union])). 4.05/4.29 fof(c_0_5666, plain, ![X7794, X7795, X7796]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X7795)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X7794))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X7796,X7795,X7794)), inference(variable_rename,[status(thm)],[fact_com_Osize_I13_J])). 4.05/4.29 cnf(c_0_5667, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X1,X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_4756])). 4.05/4.29 cnf(c_0_5668, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_4757]), ['final']). 4.05/4.29 cnf(c_0_5669, 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_4758]), ['final']). 4.05/4.29 cnf(c_0_5670, 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_4759, c_0_4760]), ['final']). 4.05/4.29 fof(c_0_5671, plain, ![X2188, X2189]:hAPP(c_Set_OPow(X2189),X2188)=hAPP(c_Set_OCollect(tc_fun(X2189,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X2189,tc_HOL_Obool),tc_fun(X2189,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X2189,tc_HOL_Obool))),X2188)), inference(variable_rename,[status(thm)],[fact_Pow__def])). 4.05/4.29 fof(c_0_5672, plain, ![X11912, X11913, X11914, X11915, X11916, X11917]:hAPP(c_Set_Ovimage(X11917,X11916,hAPP(c_Fun_Ocomp(X11915,X11916,X11917,X11914),X11913)),X11912)=hAPP(c_Set_Ovimage(X11917,X11915,X11913),hAPP(c_Set_Ovimage(X11915,X11916,X11914),X11912)), inference(variable_rename,[status(thm)],[fact_vimage__compose])). 4.05/4.29 fof(c_0_5673, plain, ![X17136, X17137, X17138, X17139]:hAPP(c_Set_Ovimage(X17139,X17138,X17137),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17138,tc_HOL_Obool)),X17136))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17139,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X17139,X17138,X17137),X17136)), inference(variable_rename,[status(thm)],[fact_vimage__Compl])). 4.05/4.29 fof(c_0_5674, plain, ![X5766, X5767]:hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X5767),X5766)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5767,X5766))=c_Divides_Odivmod__nat(X5767,X5766), inference(variable_rename,[status(thm)],[fact_divmod__nat__div__mod])). 4.05/4.29 fof(c_0_5675, plain, ![X17244, X17245, X17246]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X17245)),c_Com_Ocom_Ocom__size(X17244))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X17246,X17245,X17244)), inference(variable_rename,[status(thm)],[fact_com_Osize_I5_J])). 4.05/4.29 cnf(c_0_5676, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_4761])). 4.05/4.29 fof(c_0_5677, plain, ![X7553, X7554, X7555, X7556]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7555,tc_HOL_Obool)),X7553),hAPP(c_Set_Oimage(X7556,X7555,X7554),c_Orderings_Otop__class_Otop(tc_fun(X7556,tc_HOL_Obool))))=hAPP(c_Set_Oimage(X7556,X7555,X7554),hAPP(c_Set_Ovimage(X7556,X7555,X7554),X7553)), inference(variable_rename,[status(thm)],[fact_image__vimage__eq])). 4.05/4.29 fof(c_0_5678, plain, ![X9249, X9250, X9251, X9252, X9253]:((X9253!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X9252,X9251,X9250),X9253),X9249)=hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X9251),X9252),c_List_Olist_ONil(X9251)),X9249))&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X9253|hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X9252,X9251,X9250),X9253),X9249)=hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X9251),X9252),tc_prod(X9251,X9252),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X9251),X9252),c_List_Olist_ONil(X9251)),X9249),hAPP(c_Product__Type_Oprod_Oprod__case(X9251,X9252,tc_prod(tc_List_Olist(X9251),X9252)),hAPP(hAPP(c_COMBC(X9251,tc_fun(X9252,tc_prod(tc_List_Olist(X9251),X9252)),tc_fun(X9252,tc_prod(tc_List_Olist(X9251),X9252))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X9251),X9252),tc_prod(tc_List_Olist(X9251),X9252)),tc_fun(tc_fun(X9252,tc_prod(tc_List_Olist(X9251),X9252)),tc_fun(X9252,tc_prod(tc_List_Olist(X9251),X9252))),X9251),c_COMBB(tc_prod(tc_List_Olist(X9251),X9252),tc_prod(tc_List_Olist(X9251),X9252),X9252)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X9251),tc_fun(X9252,tc_prod(tc_List_Olist(X9251),X9252))),tc_fun(tc_prod(tc_List_Olist(X9251),X9252),tc_prod(tc_List_Olist(X9251),X9252)),X9251),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X9251),X9252,tc_prod(tc_List_Olist(X9251),X9252))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X9251),tc_List_Olist(X9251)),tc_fun(tc_List_Olist(X9251),tc_fun(X9252,tc_prod(tc_List_Olist(X9251),X9252))),X9251),hAPP(c_COMBB(tc_List_Olist(X9251),tc_fun(X9252,tc_prod(tc_List_Olist(X9251),X9252)),tc_List_Olist(X9251)),c_Product__Type_OPair(tc_List_Olist(X9251),X9252))),c_List_Olist_OCons(X9251))))),hAPP(c_Lazy__Sequence_Oanamorph(X9252,X9251,X9250),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X9253),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(X9250,X9249)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_anamorph_Osimps])])])). 4.05/4.29 fof(c_0_5679, plain, ![X3354, X3355]:hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3355,X3355),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3354)=c_Relation_OId(X3355), inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I1_J])). 4.05/4.29 fof(c_0_5680, plain, ![X16389, X16390]:c_List_Olenlex(X16390,X16389)=hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X16390),tc_List_Olist(X16390))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X16390),tc_List_Olist(X16390),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X16390),tc_fun(tc_List_Olist(X16390),tc_HOL_Obool),tc_fun(tc_List_Olist(X16390),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X16390),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X16390),tc_HOL_Obool),tc_fun(tc_List_Olist(X16390),tc_HOL_Obool)),tc_List_Olist(X16390)),c_COMBS(tc_List_Olist(X16390),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X16390),tc_HOL_Obool),tc_fun(tc_List_Olist(X16390),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X16390)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X16390)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X16390),tc_fun(tc_List_Olist(X16390),tc_Nat_Onat),tc_fun(tc_List_Olist(X16390),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X16390),tc_Nat_Onat),tc_fun(tc_List_Olist(X16390),tc_HOL_Obool)),tc_List_Olist(X16390)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X16390))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X16390)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X16390))))),c_Nat_Osize__class_Osize(tc_List_Olist(X16390)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X16390),tc_fun(tc_List_Olist(X16390),tc_HOL_Obool),tc_fun(tc_List_Olist(X16390),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X16390),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X16390),tc_HOL_Obool),tc_fun(tc_List_Olist(X16390),tc_HOL_Obool)),tc_List_Olist(X16390)),c_COMBS(tc_List_Olist(X16390),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X16390),tc_HOL_Obool),tc_fun(tc_List_Olist(X16390),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X16390)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X16390)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X16390),tc_fun(tc_List_Olist(X16390),tc_Nat_Onat),tc_fun(tc_List_Olist(X16390),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X16390),tc_Nat_Onat),tc_fun(tc_List_Olist(X16390),tc_HOL_Obool)),tc_List_Olist(X16390)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X16390))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X16390)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X16390))))),c_Nat_Osize__class_Osize(tc_List_Olist(X16390)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X16390),tc_fun(tc_prod(tc_List_Olist(X16390),tc_List_Olist(X16390)),tc_HOL_Obool),tc_fun(tc_List_Olist(X16390),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X16390),tc_fun(tc_fun(tc_prod(tc_List_Olist(X16390),tc_List_Olist(X16390)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X16390),tc_List_Olist(X16390)),tc_HOL_Obool),tc_fun(tc_List_Olist(X16390),tc_HOL_Obool)),tc_List_Olist(X16390)),c_COMBC(tc_List_Olist(X16390),tc_fun(tc_prod(tc_List_Olist(X16390),tc_List_Olist(X16390)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X16390),tc_prod(tc_List_Olist(X16390),tc_List_Olist(X16390))),tc_fun(tc_List_Olist(X16390),tc_fun(tc_fun(tc_prod(tc_List_Olist(X16390),tc_List_Olist(X16390)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X16390)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X16390),tc_List_Olist(X16390)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X16390),tc_List_Olist(X16390)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X16390)),c_member(tc_prod(tc_List_Olist(X16390),tc_List_Olist(X16390))))),c_Product__Type_OPair(tc_List_Olist(X16390),tc_List_Olist(X16390))))),c_List_Olex(X16390,X16389)))))), inference(variable_rename,[status(thm)],[fact_lenlex__conv])). 4.05/4.29 fof(c_0_5681, plain, ![X17526, X17527, X17528]:c_List_Oset__Cons(X17528,X17527,X17526)=hAPP(c_Set_OCollect(tc_List_Olist(X17528)),hAPP(hAPP(c_COMBB(tc_fun(X17528,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X17528)),c_HOL_OEx(X17528)),hAPP(hAPP(c_COMBB(tc_fun(X17528,tc_fun(tc_List_Olist(X17528),tc_HOL_Obool)),tc_fun(X17528,tc_HOL_Obool),tc_List_Olist(X17528)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X17528),tc_HOL_Obool),tc_HOL_Obool,X17528),c_HOL_OEx(tc_List_Olist(X17528)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X17528),tc_fun(X17528,tc_fun(tc_List_Olist(X17528),tc_HOL_Obool)),tc_fun(X17528,tc_fun(tc_List_Olist(X17528),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X17528,tc_fun(tc_fun(tc_List_Olist(X17528),tc_HOL_Obool),tc_fun(tc_List_Olist(X17528),tc_HOL_Obool))),tc_fun(tc_fun(X17528,tc_fun(tc_List_Olist(X17528),tc_HOL_Obool)),tc_fun(X17528,tc_fun(tc_List_Olist(X17528),tc_HOL_Obool))),tc_List_Olist(X17528)),c_COMBS(X17528,tc_fun(tc_List_Olist(X17528),tc_HOL_Obool),tc_fun(tc_List_Olist(X17528),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X17528,tc_fun(tc_List_Olist(X17528),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X17528,tc_fun(tc_fun(tc_List_Olist(X17528),tc_HOL_Obool),tc_fun(tc_List_Olist(X17528),tc_HOL_Obool))),tc_List_Olist(X17528)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X17528),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X17528),tc_HOL_Obool),tc_fun(tc_List_Olist(X17528),tc_HOL_Obool)),X17528),c_COMBS(tc_List_Olist(X17528),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X17528,tc_fun(tc_List_Olist(X17528),tc_HOL_Obool)),tc_fun(X17528,tc_fun(tc_List_Olist(X17528),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X17528)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X17528),tc_HOL_Obool),tc_fun(tc_List_Olist(X17528),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X17528),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X17528)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X17528),tc_fun(X17528,tc_fun(tc_List_Olist(X17528),tc_List_Olist(X17528))),tc_fun(X17528,tc_fun(tc_List_Olist(X17528),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X17528),tc_List_Olist(X17528)),tc_fun(tc_List_Olist(X17528),tc_HOL_Obool)),tc_fun(tc_fun(X17528,tc_fun(tc_List_Olist(X17528),tc_List_Olist(X17528))),tc_fun(X17528,tc_fun(tc_List_Olist(X17528),tc_HOL_Obool))),tc_List_Olist(X17528)),c_COMBB(tc_fun(tc_List_Olist(X17528),tc_List_Olist(X17528)),tc_fun(tc_List_Olist(X17528),tc_HOL_Obool),X17528)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X17528),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X17528),tc_List_Olist(X17528)),tc_fun(tc_List_Olist(X17528),tc_HOL_Obool)),tc_List_Olist(X17528)),c_COMBB(tc_List_Olist(X17528),tc_HOL_Obool,tc_List_Olist(X17528))),c_fequal))),c_List_Olist_OCons(X17528)))))),hAPP(hAPP(c_COMBC(X17528,tc_fun(tc_List_Olist(X17528),tc_HOL_Obool),tc_fun(tc_List_Olist(X17528),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X17528),tc_HOL_Obool),tc_fun(tc_List_Olist(X17528),tc_HOL_Obool)),X17528),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X17528))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X17528),c_fconj),hAPP(hAPP(c_COMBC(X17528,tc_fun(X17528,tc_HOL_Obool),tc_HOL_Obool),c_member(X17528)),X17527)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X17528),tc_fun(tc_List_Olist(X17528),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X17528))),X17526)))))), inference(variable_rename,[status(thm)],[fact_set__Cons__def])). 4.05/4.29 fof(c_0_5682, plain, ![X15665, X15666, X15667, X15668, X15669]:hAPP(c_Set_OCollect(tc_prod(X15669,X15667)),hAPP(c_Product__Type_Oprod_Oprod__case(X15669,X15667,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X15667,tc_fun(X15668,tc_HOL_Obool)),tc_fun(X15667,tc_HOL_Obool),X15669),hAPP(c_COMBB(tc_fun(X15668,tc_HOL_Obool),tc_HOL_Obool,X15667),c_HOL_OEx(X15668))),hAPP(hAPP(c_COMBC(X15669,tc_fun(X15667,tc_fun(X15668,tc_HOL_Obool)),tc_fun(X15667,tc_fun(X15668,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X15668,tc_HOL_Obool),tc_fun(X15668,tc_HOL_Obool)),tc_fun(tc_fun(X15667,tc_fun(X15668,tc_HOL_Obool)),tc_fun(X15667,tc_fun(X15668,tc_HOL_Obool))),X15669),c_COMBB(tc_fun(X15668,tc_HOL_Obool),tc_fun(X15668,tc_HOL_Obool),X15667)),hAPP(hAPP(c_COMBB(tc_fun(X15668,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X15668,tc_HOL_Obool),tc_fun(X15668,tc_HOL_Obool)),X15669),c_COMBS(X15668,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15668,tc_HOL_Obool),tc_fun(X15668,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X15669),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X15668),c_fconj)),hAPP(hAPP(c_COMBC(X15669,tc_fun(tc_prod(X15669,X15668),tc_HOL_Obool),tc_fun(X15668,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15668,tc_fun(tc_fun(tc_prod(X15669,X15668),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X15669,X15668),tc_HOL_Obool),tc_fun(X15668,tc_HOL_Obool)),X15669),c_COMBC(X15668,tc_fun(tc_prod(X15669,X15668),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15668,tc_prod(X15669,X15668)),tc_fun(X15668,tc_fun(tc_fun(tc_prod(X15669,X15668),tc_HOL_Obool),tc_HOL_Obool)),X15669),hAPP(c_COMBB(tc_prod(X15669,X15668),tc_fun(tc_fun(tc_prod(X15669,X15668),tc_HOL_Obool),tc_HOL_Obool),X15668),c_member(tc_prod(X15669,X15668)))),c_Product__Type_OPair(X15669,X15668)))),X15666))))),hAPP(hAPP(c_COMBC(X15667,tc_fun(tc_prod(X15668,X15667),tc_HOL_Obool),tc_fun(X15668,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15668,tc_fun(tc_fun(tc_prod(X15668,X15667),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X15668,X15667),tc_HOL_Obool),tc_fun(X15668,tc_HOL_Obool)),X15667),c_COMBC(X15668,tc_fun(tc_prod(X15668,X15667),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15668,tc_prod(X15668,X15667)),tc_fun(X15668,tc_fun(tc_fun(tc_prod(X15668,X15667),tc_HOL_Obool),tc_HOL_Obool)),X15667),hAPP(c_COMBB(tc_prod(X15668,X15667),tc_fun(tc_fun(tc_prod(X15668,X15667),tc_HOL_Obool),tc_HOL_Obool),X15668),c_member(tc_prod(X15668,X15667)))),hAPP(c_COMBC(X15668,X15667,tc_prod(X15668,X15667)),c_Product__Type_OPair(X15668,X15667))))),X15665)))))=hAPP(hAPP(c_Relation_Orel__comp(X15669,X15668,X15667),X15666),X15665), inference(variable_rename,[status(thm)],[fact_rel__comp__def])). 4.05/4.29 cnf(c_0_5683, plain, (c_Divides_Oadjust(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)))))))), inference(split_conjunct,[status(thm)],[c_0_4762])). 4.05/4.29 fof(c_0_5684, plain, ![X11190, X11191]:hAPP(c_Set_OCollect(tc_fun(X11191,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X11191,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X11191,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X11191,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X11191,tc_HOL_Obool),tc_fun(tc_fun(X11191,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X11191,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X11191,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X11191,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X11191,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X11191,tc_HOL_Obool)),c_COMBS(tc_fun(X11191,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X11191,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X11191,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X11191,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X11191,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X11191,tc_HOL_Obool),tc_fun(tc_fun(X11191,tc_HOL_Obool),tc_fun(X11191,tc_HOL_Obool)),tc_fun(tc_fun(X11191,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X11191,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X11191,tc_HOL_Obool),tc_fun(X11191,tc_HOL_Obool)),tc_fun(tc_fun(X11191,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X11191,tc_HOL_Obool)),c_COMBB(tc_fun(X11191,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X11191,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X11191,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X11191,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X11191,tc_HOL_Obool)),hAPP(c_member(tc_fun(X11191,tc_HOL_Obool)),X11190)),c_Set_OPow(X11191)))))=hAPP(c_Set_OPow(X11191),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11191,tc_HOL_Obool)),X11190)), inference(variable_rename,[status(thm)],[fact_Pow__Compl])). 4.05/4.29 fof(c_0_5685, plain, ![X3552, X3553, X3554]:hAPP(c_List_Olexn(X3554,X3553),hAPP(c_Nat_OSuc,X3552))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X3554),tc_List_Olist(X3554)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X3554,tc_List_Olist(X3554)),tc_prod(X3554,tc_List_Olist(X3554))),tc_prod(tc_List_Olist(X3554),tc_List_Olist(X3554)),c_Product__Type_Omap__pair(tc_prod(X3554,tc_List_Olist(X3554)),tc_List_Olist(X3554),tc_prod(X3554,tc_List_Olist(X3554)),tc_List_Olist(X3554),hAPP(c_Product__Type_Oprod_Oprod__case(X3554,tc_List_Olist(X3554),tc_List_Olist(X3554)),c_List_Olist_OCons(X3554)),hAPP(c_Product__Type_Oprod_Oprod__case(X3554,tc_List_Olist(X3554),tc_List_Olist(X3554)),c_List_Olist_OCons(X3554)))),c_Wellfounded_Olex__prod(X3554,tc_List_Olist(X3554),X3553,hAPP(c_List_Olexn(X3554,X3553),X3552)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X3554),tc_List_Olist(X3554))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X3554),tc_List_Olist(X3554),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X3554),tc_fun(tc_List_Olist(X3554),tc_HOL_Obool),tc_fun(tc_List_Olist(X3554),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X3554),tc_HOL_Obool),tc_fun(tc_List_Olist(X3554),tc_HOL_Obool)),tc_List_Olist(X3554)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X3554))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X3554)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X3554),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X3554)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X3554)))),hAPP(c_Nat_OSuc,X3552))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X3554),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X3554)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X3554)))),hAPP(c_Nat_OSuc,X3552)))))), inference(variable_rename,[status(thm)],[fact_lexn_Osimps_I2_J])). 4.05/4.29 fof(c_0_5686, plain, ![X17052, X17053, X17054, X17055]:hAPP(c_Set_OCollect(tc_prod(X17055,X17054)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X17055,X17054)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X17055,X17054),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(X17055,X17054)),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(X17055,X17054)),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(X17055,X17054),tc_fun(tc_Nat_Onat,tc_prod(X17055,X17054)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X17055,X17054),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X17055,X17054)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X17055,X17054)),c_COMBB(tc_prod(X17055,X17054),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X17054,tc_prod(X17055,X17054)),hAPP(hAPP(c_COMBB(X17055,tc_fun(X17054,tc_prod(X17055,X17054)),tc_Nat_Onat),c_Product__Type_OPair(X17055,X17054)),hAPP(c_List_Onth(X17055),X17053))),hAPP(c_List_Onth(X17054),X17052)))))),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(X17055)),X17053)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17054)),X17052))))))=hAPP(c_List_Oset(tc_prod(X17055,X17054)),hAPP(hAPP(c_List_Ozip(X17055,X17054),X17053),X17052)), inference(variable_rename,[status(thm)],[fact_set__zip])). 4.05/4.29 fof(c_0_5687, plain, ![X13758, X13759, X13760, X13761]:c_List_Ofoldr(tc_prod(X13761,X13760),tc_fun(X13761,tc_Option_Ooption(X13760)),hAPP(c_Product__Type_Oprod_Oprod__case(X13761,X13760,tc_fun(tc_fun(X13761,tc_Option_Ooption(X13760)),tc_fun(X13761,tc_Option_Ooption(X13760)))),hAPP(hAPP(c_COMBC(X13761,tc_fun(X13760,tc_Option_Ooption(X13760)),tc_fun(X13760,tc_fun(tc_fun(X13761,tc_Option_Ooption(X13760)),tc_fun(X13761,tc_Option_Ooption(X13760))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X13760),tc_fun(tc_fun(X13761,tc_Option_Ooption(X13760)),tc_fun(X13761,tc_Option_Ooption(X13760)))),tc_fun(tc_fun(X13760,tc_Option_Ooption(X13760)),tc_fun(X13760,tc_fun(tc_fun(X13761,tc_Option_Ooption(X13760)),tc_fun(X13761,tc_Option_Ooption(X13760))))),X13761),c_COMBB(tc_Option_Ooption(X13760),tc_fun(tc_fun(X13761,tc_Option_Ooption(X13760)),tc_fun(X13761,tc_Option_Ooption(X13760))),X13760)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X13761,tc_Option_Ooption(X13760)),tc_fun(tc_Option_Ooption(X13760),tc_fun(X13761,tc_Option_Ooption(X13760)))),tc_fun(tc_Option_Ooption(X13760),tc_fun(tc_fun(X13761,tc_Option_Ooption(X13760)),tc_fun(X13761,tc_Option_Ooption(X13760)))),X13761),c_COMBC(tc_fun(X13761,tc_Option_Ooption(X13760)),tc_Option_Ooption(X13760),tc_fun(X13761,tc_Option_Ooption(X13760)))),hAPP(c_COMBC(tc_fun(X13761,tc_Option_Ooption(X13760)),X13761,tc_fun(tc_Option_Ooption(X13760),tc_fun(X13761,tc_Option_Ooption(X13760)))),c_Fun_Ofun__upd(X13761,tc_Option_Ooption(X13760)))))),c_Option_Ooption_OSome(X13760))),X13758,X13759)=c_Map_Omap__add(X13761,X13760,X13759,hAPP(c_Map_Omap__of(X13761,X13760),X13758)), inference(variable_rename,[status(thm)],[fact_map__add__map__of__foldr])). 4.05/4.29 fof(c_0_5688, plain, ![X15932, X15933]: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,X15933))),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),X15932)))))),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)),X15932))),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)),X15932))))),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)),X15932)))),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),X15932))),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(X15933,X15932), inference(variable_rename,[status(thm)],[fact_divmod__int__rel__def])). 4.05/4.29 cnf(c_0_5689, plain, (hAPP(c_Divides_Oadjust(X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X1)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_4763])). 4.05/4.29 cnf(c_0_5690, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X1),X2),hAPP(c_Nitpick_Odenom(X1),X3))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X1),tc_Int_Oint),c_Nitpick_Ofrac(X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),X2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X1),X2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X1),X3))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X1),X3)))))),c_COMBI(tc_Int_Oint)))=c_Nitpick_Oplus__frac(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_4764])). 4.05/4.29 fof(c_0_5691, plain, ![X13986, X13987, X13988]:hAPP(c_List_Oset(X13988),c_List_Osublist(X13988,X13987,X13986))=hAPP(c_Set_OCollect(X13988),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X13988),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X13988,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)),X13988),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)),X13988),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X13988,tc_fun(tc_Nat_Onat,X13988),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13988,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X13988),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X13988),c_COMBB(X13988,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X13988),X13987))))),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(X13988)),X13987)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X13986))))), inference(variable_rename,[status(thm)],[fact_set__sublist])). 4.05/4.29 fof(c_0_5692, plain, ![X11251, X11252, X11253, X11254]:hAPP(c_Set_OCollect(tc_prod(X11253,X11253)),hAPP(c_Product__Type_Oprod_Oprod__case(X11253,X11253,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X11253,tc_fun(tc_prod(X11254,X11254),tc_HOL_Obool),tc_fun(X11253,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11253,tc_fun(tc_fun(tc_prod(X11254,X11254),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X11254,X11254),tc_HOL_Obool),tc_fun(X11253,tc_HOL_Obool)),X11253),c_COMBC(X11253,tc_fun(tc_prod(X11254,X11254),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11253,tc_prod(X11254,X11254)),tc_fun(X11253,tc_fun(tc_fun(tc_prod(X11254,X11254),tc_HOL_Obool),tc_HOL_Obool)),X11253),hAPP(c_COMBB(tc_prod(X11254,X11254),tc_fun(tc_fun(tc_prod(X11254,X11254),tc_HOL_Obool),tc_HOL_Obool),X11253),c_member(tc_prod(X11254,X11254)))),hAPP(hAPP(c_COMBC(X11253,tc_fun(X11253,X11254),tc_fun(X11253,tc_prod(X11254,X11254))),hAPP(hAPP(c_COMBB(tc_fun(X11254,tc_prod(X11254,X11254)),tc_fun(tc_fun(X11253,X11254),tc_fun(X11253,tc_prod(X11254,X11254))),X11253),c_COMBB(X11254,tc_prod(X11254,X11254),X11253)),hAPP(hAPP(c_COMBB(X11254,tc_fun(X11254,tc_prod(X11254,X11254)),X11253),c_Product__Type_OPair(X11254,X11254)),X11251))),X11251)))),X11252)))=hAPP(hAPP(c_Relation_Oinv__image(X11254,X11253),X11252),X11251), inference(variable_rename,[status(thm)],[fact_inv__image__def])). 4.05/4.29 cnf(c_0_5693, 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_4765])). 4.05/4.29 cnf(c_0_5694, 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_4766, c_0_4767])). 4.05/4.29 cnf(c_0_5695, 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_4768, c_0_4523]), ['final']). 4.05/4.29 cnf(c_0_5696, 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_4769, c_0_4523]), ['final']). 4.05/4.29 cnf(c_0_5697, 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_4770, c_0_4767])). 4.05/4.29 fof(c_0_5698, plain, ![X12099, X12100, X12101]:hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X12101,X12100),X12099)=hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X12101,tc_Lazy__Sequence_Olazy__sequence(X12101)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X12101,tc_Lazy__Sequence_Olazy__sequence(X12101),tc_Nat_Onat),hAPP(hAPP(c_COMBC(X12101,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X12101),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X12101),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X12101),tc_Nat_Onat)),X12101),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X12101),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X12101),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X12101),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X12101),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X12101)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X12101,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X12101),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X12101),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X12101),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X12101),tc_Nat_Onat)),X12101),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X12101))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X12101),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X12100))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X12101,X12100))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X12101),X12099)), inference(variable_rename,[status(thm)],[fact_lazy__sequence__size__code])). 4.05/4.29 fof(c_0_5699, plain, ![X1776, X1777, X1778, X1779, X1780]:hAPP(c_Option_Ooption_Ooption__case(X1780,tc_prod(X1779,tc_Lazy__Sequence_Olazy__sequence(X1779)),X1778,hAPP(c_Product__Type_Oprod_Oprod__case(X1779,tc_Lazy__Sequence_Olazy__sequence(X1779),X1780),X1777)),hAPP(c_Lazy__Sequence_Oyield(X1779),X1776))=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X1780,X1779,X1778,X1777,X1776), inference(variable_rename,[status(thm)],[fact_seq__case])). 4.05/4.29 cnf(c_0_5700, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),c_List_Ofoldr(tc_List_Olist(X3),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3))),X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_List_Ofoldr(tc_List_Olist(X3),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X3),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X3)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_List_Olist(X3),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X3)))),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(split_conjunct,[status(thm)],[c_0_4771])). 4.05/4.29 fof(c_0_5701, plain, ![X16629, X16630]:hAPP(c_Set_OCollect(X16630),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X16630),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X16630,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)),X16630),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)),X16630),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X16630,tc_fun(tc_Nat_Onat,X16630),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16630,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X16630),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X16630),c_COMBB(X16630,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X16630),X16629))))),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(X16630)),X16629)))))=hAPP(c_List_Oset(X16630),X16629), inference(variable_rename,[status(thm)],[fact_set__conv__nth])). 4.05/4.29 cnf(c_0_5702, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X1,X3,X4),X5))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X3,X4)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5)))))=hAPP(c_Nat_Onat_Onat__rec(X1,X3,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X5))), inference(split_conjunct,[status(thm)],[c_0_4772])). 4.05/4.29 fof(c_0_5703, plain, ![X17449]:hAPP(c_Set_OCollect(tc_prod(tc_fun(X17449,tc_HOL_Obool),tc_fun(X17449,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X17449,tc_HOL_Obool),tc_fun(X17449,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X17449,tc_HOL_Obool),tc_fun(tc_fun(X17449,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X17449,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X17449,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X17449,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X17449,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X17449,tc_HOL_Obool)),c_COMBS(tc_fun(X17449,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X17449,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X17449,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X17449,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X17449,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X17449,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X17449))))=c_Wellfounded_Ofinite__psubset(X17449), inference(variable_rename,[status(thm)],[fact_finite__psubset__def])). 4.05/4.29 fof(c_0_5704, plain, ![X2948, X2949, X2950]:hAPP(c_Set_OCollect(tc_prod(X2949,X2950)),hAPP(c_Product__Type_Oprod_Oprod__case(X2949,X2950,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2949,tc_fun(tc_prod(X2950,X2949),tc_HOL_Obool),tc_fun(X2950,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2950,tc_fun(tc_fun(tc_prod(X2950,X2949),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2950,X2949),tc_HOL_Obool),tc_fun(X2950,tc_HOL_Obool)),X2949),c_COMBC(X2950,tc_fun(tc_prod(X2950,X2949),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2950,tc_prod(X2950,X2949)),tc_fun(X2950,tc_fun(tc_fun(tc_prod(X2950,X2949),tc_HOL_Obool),tc_HOL_Obool)),X2949),hAPP(c_COMBB(tc_prod(X2950,X2949),tc_fun(tc_fun(tc_prod(X2950,X2949),tc_HOL_Obool),tc_HOL_Obool),X2950),c_member(tc_prod(X2950,X2949)))),hAPP(c_COMBC(X2950,X2949,tc_prod(X2950,X2949)),c_Product__Type_OPair(X2950,X2949))))),X2948)))=hAPP(c_Relation_Oconverse(X2950,X2949),X2948), inference(variable_rename,[status(thm)],[fact_converse__def])). 4.05/4.29 fof(c_0_5705, plain, ![X1121]:hAPP(c_Int_Onat,X1121)=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,X1121)),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)))))), inference(variable_rename,[status(thm)],[fact_nat__def])). 4.05/4.29 fof(c_0_5706, plain, ![X6357, X6358, X6359, X6360]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6360,tc_fun(X6359,tc_HOL_Obool)),X6358),X6357)=hAPP(c_Set_OCollect(X6359),hAPP(hAPP(c_COMBB(tc_fun(X6360,tc_HOL_Obool),tc_HOL_Obool,X6359),c_HOL_OAll(X6360)),hAPP(hAPP(c_COMBB(tc_fun(X6360,tc_HOL_Obool),tc_fun(X6360,tc_HOL_Obool),X6359),hAPP(c_COMBS(X6360,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6360),c_fimplies),hAPP(hAPP(c_COMBC(X6360,tc_fun(X6360,tc_HOL_Obool),tc_HOL_Obool),c_member(X6360)),X6358)))),hAPP(hAPP(c_COMBC(X6359,tc_fun(X6360,tc_fun(X6359,tc_HOL_Obool)),tc_fun(X6360,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X6359,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X6360,tc_fun(X6359,tc_HOL_Obool)),tc_fun(X6360,tc_HOL_Obool)),X6359),c_COMBB(tc_fun(X6359,tc_HOL_Obool),tc_HOL_Obool,X6360)),c_member(X6359))),X6357)))), inference(variable_rename,[status(thm)],[fact_INTER__def])). 4.05/4.29 fof(c_0_5707, plain, ![X11174, X11175, X11176]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11176,tc_fun(tc_fun(X11176,tc_HOL_Obool),tc_HOL_Obool)),X11175),hAPP(hAPP(c_COMBC(X11176,tc_fun(tc_fun(X11176,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X11176,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11176,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X11176,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X11176,tc_HOL_Obool),tc_HOL_Obool)),X11176),c_Set_Oinsert(tc_fun(X11176,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X11176,tc_HOL_Obool),tc_fun(X11176,tc_HOL_Obool),X11176),c_Relation_OImage(X11176,X11176,X11174)),hAPP(hAPP(c_COMBC(X11176,tc_fun(X11176,tc_HOL_Obool),tc_fun(X11176,tc_HOL_Obool)),c_Set_Oinsert(X11176)),c_Orderings_Obot__class_Obot(tc_fun(X11176,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X11176,tc_HOL_Obool),tc_HOL_Obool))))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X11176),X11175),X11174), inference(variable_rename,[status(thm)],[fact_quotient__def])). 4.05/4.29 fof(c_0_5708, plain, ![X17059, X17060, X17061, X17062]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X17062,tc_fun(X17061,tc_HOL_Obool)),X17059),hAPP(hAPP(c_COMBC(X17062,tc_fun(X17061,tc_HOL_Obool),tc_fun(X17061,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X17061,tc_fun(tc_fun(X17061,tc_HOL_Obool),tc_fun(X17061,tc_HOL_Obool)),X17062),c_Set_Oinsert(X17061)),X17060)),c_Orderings_Obot__class_Obot(tc_fun(X17061,tc_HOL_Obool))))=hAPP(c_Set_Oimage(X17062,X17061,X17060),X17059), inference(variable_rename,[status(thm)],[fact_image__eq__UN])). 4.05/4.29 fof(c_0_5709, plain, ![X3671, X3672, X3673]:hAPP(c_List_Oset(tc_List_Olist(X3673)),c_Enum_On__lists(X3673,X3672,X3671))=hAPP(c_Set_OCollect(tc_List_Olist(X3673)),hAPP(hAPP(c_COMBS(tc_List_Olist(X3673),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X3673)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X3673),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X3673)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X3673)))),X3672))),hAPP(hAPP(c_COMBC(tc_List_Olist(X3673),tc_fun(X3673,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X3673,tc_HOL_Obool),tc_fun(tc_fun(X3673,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X3673)),c_Orderings_Oord__class_Oless__eq(tc_fun(X3673,tc_HOL_Obool))),c_List_Oset(X3673))),hAPP(c_List_Oset(X3673),X3671)))), inference(variable_rename,[status(thm)],[fact_set__n__lists])). 4.05/4.29 fof(c_0_5710, plain, ![X15058, X15059, X15060, X15061, X15062, X15063, X15064, X15065]:hAPP(hAPP(c_List_Omap(tc_prod(X15063,X15060),tc_prod(X15065,X15064)),hAPP(c_Product__Type_Oprod_Oprod__case(X15063,X15060,tc_prod(X15065,X15064)),hAPP(hAPP(c_COMBC(X15063,tc_fun(X15060,X15064),tc_fun(X15060,tc_prod(X15065,X15064))),hAPP(hAPP(c_COMBB(tc_fun(X15064,tc_prod(X15065,X15064)),tc_fun(tc_fun(X15060,X15064),tc_fun(X15060,tc_prod(X15065,X15064))),X15063),c_COMBB(X15064,tc_prod(X15065,X15064),X15060)),hAPP(hAPP(c_COMBB(X15065,tc_fun(X15064,tc_prod(X15065,X15064)),X15063),c_Product__Type_OPair(X15065,X15064)),X15062))),X15059))),hAPP(hAPP(c_List_Ozip(X15063,X15060),X15061),X15058))=hAPP(hAPP(c_List_Ozip(X15065,X15064),hAPP(hAPP(c_List_Omap(X15063,X15065),X15062),X15061)),hAPP(hAPP(c_List_Omap(X15060,X15064),X15059),X15058)), inference(variable_rename,[status(thm)],[fact_zip__map__map])). 4.05/4.29 fof(c_0_5711, plain, ![X7412, X7413, X7414, X7415, X7416, X7417]:hAPP(c_Product__Type_Oprod_Oprod__case(X7417,X7415,tc_prod(X7416,X7414)),hAPP(hAPP(c_COMBC(X7417,tc_fun(X7415,X7414),tc_fun(X7415,tc_prod(X7416,X7414))),hAPP(hAPP(c_COMBB(tc_fun(X7414,tc_prod(X7416,X7414)),tc_fun(tc_fun(X7415,X7414),tc_fun(X7415,tc_prod(X7416,X7414))),X7417),c_COMBB(X7414,tc_prod(X7416,X7414),X7415)),hAPP(hAPP(c_COMBB(X7416,tc_fun(X7414,tc_prod(X7416,X7414)),X7417),c_Product__Type_OPair(X7416,X7414)),X7413))),X7412))=c_Product__Type_Omap__pair(X7417,X7416,X7415,X7414,X7413,X7412), inference(variable_rename,[status(thm)],[fact_map__pair__def])). 4.05/4.29 cnf(c_0_5712, plain, (c_Nat_Onat_Onat__case(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)),c_Nat_Onat_Onat__case(X1,X2,X3,X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,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))))), inference(split_conjunct,[status(thm)],[c_0_4773])). 4.05/4.29 cnf(c_0_5713, plain, (c_Complete__Lattice_OInf__class_OInf(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_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))))), inference(split_conjunct,[status(thm)],[c_0_4774])). 4.05/4.29 fof(c_0_5714, plain, ![X3387, X3388, X3389, X3390]: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),X3390),X3388)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3389),X3387))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))=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),X3390),X3389)),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),X3388),X3387)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[fact_add])). 4.05/4.29 cnf(c_0_5715, plain, (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)))))=c_Relation_OId(X1)), inference(split_conjunct,[status(thm)],[c_0_4775])). 4.05/4.29 cnf(c_0_5716, plain, (c_Relation_OId(X1)=c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_4776])). 4.05/4.29 cnf(c_0_5717, 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_4777])). 4.05/4.29 cnf(c_0_5718, 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)),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(split_conjunct,[status(thm)],[c_0_4778])). 4.05/4.29 cnf(c_0_5719, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X1))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),X2))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))), inference(split_conjunct,[status(thm)],[c_0_4779])). 4.05/4.29 fof(c_0_5720, plain, ![X9722, X9723, X9724]:c_Enum_On__lists(X9724,hAPP(c_Nat_OSuc,X9723),X9722)=c_List_Oconcat(tc_List_Olist(X9724),hAPP(hAPP(c_List_Omap(tc_List_Olist(X9724),tc_List_Olist(tc_List_Olist(X9724))),hAPP(hAPP(c_COMBC(tc_List_Olist(X9724),tc_List_Olist(X9724),tc_List_Olist(tc_List_Olist(X9724))),hAPP(hAPP(c_COMBB(tc_fun(X9724,tc_List_Olist(X9724)),tc_fun(tc_List_Olist(X9724),tc_List_Olist(tc_List_Olist(X9724))),tc_List_Olist(X9724)),c_List_Omap(X9724,tc_List_Olist(X9724))),hAPP(c_COMBC(X9724,tc_List_Olist(X9724),tc_List_Olist(X9724)),c_List_Olist_OCons(X9724)))),X9722)),c_Enum_On__lists(X9724,X9723,X9722))), inference(variable_rename,[status(thm)],[fact_n__lists_Osimps_I2_J])). 4.05/4.29 cnf(c_0_5721, 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_4780])). 4.05/4.29 fof(c_0_5722, plain, ![X9692, X9693, X9694, X9695, X9696]:c_Map_Odom(X9696,X9695,c_Fun_Ooverride__on(X9696,tc_Option_Ooption(X9695),X9694,X9693,X9692))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9696,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9696,tc_HOL_Obool)),c_Map_Odom(X9696,X9695,X9694)),hAPP(c_Set_OCollect(X9696),hAPP(hAPP(c_COMBC(X9696,tc_fun(X9696,tc_HOL_Obool),tc_HOL_Obool),c_member(X9696)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9696,tc_HOL_Obool)),X9692),c_Map_Odom(X9696,X9695,X9693)))))),hAPP(c_Set_OCollect(X9696),hAPP(hAPP(c_COMBC(X9696,tc_fun(X9696,tc_HOL_Obool),tc_HOL_Obool),c_member(X9696)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9696,tc_HOL_Obool)),X9692),c_Map_Odom(X9696,X9695,X9693))))), inference(variable_rename,[status(thm)],[fact_dom__override__on])). 4.05/4.29 fof(c_0_5723, plain, ![X14637, X14638]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14638,tc_fun(tc_prod(X14638,X14638),tc_HOL_Obool)),X14637),hAPP(hAPP(c_COMBC(X14638,tc_fun(tc_prod(X14638,X14638),tc_HOL_Obool),tc_fun(tc_prod(X14638,X14638),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X14638,X14638),tc_fun(tc_fun(tc_prod(X14638,X14638),tc_HOL_Obool),tc_fun(tc_prod(X14638,X14638),tc_HOL_Obool)),X14638),c_Set_Oinsert(tc_prod(X14638,X14638))),hAPP(hAPP(c_COMBS(X14638,X14638,tc_prod(X14638,X14638)),c_Product__Type_OPair(X14638,X14638)),c_COMBI(X14638)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X14638,X14638),tc_HOL_Obool))))=c_Relation_OId__on(X14638,X14637), inference(variable_rename,[status(thm)],[fact_Id__on__def])). 4.05/4.29 cnf(c_0_5724, 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_4781])). 4.05/4.29 cnf(c_0_5725, 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_4782])). 4.05/4.29 cnf(c_0_5726, 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_4783])). 4.05/4.29 cnf(c_0_5727, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),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),X1)),c_Int_Onat))))), inference(split_conjunct,[status(thm)],[c_0_4784])). 4.05/4.29 cnf(c_0_5728, 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_4785])). 4.05/4.29 cnf(c_0_5729, 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_4786])). 4.05/4.29 cnf(c_0_5730, plain, (c_List_Osublist(X1,X2,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)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X3)),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X2),c_List_Oupt(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_4787])). 4.05/4.29 cnf(c_0_5731, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(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_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I3_J])). 4.05/4.29 fof(c_0_5732, plain, ![X9775, X9776, X9777, X9778]:hAPP(hAPP(c_Product__Type_OPair(X9778,X9777),X9776),X9775)=c_Hilbert__Choice_OEps(tc_prod(X9778,X9777),hAPP(c_Product__Type_Oprod_Oprod__case(X9778,X9777,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X9778,tc_fun(X9777,tc_HOL_Obool),tc_fun(X9777,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X9777,tc_HOL_Obool),tc_fun(X9777,tc_HOL_Obool)),X9778),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X9777)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X9778),c_fconj),hAPP(c_fequal,X9776)))),hAPP(c_fequal,X9775)))), inference(variable_rename,[status(thm)],[fact_Eps__split__eq])). 4.05/4.29 cnf(c_0_5733, plain, (c_HOL_OThe(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(c_fequal,X3)))),hAPP(c_fequal,X4))))=hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_4788])). 4.05/4.29 fof(c_0_5734, plain, ![X3149, X3150]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X3150,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(X3150,tc_HOL_Obool)),tc_fun(X3150,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X3150,tc_HOL_Obool)),tc_fun(X3150,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X3150,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X3149))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X3150,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X3149), inference(variable_rename,[status(thm)],[fact_UN__UN__finite__eq])). 4.05/4.29 fof(c_0_5735, plain, ![X6333, X6334, X6335, X6336, X6337, X6338]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6335,tc_fun(X6337,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6338,tc_fun(X6335,tc_HOL_Obool)),X6336),X6334)),X6333)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6338,tc_fun(X6337,tc_HOL_Obool)),X6336),hAPP(hAPP(c_COMBC(X6338,tc_fun(X6335,tc_fun(X6337,tc_HOL_Obool)),tc_fun(X6337,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6335,tc_HOL_Obool),tc_fun(tc_fun(X6335,tc_fun(X6337,tc_HOL_Obool)),tc_fun(X6337,tc_HOL_Obool)),X6338),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6335,tc_fun(X6337,tc_HOL_Obool))),X6334)),X6333)), inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I9_J])). 4.05/4.29 fof(c_0_5736, plain, ![X4531, X4532, X4533, X4534]:hAPP(hAPP(c_List_Oappend(X4534),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X4534)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4531)),hAPP(hAPP(c_List_Olist_OCons(X4534),X4533),c_List_Olist_ONil(X4534))),c_List_Olist_ONil(X4534))),c_List_Osublist(X4534,X4532,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)),X4531))))=c_List_Osublist(X4534,hAPP(hAPP(c_List_Olist_OCons(X4534),X4533),X4532),X4531), inference(variable_rename,[status(thm)],[fact_sublist__Cons])). 4.05/4.29 fof(c_0_5737, plain, ![X12659, X12660, X12661]:c_List_Olistsp(X12661,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12661,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X12661,tc_fun(X12661,tc_HOL_Obool),tc_HOL_Obool),c_member(X12661)),X12660)),hAPP(hAPP(c_COMBC(X12661,tc_fun(X12661,tc_HOL_Obool),tc_HOL_Obool),c_member(X12661)),X12659)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X12661),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X12661),tc_fun(tc_List_Olist(X12661),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X12661))),c_List_Olists(X12661,X12660))),hAPP(hAPP(c_COMBC(tc_List_Olist(X12661),tc_fun(tc_List_Olist(X12661),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X12661))),c_List_Olists(X12661,X12659))), inference(variable_rename,[status(thm)],[fact_lists__Int__eq])). 4.05/4.29 fof(c_0_5738, plain, ![X5426, X5427, X5428, X5429]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5429,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5429,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5429,tc_HOL_Obool)),X5428),X5427)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5429,tc_HOL_Obool)),X5427),X5426))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5429,tc_HOL_Obool)),X5426),X5428))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5429,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5429,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5429,tc_HOL_Obool)),X5428),X5427)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5429,tc_HOL_Obool)),X5427),X5426))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5429,tc_HOL_Obool)),X5426),X5428)), inference(variable_rename,[status(thm)],[fact_Un__Int__crazy])). 4.05/4.29 fof(c_0_5739, plain, ![X12740, X12741, X12742, X12743]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12743,tc_HOL_Obool)),X12742),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12743,tc_HOL_Obool)),X12741),X12740))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12743,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12743,tc_HOL_Obool)),X12742),X12741)),X12740), inference(variable_rename,[status(thm)],[fact_Int__assoc])). 4.05/4.29 cnf(c_0_5740, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))), inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I4_J])). 4.05/4.29 fof(c_0_5741, plain, ![X14497, X14498]:c_List_Olenlex(X14498,X14497)=hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X14498)),tc_List_Olist(X14498)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X14498),c_Wellfounded_Oless__than,c_List_Olex(X14498,X14497))),hAPP(hAPP(c_COMBS(tc_List_Olist(X14498),tc_List_Olist(X14498),tc_prod(tc_Nat_Onat,tc_List_Olist(X14498))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X14498),tc_prod(tc_Nat_Onat,tc_List_Olist(X14498))),tc_List_Olist(X14498)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X14498))),c_Nat_Osize__class_Osize(tc_List_Olist(X14498)))),c_COMBI(tc_List_Olist(X14498)))), inference(variable_rename,[status(thm)],[fact_lenlex__def])). 4.05/4.29 fof(c_0_5742, plain, ![X5636, X5637, X5638]:hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X5638),X5638),c_Wellfounded_Olex__prod(tc_Nat_Onat,X5638,c_Wellfounded_Oless__than,X5636)),hAPP(hAPP(c_COMBS(X5638,X5638,tc_prod(tc_Nat_Onat,X5638)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X5638,tc_prod(tc_Nat_Onat,X5638)),X5638),c_Product__Type_OPair(tc_Nat_Onat,X5638)),X5637)),c_COMBI(X5638)))=c_Wellfounded_Omlex__prod(X5638,X5637,X5636), inference(variable_rename,[status(thm)],[fact_mlex__prod__def])). 4.05/4.29 fof(c_0_5743, plain, ![X7836, X7837, X7838, X7839]:hAPP(hAPP(c_List_Oappend(X7839),c_List_Osublist(X7839,X7838,X7836)),c_List_Osublist(X7839,X7837,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(X7839)),X7838)))),X7836))))=c_List_Osublist(X7839,hAPP(hAPP(c_List_Oappend(X7839),X7838),X7837),X7836), inference(variable_rename,[status(thm)],[fact_sublist__append])). 4.05/4.29 cnf(c_0_5744, 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)),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(split_conjunct,[status(thm)],[c_0_4789])). 4.05/4.29 fof(c_0_5745, plain, ![X11608, X11609]:hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X11609)),X11608)=hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X11609,tc_Lazy__Sequence_Olazy__sequence(X11609)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X11609,tc_Lazy__Sequence_Olazy__sequence(X11609),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X11609),tc_Nat_Onat),X11609),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X11609),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(X11609)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X11609)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(c_Lazy__Sequence_Oyield(X11609),X11608)), inference(variable_rename,[status(thm)],[fact_size__code])). 4.05/4.29 fof(c_0_5746, plain, ![X13540, X13541]: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),X13540),X13541)),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),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),X13541),X13540)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[fact_minus])). 4.05/4.29 fof(c_0_5747, plain, ![X10478, X10479]:c_Random_Oselect(X10479,X10478)=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(X10479,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(X10479)),X10478)))),hAPP(hAPP(c_COMBB(X10479,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X10479,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X10479,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10479,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X10479),X10478)),c_Code__Numeral_Onat__of))), inference(variable_rename,[status(thm)],[fact_select__def])). 4.05/4.29 fof(c_0_5748, plain, ![X16341, X16342, X16343]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16343)),hAPP(c_List_Ofilter(X16343,X16342),X16341))=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(X16343)),X16341)))),hAPP(hAPP(c_COMBB(X16343,tc_HOL_Obool,tc_Nat_Onat),X16342),hAPP(c_List_Onth(X16343),X16341))))), inference(variable_rename,[status(thm)],[fact_length__filter__conv__card])). 4.05/4.29 cnf(c_0_5749, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2))=c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4790])). 4.05/4.29 cnf(c_0_5750, 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_4791])). 4.05/4.29 cnf(c_0_5751, 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_4792])). 4.05/4.29 cnf(c_0_5752, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4793, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_5753, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))=X1), inference(rw,[status(thm)],[c_0_4794, c_0_4795]), ['final']). 4.05/4.29 fof(c_0_5754, plain, ![X1109, X1110, X1111, X1112, X1113, X1114]:hAPP(c_Set_Ovimage(X1114,tc_prod(X1113,X1112),X1111),hAPP(hAPP(c_Product__Type_OSigma(X1113,X1112),X1110),hAPP(c_COMBK(tc_fun(X1112,tc_HOL_Obool),X1113),X1109)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1114,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1114,X1113,hAPP(c_Fun_Ocomp(tc_prod(X1113,X1112),X1113,X1114,c_Product__Type_Ofst(X1113,X1112)),X1111)),X1110)),hAPP(c_Set_Ovimage(X1114,X1112,hAPP(c_Fun_Ocomp(tc_prod(X1113,X1112),X1112,X1114,c_Product__Type_Osnd(X1113,X1112)),X1111)),X1109)), inference(variable_rename,[status(thm)],[fact_vimage__Times])). 4.05/4.29 fof(c_0_5755, plain, ![X10317, X10318, X10319, X10320]:hAPP(hAPP(c_List_Omap(X10320,X10319),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X10319),X10319,X10320,c_Option_Othe(X10319)),X10318)),hAPP(c_List_Ofilter(X10320,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10320),c_fNot),hAPP(hAPP(c_COMBC(X10320,tc_Option_Ooption(X10319),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X10319),tc_fun(tc_Option_Ooption(X10319),tc_HOL_Obool),X10320),c_fequal),X10318)),c_Option_Ooption_ONone(X10319)))),X10317))=c_List_Omap__filter(X10320,X10319,X10318,X10317), inference(variable_rename,[status(thm)],[fact_map__filter__def])). 4.05/4.29 cnf(c_0_5756, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3)),c_Option_Ooption_ONone(X2))))=c_Map_Odom(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_4796])). 4.05/4.29 cnf(c_0_5757, 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_4797])). 4.05/4.29 cnf(c_0_5758, 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_4798])). 4.05/4.29 cnf(c_0_5759, 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_4799])). 4.05/4.29 fof(c_0_5760, plain, ![X9122, X9123, X9124, X9125, X9126]:((X9126!=c_Orderings_Obot__class_Obot(tc_fun(X9125,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X9124,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9125,tc_fun(X9124,tc_HOL_Obool)),X9126),hAPP(hAPP(c_COMBC(X9125,tc_fun(X9124,tc_HOL_Obool),tc_fun(X9124,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9124,tc_HOL_Obool),tc_fun(tc_fun(X9124,tc_HOL_Obool),tc_fun(X9124,tc_HOL_Obool)),X9125),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9124,tc_HOL_Obool))),X9123)),X9122)))&(c_Orderings_Obot__class_Obot(tc_fun(X9125,tc_HOL_Obool))=X9126|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9125,tc_fun(X9124,tc_HOL_Obool)),X9126),hAPP(hAPP(c_COMBC(X9125,tc_fun(X9124,tc_HOL_Obool),tc_fun(X9124,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9124,tc_HOL_Obool),tc_fun(tc_fun(X9124,tc_HOL_Obool),tc_fun(X9124,tc_HOL_Obool)),X9125),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9124,tc_HOL_Obool))),X9123)),X9122))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9124,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9125,tc_fun(X9124,tc_HOL_Obool)),X9126),X9123)),X9122))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__simps_I2_J])])])). 4.05/4.29 cnf(c_0_5761, plain, (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)))=c_Transitive__Closure_Ortrancl(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_4800])). 4.05/4.29 cnf(c_0_5762, 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_4801])). 4.05/4.29 fof(c_0_5763, plain, ![X6398, X6399, X6400]:c_Map_Oran(X6400,X6399,X6398)=hAPP(c_Set_OCollect(X6399),hAPP(hAPP(c_COMBB(tc_fun(X6400,tc_HOL_Obool),tc_HOL_Obool,X6399),c_HOL_OEx(X6400)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X6399),tc_fun(X6400,tc_HOL_Obool),X6399),hAPP(c_COMBC(X6400,tc_Option_Ooption(X6399),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X6399),tc_fun(tc_Option_Ooption(X6399),tc_HOL_Obool),X6400),c_fequal),X6398))),c_Option_Ooption_OSome(X6399)))), inference(variable_rename,[status(thm)],[fact_ran__def])). 4.05/4.29 fof(c_0_5764, plain, ![X8670, X8671, X8672, X8673]:c_List_Oconcat(X8673,hAPP(hAPP(c_List_Omap(X8672,tc_List_Olist(X8673)),hAPP(hAPP(c_COMBC(X8672,tc_List_Olist(X8673),tc_List_Olist(X8673)),hAPP(hAPP(c_COMBB(X8673,tc_fun(tc_List_Olist(X8673),tc_List_Olist(X8673)),X8672),c_List_Olist_OCons(X8673)),X8671)),c_List_Olist_ONil(X8673))),X8670))=hAPP(hAPP(c_List_Omap(X8672,X8673),X8671),X8670), inference(variable_rename,[status(thm)],[fact_concat__map__singleton])). 4.05/4.29 fof(c_0_5765, plain, ![X14349, X14350, X14351, X14352]:hAPP(c_Relation_OImage(tc_List_Olist(X14352),tc_List_Olist(X14352),c_List_Olistrel(X14352,X14351)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X14352)),hAPP(hAPP(c_List_Olist_OCons(X14352),X14350),X14349)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X14352),tc_HOL_Obool))))=c_List_Oset__Cons(X14352,hAPP(c_Relation_OImage(X14352,X14352,X14351),hAPP(hAPP(c_Set_Oinsert(X14352),X14350),c_Orderings_Obot__class_Obot(tc_fun(X14352,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X14352),tc_List_Olist(X14352),c_List_Olistrel(X14352,X14351)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X14352)),X14349),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X14352),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_listrel__Cons])). 4.05/4.29 cnf(c_0_5766, plain, (hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))=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))))), inference(split_conjunct,[status(thm)],[c_0_4802])). 4.05/4.29 cnf(c_0_5767, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J])). 4.05/4.29 cnf(c_0_5768, 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_4803])). 4.05/4.29 cnf(c_0_5769, plain, (hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), inference(split_conjunct,[status(thm)],[fact_card__UNIV__bool])). 4.05/4.29 fof(c_0_5770, plain, ![X12317]:c_Int_Oint__ge__less__than2(X12317)=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),X12317)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))), inference(variable_rename,[status(thm)],[fact_int__ge__less__than2__def])). 4.05/4.29 cnf(c_0_5771, 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_4804])). 4.05/4.29 fof(c_0_5772, plain, ![X15480, X15481, X15482]: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),X15482),X15480)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X15481),X15480))),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,X15482,X15480)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X15481,X15480))),X15480))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15482),X15481)),X15480), inference(variable_rename,[status(thm)],[fact_zdiv__zadd1__eq])). 4.05/4.29 fof(c_0_5773, plain, ![X10870, X10871, X10872]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10872),X10871)),X10870)=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),X10872),X10870)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X10871),X10870))),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,X10872,X10870)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10871,X10870))),X10870)), inference(variable_rename,[status(thm)],[fact_div__add1__eq])). 4.05/4.29 fof(c_0_5774, plain, ![X3349, X3350, X3351]:hAPP(c_List_Orotate(X3351,X3350),hAPP(c_List_Orev(X3351),X3349))=hAPP(c_List_Orev(X3351),hAPP(c_List_Orotate(X3351,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3351)),X3349)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3350,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3351)),X3349)))),X3349)), inference(variable_rename,[status(thm)],[fact_rotate__rev])). 4.05/4.29 cnf(c_0_5775, 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_OBit1(X1)),c_Int_OBit1(X2))), inference(split_conjunct,[status(thm)],[c_0_4805])). 4.05/4.29 fof(c_0_5776, plain, ![X697, X698, X699]:hAPP(hAPP(c_Set_Oinsert(X699),X698),hAPP(c_Set_OCollect(X699),X697))=hAPP(c_Set_OCollect(X699),hAPP(hAPP(c_COMBS(X699,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X699),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X699),c_fNot),hAPP(hAPP(c_COMBC(X699,X699,tc_HOL_Obool),c_fequal),X698)))),X697)), inference(variable_rename,[status(thm)],[fact_insert__Collect])). 4.05/4.29 cnf(c_0_5777, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J])). 4.05/4.29 cnf(c_0_5778, plain, (c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J])). 4.05/4.29 fof(c_0_5779, plain, ![X4143]: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),X4143),c_Int_Onat))))=hAPP(c_Set_OCollect(tc_Nat_Onat),X4143), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J])). 4.05/4.29 fof(c_0_5780, plain, ![X568, X569, X570]:hAPP(c_List_Oset(X570),hAPP(c_List_Ofilter(X570,X569),X568))=hAPP(c_Set_OCollect(X570),hAPP(hAPP(c_COMBS(X570,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X570),c_fconj),hAPP(hAPP(c_COMBC(X570,tc_fun(X570,tc_HOL_Obool),tc_HOL_Obool),c_member(X570)),hAPP(c_List_Oset(X570),X568)))),X569)), inference(variable_rename,[status(thm)],[fact_set__filter])). 4.05/4.29 cnf(c_0_5781, 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_4806])). 4.05/4.29 fof(c_0_5782, plain, ![X2100, X2101, X2102]:hAPP(c_List_Orotate(X2102,X2101),X2100)=hAPP(hAPP(c_List_Oappend(X2102),hAPP(hAPP(c_List_Odrop(X2102),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2101,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2102)),X2100))),X2100)),hAPP(hAPP(c_List_Otake(X2102),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2101,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2102)),X2100))),X2100)), inference(variable_rename,[status(thm)],[fact_rotate__drop__take])). 4.05/4.29 cnf(c_0_5783, plain, (c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X1))), inference(split_conjunct,[status(thm)],[c_0_4807])). 4.05/4.29 fof(c_0_5784, plain, ![X4371, X4372, X4373]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4372),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4373),X4371))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4373),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4372),X4371)), inference(variable_rename,[status(thm)],[fact_zadd__left__commute])). 4.05/4.29 fof(c_0_5785, plain, ![X6665, X6666]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6666),X6665)=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),X6666),X6665)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[fact_nat])). 4.05/4.29 fof(c_0_5786, plain, ![X5754, X5755, X5756]:c_HOL_OThe(tc_prod(X5756,X5755),hAPP(hAPP(c_COMBS(tc_prod(X5756,X5755),X5755,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5756,tc_fun(X5755,tc_HOL_Obool),tc_prod(X5756,X5755)),X5754),c_Product__Type_Ofst(X5756,X5755))),c_Product__Type_Osnd(X5756,X5755)))=c_HOL_OThe(tc_prod(X5756,X5755),hAPP(c_Product__Type_Oprod_Oprod__case(X5756,X5755,tc_HOL_Obool),X5754)), inference(variable_rename,[status(thm)],[fact_The__split])). 4.05/4.29 fof(c_0_5787, plain, ![X7378]: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),X7378),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)))),X7378)), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J])). 4.05/4.29 fof(c_0_5788, plain, ![X2346, X2347, X2348]:hAPP(hAPP(c_Equiv__Relations_Oquotient(X2348),hAPP(hAPP(c_Set_Oinsert(X2348),X2347),c_Orderings_Obot__class_Obot(tc_fun(X2348,tc_HOL_Obool)))),X2346)=hAPP(hAPP(c_Set_Oinsert(tc_fun(X2348,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2348,X2348,X2346),hAPP(hAPP(c_Set_Oinsert(X2348),X2347),c_Orderings_Obot__class_Obot(tc_fun(X2348,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2348,tc_HOL_Obool),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_singleton__quotient])). 4.05/4.29 cnf(c_0_5789, plain, (c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J])). 4.05/4.29 cnf(c_0_5790, 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_4808])). 4.05/4.29 cnf(c_0_5791, plain, (c_Nitpick_Onat__lcm(X1,X2)=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))), inference(split_conjunct,[status(thm)],[c_0_4809])). 4.05/4.29 cnf(c_0_5792, plain, (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)))=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)))), inference(split_conjunct,[status(thm)],[c_0_4810])). 4.05/4.29 cnf(c_0_5793, 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_4811])). 4.05/4.29 cnf(c_0_5794, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4812, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_5795, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4813, c_0_4814]), c_0_4427]), c_0_4795])). 4.05/4.29 cnf(c_0_5796, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4815, c_0_4505]), c_0_4795]), ['final']). 4.05/4.29 cnf(c_0_5797, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1))=c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))), inference(split_conjunct,[status(thm)],[c_0_4816])). 4.05/4.29 fof(c_0_5798, plain, ![X2594]: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),X2594),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2594), inference(variable_rename,[status(thm)],[fact_int__def])). 4.05/4.29 cnf(c_0_5799, plain, (hAPP(c_List_Orev(X1),c_List_Oconcat(X1,X2))=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)))), inference(split_conjunct,[status(thm)],[c_0_4817])). 4.05/4.29 fof(c_0_5800, plain, ![X17123, X17124, X17125, X17126]:hAPP(c_List_Orev(X17126),hAPP(hAPP(c_List_Omap(X17125,X17126),X17124),X17123))=hAPP(hAPP(c_List_Omap(X17125,X17126),X17124),hAPP(c_List_Orev(X17125),X17123)), inference(variable_rename,[status(thm)],[fact_rev__map])). 4.05/4.29 fof(c_0_5801, plain, ![X2069, X2070, X2071, X2072]:hAPP(c_Relation_OField(X2072),hAPP(hAPP(c_Set_Oinsert(tc_prod(X2072,X2072)),hAPP(hAPP(c_Product__Type_OPair(X2072,X2072),X2071),X2070)),X2069))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2072,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X2072),X2071),hAPP(hAPP(c_Set_Oinsert(X2072),X2070),c_Orderings_Obot__class_Obot(tc_fun(X2072,tc_HOL_Obool))))),hAPP(c_Relation_OField(X2072),X2069)), inference(variable_rename,[status(thm)],[fact_Field__insert])). 4.05/4.29 cnf(c_0_5802, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X1))=c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))), inference(split_conjunct,[status(thm)],[c_0_4818])). 4.05/4.29 fof(c_0_5803, plain, ![X3656]:X3656=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),esk114_1(X3656)),esk115_1(X3656))),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])])])). 4.05/4.29 fof(c_0_5804, plain, ![X11527, X11528, X11529, X11530]:hAPP(c_List_Orotate(X11530,X11529),hAPP(c_List_Orotate(X11530,X11528),X11527))=hAPP(c_List_Orotate(X11530,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11529),X11528)),X11527), inference(variable_rename,[status(thm)],[fact_rotate__rotate])). 4.05/4.29 fof(c_0_5805, plain, ![X7905, X7906]:c_HOL_OThe(X7906,hAPP(hAPP(c_COMBB(tc_fun(X7906,tc_HOL_Obool),tc_HOL_Obool,X7906),hAPP(c_fequal,X7905)),hAPP(hAPP(c_COMBC(X7906,tc_fun(X7906,tc_HOL_Obool),tc_fun(X7906,tc_HOL_Obool)),c_Set_Oinsert(X7906)),c_Orderings_Obot__class_Obot(tc_fun(X7906,tc_HOL_Obool)))))=c_Set_Othe__elem(X7906,X7905), inference(variable_rename,[status(thm)],[fact_the__elem__def])). 4.05/4.29 cnf(c_0_5806, plain, (c_Transitive__Closure_Otrancl(X1,X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Otrancl(X1,X2)),X2))), inference(split_conjunct,[status(thm)],[c_0_4819])). 4.05/4.29 fof(c_0_5807, plain, ![X4798, X4799, X4800, X4801, X4802, X4803, X4804]:hAPP(hAPP(c_Relation_Orel__comp(X4804,X4803,X4802),hAPP(hAPP(c_Relation_Orel__comp(X4804,X4801,X4803),X4800),X4799)),X4798)=hAPP(hAPP(c_Relation_Orel__comp(X4804,X4801,X4802),X4800),hAPP(hAPP(c_Relation_Orel__comp(X4801,X4803,X4802),X4799),X4798)), inference(variable_rename,[status(thm)],[fact_O__assoc])). 4.05/4.29 fof(c_0_5808, plain, ![X11361, X11362, X11363]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11363)),hAPP(c_List_Ofilter(X11363,X11362),X11361))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11363)),hAPP(c_List_Ofilter(X11363,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11363),c_fNot),X11362)),X11361)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11363)),X11361), inference(variable_rename,[status(thm)],[fact_sum__length__filter__compl])). 4.05/4.29 fof(c_0_5809, plain, ![X8658, X8659, X8660]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8660)),hAPP(hAPP(c_List_Oappend(X8660),X8659),X8658))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8660)),X8659)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8660)),X8658)), inference(variable_rename,[status(thm)],[fact_length__append])). 4.05/4.29 fof(c_0_5810, plain, ![X2493, X2494]: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),X2494)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2493))))), inference(variable_rename,[status(thm)],[fact_finite__M__bounded__by__nat])). 4.05/4.29 fof(c_0_5811, plain, ![X7406, X7407, X7408, X7409, X7410, X7411]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7408,tc_fun(X7411,tc_HOL_Obool)),X7407),hAPP(hAPP(c_COMBB(tc_fun(X7410,tc_HOL_Obool),tc_fun(X7411,tc_HOL_Obool),X7408),c_Set_Ovimage(X7411,X7410,X7409)),X7406))=hAPP(c_Set_Ovimage(X7411,X7410,X7409),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7408,tc_fun(X7410,tc_HOL_Obool)),X7407),X7406)), inference(variable_rename,[status(thm)],[fact_vimage__UN])). 4.05/4.29 fof(c_0_5812, plain, ![X4464, X4465, X4466, X4467]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4467,tc_HOL_Obool)),X4466),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4467,tc_HOL_Obool)),X4465),X4464))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4467,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4467,tc_HOL_Obool)),X4466),X4465)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4467,tc_HOL_Obool)),X4466),X4464)), inference(variable_rename,[status(thm)],[fact_Diff__Un])). 4.05/4.29 cnf(c_0_5813, 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_4820])). 4.05/4.29 cnf(c_0_5814, 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_4821, c_0_4822])). 4.05/4.29 fof(c_0_5815, plain, ![X11418, X11419, X11420, X11421, X11422, X11423]:hAPP(c_Set_Ovimage(X11423,X11422,X11421),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11420,tc_fun(X11422,tc_HOL_Obool)),X11419),X11418))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11420,tc_fun(X11423,tc_HOL_Obool)),X11419),hAPP(hAPP(c_COMBB(tc_fun(X11422,tc_HOL_Obool),tc_fun(X11423,tc_HOL_Obool),X11420),c_Set_Ovimage(X11423,X11422,X11421)),X11418)), inference(variable_rename,[status(thm)],[fact_vimage__INT])). 4.05/4.29 fof(c_0_5816, plain, ![X4686, X4687, X4688, X4689, X4690]:((X4690=c_Orderings_Obot__class_Obot(tc_fun(X4689,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4689,tc_fun(X4688,tc_HOL_Obool)),X4690),hAPP(hAPP(c_COMBB(tc_fun(X4688,tc_HOL_Obool),tc_fun(X4688,tc_HOL_Obool),X4689),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4688,tc_HOL_Obool)),X4687)),X4686))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4688,tc_HOL_Obool)),X4687),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4689,tc_fun(X4688,tc_HOL_Obool)),X4690),X4686)))&(X4690!=c_Orderings_Obot__class_Obot(tc_fun(X4689,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4689,tc_fun(X4688,tc_HOL_Obool)),X4690),hAPP(hAPP(c_COMBB(tc_fun(X4688,tc_HOL_Obool),tc_fun(X4688,tc_HOL_Obool),X4689),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4688,tc_HOL_Obool)),X4687)),X4686))=c_Orderings_Obot__class_Obot(tc_fun(X4688,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__simps_I3_J])])])). 4.05/4.29 fof(c_0_5817, plain, ![X17667, X17668, X17669, X17670]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17670,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17670,tc_HOL_Obool)),X17669),X17668)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17670,tc_HOL_Obool)),X17669),X17667))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17670,tc_HOL_Obool)),X17669),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17670,tc_HOL_Obool)),X17668),X17667)), inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib])). 4.05/4.29 fof(c_0_5818, plain, ![X1523, X1524, X1525, X1526, X1527, X1528]:(X1526!=hAPP(hAPP(c_List_Olist_OCons(X1525),X1527),X1528)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1525),tc_List_Olist(X1525))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1525),tc_List_Olist(X1525)),X1524),hAPP(hAPP(c_List_Oappend(X1525),X1524),X1526))),c_List_Olexord(X1525,X1523)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__rightI])])])). 4.05/4.29 fof(c_0_5819, plain, ![X2624, X2625, X2626]:c_List_Oconcat(X2626,hAPP(hAPP(c_List_Omap(tc_List_Olist(X2626),tc_List_Olist(X2626)),c_List_Ofilter(X2626,X2625)),X2624))=hAPP(c_List_Ofilter(X2626,X2625),c_List_Oconcat(X2626,X2624)), inference(variable_rename,[status(thm)],[fact_filter__concat])). 4.05/4.29 fof(c_0_5820, plain, ![X13317, X13318, X13319]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13319,tc_HOL_Obool)),X13318),X13317)=c_Complete__Lattice_OInf__class_OInf(tc_fun(X13319,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X13319,tc_HOL_Obool)),X13318),hAPP(hAPP(c_Set_Oinsert(tc_fun(X13319,tc_HOL_Obool)),X13317),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X13319,tc_HOL_Obool),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_Int__eq__Inter])). 4.05/4.29 fof(c_0_5821, plain, ![X856, X857, X858]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X858,tc_HOL_Obool)),X857),X856)=c_Complete__Lattice_OSup__class_OSup(tc_fun(X858,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X858,tc_HOL_Obool)),X857),hAPP(hAPP(c_Set_Oinsert(tc_fun(X858,tc_HOL_Obool)),X856),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X858,tc_HOL_Obool),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_Un__eq__Union])). 4.05/4.29 fof(c_0_5822, plain, ![X13847, X13848, X13849, X13850, X13851]:((c_Orderings_Obot__class_Obot(tc_fun(X13850,tc_HOL_Obool))=X13851|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13850,tc_fun(X13849,tc_HOL_Obool)),X13851),hAPP(hAPP(c_COMBB(tc_fun(X13849,tc_HOL_Obool),tc_fun(X13849,tc_HOL_Obool),X13850),hAPP(c_Set_Oinsert(X13849),X13848)),X13847))=hAPP(hAPP(c_Set_Oinsert(X13849),X13848),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13850,tc_fun(X13849,tc_HOL_Obool)),X13851),X13847)))&(X13851!=c_Orderings_Obot__class_Obot(tc_fun(X13850,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13850,tc_fun(X13849,tc_HOL_Obool)),X13851),hAPP(hAPP(c_COMBB(tc_fun(X13849,tc_HOL_Obool),tc_fun(X13849,tc_HOL_Obool),X13850),hAPP(c_Set_Oinsert(X13849),X13848)),X13847))=c_Orderings_Obot__class_Obot(tc_fun(X13849,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__simps_I1_J])])])). 4.05/4.29 cnf(c_0_5823, 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_4823])). 4.05/4.29 fof(c_0_5824, plain, ![X7850, X7851, X7852, X7853, X7854]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X7852,hAPP(c_Product__Type_Ofst(X7854,X7853),X7850))),hAPP(X7851,hAPP(c_Product__Type_Osnd(X7854,X7853),X7850)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Product__Type_Oprod_Oprod__size(X7854,X7853,X7852,X7851,X7850), inference(variable_rename,[status(thm)],[fact_prod__size__simp])). 4.05/4.29 cnf(c_0_5825, 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_4824])). 4.05/4.29 cnf(c_0_5826, 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_4613])). 4.05/4.29 fof(c_0_5827, plain, ![X1068, X1069, X1070, X1073, X1074, X1075, X1076, X1077]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1070),tc_List_Olist(X1070))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1070),tc_List_Olist(X1070)),c_List_Olist_ONil(X1070)),X1069)),c_List_Olexord(X1070,X1068)))|hAPP(hAPP(c_List_Olist_OCons(X1070),esk26_3(X1068,X1069,X1070)),esk27_3(X1068,X1069,X1070))=X1069)&(hAPP(hAPP(c_List_Olist_OCons(X1075),X1076),X1077)!=X1074|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1075),tc_List_Olist(X1075))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1075),tc_List_Olist(X1075)),c_List_Olist_ONil(X1075)),X1074)),c_List_Olexord(X1075,X1073))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__Nil__left])])])])])). 4.05/4.29 cnf(c_0_5828, 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_4825])). 4.05/4.29 cnf(c_0_5829, 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_4826])). 4.05/4.29 cnf(c_0_5830, plain, (c_List_Oembed__list(X1)=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)), inference(split_conjunct,[status(thm)],[c_0_4827])). 4.05/4.29 fof(c_0_5831, plain, ![X12112, X12113, X12114, X12115, X12116]:hAPP(hAPP(c_List_Omap(X12116,X12115),X12114),hAPP(hAPP(c_List_Oappend(X12116),X12113),X12112))=hAPP(hAPP(c_List_Oappend(X12115),hAPP(hAPP(c_List_Omap(X12116,X12115),X12114),X12113)),hAPP(hAPP(c_List_Omap(X12116,X12115),X12114),X12112)), inference(variable_rename,[status(thm)],[fact_map__append])). 4.05/4.29 fof(c_0_5832, plain, ![X11569, X11570]: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),X11570)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X11569))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X11570),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X11569)))=c_Divides_Opdivmod(X11570,X11569), inference(variable_rename,[status(thm)],[fact_pdivmod__def])). 4.05/4.29 fof(c_0_5833, plain, ![X13382, X13383]:c_Divides_Odivmod__int(X13383,X13382)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X13383),X13382)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X13383,X13382)), inference(variable_rename,[status(thm)],[fact_divmod__int__mod__div])). 4.05/4.29 fof(c_0_5834, plain, ![X5087, X5088]:hAPP(c_Relation_OImage(tc_List_Olist(X5088),tc_List_Olist(X5088),c_List_Olistrel(X5088,X5087)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5088)),c_List_Olist_ONil(X5088)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5088),tc_HOL_Obool))))=hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5088)),c_List_Olist_ONil(X5088)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5088),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_listrel__Nil])). 4.05/4.29 cnf(c_0_5835, 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_4828])). 4.05/4.29 fof(c_0_5836, plain, ![X13754, X13755]:X13754=hAPP(c_List_Orev(X13755),hAPP(c_List_Orev(X13755),X13754)), inference(variable_rename,[status(thm)],[fact_rev__rev__ident])). 4.05/4.29 fof(c_0_5837, plain, ![X17095, X17096, X17097]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17096),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X17097),X17096),X17095))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17097,X17096))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17097,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17096),X17095)), inference(variable_rename,[status(thm)],[fact_mod__mult2__eq])). 4.05/4.29 fof(c_0_5838, plain, ![X2605, X2606, X2607]:hAPP(c_List_Orotate(X2607,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2606,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2607)),X2605))),X2605)=hAPP(c_List_Orotate(X2607,X2606),X2605), inference(variable_rename,[status(thm)],[fact_rotate__conv__mod])). 4.05/4.29 fof(c_0_5839, plain, ![X13182, X13183]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X13183),hAPP(c_Nat_OSuc,X13182))=c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X13182),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)),X13182)),X13183), inference(variable_rename,[status(thm)],[fact_max__Suc2])). 4.05/4.29 fof(c_0_5840, plain, ![X14807, X14808, X14809]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14809,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X14809,tc_HOL_Obool),X14808)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X14809,tc_HOL_Obool),X14807))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X14809,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X14809,tc_HOL_Obool),tc_HOL_Obool)),X14808),X14807)), inference(variable_rename,[status(thm)],[fact_Union__Un__distrib])). 4.05/4.29 fof(c_0_5841, plain, ![X640, X641, X642]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X642,tc_HOL_Obool)),X641),c_Complete__Lattice_OSup__class_OSup(tc_fun(X642,tc_HOL_Obool),X640))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X642,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X642,tc_HOL_Obool)),X641),X640)), inference(variable_rename,[status(thm)],[fact_Union__insert])). 4.05/4.29 fof(c_0_5842, plain, ![X2830, X2831, X2832]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X2832,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X2832,tc_HOL_Obool),tc_HOL_Obool)),X2831),X2830))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2832,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X2832,tc_HOL_Obool),X2831)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X2832,tc_HOL_Obool),X2830)), inference(variable_rename,[status(thm)],[fact_Inter__Un__distrib])). 4.05/4.29 fof(c_0_5843, plain, ![X13462, X13463, X13464]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X13464,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X13464,tc_HOL_Obool)),X13463),X13462))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13464,tc_HOL_Obool)),X13463),c_Complete__Lattice_OInf__class_OInf(tc_fun(X13464,tc_HOL_Obool),X13462)), inference(variable_rename,[status(thm)],[fact_Inter__insert])). 4.05/4.29 fof(c_0_5844, plain, ![X9316, X9317, X9318]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9318,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9318,tc_HOL_Obool)),X9317),X9316))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9318,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9318,tc_HOL_Obool)),X9317)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9318,tc_HOL_Obool)),X9316)), inference(variable_rename,[status(thm)],[fact_Compl__Un])). 4.05/4.29 fof(c_0_5845, plain, ![X3679, X3680, X3681, X3682, X3683]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3683,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X3683,X3682,X3681),X3680)),hAPP(c_Set_Ovimage(X3683,X3682,X3681),X3679))=hAPP(c_Set_Ovimage(X3683,X3682,X3681),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3682,tc_HOL_Obool)),X3680),X3679)), inference(variable_rename,[status(thm)],[fact_vimage__Int])). 4.05/4.29 fof(c_0_5846, plain, ![X17626, X17627, X17628, X17629, X17630]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17630,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X17630,X17629,X17628),X17627)),hAPP(c_Set_Ovimage(X17630,X17629,X17628),X17626))=hAPP(c_Set_Ovimage(X17630,X17629,X17628),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17629,tc_HOL_Obool)),X17627),X17626)), inference(variable_rename,[status(thm)],[fact_vimage__Un])). 4.05/4.29 fof(c_0_5847, plain, ![X2781, X2782, X2783, X2784, X2785]:hAPP(c_Set_Ovimage(X2785,X2784,X2783),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2784,tc_HOL_Obool)),X2782),X2781))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2785,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X2785,X2784,X2783),X2782)),hAPP(c_Set_Ovimage(X2785,X2784,X2783),X2781)), inference(variable_rename,[status(thm)],[fact_vimage__Diff])). 4.05/4.29 fof(c_0_5848, plain, ![X15016, X15017]: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)),X15016)),X15017)=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X15017),hAPP(c_Nat_OSuc,X15016)), inference(variable_rename,[status(thm)],[fact_min__Suc2])). 4.05/4.29 fof(c_0_5849, plain, ![X16114, X16115, X16116]:hAPP(hAPP(c_Relation_Orel__comp(X16116,X16116,X16116),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X16116,X16116),tc_HOL_Obool),X16114),X16115)),X16115)=hAPP(hAPP(c_Relation_Orel__comp(X16116,X16116,X16116),X16115),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X16116,X16116),tc_HOL_Obool),X16114),X16115)), inference(variable_rename,[status(thm)],[fact_rel__pow__commute])). 4.05/4.29 fof(c_0_5850, plain, ![X1813, X1814, X1815]:hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1815,X1815),tc_HOL_Obool),hAPP(c_Nat_OSuc,X1814)),X1813)=hAPP(hAPP(c_Relation_Orel__comp(X1815,X1815,X1815),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1815,X1815),tc_HOL_Obool),X1814),X1813)),X1813), inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I2_J])). 4.05/4.29 fof(c_0_5851, plain, ![X8087, X8088, X8089, X8090, X8091]:(X8087!=hAPP(c_Set_Oimage(X8091,X8090,X8089),X8088)|hAPP(c_Set_OPow(X8090),X8087)=hAPP(c_Set_Oimage(tc_fun(X8091,tc_HOL_Obool),tc_fun(X8090,tc_HOL_Obool),c_Set_Oimage(X8091,X8090,X8089)),hAPP(c_Set_OPow(X8091),X8088))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Pow__surj])])). 4.05/4.29 fof(c_0_5852, plain, ![X1420, X1421, X1422, X1423, X1425, X1426, X1427, X1428, X1429]:((c_Map_Odom(X1423,X1422,X1421)!=hAPP(hAPP(c_Set_Oinsert(X1423),X1420),c_Orderings_Obot__class_Obot(tc_fun(X1423,tc_HOL_Obool)))|X1421=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1423,tc_Option_Ooption(X1422)),hAPP(c_COMBK(tc_Option_Ooption(X1422),X1423),c_Option_Ooption_ONone(X1422))),X1420),hAPP(c_Option_Ooption_OSome(X1422),esk43_4(X1420,X1421,X1422,X1423))))&(X1426!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1428,tc_Option_Ooption(X1427)),hAPP(c_COMBK(tc_Option_Ooption(X1427),X1428),c_Option_Ooption_ONone(X1427))),X1425),hAPP(c_Option_Ooption_OSome(X1427),X1429))|c_Map_Odom(X1428,X1427,X1426)=hAPP(hAPP(c_Set_Oinsert(X1428),X1425),c_Orderings_Obot__class_Obot(tc_fun(X1428,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)],[fact_dom__eq__singleton__conv])])])])])). 4.05/4.29 fof(c_0_5853, plain, ![X13368, X13369, X13370, X13371, X13372]:c_Lazy__Sequence_Ohb__bind(X13372,X13371,hAPP(X13370,X13368),hAPP(hAPP(c_COMBC(X13372,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X13371))),X13369),X13368))=hAPP(c_New__DSequence_Oneg__bind(X13372,X13371,X13370,X13369),X13368), inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__bind__def])). 4.05/4.29 fof(c_0_5854, plain, ![X6306, X6307, X6308, X6309]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6308)),X6306)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6309)),hAPP(hAPP(c_List_Omap(X6308,X6309),X6307),X6306)), inference(variable_rename,[status(thm)],[fact_length__map])). 4.05/4.29 fof(c_0_5855, plain, ![X7099, X7100]:c_Relation_Orefl__on(X7100,c_Orderings_Otop__class_Otop(tc_fun(X7100,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7100,X7100),tc_HOL_Obool)),X7099),c_Relation_OId(X7100))), inference(variable_rename,[status(thm)],[fact_refl__reflcl])). 4.05/4.29 fof(c_0_5856, plain, ![X11687, X11688, X11689, X11690]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X11689,tc_HOL_Obool),tc_fun(X11690,tc_HOL_Obool)),X11687),c_Set_Ovimage(X11690,X11689,X11688))=hAPP(c_Set_Ovimage(X11690,X11689,X11688),c_Complete__Lattice_OSup__class_OSup(tc_fun(X11689,tc_HOL_Obool),X11687)), inference(variable_rename,[status(thm)],[fact_vimage__Union])). 4.05/4.29 fof(c_0_5857, plain, ![X7464, X7465, X7466, X7467]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7467)),X7465)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7466)),X7464))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X7467,X7466))),hAPP(hAPP(c_List_Ozip(X7467,X7466),X7465),X7464)), inference(variable_rename,[status(thm)],[fact_length__zip])). 4.05/4.29 fof(c_0_5858, plain, ![X12236, X12237, X12238]:hAPP(c_Set_OCollect(X12238),hAPP(hAPP(c_COMBB(tc_fun(X12237,tc_HOL_Obool),tc_HOL_Obool,X12238),c_HOL_OEx(X12237)),X12236))=hAPP(c_Relation_ODomain(X12238,X12237),hAPP(c_Set_OCollect(tc_prod(X12238,X12237)),hAPP(c_Product__Type_Oprod_Oprod__case(X12238,X12237,tc_HOL_Obool),X12236))), inference(variable_rename,[status(thm)],[fact_Domain__Collect__split])). 4.05/4.29 fof(c_0_5859, plain, ![X7824, X7825]:hAPP(c_List_Oset(X7825),c_List_Oconcat(X7825,X7824))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X7825),tc_fun(X7825,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X7825)),X7824)),c_List_Oset(X7825)), inference(variable_rename,[status(thm)],[fact_set__concat])). 4.05/4.29 fof(c_0_5860, plain, ![X9042]: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)),X9042))=X9042, inference(variable_rename,[status(thm)],[fact_transfer__int__nat__set__return__embed])). 4.05/4.29 fof(c_0_5861, plain, ![X14554]:hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14554))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X14554)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14554)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_greaterThan__Suc])). 4.05/4.29 fof(c_0_5862, plain, ![X3399, X3400, X3401]:hAPP(c_List_Orotate(X3401,hAPP(c_Nat_OSuc,X3400)),X3399)=hAPP(c_List_Orotate1(X3401),hAPP(c_List_Orotate(X3401,X3400),X3399)), inference(variable_rename,[status(thm)],[fact_rotate__Suc])). 4.05/4.29 fof(c_0_5863, plain, ![X13373, X13374, X13375]:hBOOL(hAPP(c_Finite__Set_Ofinite(X13375),c_Map_Odom(X13375,X13374,hAPP(c_Map_Omap__of(X13375,X13374),X13373)))), inference(variable_rename,[status(thm)],[fact_finite__dom__map__of])). 4.05/4.29 fof(c_0_5864, plain, ![X17363, X17364, X17365, X17366, X17367, X17368]:((X17367=X17368|hAPP(hAPP(c_Map_Omap__of(X17366,X17365),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X17366,X17365)),hAPP(hAPP(c_Product__Type_OPair(X17366,X17365),X17368),X17364)),X17363)),X17367)=hAPP(hAPP(c_Map_Omap__of(X17366,X17365),X17363),X17367))&(X17368!=X17367|hAPP(c_Option_Ooption_OSome(X17365),X17364)=hAPP(hAPP(c_Map_Omap__of(X17366,X17365),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X17366,X17365)),hAPP(hAPP(c_Product__Type_OPair(X17366,X17365),X17368),X17364)),X17363)),X17367))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__Cons__code_I2_J])])). 4.05/4.29 fof(c_0_5865, plain, ![X1106]:hAPP(c_Set_OPow(X1106),c_Orderings_Obot__class_Obot(tc_fun(X1106,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(tc_fun(X1106,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1106,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1106,tc_HOL_Obool),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Pow__empty])). 4.05/4.29 fof(c_0_5866, plain, ![X15634, X15635, X15636, X15637, X15638]:((X15638!=c_Orderings_Obot__class_Obot(tc_fun(X15637,tc_HOL_Obool))|hAPP(hAPP(c_Set_Oinsert(X15636),X15635),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15637,tc_fun(X15636,tc_HOL_Obool)),X15638),X15634))=hAPP(hAPP(c_Set_Oinsert(X15636),X15635),c_Orderings_Obot__class_Obot(tc_fun(X15636,tc_HOL_Obool))))&(c_Orderings_Obot__class_Obot(tc_fun(X15637,tc_HOL_Obool))=X15638|hAPP(hAPP(c_Set_Oinsert(X15636),X15635),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15637,tc_fun(X15636,tc_HOL_Obool)),X15638),X15634))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15637,tc_fun(X15636,tc_HOL_Obool)),X15638),hAPP(hAPP(c_COMBB(tc_fun(X15636,tc_HOL_Obool),tc_fun(X15636,tc_HOL_Obool),X15637),hAPP(c_Set_Oinsert(X15636),X15635)),X15634)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I1_J])])). 4.05/4.29 fof(c_0_5867, plain, ![X3902, X3903, X3904, X3905, X3906, X3907]:c_List_Oreplicate(tc_prod(X3907,X3906),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X3905),X3903),hAPP(hAPP(c_Product__Type_OPair(X3907,X3906),X3904),X3902))=hAPP(hAPP(c_List_Ozip(X3907,X3906),c_List_Oreplicate(X3907,X3905,X3904)),c_List_Oreplicate(X3906,X3903,X3902)), inference(variable_rename,[status(thm)],[fact_zip__replicate])). 4.05/4.29 fof(c_0_5868, plain, ![X9596, X9597]:c_Transitive__Closure_Ortrancl(X9597,X9596)=c_Transitive__Closure_Ortrancl(X9597,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X9597,X9597),tc_HOL_Obool)),X9596),c_Relation_OId(X9597))), inference(variable_rename,[status(thm)],[fact_rtrancl__r__diff__Id])). 4.05/4.29 fof(c_0_5869, plain, ![X12577, X12578]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X12578,X12578),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X12578,X12577)),c_Relation_OId(X12578))=c_Transitive__Closure_Ortrancl(X12578,X12577), inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl__absorb])). 4.05/4.29 fof(c_0_5870, plain, ![X4613]:hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4613))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X4613)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X4613),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_atLeast__Suc])). 4.05/4.29 fof(c_0_5871, plain, ![X9038]:hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X9038)=hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X9038)), inference(variable_rename,[status(thm)],[fact_atLeast__Suc__greaterThan])). 4.05/4.29 fof(c_0_5872, plain, ![X6723, X6724]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X6724)),X6723)=c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X6724),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),X6724)),X6723), inference(variable_rename,[status(thm)],[fact_max__Suc1])). 4.05/4.29 fof(c_0_5873, plain, ![X8941, X8942, X8943]:hAPP(hAPP(c_List_Oappend(X8943),c_List_OtakeWhile(X8943,X8942,X8941)),c_List_OdropWhile(X8943,X8942,X8941))=X8941, inference(variable_rename,[status(thm)],[fact_takeWhile__dropWhile__id])). 4.05/4.29 fof(c_0_5874, plain, ![X12885, X12886]:X12885=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X12886),hAPP(c_List_Onth(X12886),X12885)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12886)),X12885))), inference(variable_rename,[status(thm)],[fact_map__nth])). 4.05/4.29 fof(c_0_5875, plain, ![X1050, X1051, X1052]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1052),X1051)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1050),X1051))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1052),X1050)),X1051), inference(variable_rename,[status(thm)],[fact_min__diff])). 4.05/4.29 fof(c_0_5876, plain, ![X11856, X11857, X11858, X11859]:((c_Orderings_Obot__class_Obot(tc_fun(X11858,tc_HOL_Obool))=X11859|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11858,tc_fun(X11857,tc_HOL_Obool)),X11859),hAPP(c_COMBK(tc_fun(X11857,tc_HOL_Obool),X11858),X11856))=X11856)&(X11859!=c_Orderings_Obot__class_Obot(tc_fun(X11858,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X11857,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11858,tc_fun(X11857,tc_HOL_Obool)),X11859),hAPP(c_COMBK(tc_fun(X11857,tc_HOL_Obool),X11858),X11856)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__constant])])])). 4.05/4.29 fof(c_0_5877, plain, ![X1434, X1435]: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),X1435)),X1434)=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1435)),X1434), inference(variable_rename,[status(thm)],[fact_min__Suc1])). 4.05/4.29 fof(c_0_5878, plain, ![X14253, X14254, X14255]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14255)),X14253)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14255)),hAPP(hAPP(c_List_Olist_OCons(X14255),X14254),X14253)), inference(variable_rename,[status(thm)],[fact_list_Osize_I4_J])). 4.05/4.29 fof(c_0_5879, plain, ![X10788, X10789, X10790]: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(X10790,tc_Nat_Onat),X10789),X10788))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10790)),X10788))=c_List_Olist_Olist__size(X10790,X10789,X10788), inference(variable_rename,[status(thm)],[fact_list__size__conv__listsum])). 4.05/4.29 fof(c_0_5880, plain, ![X15245, X15246, X15247]:c_List_Oreplicate(X15247,X15245,X15246)=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X15247),hAPP(c_COMBK(X15247,tc_Nat_Onat),X15246)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15245)), inference(variable_rename,[status(thm)],[fact_map__replicate__trivial])). 4.05/4.29 fof(c_0_5881, plain, ![X1016, X1017]:c_Relation_Oirrefl(X1017,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1017,X1017),tc_HOL_Obool)),X1016),c_Relation_OId(X1017))), inference(variable_rename,[status(thm)],[fact_irrefl__diff__Id])). 4.05/4.29 fof(c_0_5882, plain, ![X5772, X5773, X5774, X5775, X5776, X5777]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X5775,X5773)),hAPP(X5774,X5772))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Nitpick_Opair__box_Opair__box__size(X5777,X5776,X5775,X5774,c_Nitpick_Opair__box_OPairBox(X5777,X5776,X5773,X5772)), inference(variable_rename,[status(thm)],[fact_pair__box_Osize_I1_J])). 4.05/4.29 fof(c_0_5883, plain, ![X3674, X3675, X3676, X3677, X3678]:((X3678!=c_Orderings_Obot__class_Obot(tc_fun(X3677,tc_HOL_Obool))|X3674=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3676,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3677,tc_fun(X3676,tc_HOL_Obool)),X3678),X3675)),X3674))&(c_Orderings_Obot__class_Obot(tc_fun(X3677,tc_HOL_Obool))=X3678|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3676,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3677,tc_fun(X3676,tc_HOL_Obool)),X3678),X3675)),X3674)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3677,tc_fun(X3676,tc_HOL_Obool)),X3678),hAPP(hAPP(c_COMBC(X3677,tc_fun(X3676,tc_HOL_Obool),tc_fun(X3676,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3676,tc_HOL_Obool),tc_fun(tc_fun(X3676,tc_HOL_Obool),tc_fun(X3676,tc_HOL_Obool)),X3677),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3676,tc_HOL_Obool))),X3675)),X3674)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__extend__simps_I2_J])])])). 4.05/4.29 fof(c_0_5884, plain, ![X6987, X6988, X6989, X6990, X6991]:((c_Orderings_Obot__class_Obot(tc_fun(X6990,tc_HOL_Obool))!=X6991|X6988=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6989,tc_HOL_Obool)),X6988),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6990,tc_fun(X6989,tc_HOL_Obool)),X6991),X6987)))&(X6991=c_Orderings_Obot__class_Obot(tc_fun(X6990,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6989,tc_HOL_Obool)),X6988),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6990,tc_fun(X6989,tc_HOL_Obool)),X6991),X6987))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6990,tc_fun(X6989,tc_HOL_Obool)),X6991),hAPP(hAPP(c_COMBB(tc_fun(X6989,tc_HOL_Obool),tc_fun(X6989,tc_HOL_Obool),X6990),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6989,tc_HOL_Obool)),X6988)),X6987)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__extend__simps_I3_J])])])). 4.05/4.29 fof(c_0_5885, plain, ![X3268, X3269, X3270, X3271, X3272]:((X3272=c_Orderings_Obot__class_Obot(tc_fun(X3271,tc_HOL_Obool))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3270,tc_HOL_Obool)),X3269),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3271,tc_fun(X3270,tc_HOL_Obool)),X3272),X3268))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3271,tc_fun(X3270,tc_HOL_Obool)),X3272),hAPP(hAPP(c_COMBB(tc_fun(X3270,tc_HOL_Obool),tc_fun(X3270,tc_HOL_Obool),X3271),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3270,tc_HOL_Obool)),X3269)),X3268)))&(X3272!=c_Orderings_Obot__class_Obot(tc_fun(X3271,tc_HOL_Obool))|X3269=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3270,tc_HOL_Obool)),X3269),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3271,tc_fun(X3270,tc_HOL_Obool)),X3272),X3268)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__extend__simps_I4_J])])])). 4.05/4.29 fof(c_0_5886, plain, ![X10822, X10823, X10824]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X10824)),X10823)),hAPP(c_Nat_OSuc,X10822))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X10824),X10823)),X10822), inference(variable_rename,[status(thm)],[fact_Suc__diff__diff])). 4.05/4.29 fof(c_0_5887, plain, ![X15326, X15327, X15328, X15329]:(((X15327!=c_Orderings_Obot__class_Obot(tc_fun(X15329,tc_HOL_Obool))|hAPP(hAPP(c_Product__Type_OSigma(X15329,X15328),X15327),hAPP(c_COMBK(tc_fun(X15328,tc_HOL_Obool),X15329),X15326))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X15329,X15328),tc_HOL_Obool)))&(c_Orderings_Obot__class_Obot(tc_fun(X15328,tc_HOL_Obool))!=X15326|hAPP(hAPP(c_Product__Type_OSigma(X15329,X15328),X15327),hAPP(c_COMBK(tc_fun(X15328,tc_HOL_Obool),X15329),X15326))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X15329,X15328),tc_HOL_Obool))))&(hAPP(hAPP(c_Product__Type_OSigma(X15329,X15328),X15327),hAPP(c_COMBK(tc_fun(X15328,tc_HOL_Obool),X15329),X15326))!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X15329,X15328),tc_HOL_Obool))|(X15327=c_Orderings_Obot__class_Obot(tc_fun(X15329,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X15328,tc_HOL_Obool))=X15326))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__empty])])])). 4.05/4.29 cnf(c_0_5888, 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_4829])). 4.05/4.29 fof(c_0_5889, plain, ![X16549, X16550, X16551, X16552]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16552,tc_HOL_Obool)),hAPP(c_Set_Oimage(X16551,X16552,X16550),hAPP(c_Set_Ovimage(X16551,X16552,X16550),X16549))),X16549)), inference(variable_rename,[status(thm)],[fact_image__vimage__subset])). 4.05/4.29 fof(c_0_5890, plain, ![X7971, X7972, X7973]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7973)),X7972)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7973)),X7971))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7973)),c_List_Osplice(X7973,X7972,X7971)), inference(variable_rename,[status(thm)],[fact_length__splice])). 4.05/4.29 fof(c_0_5891, plain, ![X17612, X17613, X17614]:hAPP(c_Set_Ovimage(X17614,X17613,X17612),c_Orderings_Otop__class_Otop(tc_fun(X17613,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X17614,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_vimage__UNIV])). 4.05/4.29 fof(c_0_5892, plain, ![X8571, X8572, X8573]:c_Orderings_Obot__class_Obot(tc_fun(X8573,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X8573,X8572,X8571),c_Orderings_Obot__class_Obot(tc_fun(X8572,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_vimage__empty])). 4.05/4.29 fof(c_0_5893, plain, ![X6586, X6587]:hAPP(c_Set_Ovimage(X6587,X6587,c_Fun_Oid(X6587)),X6586)=X6586, inference(variable_rename,[status(thm)],[fact_vimage__id])). 4.05/4.29 fof(c_0_5894, plain, ![X15401, X15402]:X15401=hAPP(c_Set_Ovimage(X15402,X15402,c_COMBI(X15402)),X15401), inference(variable_rename,[status(thm)],[fact_vimage__ident])). 4.05/4.29 fof(c_0_5895, plain, ![X13465, X13466, X13467]:c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13466),X13467),X13465)=hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X13467),c_List_Oupt(X13466,X13465)), inference(variable_rename,[status(thm)],[fact_drop__upt])). 4.05/4.29 fof(c_0_5896, plain, ![X15055]:hAPP(c_Finite__Set_Ocard(X15055),c_Orderings_Obot__class_Obot(tc_fun(X15055,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_card_Oempty])). 4.05/4.29 fof(c_0_5897, plain, ![X7196, X7197]:~hBOOL(hAPP(hAPP(c_member(X7197),X7196),c_Orderings_Obot__class_Obot(tc_fun(X7197,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_empty__iff])])). 4.05/4.29 fof(c_0_5898, plain, ![X12293, X12294, X12295]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12295)),hAPP(c_List_Orotate(X12295,X12294),X12293))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12295)),X12293), inference(variable_rename,[status(thm)],[fact_length__rotate])). 4.05/4.29 fof(c_0_5899, plain, ![X2710, X2711, X2712, X2713, X2714]:c_Map_Omap__comp(X2714,X2713,X2712,hAPP(c_COMBK(tc_Option_Ooption(X2713),X2714),c_Option_Ooption_ONone(X2713)),X2711,X2710)=c_Option_Ooption_ONone(X2713), inference(variable_rename,[status(thm)],[fact_map__comp__empty_I2_J])). 4.05/4.29 fof(c_0_5900, plain, ![X3517, X3518]:c_List_Oconcat(X3518,c_List_Oreplicate(tc_List_Olist(X3518),X3517,c_List_Olist_ONil(X3518)))=c_List_Olist_ONil(X3518), inference(variable_rename,[status(thm)],[fact_concat__replicate__trivial])). 4.05/4.29 fof(c_0_5901, plain, ![X8559, X8560]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8559),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8560),X8559))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8560,X8559))=X8560, inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality])). 4.05/4.29 fof(c_0_5902, plain, ![X1347]: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),X1347)))=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),X1347)), inference(variable_rename,[status(thm)],[fact_one__div__nat__number__of])). 4.05/4.29 fof(c_0_5903, plain, ![X17168]:hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17168))=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),X17168))), inference(variable_rename,[status(thm)],[fact_lessThan__Suc__eq__insert__0])). 4.05/4.29 cnf(c_0_5904, 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_4830])). 4.05/4.29 cnf(c_0_5905, 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)), inference(split_conjunct,[status(thm)],[c_0_4831]), ['final']). 4.05/4.29 fof(c_0_5906, plain, ![X11118, X11119, X11120]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X11120|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11120),X11119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11120),X11118))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X11119),X11118))&(X11120!=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),X11120),X11119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11120),X11118)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__mult__div__cancel__disj])])])). 4.05/4.29 fof(c_0_5907, plain, ![X4870]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4870)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_mult__0])). 4.05/4.29 fof(c_0_5908, plain, ![X11177, X11178]:hAPP(hAPP(c_Nitpick_Oint__gcd,X11178),X11177)=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),X11178)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X11177)))), inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__gcd__def])). 4.05/4.29 fof(c_0_5909, plain, ![X15084]:hAPP(c_Relation_Oconverse(X15084,X15084),c_Relation_OId(X15084))=c_Relation_OId(X15084), inference(variable_rename,[status(thm)],[fact_converse__Id])). 4.05/4.29 fof(c_0_5910, plain, ![X8064, X8065]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X8065))),c_Enum_Osublists(X8065,X8064))=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(X8065)),X8064)), inference(variable_rename,[status(thm)],[fact_length__sublists])). 4.05/4.29 fof(c_0_5911, plain, ![X17496, X17497]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17497),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X17497),X17496)),X17496))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17497,X17496), inference(variable_rename,[status(thm)],[fact_Divides_Omod__div__equality_H])). 4.05/4.29 fof(c_0_5912, plain, ![X1155, X1156]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1155),X1156)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1156),X1155), inference(variable_rename,[status(thm)],[fact_nat__mult__commute])). 4.05/4.29 fof(c_0_5913, plain, ![X12975, X12976]:c_Divides_Odiv__class_Omod(tc_Int_Oint,X12976,X12975)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12976),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12976),X12975)),X12975)), inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality_H])). 4.05/4.29 cnf(c_0_5914, plain, (hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Otrancl(X1,X2))=hAPP(c_Relation_ORange(X1,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_4832])). 4.05/4.29 cnf(c_0_5915, plain, (hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Otrancl(X1,X2))=hAPP(c_Relation_ODomain(X1,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_4833])). 4.05/4.29 fof(c_0_5916, plain, ![X10690, X10691, X10692]:hAPP(c_List_Oset(X10692),hAPP(c_List_Orotate(X10692,X10691),X10690))=hAPP(c_List_Oset(X10692),X10690), inference(variable_rename,[status(thm)],[fact_set__rotate])). 4.05/4.29 fof(c_0_5917, plain, ![X12570, X12571, X12572, X12573]:hAPP(hAPP(c_List_Otake(X12573),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X12572),X12571)),X12570)=hAPP(hAPP(c_List_Otake(X12573),X12572),hAPP(hAPP(c_List_Otake(X12573),X12571),X12570)), inference(variable_rename,[status(thm)],[fact_take__take])). 4.05/4.29 cnf(c_0_5918, 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_4834])). 4.05/4.29 fof(c_0_5919, plain, ![X3884, X3885]:c_Hilbert__Choice_OEps(X3885,hAPP(hAPP(c_COMBC(X3885,X3885,tc_HOL_Obool),c_fequal),X3884))=X3884, inference(variable_rename,[status(thm)],[fact_some__eq__trivial])). 4.05/4.29 fof(c_0_5920, plain, ![X8797, X8798, X8799]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X8799)),X8797)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X8799)),c_Lazy__Sequence_Olazy__sequence_OInsert(X8799,X8798,X8797)), inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I4_J])). 4.05/4.29 fof(c_0_5921, plain, ![X7153]:hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X7153)),c_List_Olist_ONil(X7153)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X7153),tc_HOL_Obool)))=c_List_Olists(X7153,c_Orderings_Obot__class_Obot(tc_fun(X7153,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_lists__empty])). 4.05/4.29 fof(c_0_5922, plain, ![X10471, X10472, X10473, X10474]:((X10472!=X10471|hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10474,X10473,hAPP(hAPP(c_Set_Oinsert(X10474),X10472),c_Orderings_Obot__class_Obot(tc_fun(X10474,tc_HOL_Obool)))),X10471)))&(~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10474,X10473,hAPP(hAPP(c_Set_Oinsert(X10474),X10472),c_Orderings_Obot__class_Obot(tc_fun(X10474,tc_HOL_Obool)))),X10471))|X10472=X10471)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1Set__sing])])). 4.05/4.29 fof(c_0_5923, plain, ![X9167]:c_List_Olistset(X9167,c_List_Olist_ONil(tc_fun(X9167,tc_HOL_Obool)))=hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X9167)),c_List_Olist_ONil(X9167)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X9167),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_listset_Osimps_I1_J])). 4.05/4.29 fof(c_0_5924, plain, ![X6060, X6061, X6062]:X6060=hAPP(hAPP(c_Relation_Orel__comp(X6062,X6062,X6061),c_Relation_OId(X6062)),X6060), inference(variable_rename,[status(thm)],[fact_Id__O__R])). 4.05/4.29 fof(c_0_5925, plain, ![X16670, X16671, X16672]:X16670=hAPP(hAPP(c_Relation_Orel__comp(X16672,X16671,X16671),X16670),c_Relation_OId(X16671)), inference(variable_rename,[status(thm)],[fact_R__O__Id])). 4.05/4.29 fof(c_0_5926, plain, ![X4709, X4710, X4711, X4712]:(hAPP(c_Set_Oimage(tc_Nat_Onat,X4711,X4710),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)),X4709)))!=X4712|hBOOL(hAPP(c_Finite__Set_Ofinite(X4711),X4712))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__seg__image__imp__finite])])])). 4.05/4.29 fof(c_0_5927, plain, ![X8446, X8447, X8448, X8451, X8452, X8453, X8454, X8455]:((~hBOOL(hAPP(hAPP(c_member(X8448),X8447),hAPP(c_List_Oset(X8448),X8446)))|X8446=hAPP(hAPP(c_List_Oappend(X8448),esk271_3(X8446,X8447,X8448)),hAPP(hAPP(c_List_Olist_OCons(X8448),X8447),esk272_3(X8446,X8447,X8448))))&(X8451!=hAPP(hAPP(c_List_Oappend(X8453),X8454),hAPP(hAPP(c_List_Olist_OCons(X8453),X8452),X8455))|hBOOL(hAPP(hAPP(c_member(X8453),X8452),hAPP(c_List_Oset(X8453),X8451))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__conv__decomp])])])])])). 4.05/4.29 cnf(c_0_5928, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X1))), inference(split_conjunct,[status(thm)],[c_0_4835])). 4.05/4.29 fof(c_0_5929, plain, ![X16650, X16651, X16652, X16653]:((X16653=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16652)),X16651)),c_Groups_Oone__class_Oone(tc_Nat_Onat))|hAPP(hAPP(c_List_Olist__update(X16652,c_List_Obutlast(X16652,X16651)),X16653),X16650)=c_List_Obutlast(X16652,hAPP(hAPP(c_List_Olist__update(X16652,X16651),X16653),X16650)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16652)),X16651)),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=X16653|c_List_Obutlast(X16652,X16651)=c_List_Obutlast(X16652,hAPP(hAPP(c_List_Olist__update(X16652,X16651),X16653),X16650)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_butlast__list__update])])])). 4.05/4.29 fof(c_0_5930, plain, ![X15101]: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),X15101)))=hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X15101), inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I1_J])). 4.05/4.29 fof(c_0_5931, plain, ![X16227, X16228, X16229, X16230]:((X16228!=c_Orderings_Obot__class_Obot(tc_fun(X16230,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X16229,tc_HOL_Obool))!=X16227|c_Sum__Type_OPlus(X16230,X16229,X16228,X16227)=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X16230,X16229),tc_HOL_Obool)))&((X16228=c_Orderings_Obot__class_Obot(tc_fun(X16230,tc_HOL_Obool))|c_Sum__Type_OPlus(X16230,X16229,X16228,X16227)!=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X16230,X16229),tc_HOL_Obool)))&(c_Orderings_Obot__class_Obot(tc_fun(X16229,tc_HOL_Obool))=X16227|c_Sum__Type_OPlus(X16230,X16229,X16228,X16227)!=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X16230,X16229),tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Plus__eq__empty__conv])])])). 4.05/4.29 cnf(c_0_5932, plain, (hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X2,X1))), inference(split_conjunct,[status(thm)],[c_0_4836])). 4.05/4.29 cnf(c_0_5933, 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_4837]), ['final']). 4.05/4.29 cnf(c_0_5934, plain, (hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4838])). 4.05/4.29 cnf(c_0_5935, 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_4839])). 4.05/4.29 cnf(c_0_5936, 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])). 4.05/4.29 cnf(c_0_5937, 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_4840])). 4.05/4.29 fof(c_0_5938, plain, ![X2315]: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)),X2315)))), inference(variable_rename,[status(thm)],[fact_finite__Collect__less__nat])). 4.05/4.29 fof(c_0_5939, plain, ![X5436]: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)),X5436)))), inference(variable_rename,[status(thm)],[fact_finite__Collect__le__nat])). 4.05/4.29 cnf(c_0_5940, plain, (c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls))), inference(split_conjunct,[status(thm)],[fact_one__code__numeral__code])). 4.05/4.29 cnf(c_0_5941, plain, (c_List_Olist_ONil(X2)=hAPP(c_List_Orotate(X2,X3),X1)|X1!=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_4841])). 4.05/4.29 cnf(c_0_5942, plain, (c_List_Orotate(X1,X2)=hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1))), inference(split_conjunct,[status(thm)],[c_0_4842])). 4.05/4.29 fof(c_0_5943, plain, ![X1966, X1967, X1968]:((X1967!=hAPP(hAPP(c_List_Olist_OCons(X1968),X1966),c_List_Olist_ONil(X1968))|hAPP(c_List_Orev(X1968),X1967)=hAPP(hAPP(c_List_Olist_OCons(X1968),X1966),c_List_Olist_ONil(X1968)))&(hAPP(c_List_Orev(X1968),X1967)!=hAPP(hAPP(c_List_Olist_OCons(X1968),X1966),c_List_Olist_ONil(X1968))|X1967=hAPP(hAPP(c_List_Olist_OCons(X1968),X1966),c_List_Olist_ONil(X1968)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__singleton__conv])])). 4.05/4.29 fof(c_0_5944, plain, ![X2800, X2801]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2801),X2800)=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X2801,X2800)), inference(variable_rename,[status(thm)],[fact_div__nat__def])). 4.05/4.29 fof(c_0_5945, plain, ![X15806, X15807]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X15807),X15806)=hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X15807,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15806),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(variable_rename,[status(thm)],[fact_atLeastLessThan__upto])). 4.05/4.29 fof(c_0_5946, plain, ![X14622, X14623]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X14623,X14622))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14622),X14623), inference(variable_rename,[status(thm)],[fact_length__upt])). 4.05/4.29 fof(c_0_5947, plain, ![X3231, X3232, X3233, X3234]:hAPP(hAPP(c_List_Otake(X3234),X3233),c_List_Oreplicate(X3234,X3232,X3231))=c_List_Oreplicate(X3234,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X3233),X3232),X3231), inference(variable_rename,[status(thm)],[fact_take__replicate])). 4.05/4.29 fof(c_0_5948, plain, ![X10131, X10132]:hAPP(c_Relation_OImage(X10132,X10132,c_Relation_OId(X10132)),X10131)=X10131, inference(variable_rename,[status(thm)],[fact_Image__Id])). 4.05/4.29 cnf(c_0_5949, 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_4843])). 4.05/4.29 fof(c_0_5950, plain, ![X7294, X7295]:hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X7295,X7294))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X7295,X7294), inference(variable_rename,[status(thm)],[fact_mod__nat__def])). 4.05/4.29 fof(c_0_5951, plain, ![X5191]:hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5191)=c_Divides_Odivmod__nat(X5191,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_divmod__nat__zero])). 4.05/4.29 fof(c_0_5952, plain, ![X9354, X9355, X9356]:c_Option_Ooption_Ooption__size(X9356,X9355,hAPP(c_Option_Ooption_OSome(X9356),X9354))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X9355,X9354)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_option_Osize_I2_J])). 4.05/4.29 fof(c_0_5953, plain, ![X2823, X2824]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X2824)),hAPP(c_Code__Numeral_Onat__of,X2823)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X2824),X2823), inference(variable_rename,[status(thm)],[fact_minus__code__numeral__def])). 4.05/4.29 fof(c_0_5954, plain, ![X323, X324]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X324)),hAPP(c_Code__Numeral_Onat__of,X323)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X324),X323), inference(variable_rename,[status(thm)],[fact_div__code__numeral__def])). 4.05/4.29 fof(c_0_5955, plain, ![X12478, X12479]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X12479),X12478)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X12479)),hAPP(c_Code__Numeral_Onat__of,X12478))), inference(variable_rename,[status(thm)],[fact_times__code__numeral__def])). 4.05/4.29 fof(c_0_5956, plain, ![X9163, X9164]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X9164),X9163)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X9164)),hAPP(c_Code__Numeral_Onat__of,X9163))), inference(variable_rename,[status(thm)],[fact_plus__code__numeral__def])). 4.05/4.29 fof(c_0_5957, plain, ![X3230]:c_Wellfounded_OwfP(X3230,hAPP(c_COMBK(tc_fun(X3230,tc_HOL_Obool),X3230),hAPP(c_COMBK(tc_HOL_Obool,X3230),c_fFalse))), inference(variable_rename,[status(thm)],[fact_wfP__empty])). 4.05/4.29 cnf(c_0_5958, 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_4844])). 4.05/4.29 fof(c_0_5959, plain, ![X16695, X16696, X16697]:hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X16697,X16696,X16695))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X16695)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_com_Osize_I11_J])). 4.05/4.29 cnf(c_0_5960, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X1))), inference(split_conjunct,[status(thm)],[c_0_4845])). 4.05/4.29 fof(c_0_5961, plain, ![X6014]:hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X6014))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X6014)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X6014)), inference(variable_rename,[status(thm)],[fact_atMost__Suc])). 4.05/4.29 fof(c_0_5962, plain, ![X16505, X16506, X16508, X16509, X16510]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16506),X16505))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16506),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk495_2(X16505,X16506))))=X16505)&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16509),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X16510)))!=X16508|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16509),X16508)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__iff__Suc__zadd])])])])])). 4.05/4.29 fof(c_0_5963, plain, ![X10044, X10045]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X10045)),hAPP(c_Nat_OSuc,X10044))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X10045),X10044)), inference(variable_rename,[status(thm)],[fact_min__Suc__Suc])). 4.05/4.29 fof(c_0_5964, plain, ![X15008, X15009]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X15009)),hAPP(c_Code__Numeral_Oof__nat,X15008))=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15009),X15008)), inference(variable_rename,[status(thm)],[fact_times__code__numeral__code])). 4.05/4.29 fof(c_0_5965, plain, ![X7680, X7681]:hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X7681)),hAPP(c_Nat_OSuc,X7680))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X7681),X7680)), inference(variable_rename,[status(thm)],[fact_max__Suc__Suc])). 4.05/4.29 fof(c_0_5966, plain, ![X1010, X1011]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1011),X1010))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1011)),hAPP(c_Code__Numeral_Oof__nat,X1010)), inference(variable_rename,[status(thm)],[fact_plus__code__numeral__code])). 4.05/4.29 cnf(c_0_5967, 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_4846])). 4.05/4.29 fof(c_0_5968, plain, ![X7983, X7984]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7984),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7983),c_Groups_Oone__class_Oone(tc_Int_Oint))))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7984),X7983))|X7984=X7983))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7984),X7983))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7984),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7983),c_Groups_Oone__class_Oone(tc_Int_Oint)))))&(X7984!=X7983|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7984),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7983),c_Groups_Oone__class_Oone(tc_Int_Oint))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__add1__eq])])])). 4.05/4.29 fof(c_0_5969, plain, ![X8468, X8469, X8470]:((c_Orderings_Obot__class_Obot(tc_fun(X8470,tc_HOL_Obool))!=X8469|hAPP(hAPP(c_Equiv__Relations_Oquotient(X8470),X8469),X8468)=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X8470,tc_HOL_Obool),tc_HOL_Obool)))&(hAPP(hAPP(c_Equiv__Relations_Oquotient(X8470),X8469),X8468)!=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X8470,tc_HOL_Obool),tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X8470,tc_HOL_Obool))=X8469)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__is__empty2])])). 4.05/4.29 fof(c_0_5970, plain, ![X14141, X14142]:hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X14142,X14141),c_Divides_Odivmod__nat(X14142,X14141))), inference(variable_rename,[status(thm)],[fact_divmod__nat__rel__divmod__nat])). 4.05/4.29 fof(c_0_5971, plain, ![X8437, X8438]:hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X8438),X8437))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X8437),X8438)), inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan__int])). 4.05/4.29 cnf(c_0_5972, 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_4847])). 4.05/4.29 fof(c_0_5973, plain, ![X8729, X8730, X8731, X8732, X8733]:((X8729!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8730),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X8731))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8730),X8729)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8733),X8732))|X8732=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8733),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk278_2(X8732,X8733))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__iff__zadd])])])])])). 4.05/4.29 fof(c_0_5974, plain, ![X950]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X950)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X950), inference(variable_rename,[status(thm)],[fact_mult__Min])). 4.05/4.29 fof(c_0_5975, plain, ![X16918, X16919, X16920, X16921, X16922]:hAPP(hAPP(c_Finite__Set_Ofold(X16922,X16921,X16920),X16919),X16918)=c_HOL_OThe(X16921,c_Finite__Set_Ofold__graph(X16922,X16921,X16920,X16919,X16918)), inference(variable_rename,[status(thm)],[fact_fold__def])). 4.05/4.29 fof(c_0_5976, plain, ![X15657, X15658]:hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X15658),hAPP(c_Code__Numeral_Onat__of,X15657)))=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X15658,X15657), inference(variable_rename,[status(thm)],[fact_mod__code__numeral__def])). 4.05/4.29 fof(c_0_5977, plain, ![X8739, X8740]:hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X8740,X8739))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X8739)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_com_Osize_I14_J])). 4.05/4.29 cnf(c_0_5978, 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_4848])). 4.05/4.29 fof(c_0_5979, plain, ![X6655, X6656]:hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6656),X6655))=hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X6656)),hAPP(c_Code__Numeral_Oof__nat,X6655)), inference(variable_rename,[status(thm)],[fact_subtract__code__numeral__code])). 4.05/4.29 cnf(c_0_5980, 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_4849])). 4.05/4.29 cnf(c_0_5981, 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)), inference(split_conjunct,[status(thm)],[c_0_4850]), ['final']). 4.05/4.29 fof(c_0_5982, plain, ![X8847, X8848]:hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X8848,X8847))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X8847)),X8848), inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost])). 4.05/4.29 fof(c_0_5983, plain, ![X15149]:c_Relation_Osingle__valued(X15149,X15149,c_Relation_OId(X15149)), inference(variable_rename,[status(thm)],[fact_single__valued__Id])). 4.05/4.29 fof(c_0_5984, plain, ![X3324]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X3324)),c_Groups_Oone__class_Oone(tc_Int_Oint)))|X3324=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(X3324!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X3324)),c_Groups_Oone__class_Oone(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zabs__less__one__iff])])). 4.05/4.29 cnf(c_0_5985, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X1)), inference(split_conjunct,[status(thm)],[c_0_4851])). 4.05/4.29 fof(c_0_5986, plain, ![X12217, X12218]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X12218|c_Divides_Opdivmod(X12217,X12218)=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),X12217)))&(X12218=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X12217),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X12218))=c_Divides_Opdivmod(X12217,X12218))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__posDivAlg])])). 4.05/4.29 fof(c_0_5987, plain, ![X3136]:hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3136))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X3136),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3136)), inference(variable_rename,[status(thm)],[fact_lessThan__Suc])). 4.05/4.29 fof(c_0_5988, plain, ![X8166, X8167]:c_Fun_Oid(tc_prod(X8167,X8166))=c_Product__Type_Oapfst(X8167,X8167,X8166,c_Fun_Oid(X8167)), inference(variable_rename,[status(thm)],[fact_apfst__id])). 4.05/4.29 fof(c_0_5989, plain, ![X11197]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X11197)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X11197)), inference(variable_rename,[status(thm)],[fact_nat_Osize_I2_J])). 4.05/4.29 fof(c_0_5990, plain, ![X17545, X17546, X17547]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X17545)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X17547,X17546,X17545)), inference(variable_rename,[status(thm)],[fact_com_Osize_I3_J])). 4.05/4.29 fof(c_0_5991, plain, ![X4908, X4909, X4911, X4912, X4913]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4909),X4908))|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4909),esk151_2(X4908,X4909)))=X4908)&(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4912),X4913))!=X4911|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4912),X4911)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add])])])])])). 4.05/4.29 fof(c_0_5992, plain, ![X2598, X2599, X2600]:((hAPP(c_COMBK(tc_Option_Ooption(X2599),X2600),c_Option_Ooption_ONone(X2599))!=X2598|c_Map_Odom(X2600,X2599,X2598)=c_Orderings_Obot__class_Obot(tc_fun(X2600,tc_HOL_Obool)))&(c_Map_Odom(X2600,X2599,X2598)!=c_Orderings_Obot__class_Obot(tc_fun(X2600,tc_HOL_Obool))|hAPP(c_COMBK(tc_Option_Ooption(X2599),X2600),c_Option_Ooption_ONone(X2599))=X2598)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dom__eq__empty__conv])])). 4.05/4.29 fof(c_0_5993, plain, ![X4891, X4892, X4893, X4894, X4895]:((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X4895|hAPP(c_Product__Type_OPair(X4894,X4893),X4891)=hAPP(c_Random_Oiterate(X4894,X4893,X4895,X4892),X4891))&(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X4895|hAPP(c_Random_Oiterate(X4894,X4893,X4895,X4892),X4891)=hAPP(hAPP(c_Product__Type_Oscomp(X4893,X4894,X4893,tc_prod(X4894,X4893)),hAPP(X4892,X4891)),c_Random_Oiterate(X4894,X4893,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X4895),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X4892)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_iterate_Osimps])])])). 4.05/4.29 fof(c_0_5994, plain, ![X2217, X2218, X2219, X2220]:((hAPP(c_Set_Oimage(X2219,X2220,X2218),X2217)!=c_Orderings_Obot__class_Obot(tc_fun(X2220,tc_HOL_Obool))|X2217=c_Orderings_Obot__class_Obot(tc_fun(X2219,tc_HOL_Obool)))&(X2217!=c_Orderings_Obot__class_Obot(tc_fun(X2219,tc_HOL_Obool))|hAPP(c_Set_Oimage(X2219,X2220,X2218),X2217)=c_Orderings_Obot__class_Obot(tc_fun(X2220,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__is__image])])). 4.05/4.29 fof(c_0_5995, plain, ![X12685, X12686, X12687]:((X12687!=c_List_Olist_ONil(X12686)|c_List_Obutlast(X12686,hAPP(hAPP(c_List_Olist_OCons(X12686),X12685),X12687))=c_List_Olist_ONil(X12686))&(c_List_Olist_ONil(X12686)=X12687|hAPP(hAPP(c_List_Olist_OCons(X12686),X12685),c_List_Obutlast(X12686,X12687))=c_List_Obutlast(X12686,hAPP(hAPP(c_List_Olist_OCons(X12686),X12685),X12687)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast_Osimps_I2_J])])). 4.05/4.29 fof(c_0_5996, plain, ![X5648, X5649, X5650]:((X5648!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5650,X5649),tc_HOL_Obool))|hAPP(c_Relation_ODomain(X5650,X5649),X5648)=c_Orderings_Obot__class_Obot(tc_fun(X5650,tc_HOL_Obool)))&(hAPP(c_Relation_ODomain(X5650,X5649),X5648)!=c_Orderings_Obot__class_Obot(tc_fun(X5650,tc_HOL_Obool))|X5648=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5650,X5649),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__empty__iff])])). 4.05/4.29 fof(c_0_5997, plain, ![X15028, X15029, X15030]:((X15028!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X15030,X15029),tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X15029,tc_HOL_Obool))=hAPP(c_Relation_ORange(X15030,X15029),X15028))&(c_Orderings_Obot__class_Obot(tc_fun(X15029,tc_HOL_Obool))!=hAPP(c_Relation_ORange(X15030,X15029),X15028)|X15028=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X15030,X15029),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Range__empty__iff])])). 4.05/4.29 fof(c_0_5998, plain, ![X11044, X11045, X11046, X11047]:((X11046!=X11047|X11044=c_List_Oremove1(X11045,X11047,hAPP(hAPP(c_List_Olist_OCons(X11045),X11046),X11044)))&(X11047=X11046|hAPP(hAPP(c_List_Olist_OCons(X11045),X11046),c_List_Oremove1(X11045,X11047,X11044))=c_List_Oremove1(X11045,X11047,hAPP(hAPP(c_List_Olist_OCons(X11045),X11046),X11044)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1_Osimps_I2_J])])). 4.05/4.29 fof(c_0_5999, plain, ![X14200, X14201]:hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X14201,X14200))), inference(variable_rename,[status(thm)],[fact_distinct__upt])). 4.05/4.29 cnf(c_0_6000, plain, (hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_4852])). 4.05/4.29 fof(c_0_6001, plain, ![X11789, X11790, X11791]:c_List_Osublist(X11791,X11790,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X11789))=hAPP(hAPP(c_List_Otake(X11791),X11789),X11790), inference(variable_rename,[status(thm)],[fact_sublist__upt__eq__take])). 4.05/4.29 fof(c_0_6002, plain, ![X9001]:hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X9001), inference(variable_rename,[status(thm)],[fact_power__Suc__0])). 4.05/4.29 fof(c_0_6003, plain, ![X11880]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X11880)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11880),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)), inference(variable_rename,[status(thm)],[fact_zdiv__minus1__right])). 4.05/4.29 fof(c_0_6004, plain, ![X913, X914, X915, X916, X917]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X913),X915)!=X914|c_Divides_Odiv__class_Omod(tc_Int_Oint,X914,X913)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(c_Divides_Odiv__class_Omod(tc_Int_Oint,X917,X916)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X916),esk22_2(X916,X917))=X917)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__eq__0__iff])])])])])). 4.05/4.29 fof(c_0_6005, plain, ![X6138, X6139, X6141, X6142, X6143]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X6139,X6138)|X6139=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6138),esk186_2(X6138,X6139)))&(X6142!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6141),X6143)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X6142,X6141))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__eq__0__iff])])])])])). 4.05/4.29 fof(c_0_6006, plain, ![X16271, X16272, X16273]:(X16273!=c_List_Olist_ONil(X16272)|X16271=c_List_Olast(X16272,hAPP(hAPP(c_List_Olist_OCons(X16272),X16271),X16273))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_last__ConsL])])])). 4.05/4.29 fof(c_0_6007, plain, ![X1226, X1227]:c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X1227,X1226))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1226)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_com_Osize_I6_J])). 4.05/4.29 fof(c_0_6008, plain, ![X16500, X16501, X16502, X16503, X16504]:((c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X16504|hAPP(c_New__DSequence_Opos__decr__bind(X16503,X16502,X16501,X16500),X16504)=c_Lazy__Sequence_Oempty(X16502))&(X16504=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hAPP(c_Lazy__Sequence_Obind(X16503,X16502,hAPP(X16501,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X16504),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X16503,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X16502)),X16500),X16504))=hAPP(c_New__DSequence_Opos__decr__bind(X16503,X16502,X16501,X16500),X16504))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_New__DSequence_Opos__decr__bind__def])])])). 4.05/4.29 cnf(c_0_6009, plain, (c_Code__Numeral_Onat__of__aux(X1,X2)=X2|X1!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[c_0_4680])). 4.05/4.29 fof(c_0_6010, plain, ![X7511, X7512]:c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X7512,X7511)), inference(variable_rename,[status(thm)],[fact_sorted__upt])). 4.05/4.29 fof(c_0_6011, plain, ![X9134]: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),X9134))), inference(variable_rename,[status(thm)],[fact_nat__zminus__int])). 4.05/4.29 fof(c_0_6012, plain, ![X3308, X3309, X3310]:c_HOL_OThe(X3310,c_Finite__Set_Ofold1Set(X3310,X3309,X3308))=hAPP(c_Finite__Set_Ofold1(X3310,X3309),X3308), inference(variable_rename,[status(thm)],[fact_fold1__def])). 4.05/4.29 fof(c_0_6013, plain, ![X15106, X15107]:c_Wellfounded_Owf(X15107,hAPP(c_Wellfounded_Omeasure(X15107),X15106)), inference(variable_rename,[status(thm)],[fact_wf__measure])). 4.05/4.29 fof(c_0_6014, plain, ![X16668, X16669]:((X16669=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X16668),X16669)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16668),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X16668),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16669),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))&(X16669!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X16668),X16669)=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])])])). 4.05/4.29 fof(c_0_6015, plain, ![X3056]:X3056=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3056),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_div__1])). 4.05/4.29 fof(c_0_6016, plain, ![X5597]:c_Divides_Odiv__class_Omod(tc_Int_Oint,X5597,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))=c_Groups_Ozero__class_Ozero(tc_Int_Oint), inference(variable_rename,[status(thm)],[fact_zmod__minus1__right])). 4.05/4.29 fof(c_0_6017, plain, ![X424]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X424,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[fact_mod__1])). 4.05/4.29 fof(c_0_6018, plain, ![X16164, X16165, X16166, X16167]:((~c_List_Olist__all2(X16167,X16166,X16165,X16164,c_List_Olist_ONil(X16166))|c_List_Olist_ONil(X16167)=X16164)&(c_List_Olist_ONil(X16167)!=X16164|c_List_Olist__all2(X16167,X16166,X16165,X16164,c_List_Olist_ONil(X16166)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Nil2])])). 4.05/4.29 fof(c_0_6019, plain, ![X4820, X4821, X4822, X4823]:((~hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X4823),X4822),X4821),X4820))|(hBOOL(hAPP(X4821,X4820))|X4820=X4822))&((~hBOOL(hAPP(X4821,X4820))|hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X4823),X4822),X4821),X4820)))&(X4820!=X4822|hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X4823),X4822),X4821),X4820))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])])). 4.05/4.29 fof(c_0_6020, plain, ![X12369, X12370, X12371]:((X12370!=X12369|hBOOL(hAPP(hAPP(c_member(X12371),X12370),hAPP(c_fequal,X12369))))&(~hBOOL(hAPP(hAPP(c_member(X12371),X12370),hAPP(c_fequal,X12369)))|X12370=X12369)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])])). 4.05/4.29 fof(c_0_6021, plain, ![X4280]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4280), inference(variable_rename,[status(thm)],[fact_min__0L])). 4.05/4.29 fof(c_0_6022, plain, ![X15664]:hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X15664),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_min__0R])). 4.05/4.29 fof(c_0_6023, plain, ![X9706]:X9706=hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X9706)), inference(variable_rename,[status(thm)],[fact_nat__int])). 4.05/4.29 fof(c_0_6024, plain, ![X9224, X9225, X9226]:((~c_List_Olist__all2(X9224,X9224,c_fequal,X9226,X9225)|X9225=X9226)&(X9225!=X9226|c_List_Olist__all2(X9224,X9224,c_fequal,X9226,X9225))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__eq])])). 4.05/4.29 fof(c_0_6025, plain, ![X1309]:X1309=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1309), inference(variable_rename,[status(thm)],[fact_max__0L])). 4.05/4.29 fof(c_0_6026, plain, ![X11088]:X11088=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X11088),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_max__0R])). 4.05/4.29 fof(c_0_6027, plain, ![X16660]:X16660=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X16660),c_Int_OPls), inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I1_J])). 4.05/4.29 fof(c_0_6028, plain, ![X7125]:c_Int_OPls=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X7125), inference(variable_rename,[status(thm)],[fact_mult__Pls])). 4.05/4.29 fof(c_0_6029, plain, ![X14504, X14505]:((X14505!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nitpick_Onat__gcd(X14504,X14505)=X14504)&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X14505|c_Nitpick_Onat__gcd(X14504,X14505)=c_Nitpick_Onat__gcd(X14505,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X14504,X14505)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__gcd_Osimps])])])). 4.05/4.29 fof(c_0_6030, plain, ![X16716, X16717]:((X16716!=X16717|c_Random_Oinc__shift(X16717,X16716)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))&(X16716=X16717|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X16716),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=c_Random_Oinc__shift(X16717,X16716))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inc__shift__def])])])). 4.05/4.29 fof(c_0_6031, plain, ![X5956, X5957]:(hBOOL(hAPP(hAPP(c_fequal,X5957),X5956))|X5956!=X5957), inference(variable_rename,[status(thm)],[help_c__fequal__2])). 4.05/4.29 fof(c_0_6032, plain, ![X7813, X7814]:c_HOL_OThe(X7814,hAPP(c_fequal,X7813))=X7813, inference(variable_rename,[status(thm)],[fact_the__sym__eq__trivial])). 4.05/4.29 fof(c_0_6033, plain, ![X6184]:X6184=hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X6184)), inference(variable_rename,[status(thm)],[fact_nat__of__of__nat])). 4.05/4.29 fof(c_0_6034, plain, ![X12887]:X12887=hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X12887)), inference(variable_rename,[status(thm)],[fact_of__nat__nat__of])). 4.05/4.29 cnf(c_0_6035, 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_4853])). 4.05/4.29 cnf(c_0_6036, 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_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Orderings_Oord__class_Omax(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))))))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_4854])). 4.05/4.29 cnf(c_0_6037, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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_4855])). 4.05/4.29 cnf(c_0_6038, 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_4856])). 4.05/4.29 cnf(c_0_6039, 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_4857])). 4.05/4.29 cnf(c_0_6040, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|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_4858, c_0_4859])). 4.05/4.29 cnf(c_0_6041, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odivmod__int(X2,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))))), inference(rw,[status(thm)],[c_0_4860, c_0_4859])). 4.05/4.29 cnf(c_0_6042, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X2,X2)),tc_fun(tc_Int_Oint,X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X2),X2),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X2,X2)),tc_fun(tc_Int_Oint,X2)),tc_Int_Oint),c_COMBB(tc_fun(X2,X2),X2,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,X2),X2),tc_Int_Oint),c_HOL_OLet(X2,X2)),c_Int_Oring__1__class_Oof__int(X2)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X2,X2),tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X2,X2)),tc_fun(tc_fun(X2,X2),tc_fun(X2,X2)),tc_Int_Oint),c_COMBS(X2,X2,X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X2,X2),tc_fun(X2,tc_fun(X2,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X2,X2)),tc_fun(tc_fun(X2,X2),tc_fun(X2,tc_fun(X2,X2))),tc_Int_Oint),c_COMBB(X2,tc_fun(X2,X2),X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),tc_Int_Oint),c_If(X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X2,X2,X2),c_Groups_Oplus__class_Oplus(X2)),c_COMBI(X2))))),hAPP(hAPP(c_COMBC(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Oplus__class_Oplus(X2)),hAPP(hAPP(c_COMBS(X2,X2,X2),c_Groups_Oplus__class_Oplus(X2)),c_COMBI(X2)))),c_Groups_Oone__class_Oone(X2))))),c_Divides_Odivmod__int(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))=hAPP(c_Int_Oring__1__class_Oof__int(X2),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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4861, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 fof(c_0_6043, plain, ![X1380, X1381, X1382, X1383, X1384, X1385]:((~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1385,tc_fun(X1384,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1385,tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_fun(X1384,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1384,tc_fun(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_fun(X1384,tc_HOL_Obool)),X1385),c_COMBC(X1384,tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1384,tc_prod(X1385,X1384)),tc_fun(X1384,tc_fun(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_HOL_Obool)),X1385),hAPP(c_COMBB(tc_prod(X1385,X1384),tc_fun(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_HOL_Obool),X1384),c_member(tc_prod(X1385,X1384)))),c_Product__Type_OPair(X1385,X1384)))),X1383)),hAPP(hAPP(c_COMBC(X1385,tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_fun(X1384,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1384,tc_fun(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_fun(X1384,tc_HOL_Obool)),X1385),c_COMBC(X1384,tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1384,tc_prod(X1385,X1384)),tc_fun(X1384,tc_fun(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_HOL_Obool)),X1385),hAPP(c_COMBB(tc_prod(X1385,X1384),tc_fun(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_HOL_Obool),X1384),c_member(tc_prod(X1385,X1384)))),c_Product__Type_OPair(X1385,X1384)))),X1382)),X1381),X1380))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1385,X1384)),hAPP(hAPP(c_Product__Type_OPair(X1385,X1384),X1381),X1380)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool)),X1383),X1382))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X1385,X1384)),hAPP(hAPP(c_Product__Type_OPair(X1385,X1384),X1381),X1380)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool)),X1383),X1382)))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1385,tc_fun(X1384,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1385,tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_fun(X1384,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1384,tc_fun(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_fun(X1384,tc_HOL_Obool)),X1385),c_COMBC(X1384,tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1384,tc_prod(X1385,X1384)),tc_fun(X1384,tc_fun(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_HOL_Obool)),X1385),hAPP(c_COMBB(tc_prod(X1385,X1384),tc_fun(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_HOL_Obool),X1384),c_member(tc_prod(X1385,X1384)))),c_Product__Type_OPair(X1385,X1384)))),X1383)),hAPP(hAPP(c_COMBC(X1385,tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_fun(X1384,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1384,tc_fun(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_fun(X1384,tc_HOL_Obool)),X1385),c_COMBC(X1384,tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1384,tc_prod(X1385,X1384)),tc_fun(X1384,tc_fun(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_HOL_Obool)),X1385),hAPP(c_COMBB(tc_prod(X1385,X1384),tc_fun(tc_fun(tc_prod(X1385,X1384),tc_HOL_Obool),tc_HOL_Obool),X1384),c_member(tc_prod(X1385,X1384)))),c_Product__Type_OPair(X1385,X1384)))),X1382)),X1381),X1380)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2])])). 4.05/4.29 fof(c_0_6044, plain, ![X10085, X10086, X10087, X10088, X10089, X10090]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X10090,X10089)),hAPP(hAPP(c_Product__Type_OPair(X10090,X10089),X10086),X10085)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool)),X10088),X10087)))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10090,tc_fun(X10089,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X10090,tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_fun(X10089,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10089,tc_fun(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_fun(X10089,tc_HOL_Obool)),X10090),c_COMBC(X10089,tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10089,tc_prod(X10090,X10089)),tc_fun(X10089,tc_fun(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_HOL_Obool)),X10090),hAPP(c_COMBB(tc_prod(X10090,X10089),tc_fun(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_HOL_Obool),X10089),c_member(tc_prod(X10090,X10089)))),c_Product__Type_OPair(X10090,X10089)))),X10088)),hAPP(hAPP(c_COMBC(X10090,tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_fun(X10089,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10089,tc_fun(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_fun(X10089,tc_HOL_Obool)),X10090),c_COMBC(X10089,tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10089,tc_prod(X10090,X10089)),tc_fun(X10089,tc_fun(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_HOL_Obool)),X10090),hAPP(c_COMBB(tc_prod(X10090,X10089),tc_fun(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_HOL_Obool),X10089),c_member(tc_prod(X10090,X10089)))),c_Product__Type_OPair(X10090,X10089)))),X10087)),X10086),X10085)))&(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10090,tc_fun(X10089,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X10090,tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_fun(X10089,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10089,tc_fun(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_fun(X10089,tc_HOL_Obool)),X10090),c_COMBC(X10089,tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10089,tc_prod(X10090,X10089)),tc_fun(X10089,tc_fun(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_HOL_Obool)),X10090),hAPP(c_COMBB(tc_prod(X10090,X10089),tc_fun(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_HOL_Obool),X10089),c_member(tc_prod(X10090,X10089)))),c_Product__Type_OPair(X10090,X10089)))),X10088)),hAPP(hAPP(c_COMBC(X10090,tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_fun(X10089,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10089,tc_fun(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_fun(X10089,tc_HOL_Obool)),X10090),c_COMBC(X10089,tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10089,tc_prod(X10090,X10089)),tc_fun(X10089,tc_fun(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_HOL_Obool)),X10090),hAPP(c_COMBB(tc_prod(X10090,X10089),tc_fun(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool),tc_HOL_Obool),X10089),c_member(tc_prod(X10090,X10089)))),c_Product__Type_OPair(X10090,X10089)))),X10087)),X10086),X10085))|hBOOL(hAPP(hAPP(c_member(tc_prod(X10090,X10089)),hAPP(hAPP(c_Product__Type_OPair(X10090,X10089),X10086),X10085)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10090,X10089),tc_HOL_Obool)),X10088),X10087))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Un__eq2])])). 4.05/4.29 fof(c_0_6045, plain, ![X1261, X1262, X1263, X1264, X1265, X1266, X1267]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X1267,X1265)),hAPP(hAPP(c_Product__Type_OPair(X1267,X1265),X1262),X1261)),hAPP(hAPP(c_Relation_Orel__comp(X1267,X1266,X1265),X1264),X1263)))|hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X1267,X1266,X1265,hAPP(hAPP(c_COMBC(X1267,tc_fun(tc_prod(X1267,X1266),tc_HOL_Obool),tc_fun(X1266,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1266,tc_fun(tc_fun(tc_prod(X1267,X1266),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1267,X1266),tc_HOL_Obool),tc_fun(X1266,tc_HOL_Obool)),X1267),c_COMBC(X1266,tc_fun(tc_prod(X1267,X1266),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1266,tc_prod(X1267,X1266)),tc_fun(X1266,tc_fun(tc_fun(tc_prod(X1267,X1266),tc_HOL_Obool),tc_HOL_Obool)),X1267),hAPP(c_COMBB(tc_prod(X1267,X1266),tc_fun(tc_fun(tc_prod(X1267,X1266),tc_HOL_Obool),tc_HOL_Obool),X1266),c_member(tc_prod(X1267,X1266)))),c_Product__Type_OPair(X1267,X1266)))),X1264),hAPP(hAPP(c_COMBC(X1266,tc_fun(tc_prod(X1266,X1265),tc_HOL_Obool),tc_fun(X1265,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1265,tc_fun(tc_fun(tc_prod(X1266,X1265),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1266,X1265),tc_HOL_Obool),tc_fun(X1265,tc_HOL_Obool)),X1266),c_COMBC(X1265,tc_fun(tc_prod(X1266,X1265),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1265,tc_prod(X1266,X1265)),tc_fun(X1265,tc_fun(tc_fun(tc_prod(X1266,X1265),tc_HOL_Obool),tc_HOL_Obool)),X1266),hAPP(c_COMBB(tc_prod(X1266,X1265),tc_fun(tc_fun(tc_prod(X1266,X1265),tc_HOL_Obool),tc_HOL_Obool),X1265),c_member(tc_prod(X1266,X1265)))),c_Product__Type_OPair(X1266,X1265)))),X1263)),X1262),X1261)))&(~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X1267,X1266,X1265,hAPP(hAPP(c_COMBC(X1267,tc_fun(tc_prod(X1267,X1266),tc_HOL_Obool),tc_fun(X1266,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1266,tc_fun(tc_fun(tc_prod(X1267,X1266),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1267,X1266),tc_HOL_Obool),tc_fun(X1266,tc_HOL_Obool)),X1267),c_COMBC(X1266,tc_fun(tc_prod(X1267,X1266),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1266,tc_prod(X1267,X1266)),tc_fun(X1266,tc_fun(tc_fun(tc_prod(X1267,X1266),tc_HOL_Obool),tc_HOL_Obool)),X1267),hAPP(c_COMBB(tc_prod(X1267,X1266),tc_fun(tc_fun(tc_prod(X1267,X1266),tc_HOL_Obool),tc_HOL_Obool),X1266),c_member(tc_prod(X1267,X1266)))),c_Product__Type_OPair(X1267,X1266)))),X1264),hAPP(hAPP(c_COMBC(X1266,tc_fun(tc_prod(X1266,X1265),tc_HOL_Obool),tc_fun(X1265,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1265,tc_fun(tc_fun(tc_prod(X1266,X1265),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1266,X1265),tc_HOL_Obool),tc_fun(X1265,tc_HOL_Obool)),X1266),c_COMBC(X1265,tc_fun(tc_prod(X1266,X1265),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1265,tc_prod(X1266,X1265)),tc_fun(X1265,tc_fun(tc_fun(tc_prod(X1266,X1265),tc_HOL_Obool),tc_HOL_Obool)),X1266),hAPP(c_COMBB(tc_prod(X1266,X1265),tc_fun(tc_fun(tc_prod(X1266,X1265),tc_HOL_Obool),tc_HOL_Obool),X1265),c_member(tc_prod(X1266,X1265)))),c_Product__Type_OPair(X1266,X1265)))),X1263)),X1262),X1261))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1267,X1265)),hAPP(hAPP(c_Product__Type_OPair(X1267,X1265),X1262),X1261)),hAPP(hAPP(c_Relation_Orel__comp(X1267,X1266,X1265),X1264),X1263))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__comp__rel__comp__eq])])). 4.05/4.29 fof(c_0_6046, plain, ![X2226, X2227, X2228, X2229]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2229,tc_fun(X2228,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X2229,tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_fun(X2228,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2228,tc_fun(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_fun(X2228,tc_HOL_Obool)),X2229),c_COMBC(X2228,tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2228,tc_prod(X2229,X2228)),tc_fun(X2228,tc_fun(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_HOL_Obool)),X2229),hAPP(c_COMBB(tc_prod(X2229,X2228),tc_fun(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_HOL_Obool),X2228),c_member(tc_prod(X2229,X2228)))),c_Product__Type_OPair(X2229,X2228)))),X2227)),hAPP(hAPP(c_COMBC(X2229,tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_fun(X2228,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2228,tc_fun(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_fun(X2228,tc_HOL_Obool)),X2229),c_COMBC(X2228,tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2228,tc_prod(X2229,X2228)),tc_fun(X2228,tc_fun(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_HOL_Obool)),X2229),hAPP(c_COMBB(tc_prod(X2229,X2228),tc_fun(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_HOL_Obool),X2228),c_member(tc_prod(X2229,X2228)))),c_Product__Type_OPair(X2229,X2228)))),X2226)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool)),X2227),X2226)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool)),X2227),X2226))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2229,tc_fun(X2228,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X2229,tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_fun(X2228,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2228,tc_fun(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_fun(X2228,tc_HOL_Obool)),X2229),c_COMBC(X2228,tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2228,tc_prod(X2229,X2228)),tc_fun(X2228,tc_fun(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_HOL_Obool)),X2229),hAPP(c_COMBB(tc_prod(X2229,X2228),tc_fun(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_HOL_Obool),X2228),c_member(tc_prod(X2229,X2228)))),c_Product__Type_OPair(X2229,X2228)))),X2227)),hAPP(hAPP(c_COMBC(X2229,tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_fun(X2228,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2228,tc_fun(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_fun(X2228,tc_HOL_Obool)),X2229),c_COMBC(X2228,tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2228,tc_prod(X2229,X2228)),tc_fun(X2228,tc_fun(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_HOL_Obool)),X2229),hAPP(c_COMBB(tc_prod(X2229,X2228),tc_fun(tc_fun(tc_prod(X2229,X2228),tc_HOL_Obool),tc_HOL_Obool),X2228),c_member(tc_prod(X2229,X2228)))),c_Product__Type_OPair(X2229,X2228)))),X2226))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])])). 4.05/4.29 cnf(c_0_6047, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),hAPP(hAPP(c_COMBS(X4,tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_fun(tc_fun(X2,tc_HOL_Obool),X1),X4),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1)),hAPP(c_COMBC(X2,X4,X1),X6))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4),c_Set_OCollect(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)))),hAPP(c_COMBC(X2,X4,tc_HOL_Obool),X7))))),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBS(X2,tc_fun(X4,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X4,X1),tc_fun(tc_fun(X4,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1)),X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X2),c_Set_OCollect(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X2),hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X5)))),X7)))),X3)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5))), inference(split_conjunct,[status(thm)],[c_0_4862])). 4.05/4.29 cnf(c_0_6048, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)),X3))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4863, c_0_4474]), c_0_4474]), c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6049, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4864, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4867]), ['final']). 4.05/4.29 cnf(c_0_6050, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)),X3))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4868, c_0_4474]), c_0_4474]), c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6051, 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_4869])). 4.05/4.29 cnf(c_0_6052, 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_4870])). 4.05/4.29 cnf(c_0_6053, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|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_4871])). 4.05/4.29 cnf(c_0_6054, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,X2))|~class_Groups_Olinordered__ab__semigroup__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4872])). 4.05/4.29 cnf(c_0_6055, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4873, c_0_4474]), c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6056, 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_4874])). 4.05/4.29 fof(c_0_6057, plain, ![X9069, X9070, X9071, X9072, X9073, X9074]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X9073,X9072)),hAPP(hAPP(c_Product__Type_OPair(X9073,X9072),X9070),X9069)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9074,tc_fun(tc_prod(X9073,X9072),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X9074,tc_HOL_Obool))),X9071)))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9074,tc_fun(X9073,tc_fun(X9072,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X9074,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X9073,X9072),tc_HOL_Obool),tc_fun(X9073,tc_fun(X9072,tc_HOL_Obool)),X9074),hAPP(c_COMBC(X9073,tc_fun(tc_prod(X9073,X9072),tc_HOL_Obool),tc_fun(X9072,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9072,tc_fun(tc_fun(tc_prod(X9073,X9072),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9073,X9072),tc_HOL_Obool),tc_fun(X9072,tc_HOL_Obool)),X9073),c_COMBC(X9072,tc_fun(tc_prod(X9073,X9072),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9072,tc_prod(X9073,X9072)),tc_fun(X9072,tc_fun(tc_fun(tc_prod(X9073,X9072),tc_HOL_Obool),tc_HOL_Obool)),X9073),hAPP(c_COMBB(tc_prod(X9073,X9072),tc_fun(tc_fun(tc_prod(X9073,X9072),tc_HOL_Obool),tc_HOL_Obool),X9072),c_member(tc_prod(X9073,X9072)))),c_Product__Type_OPair(X9073,X9072))))),X9071)),X9070),X9069)))&(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9074,tc_fun(X9073,tc_fun(X9072,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X9074,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X9073,X9072),tc_HOL_Obool),tc_fun(X9073,tc_fun(X9072,tc_HOL_Obool)),X9074),hAPP(c_COMBC(X9073,tc_fun(tc_prod(X9073,X9072),tc_HOL_Obool),tc_fun(X9072,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9072,tc_fun(tc_fun(tc_prod(X9073,X9072),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9073,X9072),tc_HOL_Obool),tc_fun(X9072,tc_HOL_Obool)),X9073),c_COMBC(X9072,tc_fun(tc_prod(X9073,X9072),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X9072,tc_prod(X9073,X9072)),tc_fun(X9072,tc_fun(tc_fun(tc_prod(X9073,X9072),tc_HOL_Obool),tc_HOL_Obool)),X9073),hAPP(c_COMBB(tc_prod(X9073,X9072),tc_fun(tc_fun(tc_prod(X9073,X9072),tc_HOL_Obool),tc_HOL_Obool),X9072),c_member(tc_prod(X9073,X9072)))),c_Product__Type_OPair(X9073,X9072))))),X9071)),X9070),X9069))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9073,X9072)),hAPP(hAPP(c_Product__Type_OPair(X9073,X9072),X9070),X9069)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9074,tc_fun(tc_prod(X9073,X9072),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X9074,tc_HOL_Obool))),X9071))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq2])])). 4.05/4.29 fof(c_0_6058, plain, ![X2747, X2748, X2749, X2750, X2751, X2752]:((~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2752,tc_fun(X2751,tc_fun(X2750,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X2752,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2751,X2750),tc_HOL_Obool),tc_fun(X2751,tc_fun(X2750,tc_HOL_Obool)),X2752),hAPP(c_COMBC(X2751,tc_fun(tc_prod(X2751,X2750),tc_HOL_Obool),tc_fun(X2750,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2750,tc_fun(tc_fun(tc_prod(X2751,X2750),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2751,X2750),tc_HOL_Obool),tc_fun(X2750,tc_HOL_Obool)),X2751),c_COMBC(X2750,tc_fun(tc_prod(X2751,X2750),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2750,tc_prod(X2751,X2750)),tc_fun(X2750,tc_fun(tc_fun(tc_prod(X2751,X2750),tc_HOL_Obool),tc_HOL_Obool)),X2751),hAPP(c_COMBB(tc_prod(X2751,X2750),tc_fun(tc_fun(tc_prod(X2751,X2750),tc_HOL_Obool),tc_HOL_Obool),X2750),c_member(tc_prod(X2751,X2750)))),c_Product__Type_OPair(X2751,X2750))))),X2749)),X2748),X2747))|hBOOL(hAPP(hAPP(c_member(tc_prod(X2751,X2750)),hAPP(hAPP(c_Product__Type_OPair(X2751,X2750),X2748),X2747)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2752,tc_fun(tc_prod(X2751,X2750),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2752,tc_HOL_Obool))),X2749))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X2751,X2750)),hAPP(hAPP(c_Product__Type_OPair(X2751,X2750),X2748),X2747)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2752,tc_fun(tc_prod(X2751,X2750),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2752,tc_HOL_Obool))),X2749)))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2752,tc_fun(X2751,tc_fun(X2750,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X2752,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2751,X2750),tc_HOL_Obool),tc_fun(X2751,tc_fun(X2750,tc_HOL_Obool)),X2752),hAPP(c_COMBC(X2751,tc_fun(tc_prod(X2751,X2750),tc_HOL_Obool),tc_fun(X2750,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2750,tc_fun(tc_fun(tc_prod(X2751,X2750),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2751,X2750),tc_HOL_Obool),tc_fun(X2750,tc_HOL_Obool)),X2751),c_COMBC(X2750,tc_fun(tc_prod(X2751,X2750),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2750,tc_prod(X2751,X2750)),tc_fun(X2750,tc_fun(tc_fun(tc_prod(X2751,X2750),tc_HOL_Obool),tc_HOL_Obool)),X2751),hAPP(c_COMBB(tc_prod(X2751,X2750),tc_fun(tc_fun(tc_prod(X2751,X2750),tc_HOL_Obool),tc_HOL_Obool),X2750),c_member(tc_prod(X2751,X2750)))),c_Product__Type_OPair(X2751,X2750))))),X2749)),X2748),X2747)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq2])])). 4.05/4.29 fof(c_0_6059, plain, ![X15207, X15208, X15209, X15210, X15212, X15213, X15214, X15215, X15216]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X15210,X15210)),esk457_4(X15207,X15208,X15209,X15210)),hAPP(c_List_Oset(tc_prod(X15210,X15210)),hAPP(hAPP(c_List_Ozip(X15210,X15210),X15209),X15208))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15210)),X15209)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15210)),X15208)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X15210),tc_List_Olist(X15210))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X15210),tc_List_Olist(X15210)),X15209),X15208)),c_List_Olistrel(X15210,X15207))))&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X15210,X15210,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X15210,tc_fun(tc_prod(X15210,X15210),tc_HOL_Obool),tc_fun(X15210,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15210,tc_fun(tc_fun(tc_prod(X15210,X15210),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X15210,X15210),tc_HOL_Obool),tc_fun(X15210,tc_HOL_Obool)),X15210),c_COMBC(X15210,tc_fun(tc_prod(X15210,X15210),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15210,tc_prod(X15210,X15210)),tc_fun(X15210,tc_fun(tc_fun(tc_prod(X15210,X15210),tc_HOL_Obool),tc_HOL_Obool)),X15210),hAPP(c_COMBB(tc_prod(X15210,X15210),tc_fun(tc_fun(tc_prod(X15210,X15210),tc_HOL_Obool),tc_HOL_Obool),X15210),c_member(tc_prod(X15210,X15210)))),c_Product__Type_OPair(X15210,X15210)))),X15207)),esk457_4(X15207,X15208,X15209,X15210)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15210)),X15209)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15210)),X15208)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X15210),tc_List_Olist(X15210))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X15210),tc_List_Olist(X15210)),X15209),X15208)),c_List_Olistrel(X15210,X15207)))))&((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15215)),X15214)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15215)),X15213)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X15215),tc_List_Olist(X15215))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X15215),tc_List_Olist(X15215)),X15214),X15213)),c_List_Olistrel(X15215,X15212))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15215,X15215)),X15216),hAPP(c_List_Oset(tc_prod(X15215,X15215)),hAPP(hAPP(c_List_Ozip(X15215,X15215),X15214),X15213))))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X15215,X15215,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X15215,tc_fun(tc_prod(X15215,X15215),tc_HOL_Obool),tc_fun(X15215,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15215,tc_fun(tc_fun(tc_prod(X15215,X15215),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X15215,X15215),tc_HOL_Obool),tc_fun(X15215,tc_HOL_Obool)),X15215),c_COMBC(X15215,tc_fun(tc_prod(X15215,X15215),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15215,tc_prod(X15215,X15215)),tc_fun(X15215,tc_fun(tc_fun(tc_prod(X15215,X15215),tc_HOL_Obool),tc_HOL_Obool)),X15215),hAPP(c_COMBB(tc_prod(X15215,X15215),tc_fun(tc_fun(tc_prod(X15215,X15215),tc_HOL_Obool),tc_HOL_Obool),X15215),c_member(tc_prod(X15215,X15215)))),c_Product__Type_OPair(X15215,X15215)))),X15212)),X15216))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X15215),tc_List_Olist(X15215))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X15215),tc_List_Olist(X15215)),X15214),X15213)),c_List_Olistrel(X15215,X15212)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__iff__zip])])])])])])). 4.05/4.29 cnf(c_0_6060, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_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_4875])). 4.05/4.29 cnf(c_0_6061, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X1))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4876, c_0_4474]), c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6062, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))=hAPP(c_Code__Numeral_Oint__of,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_4877, c_0_4474]), c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6063, 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_4878])). 4.05/4.29 cnf(c_0_6064, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_Nat_Onat,X6),c_Finite__Set_Ocard(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X6),c_Set_OCollect(X4)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool),X6),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)),X3)))),X2)))),X5)|hAPP(X1,esk148_6(X1,X2,X3,X4,X5,X6))!=hAPP(c_Finite__Set_Ocard(X6),hAPP(c_Set_OCollect(X6),hAPP(hAPP(c_COMBS(X6,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6),c_fconj),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X5))),hAPP(hAPP(c_COMBC(X6,X4,tc_HOL_Obool),X2),esk148_6(X1,X2,X3,X4,X5,X6)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5))), inference(split_conjunct,[status(thm)],[c_0_4879])). 4.05/4.29 cnf(c_0_6065, 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_4880])). 4.05/4.29 cnf(c_0_6066, 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),esk379_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_4881])). 4.05/4.29 fof(c_0_6067, plain, ![X15038, X15039, X15040, X15041, X15042]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X15041,X15042)),hAPP(hAPP(c_Product__Type_OPair(X15041,X15042),X15039),X15038)),hAPP(c_Relation_Oconverse(X15042,X15041),X15040)))|hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X15042,X15041,hAPP(hAPP(c_COMBC(X15042,tc_fun(tc_prod(X15042,X15041),tc_HOL_Obool),tc_fun(X15041,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15041,tc_fun(tc_fun(tc_prod(X15042,X15041),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X15042,X15041),tc_HOL_Obool),tc_fun(X15041,tc_HOL_Obool)),X15042),c_COMBC(X15041,tc_fun(tc_prod(X15042,X15041),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15041,tc_prod(X15042,X15041)),tc_fun(X15041,tc_fun(tc_fun(tc_prod(X15042,X15041),tc_HOL_Obool),tc_HOL_Obool)),X15042),hAPP(c_COMBB(tc_prod(X15042,X15041),tc_fun(tc_fun(tc_prod(X15042,X15041),tc_HOL_Obool),tc_HOL_Obool),X15041),c_member(tc_prod(X15042,X15041)))),c_Product__Type_OPair(X15042,X15041)))),X15040)),X15039),X15038)))&(~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X15042,X15041,hAPP(hAPP(c_COMBC(X15042,tc_fun(tc_prod(X15042,X15041),tc_HOL_Obool),tc_fun(X15041,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15041,tc_fun(tc_fun(tc_prod(X15042,X15041),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X15042,X15041),tc_HOL_Obool),tc_fun(X15041,tc_HOL_Obool)),X15042),c_COMBC(X15041,tc_fun(tc_prod(X15042,X15041),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X15041,tc_prod(X15042,X15041)),tc_fun(X15041,tc_fun(tc_fun(tc_prod(X15042,X15041),tc_HOL_Obool),tc_HOL_Obool)),X15042),hAPP(c_COMBB(tc_prod(X15042,X15041),tc_fun(tc_fun(tc_prod(X15042,X15041),tc_HOL_Obool),tc_HOL_Obool),X15041),c_member(tc_prod(X15042,X15041)))),c_Product__Type_OPair(X15042,X15041)))),X15040)),X15039),X15038))|hBOOL(hAPP(hAPP(c_member(tc_prod(X15041,X15042)),hAPP(hAPP(c_Product__Type_OPair(X15041,X15042),X15039),X15038)),hAPP(c_Relation_Oconverse(X15042,X15041),X15040))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__converse__eq])])). 4.05/4.29 cnf(c_0_6068, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hAPP(c_Code__Numeral_Oint__of,X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))|c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))!=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)],[c_0_4882, c_0_4474]), c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6069, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4883, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6070, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4884, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6071, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4885, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6072, 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_4886])). 4.05/4.29 cnf(c_0_6073, 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_4887])). 4.05/4.29 cnf(c_0_6074, 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_4888])). 4.05/4.29 fof(c_0_6075, plain, ![X8523, X8524, X8525, X8526]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X8526,tc_HOL_Obool),tc_fun(X8526,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X8526,tc_HOL_Obool),tc_fun(X8526,tc_HOL_Obool)),X8524),X8523)),c_Wellfounded_Omax__ext(X8526,X8525)))|c_Wellfounded_Omax__extp(X8526,hAPP(hAPP(c_COMBC(X8526,tc_fun(tc_prod(X8526,X8526),tc_HOL_Obool),tc_fun(X8526,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8526,tc_fun(tc_fun(tc_prod(X8526,X8526),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X8526,X8526),tc_HOL_Obool),tc_fun(X8526,tc_HOL_Obool)),X8526),c_COMBC(X8526,tc_fun(tc_prod(X8526,X8526),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8526,tc_prod(X8526,X8526)),tc_fun(X8526,tc_fun(tc_fun(tc_prod(X8526,X8526),tc_HOL_Obool),tc_HOL_Obool)),X8526),hAPP(c_COMBB(tc_prod(X8526,X8526),tc_fun(tc_fun(tc_prod(X8526,X8526),tc_HOL_Obool),tc_HOL_Obool),X8526),c_member(tc_prod(X8526,X8526)))),c_Product__Type_OPair(X8526,X8526)))),X8525),X8524,X8523))&(~c_Wellfounded_Omax__extp(X8526,hAPP(hAPP(c_COMBC(X8526,tc_fun(tc_prod(X8526,X8526),tc_HOL_Obool),tc_fun(X8526,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8526,tc_fun(tc_fun(tc_prod(X8526,X8526),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X8526,X8526),tc_HOL_Obool),tc_fun(X8526,tc_HOL_Obool)),X8526),c_COMBC(X8526,tc_fun(tc_prod(X8526,X8526),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8526,tc_prod(X8526,X8526)),tc_fun(X8526,tc_fun(tc_fun(tc_prod(X8526,X8526),tc_HOL_Obool),tc_HOL_Obool)),X8526),hAPP(c_COMBB(tc_prod(X8526,X8526),tc_fun(tc_fun(tc_prod(X8526,X8526),tc_HOL_Obool),tc_HOL_Obool),X8526),c_member(tc_prod(X8526,X8526)))),c_Product__Type_OPair(X8526,X8526)))),X8525),X8524,X8523)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X8526,tc_HOL_Obool),tc_fun(X8526,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X8526,tc_HOL_Obool),tc_fun(X8526,tc_HOL_Obool)),X8524),X8523)),c_Wellfounded_Omax__ext(X8526,X8525))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__extp__max__ext__eq])])). 4.05/4.29 cnf(c_0_6076, 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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))),c_Groups_Ozero__class_Ozero(X2)))|X3!=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4889, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6077, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))))|~class_Rings_Olinordered__idom(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4890, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6078, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))))|~class_Rings_Olinordered__idom(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4891, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6079, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4892, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6080, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),X1,X5),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X5),c_Set_OCollect(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X5),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,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,tc_HOL_Obool),X2),c_fequal),X6)))))),hAPP(c_Set_Oimage(X2,X5,X6),X3))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4893])). 4.05/4.29 fof(c_0_6081, plain, ![X11357, X11358, X11359, X11360]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X11360),tc_List_Olist(X11360))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X11360),tc_List_Olist(X11360)),X11358),X11357)),c_List_Olistrel(X11360,X11359)))|c_List_Olistrelp(X11360,hAPP(hAPP(c_COMBC(X11360,tc_fun(tc_prod(X11360,X11360),tc_HOL_Obool),tc_fun(X11360,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11360,tc_fun(tc_fun(tc_prod(X11360,X11360),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X11360,X11360),tc_HOL_Obool),tc_fun(X11360,tc_HOL_Obool)),X11360),c_COMBC(X11360,tc_fun(tc_prod(X11360,X11360),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11360,tc_prod(X11360,X11360)),tc_fun(X11360,tc_fun(tc_fun(tc_prod(X11360,X11360),tc_HOL_Obool),tc_HOL_Obool)),X11360),hAPP(c_COMBB(tc_prod(X11360,X11360),tc_fun(tc_fun(tc_prod(X11360,X11360),tc_HOL_Obool),tc_HOL_Obool),X11360),c_member(tc_prod(X11360,X11360)))),c_Product__Type_OPair(X11360,X11360)))),X11359),X11358,X11357))&(~c_List_Olistrelp(X11360,hAPP(hAPP(c_COMBC(X11360,tc_fun(tc_prod(X11360,X11360),tc_HOL_Obool),tc_fun(X11360,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11360,tc_fun(tc_fun(tc_prod(X11360,X11360),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X11360,X11360),tc_HOL_Obool),tc_fun(X11360,tc_HOL_Obool)),X11360),c_COMBC(X11360,tc_fun(tc_prod(X11360,X11360),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11360,tc_prod(X11360,X11360)),tc_fun(X11360,tc_fun(tc_fun(tc_prod(X11360,X11360),tc_HOL_Obool),tc_HOL_Obool)),X11360),hAPP(c_COMBB(tc_prod(X11360,X11360),tc_fun(tc_fun(tc_prod(X11360,X11360),tc_HOL_Obool),tc_HOL_Obool),X11360),c_member(tc_prod(X11360,X11360)))),c_Product__Type_OPair(X11360,X11360)))),X11359),X11358,X11357)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X11360),tc_List_Olist(X11360))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X11360),tc_List_Olist(X11360)),X11358),X11357)),c_List_Olistrel(X11360,X11359))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp__listrel__eq])])). 4.05/4.29 fof(c_0_6082, plain, ![X7235, X7236, X7237, X7238]:((~hBOOL(hAPP(c_Predicate_ORangeP(X7238,X7237,hAPP(hAPP(c_COMBC(X7238,tc_fun(tc_prod(X7238,X7237),tc_HOL_Obool),tc_fun(X7237,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7237,tc_fun(tc_fun(tc_prod(X7238,X7237),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7238,X7237),tc_HOL_Obool),tc_fun(X7237,tc_HOL_Obool)),X7238),c_COMBC(X7237,tc_fun(tc_prod(X7238,X7237),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7237,tc_prod(X7238,X7237)),tc_fun(X7237,tc_fun(tc_fun(tc_prod(X7238,X7237),tc_HOL_Obool),tc_HOL_Obool)),X7238),hAPP(c_COMBB(tc_prod(X7238,X7237),tc_fun(tc_fun(tc_prod(X7238,X7237),tc_HOL_Obool),tc_HOL_Obool),X7237),c_member(tc_prod(X7238,X7237)))),c_Product__Type_OPair(X7238,X7237)))),X7236)),X7235))|hBOOL(hAPP(hAPP(c_member(X7237),X7235),hAPP(c_Relation_ORange(X7238,X7237),X7236))))&(~hBOOL(hAPP(hAPP(c_member(X7237),X7235),hAPP(c_Relation_ORange(X7238,X7237),X7236)))|hBOOL(hAPP(c_Predicate_ORangeP(X7238,X7237,hAPP(hAPP(c_COMBC(X7238,tc_fun(tc_prod(X7238,X7237),tc_HOL_Obool),tc_fun(X7237,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7237,tc_fun(tc_fun(tc_prod(X7238,X7237),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X7238,X7237),tc_HOL_Obool),tc_fun(X7237,tc_HOL_Obool)),X7238),c_COMBC(X7237,tc_fun(tc_prod(X7238,X7237),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7237,tc_prod(X7238,X7237)),tc_fun(X7237,tc_fun(tc_fun(tc_prod(X7238,X7237),tc_HOL_Obool),tc_HOL_Obool)),X7238),hAPP(c_COMBB(tc_prod(X7238,X7237),tc_fun(tc_fun(tc_prod(X7238,X7237),tc_HOL_Obool),tc_HOL_Obool),X7237),c_member(tc_prod(X7238,X7237)))),c_Product__Type_OPair(X7238,X7237)))),X7236)),X7235)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq])])). 4.05/4.29 fof(c_0_6083, plain, ![X11277, X11278, X11279, X11280]:((~hBOOL(hAPP(hAPP(c_member(X11280),X11277),hAPP(c_Relation_ODomain(X11280,X11279),X11278)))|hBOOL(hAPP(c_Predicate_ODomainP(X11280,X11279,hAPP(hAPP(c_COMBC(X11280,tc_fun(tc_prod(X11280,X11279),tc_HOL_Obool),tc_fun(X11279,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11279,tc_fun(tc_fun(tc_prod(X11280,X11279),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X11280,X11279),tc_HOL_Obool),tc_fun(X11279,tc_HOL_Obool)),X11280),c_COMBC(X11279,tc_fun(tc_prod(X11280,X11279),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11279,tc_prod(X11280,X11279)),tc_fun(X11279,tc_fun(tc_fun(tc_prod(X11280,X11279),tc_HOL_Obool),tc_HOL_Obool)),X11280),hAPP(c_COMBB(tc_prod(X11280,X11279),tc_fun(tc_fun(tc_prod(X11280,X11279),tc_HOL_Obool),tc_HOL_Obool),X11279),c_member(tc_prod(X11280,X11279)))),c_Product__Type_OPair(X11280,X11279)))),X11278)),X11277)))&(~hBOOL(hAPP(c_Predicate_ODomainP(X11280,X11279,hAPP(hAPP(c_COMBC(X11280,tc_fun(tc_prod(X11280,X11279),tc_HOL_Obool),tc_fun(X11279,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11279,tc_fun(tc_fun(tc_prod(X11280,X11279),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X11280,X11279),tc_HOL_Obool),tc_fun(X11279,tc_HOL_Obool)),X11280),c_COMBC(X11279,tc_fun(tc_prod(X11280,X11279),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X11279,tc_prod(X11280,X11279)),tc_fun(X11279,tc_fun(tc_fun(tc_prod(X11280,X11279),tc_HOL_Obool),tc_HOL_Obool)),X11280),hAPP(c_COMBB(tc_prod(X11280,X11279),tc_fun(tc_fun(tc_prod(X11280,X11279),tc_HOL_Obool),tc_HOL_Obool),X11279),c_member(tc_prod(X11280,X11279)))),c_Product__Type_OPair(X11280,X11279)))),X11278)),X11277))|hBOOL(hAPP(hAPP(c_member(X11280),X11277),hAPP(c_Relation_ODomain(X11280,X11279),X11278))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq])])). 4.05/4.29 cnf(c_0_6084, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk379_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_4881])). 4.05/4.29 cnf(c_0_6085, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk391_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))|hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))=c_List_Otranspose(X2,X3)|c_List_Olist_ONil(tc_List_Olist(X2))=X3), inference(split_conjunct,[status(thm)],[c_0_4517])). 4.05/4.29 cnf(c_0_6086, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4894, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6087, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))=c_Groups_Ozero__class_Ozero(X2)|X3!=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4895, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6088, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))=c_List_Otranspose(X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk391_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4896, c_0_4519]), c_0_4519])). 4.05/4.29 cnf(c_0_6089, 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_4897, c_0_4898]), ['final']). 4.05/4.29 cnf(c_0_6090, plain, (c_List_Olist_ONil(X1)=hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Olist_ONil(X2))), inference(split_conjunct,[status(thm)],[c_0_4899]), ['final']). 4.05/4.29 fof(c_0_6091, plain, ![X14484, X14485, X14486]:((~hBOOL(hAPP(c_Wellfounded_Oaccp(X14486,hAPP(hAPP(c_COMBC(X14486,tc_fun(tc_prod(X14486,X14486),tc_HOL_Obool),tc_fun(X14486,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14486,tc_fun(tc_fun(tc_prod(X14486,X14486),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X14486,X14486),tc_HOL_Obool),tc_fun(X14486,tc_HOL_Obool)),X14486),c_COMBC(X14486,tc_fun(tc_prod(X14486,X14486),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14486,tc_prod(X14486,X14486)),tc_fun(X14486,tc_fun(tc_fun(tc_prod(X14486,X14486),tc_HOL_Obool),tc_HOL_Obool)),X14486),hAPP(c_COMBB(tc_prod(X14486,X14486),tc_fun(tc_fun(tc_prod(X14486,X14486),tc_HOL_Obool),tc_HOL_Obool),X14486),c_member(tc_prod(X14486,X14486)))),c_Product__Type_OPair(X14486,X14486)))),X14485)),X14484))|hBOOL(hAPP(hAPP(c_member(X14486),X14484),c_Wellfounded_Oacc(X14486,X14485))))&(~hBOOL(hAPP(hAPP(c_member(X14486),X14484),c_Wellfounded_Oacc(X14486,X14485)))|hBOOL(hAPP(c_Wellfounded_Oaccp(X14486,hAPP(hAPP(c_COMBC(X14486,tc_fun(tc_prod(X14486,X14486),tc_HOL_Obool),tc_fun(X14486,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14486,tc_fun(tc_fun(tc_prod(X14486,X14486),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X14486,X14486),tc_HOL_Obool),tc_fun(X14486,tc_HOL_Obool)),X14486),c_COMBC(X14486,tc_fun(tc_prod(X14486,X14486),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14486,tc_prod(X14486,X14486)),tc_fun(X14486,tc_fun(tc_fun(tc_prod(X14486,X14486),tc_HOL_Obool),tc_HOL_Obool)),X14486),hAPP(c_COMBB(tc_prod(X14486,X14486),tc_fun(tc_fun(tc_prod(X14486,X14486),tc_HOL_Obool),tc_HOL_Obool),X14486),c_member(tc_prod(X14486,X14486)))),c_Product__Type_OPair(X14486,X14486)))),X14485)),X14484)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__acc__eq])])). 4.05/4.29 cnf(c_0_6092, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk148_6(X2,X3,X4,X1,X5,X6)),X4))|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(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)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5))), inference(split_conjunct,[status(thm)],[c_0_4879])). 4.05/4.29 fof(c_0_6093, plain, ![X748, X749]:((~c_Equiv__Relations_Oequiv(X749,c_Orderings_Otop__class_Otop(tc_fun(X749,tc_HOL_Obool)),X748)|c_Equiv__Relations_Oequivp(X749,hAPP(hAPP(c_COMBC(X749,tc_fun(tc_prod(X749,X749),tc_HOL_Obool),tc_fun(X749,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X749,tc_fun(tc_fun(tc_prod(X749,X749),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X749,X749),tc_HOL_Obool),tc_fun(X749,tc_HOL_Obool)),X749),c_COMBC(X749,tc_fun(tc_prod(X749,X749),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X749,tc_prod(X749,X749)),tc_fun(X749,tc_fun(tc_fun(tc_prod(X749,X749),tc_HOL_Obool),tc_HOL_Obool)),X749),hAPP(c_COMBB(tc_prod(X749,X749),tc_fun(tc_fun(tc_prod(X749,X749),tc_HOL_Obool),tc_HOL_Obool),X749),c_member(tc_prod(X749,X749)))),c_Product__Type_OPair(X749,X749)))),X748)))&(~c_Equiv__Relations_Oequivp(X749,hAPP(hAPP(c_COMBC(X749,tc_fun(tc_prod(X749,X749),tc_HOL_Obool),tc_fun(X749,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X749,tc_fun(tc_fun(tc_prod(X749,X749),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X749,X749),tc_HOL_Obool),tc_fun(X749,tc_HOL_Obool)),X749),c_COMBC(X749,tc_fun(tc_prod(X749,X749),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X749,tc_prod(X749,X749)),tc_fun(X749,tc_fun(tc_fun(tc_prod(X749,X749),tc_HOL_Obool),tc_HOL_Obool)),X749),hAPP(c_COMBB(tc_prod(X749,X749),tc_fun(tc_fun(tc_prod(X749,X749),tc_HOL_Obool),tc_HOL_Obool),X749),c_member(tc_prod(X749,X749)))),c_Product__Type_OPair(X749,X749)))),X748))|c_Equiv__Relations_Oequiv(X749,c_Orderings_Otop__class_Otop(tc_fun(X749,tc_HOL_Obool)),X748))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__equiv])])). 4.05/4.29 cnf(c_0_6094, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))=c_List_Otranspose(X2,X3)|c_List_Olist_ONil(tc_List_Olist(X2))=X3|X1!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X2)),X3),esk391_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_4517])). 4.05/4.29 cnf(c_0_6095, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X1))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2)))))=hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),X1))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2)))))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_4900])). 4.05/4.29 cnf(c_0_6096, 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_4901, c_0_4523]), c_0_4902]), ['final']). 4.05/4.29 cnf(c_0_6097, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))=c_List_Otranspose(X2,X3)|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X2)),X3),esk391_3(X1,X2,X3)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4903, c_0_4519]), c_0_4519])). 4.05/4.29 cnf(c_0_6098, 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_4904])). 4.05/4.29 cnf(c_0_6099, 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_4905])). 4.05/4.29 cnf(c_0_6100, 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_4906, c_0_4523]), ['final']). 4.05/4.29 fof(c_0_6101, plain, ![X13545, X13546]:((~c_Wellfounded_OwfP(X13546,hAPP(hAPP(c_COMBC(X13546,tc_fun(tc_prod(X13546,X13546),tc_HOL_Obool),tc_fun(X13546,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13546,tc_fun(tc_fun(tc_prod(X13546,X13546),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X13546,X13546),tc_HOL_Obool),tc_fun(X13546,tc_HOL_Obool)),X13546),c_COMBC(X13546,tc_fun(tc_prod(X13546,X13546),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13546,tc_prod(X13546,X13546)),tc_fun(X13546,tc_fun(tc_fun(tc_prod(X13546,X13546),tc_HOL_Obool),tc_HOL_Obool)),X13546),hAPP(c_COMBB(tc_prod(X13546,X13546),tc_fun(tc_fun(tc_prod(X13546,X13546),tc_HOL_Obool),tc_HOL_Obool),X13546),c_member(tc_prod(X13546,X13546)))),c_Product__Type_OPair(X13546,X13546)))),X13545))|c_Wellfounded_Owf(X13546,X13545))&(~c_Wellfounded_Owf(X13546,X13545)|c_Wellfounded_OwfP(X13546,hAPP(hAPP(c_COMBC(X13546,tc_fun(tc_prod(X13546,X13546),tc_HOL_Obool),tc_fun(X13546,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13546,tc_fun(tc_fun(tc_prod(X13546,X13546),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X13546,X13546),tc_HOL_Obool),tc_fun(X13546,tc_HOL_Obool)),X13546),c_COMBC(X13546,tc_fun(tc_prod(X13546,X13546),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13546,tc_prod(X13546,X13546)),tc_fun(X13546,tc_fun(tc_fun(tc_prod(X13546,X13546),tc_HOL_Obool),tc_HOL_Obool)),X13546),hAPP(c_COMBB(tc_prod(X13546,X13546),tc_fun(tc_fun(tc_prod(X13546,X13546),tc_HOL_Obool),tc_HOL_Obool),X13546),c_member(tc_prod(X13546,X13546)))),c_Product__Type_OPair(X13546,X13546)))),X13545)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__wf__eq])])). 4.05/4.29 fof(c_0_6102, plain, ![X4184, X4185, X4186, X4187]:((hAPP(hAPP(c_COMBC(X4187,tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_fun(X4186,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4186,tc_fun(tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_fun(X4186,tc_HOL_Obool)),X4187),c_COMBC(X4186,tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4186,tc_prod(X4187,X4186)),tc_fun(X4186,tc_fun(tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_HOL_Obool)),X4187),hAPP(c_COMBB(tc_prod(X4187,X4186),tc_fun(tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_HOL_Obool),X4186),c_member(tc_prod(X4187,X4186)))),c_Product__Type_OPair(X4187,X4186)))),X4184)!=hAPP(hAPP(c_COMBC(X4187,tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_fun(X4186,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4186,tc_fun(tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_fun(X4186,tc_HOL_Obool)),X4187),c_COMBC(X4186,tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4186,tc_prod(X4187,X4186)),tc_fun(X4186,tc_fun(tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_HOL_Obool)),X4187),hAPP(c_COMBB(tc_prod(X4187,X4186),tc_fun(tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_HOL_Obool),X4186),c_member(tc_prod(X4187,X4186)))),c_Product__Type_OPair(X4187,X4186)))),X4185)|X4184=X4185)&(X4184!=X4185|hAPP(hAPP(c_COMBC(X4187,tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_fun(X4186,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4186,tc_fun(tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_fun(X4186,tc_HOL_Obool)),X4187),c_COMBC(X4186,tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4186,tc_prod(X4187,X4186)),tc_fun(X4186,tc_fun(tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_HOL_Obool)),X4187),hAPP(c_COMBB(tc_prod(X4187,X4186),tc_fun(tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_HOL_Obool),X4186),c_member(tc_prod(X4187,X4186)))),c_Product__Type_OPair(X4187,X4186)))),X4184)=hAPP(hAPP(c_COMBC(X4187,tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_fun(X4186,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4186,tc_fun(tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_fun(X4186,tc_HOL_Obool)),X4187),c_COMBC(X4186,tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4186,tc_prod(X4187,X4186)),tc_fun(X4186,tc_fun(tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_HOL_Obool)),X4187),hAPP(c_COMBB(tc_prod(X4187,X4186),tc_fun(tc_fun(tc_prod(X4187,X4186),tc_HOL_Obool),tc_HOL_Obool),X4186),c_member(tc_prod(X4187,X4186)))),c_Product__Type_OPair(X4187,X4186)))),X4185))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])])). 4.05/4.29 cnf(c_0_6103, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))|~class_Groups_Omonoid__mult(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4907, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6104, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk215_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),esk214_3(X1,X2,X3)),esk215_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,esk214_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),esk215_3(X1,X2,X3))))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4908, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6105, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBS(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X4)),X5)),X6)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_Set_OCollect(X2),X4)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_OCollect(X2),X4)))))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4909])). 4.05/4.29 cnf(c_0_6106, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))), inference(split_conjunct,[status(thm)],[c_0_4910]), ['final']). 4.05/4.29 cnf(c_0_6107, 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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4911, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6108, 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_4912])). 4.05/4.29 cnf(c_0_6109, 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,esk190_4(X3,X2,X1,X4)))),hAPP(X1,esk190_4(X3,X2,X1,X4))))), inference(split_conjunct,[status(thm)],[c_0_4913])). 4.05/4.29 fof(c_0_6110, plain, ![X12897, X12898, X12899, X12900, X12901, X12902]:((hBOOL(hAPP(hAPP(c_member(X12901),esk394_6(X12897,X12898,X12899,X12900,X12901,X12902)),X12900))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12902,X12901,c_Groups_Otimes__class_Otimes(X12902)),hAPP(hAPP(c_COMBS(X12901,tc_fun(X12899,tc_HOL_Obool),X12902),hAPP(hAPP(c_COMBC(X12901,X12902,tc_fun(tc_fun(X12899,tc_HOL_Obool),X12902)),hAPP(hAPP(c_COMBB(tc_fun(X12899,X12902),tc_fun(X12902,tc_fun(tc_fun(X12899,tc_HOL_Obool),X12902)),X12901),c_Finite__Set_Ofold__image(X12902,X12899,c_Groups_Otimes__class_Otimes(X12902))),X12897)),c_Groups_Oone__class_Oone(X12902))),X12898)),c_Groups_Oone__class_Oone(X12902)),X12900)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12902,tc_prod(X12901,X12899),c_Groups_Otimes__class_Otimes(X12902)),hAPP(c_Product__Type_Oprod_Oprod__case(X12901,X12899,X12902),X12897)),c_Groups_Oone__class_Oone(X12902)),hAPP(hAPP(c_Product__Type_OSigma(X12901,X12899),X12900),X12898))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12901),X12900))|~class_Groups_Ocomm__monoid__mult(X12902))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12899),hAPP(X12898,esk394_6(X12897,X12898,X12899,X12900,X12901,X12902))))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12902,X12901,c_Groups_Otimes__class_Otimes(X12902)),hAPP(hAPP(c_COMBS(X12901,tc_fun(X12899,tc_HOL_Obool),X12902),hAPP(hAPP(c_COMBC(X12901,X12902,tc_fun(tc_fun(X12899,tc_HOL_Obool),X12902)),hAPP(hAPP(c_COMBB(tc_fun(X12899,X12902),tc_fun(X12902,tc_fun(tc_fun(X12899,tc_HOL_Obool),X12902)),X12901),c_Finite__Set_Ofold__image(X12902,X12899,c_Groups_Otimes__class_Otimes(X12902))),X12897)),c_Groups_Oone__class_Oone(X12902))),X12898)),c_Groups_Oone__class_Oone(X12902)),X12900)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12902,tc_prod(X12901,X12899),c_Groups_Otimes__class_Otimes(X12902)),hAPP(c_Product__Type_Oprod_Oprod__case(X12901,X12899,X12902),X12897)),c_Groups_Oone__class_Oone(X12902)),hAPP(hAPP(c_Product__Type_OSigma(X12901,X12899),X12900),X12898))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12901),X12900))|~class_Groups_Ocomm__monoid__mult(X12902))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__Sigma])])])])])). 4.05/4.29 fof(c_0_6111, plain, ![X668, X669, X670, X671, X672, X673, X674]:(~class_Rings_Osemiring__0(X674)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X673,X674),hAPP(hAPP(c_COMBC(X673,tc_fun(X670,tc_HOL_Obool),X674),hAPP(hAPP(c_COMBB(tc_fun(X670,X674),tc_fun(tc_fun(X670,tc_HOL_Obool),X674),X673),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X670,X674)),hAPP(hAPP(c_COMBC(X673,tc_fun(X670,X674),tc_fun(X670,X674)),hAPP(hAPP(c_COMBB(tc_fun(X674,X674),tc_fun(tc_fun(X670,X674),tc_fun(X670,X674)),X673),c_COMBB(X674,X674,X670)),hAPP(hAPP(c_COMBB(X674,tc_fun(X674,X674),X673),c_Groups_Otimes__class_Otimes(X674)),X672))),X669))),X668)),X671)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X674),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X673,X674),X672),X671)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X670,X674),X669),X668))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__product])])). 4.05/4.29 cnf(c_0_6112, 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_4914, c_0_4915]), c_0_4523])). 4.05/4.29 cnf(c_0_6113, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),hAPP(c_COMBC(X2,X1,tc_HOL_Obool),X4)))=hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),X3))),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4916, c_0_4915]), c_0_4523]), ['final']). 4.05/4.29 cnf(c_0_6114, 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_4917, c_0_4915]), c_0_4523])). 4.05/4.29 cnf(c_0_6115, 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_4546])). 4.05/4.29 cnf(c_0_6116, plain, (hBOOL(hAPP(X1,esk190_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_4913])). 4.05/4.29 cnf(c_0_6117, 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_4918, c_0_4434])). 4.05/4.29 cnf(c_0_6118, 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_4919, c_0_4523]), c_0_4523]), c_0_4920]), c_0_4523]), ['final']). 4.05/4.29 cnf(c_0_6119, 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),hAPP(hAPP(c_COMBB(X1,X1,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X1),X2)),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))),X3))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X4)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),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),X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X3))))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_4921])). 4.05/4.29 cnf(c_0_6120, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_4922]), ['final']). 4.05/4.29 cnf(c_0_6121, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk499_3(X1,X2,X3)),esk500_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(X1,esk499_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),esk500_3(X1,X2,X3))))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4923, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6122, 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_4924])). 4.05/4.29 cnf(c_0_6123, 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_4925, c_0_4915]), c_0_4915]), c_0_4926]), c_0_4523]), ['final']). 4.05/4.29 fof(c_0_6124, plain, ![X14030, X14031, X14032, X14033]:(~c_Fun_Oinj__on(X14033,tc_fun(tc_fun(X14033,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X14033,tc_fun(tc_prod(X14033,X14033),tc_HOL_Obool),tc_fun(tc_fun(X14033,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14033,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X14033,X14033),tc_HOL_Obool),tc_fun(tc_fun(X14033,tc_HOL_Obool),tc_HOL_Obool)),X14033),c_Equiv__Relations_Oquotient(X14033)),hAPP(hAPP(c_COMBC(X14033,tc_fun(X14033,tc_HOL_Obool),tc_fun(X14033,tc_HOL_Obool)),c_Set_Oinsert(X14033)),c_Orderings_Obot__class_Obot(tc_fun(X14033,tc_HOL_Obool))))),X14032),X14031)|(~hBOOL(hAPP(hAPP(c_member(X14033),X14030),X14031))|hAPP(hAPP(c_Equiv__Relations_Oquotient(X14033),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14033,tc_HOL_Obool)),X14031),hAPP(hAPP(c_Set_Oinsert(X14033),X14030),c_Orderings_Obot__class_Obot(tc_fun(X14033,tc_HOL_Obool))))),X14032)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X14033,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X14033),X14031),X14032)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X14033),hAPP(hAPP(c_Set_Oinsert(X14033),X14030),c_Orderings_Obot__class_Obot(tc_fun(X14033,tc_HOL_Obool)))),X14032)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_quotient__diff1])])])). 4.05/4.29 fof(c_0_6125, plain, ![X13884, X13885, X13886, X13887]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X13887),X13886))|(~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)),X13885),X13887)),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)),X13884),X13886)),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)),X13885),X13884)),X13886)),c_FunDef_Omax__weak))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wmax__insertI])])])). 4.05/4.29 fof(c_0_6126, plain, ![X6390, X6391, X6392, X6393]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X6393),X6392))|(~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)),X6391),X6393)),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)),X6390),X6392)),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)),X6391),X6390)),X6392)),c_FunDef_Omax__strict))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_smax__insertI])])])). 4.05/4.29 cnf(c_0_6127, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3))|~class_Groups_Omonoid__mult(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4927, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6128, 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_4928, c_0_4434])). 4.05/4.29 fof(c_0_6129, plain, ![X5877, X5878, X5879, X5880]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X5880),X5879))|(~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)),X5880),X5878)),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)),X5879),X5877)),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)),X5879),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X5878),X5877))),c_FunDef_Omin__strict))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_smin__insertI])])])). 4.05/4.29 fof(c_0_6130, plain, ![X15737, X15738, X15739, X15740]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X15740),X15739))|(~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)),X15740),X15738)),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)),X15739),X15737)),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)),X15739),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X15738),X15737))),c_FunDef_Omin__weak))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wmin__insertI])])])). 4.05/4.29 fof(c_0_6131, plain, ![X14612, X14613, X14614, X14615, X14616, X14617, X14618, X14619, X14620, X14621]:(~c_Equiv__Relations_Oequiv(X14621,X14620,X14619)|(~c_Equiv__Relations_Oequiv(X14618,X14617,X14616)|(~c_Equiv__Relations_Ocongruent2(X14621,X14618,tc_fun(X14615,tc_HOL_Obool),X14619,X14616,X14614)|(~hBOOL(hAPP(hAPP(c_member(X14621),X14613),X14620))|(~hBOOL(hAPP(hAPP(c_member(X14618),X14612),X14617))|hAPP(hAPP(X14614,X14613),X14612)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14621,tc_fun(X14615,tc_HOL_Obool)),hAPP(c_Relation_OImage(X14621,X14621,X14619),hAPP(hAPP(c_Set_Oinsert(X14621),X14613),c_Orderings_Obot__class_Obot(tc_fun(X14621,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X14618,tc_fun(X14615,tc_HOL_Obool)),tc_fun(X14615,tc_HOL_Obool),X14621),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14618,tc_fun(X14615,tc_HOL_Obool)),hAPP(c_Relation_OImage(X14618,X14618,X14616),hAPP(hAPP(c_Set_Oinsert(X14618),X14612),c_Orderings_Obot__class_Obot(tc_fun(X14618,tc_HOL_Obool)))))),X14614))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__equiv__class2])])])). 4.05/4.29 cnf(c_0_6132, 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_4929, c_0_4434])). 4.05/4.29 cnf(c_0_6133, plain, (hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1)=hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))), inference(split_conjunct,[status(thm)],[c_0_4930]), ['final']). 4.05/4.29 cnf(c_0_6134, 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_4931])). 4.05/4.29 cnf(c_0_6135, 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_4932])). 4.05/4.29 fof(c_0_6136, plain, ![X14215, X14216, X14217, X14218, X14219, X14220, X14221, X14222, X14223, X14224, X14225]:((hBOOL(hAPP(hAPP(c_member(X14225),esk433_11(X14215,X14216,X14217,X14218,X14219,X14220,X14221,X14222,X14223,X14224,X14225)),X14224))|hBOOL(hAPP(hAPP(c_member(tc_fun(X14219,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14225,tc_fun(X14219,tc_HOL_Obool)),X14217),hAPP(hAPP(c_COMBB(tc_fun(X14222,tc_fun(X14219,tc_HOL_Obool)),tc_fun(X14219,tc_HOL_Obool),X14225),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14222,tc_fun(X14219,tc_HOL_Obool)),X14216)),X14218))),X14215))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X14222,tc_HOL_Obool)),X14216),hAPP(hAPP(c_Equiv__Relations_Oquotient(X14222),X14221),X14220)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X14225,tc_HOL_Obool)),X14217),hAPP(hAPP(c_Equiv__Relations_Oquotient(X14225),X14224),X14223)))|~c_Equiv__Relations_Ocongruent2(X14225,X14222,tc_fun(X14219,tc_HOL_Obool),X14223,X14220,X14218)|~c_Equiv__Relations_Oequiv(X14222,X14221,X14220)|~c_Equiv__Relations_Oequiv(X14225,X14224,X14223))&((hBOOL(hAPP(hAPP(c_member(X14222),esk434_11(X14215,X14216,X14217,X14218,X14219,X14220,X14221,X14222,X14223,X14224,X14225)),X14221))|hBOOL(hAPP(hAPP(c_member(tc_fun(X14219,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14225,tc_fun(X14219,tc_HOL_Obool)),X14217),hAPP(hAPP(c_COMBB(tc_fun(X14222,tc_fun(X14219,tc_HOL_Obool)),tc_fun(X14219,tc_HOL_Obool),X14225),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14222,tc_fun(X14219,tc_HOL_Obool)),X14216)),X14218))),X14215))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X14222,tc_HOL_Obool)),X14216),hAPP(hAPP(c_Equiv__Relations_Oquotient(X14222),X14221),X14220)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X14225,tc_HOL_Obool)),X14217),hAPP(hAPP(c_Equiv__Relations_Oquotient(X14225),X14224),X14223)))|~c_Equiv__Relations_Ocongruent2(X14225,X14222,tc_fun(X14219,tc_HOL_Obool),X14223,X14220,X14218)|~c_Equiv__Relations_Oequiv(X14222,X14221,X14220)|~c_Equiv__Relations_Oequiv(X14225,X14224,X14223))&(~hBOOL(hAPP(hAPP(c_member(tc_fun(X14219,tc_HOL_Obool)),hAPP(hAPP(X14218,esk433_11(X14215,X14216,X14217,X14218,X14219,X14220,X14221,X14222,X14223,X14224,X14225)),esk434_11(X14215,X14216,X14217,X14218,X14219,X14220,X14221,X14222,X14223,X14224,X14225))),X14215))|hBOOL(hAPP(hAPP(c_member(tc_fun(X14219,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14225,tc_fun(X14219,tc_HOL_Obool)),X14217),hAPP(hAPP(c_COMBB(tc_fun(X14222,tc_fun(X14219,tc_HOL_Obool)),tc_fun(X14219,tc_HOL_Obool),X14225),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14222,tc_fun(X14219,tc_HOL_Obool)),X14216)),X14218))),X14215))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X14222,tc_HOL_Obool)),X14216),hAPP(hAPP(c_Equiv__Relations_Oquotient(X14222),X14221),X14220)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X14225,tc_HOL_Obool)),X14217),hAPP(hAPP(c_Equiv__Relations_Oquotient(X14225),X14224),X14223)))|~c_Equiv__Relations_Ocongruent2(X14225,X14222,tc_fun(X14219,tc_HOL_Obool),X14223,X14220,X14218)|~c_Equiv__Relations_Oequiv(X14222,X14221,X14220)|~c_Equiv__Relations_Oequiv(X14225,X14224,X14223)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__equiv__class__type2])])])])])). 4.05/4.29 cnf(c_0_6137, plain, (hAPP(c_List_Oset(tc_prod(X1,X2)),X3)=hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_Option_Ooption(X2),tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),hAPP(c_Map_Omap__of(X1,X2),X3)))),c_Option_Ooption_OSome(X2))))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_4933])). 4.05/4.29 cnf(c_0_6138, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4934, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6139, 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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4935, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6140, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4936, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6141, 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_4878])). 4.05/4.29 fof(c_0_6142, plain, ![X8565, X8566, X8567, X8568]:(~class_Smallcheck_Osmall(X8568)|~class_Smallcheck_Osmall(X8567)|hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(X8567,X8568)),X8566),X8565)=hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(X8567),hAPP(hAPP(c_COMBC(X8567,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(X8568,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X8567),c_Smallcheck_Osmall__class_Osmall(X8568)),hAPP(hAPP(c_COMBB(tc_fun(X8568,tc_prod(X8567,X8568)),tc_fun(X8568,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X8567),hAPP(c_COMBB(tc_prod(X8567,X8568),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),X8568),X8566)),c_Product__Type_OPair(X8567,X8568)))),X8565)),X8565)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_small__prod__def])])). 4.05/4.29 fof(c_0_6143, plain, ![X3920, X3921, X3922, X3923, X3924, X3925]:((hBOOL(hAPP(hAPP(c_member(X3924),esk121_6(X3920,X3921,X3922,X3923,X3924,X3925)),X3923))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3924,X3925),hAPP(hAPP(c_COMBS(X3924,tc_fun(X3922,tc_HOL_Obool),X3925),hAPP(hAPP(c_COMBB(tc_fun(X3922,X3925),tc_fun(tc_fun(X3922,tc_HOL_Obool),X3925),X3924),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3922,X3925)),X3920)),X3921)),X3923)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X3924,X3922),X3925),hAPP(c_Product__Type_Oprod_Oprod__case(X3924,X3922,X3925),X3920)),hAPP(hAPP(c_Product__Type_OSigma(X3924,X3922),X3923),X3921))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3924),X3923))|~class_Groups_Ocomm__monoid__add(X3925))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3922),hAPP(X3921,esk121_6(X3920,X3921,X3922,X3923,X3924,X3925))))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3924,X3925),hAPP(hAPP(c_COMBS(X3924,tc_fun(X3922,tc_HOL_Obool),X3925),hAPP(hAPP(c_COMBB(tc_fun(X3922,X3925),tc_fun(tc_fun(X3922,tc_HOL_Obool),X3925),X3924),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3922,X3925)),X3920)),X3921)),X3923)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X3924,X3922),X3925),hAPP(c_Product__Type_Oprod_Oprod__case(X3924,X3922,X3925),X3920)),hAPP(hAPP(c_Product__Type_OSigma(X3924,X3922),X3923),X3921))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3924),X3923))|~class_Groups_Ocomm__monoid__add(X3925))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Sigma])])])])). 4.05/4.29 cnf(c_0_6144, 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_4937])). 4.05/4.29 cnf(c_0_6145, 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_4938]), ['final']). 4.05/4.29 cnf(c_0_6146, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3)))|~class_Rings_Ocomm__semiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4939, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6147, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))!=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4940, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6148, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))),c_Groups_Ozero__class_Ozero(X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4941, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6149, plain, (X3!=c_Groups_Ozero__class_Ozero(X1)|X2!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4942, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6150, 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_4943])). 4.05/4.29 cnf(c_0_6151, 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_4944]), ['final']). 4.05/4.29 fof(c_0_6152, plain, ![X8494, X8495]:(~class_Enum_Oenum(X8494)|~class_Enum_Oenum(X8495)|hAPP(hAPP(c_List_Omap(tc_List_Olist(X8494),tc_fun(X8495,X8494)),hAPP(hAPP(c_COMBB(tc_fun(X8495,tc_Option_Ooption(X8494)),tc_fun(X8495,X8494),tc_List_Olist(X8494)),c_Fun_Ocomp(tc_Option_Ooption(X8494),X8494,X8495,c_Option_Othe(X8494))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X8495,X8494)),tc_fun(X8495,tc_Option_Ooption(X8494)),tc_List_Olist(X8494)),c_Map_Omap__of(X8495,X8494)),hAPP(c_List_Ozip(X8495,X8494),c_Enum_Oenum__class_Oenum(X8495))))),c_Enum_On__lists(X8494,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8495)),c_Enum_Oenum__class_Oenum(X8495)),c_Enum_Oenum__class_Oenum(X8494)))=c_Enum_Oenum__class_Oenum(tc_fun(X8495,X8494))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_enum__fun__def])])])). 4.05/4.29 fof(c_0_6153, plain, ![X11457, X11458, X11459]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X11458,X11459)),X11457))|c_Enum_Oex__n__lists(X11459,hAPP(hAPP(c_COMBB(tc_fun(X11458,X11459),tc_HOL_Obool,tc_List_Olist(X11459)),X11457),hAPP(hAPP(c_COMBB(tc_fun(X11458,tc_Option_Ooption(X11459)),tc_fun(X11458,X11459),tc_List_Olist(X11459)),c_Fun_Ocomp(tc_Option_Ooption(X11459),X11459,X11458,c_Option_Othe(X11459))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X11458,X11459)),tc_fun(X11458,tc_Option_Ooption(X11459)),tc_List_Olist(X11459)),c_Map_Omap__of(X11458,X11459)),hAPP(c_List_Ozip(X11458,X11459),c_Enum_Oenum__class_Oenum(X11458))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11458)),c_Enum_Oenum__class_Oenum(X11458)))|(~class_Enum_Oenum(X11458)|~class_Enum_Oenum(X11459)))&(~c_Enum_Oex__n__lists(X11459,hAPP(hAPP(c_COMBB(tc_fun(X11458,X11459),tc_HOL_Obool,tc_List_Olist(X11459)),X11457),hAPP(hAPP(c_COMBB(tc_fun(X11458,tc_Option_Ooption(X11459)),tc_fun(X11458,X11459),tc_List_Olist(X11459)),c_Fun_Ocomp(tc_Option_Ooption(X11459),X11459,X11458,c_Option_Othe(X11459))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X11458,X11459)),tc_fun(X11458,tc_Option_Ooption(X11459)),tc_List_Olist(X11459)),c_Map_Omap__of(X11458,X11459)),hAPP(c_List_Ozip(X11458,X11459),c_Enum_Oenum__class_Oenum(X11458))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11458)),c_Enum_Oenum__class_Oenum(X11458)))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X11458,X11459)),X11457))|(~class_Enum_Oenum(X11458)|~class_Enum_Oenum(X11459)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_enum__ex__fun__def])])])])). 4.05/4.29 cnf(c_0_6154, 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)),esk514_3(X3,X2,X1)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk515_3(X3,X2,X1)),esk515_3(X3,X2,X1))),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4945, c_0_4915]), c_0_4915])). 4.05/4.29 cnf(c_0_6155, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk515_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)),esk514_3(X3,X2,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4946, c_0_4915]), c_0_4915])). 4.05/4.29 fof(c_0_6156, plain, ![X12528, X12529, X12530]:((~c_Enum_Oall__n__lists(X12530,hAPP(hAPP(c_COMBB(tc_fun(X12529,X12530),tc_HOL_Obool,tc_List_Olist(X12530)),X12528),hAPP(hAPP(c_COMBB(tc_fun(X12529,tc_Option_Ooption(X12530)),tc_fun(X12529,X12530),tc_List_Olist(X12530)),c_Fun_Ocomp(tc_Option_Ooption(X12530),X12530,X12529,c_Option_Othe(X12530))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X12529,X12530)),tc_fun(X12529,tc_Option_Ooption(X12530)),tc_List_Olist(X12530)),c_Map_Omap__of(X12529,X12530)),hAPP(c_List_Ozip(X12529,X12530),c_Enum_Oenum__class_Oenum(X12529))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12529)),c_Enum_Oenum__class_Oenum(X12529)))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X12529,X12530)),X12528))|(~class_Enum_Oenum(X12529)|~class_Enum_Oenum(X12530)))&(~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X12529,X12530)),X12528))|c_Enum_Oall__n__lists(X12530,hAPP(hAPP(c_COMBB(tc_fun(X12529,X12530),tc_HOL_Obool,tc_List_Olist(X12530)),X12528),hAPP(hAPP(c_COMBB(tc_fun(X12529,tc_Option_Ooption(X12530)),tc_fun(X12529,X12530),tc_List_Olist(X12530)),c_Fun_Ocomp(tc_Option_Ooption(X12530),X12530,X12529,c_Option_Othe(X12530))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X12529,X12530)),tc_fun(X12529,tc_Option_Ooption(X12530)),tc_List_Olist(X12530)),c_Map_Omap__of(X12529,X12530)),hAPP(c_List_Ozip(X12529,X12530),c_Enum_Oenum__class_Oenum(X12529))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12529)),c_Enum_Oenum__class_Oenum(X12529)))|(~class_Enum_Oenum(X12529)|~class_Enum_Oenum(X12530)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_enum__all__fun__def])])])])). 4.05/4.29 cnf(c_0_6157, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk161_4(X1,X2,X3,X4)),esk162_4(X1,X2,X3,X4)))|hBOOL(hAPP(hAPP(hAPP(X1,esk160_4(X1,X2,X3,X4)),esk161_4(X1,X2,X3,X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk162_4(X1,X2,X3,X4)),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))|hAPP(esk160_4(X1,X2,X3,X4),esk162_4(X1,X2,X3,X4))!=c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))), inference(split_conjunct,[status(thm)],[c_0_4947])). 4.05/4.29 cnf(c_0_6158, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))),c_Groups_Ozero__class_Ozero(X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4948, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6159, 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_4949, c_0_4950])). 4.05/4.29 cnf(c_0_6160, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X2)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)))|~class_Rings_Osemiring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4951, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 fof(c_0_6161, plain, ![X8171, X8172, X8173, X8174, X8175]:((hBOOL(hAPP(hAPP(c_member(X8174),esk258_5(X8171,X8172,X8173,X8174,X8175)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8174,tc_HOL_Obool)),X8173),X8172)))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8175),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8175,X8174,c_Groups_Otimes__class_Otimes(X8175)),X8171),c_Groups_Oone__class_Oone(X8175)),X8173)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8175,X8174,c_Groups_Otimes__class_Otimes(X8175)),X8171),c_Groups_Oone__class_Oone(X8175)),X8172))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8175,X8174,c_Groups_Otimes__class_Otimes(X8175)),X8171),c_Groups_Oone__class_Oone(X8175)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8174,tc_HOL_Obool)),X8173),X8172))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8174),X8172))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8174),X8173))|~class_Groups_Ocomm__monoid__mult(X8175))&(c_Groups_Oone__class_Oone(X8175)!=hAPP(X8171,esk258_5(X8171,X8172,X8173,X8174,X8175))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8175),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8175,X8174,c_Groups_Otimes__class_Otimes(X8175)),X8171),c_Groups_Oone__class_Oone(X8175)),X8173)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8175,X8174,c_Groups_Otimes__class_Otimes(X8175)),X8171),c_Groups_Oone__class_Oone(X8175)),X8172))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8175,X8174,c_Groups_Otimes__class_Otimes(X8175)),X8171),c_Groups_Oone__class_Oone(X8175)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8174,tc_HOL_Obool)),X8173),X8172))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8174),X8172))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8174),X8173))|~class_Groups_Ocomm__monoid__mult(X8175))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__Un__one])])])])])). 4.05/4.29 cnf(c_0_6162, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))),c_Groups_Ozero__class_Ozero(X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4952, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6163, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4953, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6164, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4954, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6165, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Hilbert__Choice_OEps(tc_List_Olist(X1),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_List_Oset(X1))),X2))),c_List_Odistinct(X1))))=c_Nitpick_Ocard_H(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_4955])). 4.05/4.29 cnf(c_0_6166, 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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4956, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6167, 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),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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3))|~class_Rings_Ocomm__semiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4957, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 fof(c_0_6168, plain, ![X12522, X12523, X12524, X12525, X12526, X12527]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X12527,tc_HOL_Obool),tc_fun(X12527,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X12527,tc_HOL_Obool),tc_fun(X12527,tc_HOL_Obool)),X12526),X12525)),c_Wellfounded_Omax__ext(X12527,X12524)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X12527,tc_HOL_Obool),tc_fun(X12527,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X12527,tc_HOL_Obool),tc_fun(X12527,tc_HOL_Obool)),X12523),X12522)),c_Wellfounded_Omax__ext(X12527,X12524)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X12527,tc_HOL_Obool),tc_fun(X12527,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X12527,tc_HOL_Obool),tc_fun(X12527,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12527,tc_HOL_Obool)),X12526),X12523)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12527,tc_HOL_Obool)),X12525),X12522))),c_Wellfounded_Omax__ext(X12527,X12524))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__additive])])). 4.05/4.29 cnf(c_0_6169, 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)),X6)),X3)=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))))|~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_4958])). 4.05/4.29 fof(c_0_6170, plain, ![X9492, X9493, X9494, X9495, X9496]:(~class_Groups_Ocomm__monoid__mult(X9496)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9495),X9494))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9495),X9493))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9496),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X9496,X9495,c_Groups_Otimes__class_Otimes(X9496)),X9492),c_Groups_Oone__class_Oone(X9496)),X9494)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X9496,X9495,c_Groups_Otimes__class_Otimes(X9496)),X9492),c_Groups_Oone__class_Oone(X9496)),X9493))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9496),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X9496,X9495,c_Groups_Otimes__class_Otimes(X9496)),X9492),c_Groups_Oone__class_Oone(X9496)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9495,tc_HOL_Obool)),X9494),X9493))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X9496,X9495,c_Groups_Otimes__class_Otimes(X9496)),X9492),c_Groups_Oone__class_Oone(X9496)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9495,tc_HOL_Obool)),X9494),X9493)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__Un__Int])])])). 4.05/4.29 cnf(c_0_6171, plain, (hAPP(c_Divides_Oadjust(X2),c_Divides_OnegDivAlg(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)))=c_Divides_OnegDivAlg(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4959, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 fof(c_0_6172, plain, ![X10671, X10672, X10673, X10674, X10675]:(~class_Groups_Ocomm__monoid__mult(X10675)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10674),X10673))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10675),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10675,X10674,c_Groups_Otimes__class_Otimes(X10675)),X10672),c_Groups_Oone__class_Oone(X10675)),X10673)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10675,X10674,c_Groups_Otimes__class_Otimes(X10675)),X10671),c_Groups_Oone__class_Oone(X10675)),X10673))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10675,X10674,c_Groups_Otimes__class_Otimes(X10675)),hAPP(hAPP(c_COMBS(X10674,X10675,X10675),hAPP(hAPP(c_COMBB(X10675,tc_fun(X10675,X10675),X10674),c_Groups_Otimes__class_Otimes(X10675)),X10672)),X10671)),c_Groups_Oone__class_Oone(X10675)),X10673))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__distrib])])])). 4.05/4.29 cnf(c_0_6173, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4960, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.29 fof(c_0_6174, plain, ![X461, X462, X463, X464, X465]:((hBOOL(hAPP(hAPP(c_member(X464),esk6_5(X461,X462,X463,X464,X465)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X464,tc_HOL_Obool)),X463),X462)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X464,X465),X461),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X464,tc_HOL_Obool)),X463),X462))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X465),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X464,X465),X461),X463)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X464,X465),X461),X462))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X464,X465),X461),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X464,tc_HOL_Obool)),X463),X462)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X464),X462))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X464),X463))|~class_Fields_Ofield(X465))&(c_Groups_Ozero__class_Ozero(X465)=hAPP(X461,esk6_5(X461,X462,X463,X464,X465))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X464,X465),X461),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X464,tc_HOL_Obool)),X463),X462))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X465),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X464,X465),X461),X463)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X464,X465),X461),X462))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X464,X465),X461),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X464,tc_HOL_Obool)),X463),X462)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X464),X462))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X464),X463))|~class_Fields_Ofield(X465))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__Un])])])])])). 4.05/4.29 cnf(c_0_6175, 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),esk333_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_4961])). 4.05/4.29 fof(c_0_6176, plain, ![X12129, X12130, X12131, X12132, X12133, X12134]:(~class_Groups_Ocomm__monoid__mult(X12134)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12133,X12134),hAPP(hAPP(c_COMBC(X12133,tc_fun(X12132,tc_HOL_Obool),X12134),hAPP(hAPP(c_COMBB(tc_fun(X12132,X12134),tc_fun(tc_fun(X12132,tc_HOL_Obool),X12134),X12133),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12132,X12134)),X12131)),X12130)),X12129)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X12133,X12132),X12134),hAPP(c_Product__Type_Oprod_Oprod__case(X12133,X12132,X12134),X12131)),hAPP(hAPP(c_Product__Type_OSigma(X12133,X12132),X12129),hAPP(c_COMBK(tc_fun(X12132,tc_HOL_Obool),X12133),X12130)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__cartesian__product])])). 4.05/4.29 cnf(c_0_6177, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),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_4962, c_0_4434])). 4.05/4.29 cnf(c_0_6178, 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_4963, c_0_4434])). 4.05/4.29 fof(c_0_6179, plain, ![X10758, X10759, X10760, X10761, X10762, X10763]:(~class_Groups_Ocomm__monoid__add(X10763)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10762,X10763),hAPP(hAPP(c_COMBC(X10762,tc_fun(X10761,tc_HOL_Obool),X10763),hAPP(hAPP(c_COMBB(tc_fun(X10761,X10763),tc_fun(tc_fun(X10761,tc_HOL_Obool),X10763),X10762),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10761,X10763)),X10760)),X10759)),X10758)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X10762,X10761),X10763),hAPP(c_Product__Type_Oprod_Oprod__case(X10762,X10761,X10763),X10760)),hAPP(hAPP(c_Product__Type_OSigma(X10762,X10761),X10758),hAPP(c_COMBK(tc_fun(X10761,tc_HOL_Obool),X10762),X10759)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__cartesian__product])])). 4.05/4.29 fof(c_0_6180, plain, ![X3433, X3434]:((~c_Wellfounded_Owf(X3434,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool),tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool)),X3433))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X3434,X3434,X3434),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool),tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool)),X3433)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool),tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool)),X3433))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool),tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool)),X3433)))|c_FunDef_Oreduction__pair(X3434,X3433))&((c_Wellfounded_Owf(X3434,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool),tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool)),X3433))|~c_FunDef_Oreduction__pair(X3434,X3433))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X3434,X3434,X3434),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool),tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool)),X3433)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool),tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool)),X3433))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool),tc_fun(tc_prod(X3434,X3434),tc_HOL_Obool)),X3433)))|~c_FunDef_Oreduction__pair(X3434,X3433)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pair__def])])])). 4.05/4.29 cnf(c_0_6181, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBS(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X4))),X5)),c_Groups_Ozero__class_Ozero(X1))),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_4964])). 4.05/4.29 fof(c_0_6182, plain, ![X17298, X17299, X17300, X17301, X17302, X17303]:((hBOOL(hAPP(hAPP(c_member(X17302),esk519_6(X17298,X17299,X17300,X17301,X17302,X17303)),X17301))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X17302,X17300),X17303),hAPP(c_Product__Type_Oprod_Oprod__case(X17302,X17300,X17303),X17298)),hAPP(hAPP(c_Product__Type_OSigma(X17302,X17300),X17301),X17299))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17302,X17303),hAPP(hAPP(c_COMBS(X17302,tc_fun(X17300,tc_HOL_Obool),X17303),hAPP(hAPP(c_COMBB(tc_fun(X17300,X17303),tc_fun(tc_fun(X17300,tc_HOL_Obool),X17303),X17302),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17300,X17303)),X17298)),X17299)),X17301)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X17302),X17301))|~class_Groups_Ocomm__monoid__mult(X17303))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17300),hAPP(X17299,esk519_6(X17298,X17299,X17300,X17301,X17302,X17303))))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X17302,X17300),X17303),hAPP(c_Product__Type_Oprod_Oprod__case(X17302,X17300,X17303),X17298)),hAPP(hAPP(c_Product__Type_OSigma(X17302,X17300),X17301),X17299))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17302,X17303),hAPP(hAPP(c_COMBS(X17302,tc_fun(X17300,tc_HOL_Obool),X17303),hAPP(hAPP(c_COMBB(tc_fun(X17300,X17303),tc_fun(tc_fun(X17300,tc_HOL_Obool),X17303),X17302),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17300,X17303)),X17298)),X17299)),X17301)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X17302),X17301))|~class_Groups_Ocomm__monoid__mult(X17303))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__Sigma])])])])])). 4.05/4.29 cnf(c_0_6183, plain, (hBOOL(hAPP(X1,esk321_2(X2,X1)))|hBOOL(hAPP(X2,esk321_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)))),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_4965])). 4.05/4.29 cnf(c_0_6184, 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_4966])). 4.05/4.29 cnf(c_0_6185, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk321_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)))),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_4965])). 4.05/4.29 cnf(c_0_6186, plain, (c_Divides_OposDivAlg(X2,X1)=hAPP(c_Divides_Oadjust(X1),c_Divides_OposDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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)],[c_0_4967, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 fof(c_0_6187, plain, ![X13720, X13721, X13722, X13723, X13724, X13725, X13726, X13727, X13728]:((~c_Equiv__Relations_Ocongruent(X13723,X13722,X13721,X13720)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13723,X13723)),X13724),X13721))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13723,X13723,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X13723,tc_fun(X13723,X13722),tc_fun(X13723,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13722,tc_HOL_Obool),tc_fun(tc_fun(X13723,X13722),tc_fun(X13723,tc_HOL_Obool)),X13723),c_COMBB(X13722,tc_HOL_Obool,X13723)),hAPP(hAPP(c_COMBB(X13722,tc_fun(X13722,tc_HOL_Obool),X13723),c_fequal),X13720))),X13720)),X13724))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X13728,X13728)),esk427_4(X13725,X13726,X13727,X13728)),X13726))|c_Equiv__Relations_Ocongruent(X13728,X13727,X13726,X13725))&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13728,X13728,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X13728,tc_fun(X13728,X13727),tc_fun(X13728,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X13727,tc_HOL_Obool),tc_fun(tc_fun(X13728,X13727),tc_fun(X13728,tc_HOL_Obool)),X13728),c_COMBB(X13727,tc_HOL_Obool,X13728)),hAPP(hAPP(c_COMBB(X13727,tc_fun(X13727,tc_HOL_Obool),X13728),c_fequal),X13725))),X13725)),esk427_4(X13725,X13726,X13727,X13728)))|c_Equiv__Relations_Ocongruent(X13728,X13727,X13726,X13725)))), 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_congruent__def])])])])])])])). 4.05/4.29 cnf(c_0_6188, 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_4968])). 4.05/4.29 fof(c_0_6189, plain, ![X2253, X2254, X2255, X2256, X2257]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2257),tc_List_Olist(X2257))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2257),tc_List_Olist(X2257)),hAPP(hAPP(c_List_Oappend(X2257),X2256),X2255)),hAPP(hAPP(c_List_Oappend(X2257),X2256),X2254))),c_List_Olexord(X2257,X2253)))|(hBOOL(hAPP(hAPP(c_member(tc_prod(X2257,X2257)),hAPP(hAPP(c_Product__Type_OPair(X2257,X2257),esk83_5(X2253,X2254,X2255,X2256,X2257)),esk83_5(X2253,X2254,X2255,X2256,X2257))),X2253))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2257),tc_List_Olist(X2257))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2257),tc_List_Olist(X2257)),X2255),X2254)),c_List_Olexord(X2257,X2253))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lexord__append__leftD])])])])). 4.05/4.29 fof(c_0_6190, plain, ![X11571, X11572, X11573, X11574, X11575, X11576, X11577, X11578]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X11578,X11577),tc_HOL_Obool)),X11576),hAPP(hAPP(c_Product__Type_OSigma(X11578,X11577),X11575),hAPP(c_COMBK(tc_fun(X11577,tc_HOL_Obool),X11578),X11574))))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X11577,X11573),tc_HOL_Obool)),X11572),hAPP(hAPP(c_Product__Type_OSigma(X11577,X11573),X11574),hAPP(c_COMBK(tc_fun(X11573,tc_HOL_Obool),X11577),X11571))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X11578,X11573),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X11578,X11577,X11573),X11576),X11572)),hAPP(hAPP(c_Product__Type_OSigma(X11578,X11573),X11575),hAPP(c_COMBK(tc_fun(X11573,tc_HOL_Obool),X11578),X11571)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__comp__subset__Sigma])])])). 4.05/4.29 cnf(c_0_6191, 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_4968])). 4.05/4.29 cnf(c_0_6192, 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_4969])). 4.05/4.29 cnf(c_0_6193, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3)))),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4970, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6194, 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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4971, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6195, plain, (hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X2))=hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),X1))|~hBOOL(hAPP(X1,esk321_2(X2,X1)))|~hBOOL(hAPP(X2,esk321_2(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_4965])). 4.05/4.29 cnf(c_0_6196, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4972, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 fof(c_0_6197, plain, ![X1151, X1152, X1153, X1154]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1154),X1153))|hAPP(c_Set_Oimage(X1154,X1152,X1151),X1153)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X1152,tc_HOL_Obool),X1154,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1152,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1154,tc_fun(X1152,tc_HOL_Obool),tc_fun(X1152,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X1152,tc_fun(tc_fun(X1152,tc_HOL_Obool),tc_fun(X1152,tc_HOL_Obool)),X1154),c_Set_Oinsert(X1152)),X1151)),c_Orderings_Obot__class_Obot(tc_fun(X1152,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X1152,tc_HOL_Obool))),X1153)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__eq__fold__image])])])). 4.05/4.29 cnf(c_0_6198, 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)),X2),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)),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_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_4973])). 4.05/4.29 cnf(c_0_6199, plain, (hBOOL(hAPP(X1,esk333_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_4961])). 4.05/4.29 cnf(c_0_6200, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4974, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6201, 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_4958])). 4.05/4.29 cnf(c_0_6202, 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_4975])). 4.05/4.29 cnf(c_0_6203, 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_4976, c_0_4977]), ['final']). 4.05/4.29 fof(c_0_6204, plain, ![X11967, X11968, X11969, X11970, X11971, X11972]:(~class_Groups_Ocomm__monoid__add(X11972)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11970,X11972),hAPP(hAPP(c_COMBC(X11970,tc_fun(X11971,tc_HOL_Obool),X11972),hAPP(hAPP(c_COMBB(tc_fun(X11971,X11972),tc_fun(tc_fun(X11971,tc_HOL_Obool),X11972),X11970),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11971,X11972)),hAPP(c_COMBC(X11971,X11970,X11972),X11969))),X11967)),X11968)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11971,X11972),hAPP(hAPP(c_COMBC(X11971,tc_fun(X11970,tc_HOL_Obool),X11972),hAPP(hAPP(c_COMBB(tc_fun(X11970,X11972),tc_fun(tc_fun(X11970,tc_HOL_Obool),X11972),X11971),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11970,X11972)),X11969)),X11968)),X11967)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__commute])])])). 4.05/4.29 fof(c_0_6205, plain, ![X8744, X8745, X8746, X8747, X8748, X8749, X8750, X8751]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8751)),X8750)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8749)),X8748)|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8751)),X8747)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8749)),X8748)|(hBOOL(hAPP(hAPP(c_member(X8749),X8746),hAPP(c_List_Oset(X8749),X8748)))|(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X8749,tc_Option_Ooption(X8751)),hAPP(c_Map_Omap__of(X8749,X8751),hAPP(hAPP(c_List_Ozip(X8749,X8751),X8748),X8750))),X8746),hAPP(c_Option_Ooption_OSome(X8751),X8745))!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X8749,tc_Option_Ooption(X8751)),hAPP(c_Map_Omap__of(X8749,X8751),hAPP(hAPP(c_List_Ozip(X8749,X8751),X8748),X8747))),X8746),hAPP(c_Option_Ooption_OSome(X8751),X8744))|hAPP(c_Map_Omap__of(X8749,X8751),hAPP(hAPP(c_List_Ozip(X8749,X8751),X8748),X8750))=hAPP(c_Map_Omap__of(X8749,X8751),hAPP(hAPP(c_List_Ozip(X8749,X8751),X8748),X8747)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__zip__upd])])])). 4.05/4.29 fof(c_0_6206, plain, ![X7327, X7328, X7329, X7330, X7331]:((X7331!=c_Orderings_Obot__class_Obot(tc_fun(X7330,tc_HOL_Obool))|c_Orderings_Otop__class_Otop(tc_fun(X7329,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7330,tc_fun(X7329,tc_HOL_Obool)),X7331),hAPP(hAPP(c_COMBC(X7330,tc_fun(X7329,tc_HOL_Obool),tc_fun(X7329,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7329,tc_HOL_Obool),tc_fun(tc_fun(X7329,tc_HOL_Obool),tc_fun(X7329,tc_HOL_Obool)),X7330),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7329,tc_HOL_Obool))),X7328)),X7327)))&(c_Orderings_Obot__class_Obot(tc_fun(X7330,tc_HOL_Obool))=X7331|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7329,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7330,tc_fun(X7329,tc_HOL_Obool)),X7331),X7328)),X7327)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7330,tc_fun(X7329,tc_HOL_Obool)),X7331),hAPP(hAPP(c_COMBC(X7330,tc_fun(X7329,tc_HOL_Obool),tc_fun(X7329,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X7329,tc_HOL_Obool),tc_fun(tc_fun(X7329,tc_HOL_Obool),tc_fun(X7329,tc_HOL_Obool)),X7330),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7329,tc_HOL_Obool))),X7328)),X7327)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__simps_I1_J])])])). 4.05/4.29 fof(c_0_6207, plain, ![X12985, X12986, X12987]:(~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X12987),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X12987))),X12986)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12985),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X12987))),X12986)))|hAPP(hAPP(c_List_Omap(tc_List_Olist(X12987),X12987),hAPP(hAPP(c_COMBC(tc_List_Olist(X12987),tc_Nat_Onat,X12987),c_List_Onth(X12987)),X12985)),hAPP(c_List_Ofilter(tc_List_Olist(X12987),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X12987)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12985)),c_Nat_Osize__class_Osize(tc_List_Olist(X12987)))),c_List_Otranspose(X12987,X12986)))=hAPP(hAPP(c_List_Onth(tc_List_Olist(X12987)),X12986),X12985))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transpose__column])])])). 4.05/4.29 cnf(c_0_6208, 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_4968])). 4.05/4.29 cnf(c_0_6209, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4978, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.29 cnf(c_0_6210, 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_Enum_Oenum__the(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(rw,[status(thm)],[c_0_4979, c_0_4980])). 4.05/4.29 cnf(c_0_6211, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),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_4981])). 4.05/4.29 cnf(c_0_6212, 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_4982]), ['final']). 4.05/4.29 cnf(c_0_6213, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),c_Groups_Ozero__class_Ozero(X4))),X3)=c_Groups_Ozero__class_Ozero(X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_4983])). 4.05/4.29 cnf(c_0_6214, 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_4984]), ['final']). 4.05/4.29 cnf(c_0_6215, 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_4968])). 4.05/4.30 fof(c_0_6216, plain, ![X14702, X14703, X14704, X14705, X14706]:(~c_Relation_Osingle__valued(X14706,X14706,X14705)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X14706,X14706)),hAPP(hAPP(c_Product__Type_OPair(X14706,X14706),X14704),X14703)),c_Transitive__Closure_Ortrancl(X14706,X14705)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X14706,X14706)),hAPP(hAPP(c_Product__Type_OPair(X14706,X14706),X14704),X14702)),c_Transitive__Closure_Ortrancl(X14706,X14705)))|(hBOOL(hAPP(hAPP(c_member(tc_prod(X14706,X14706)),hAPP(hAPP(c_Product__Type_OPair(X14706,X14706),X14703),X14702)),c_Transitive__Closure_Ortrancl(X14706,X14705)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X14706,X14706)),hAPP(hAPP(c_Product__Type_OPair(X14706,X14706),X14702),X14703)),c_Transitive__Closure_Ortrancl(X14706,X14705))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_single__valued__confluent])])])). 4.05/4.30 cnf(c_0_6217, 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_4985])). 4.05/4.30 cnf(c_0_6218, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))|~class_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)],[c_0_4986, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6219, 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_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4987, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_6220, plain, ![X6096, X6097, X6098, X6099, X6100]:((X6100!=c_Orderings_Obot__class_Obot(tc_fun(X6099,tc_HOL_Obool))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6098,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X6098,tc_HOL_Obool))),X6096)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6098,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6099,tc_fun(X6098,tc_HOL_Obool)),X6100),X6097)),X6096))&(X6100=c_Orderings_Obot__class_Obot(tc_fun(X6099,tc_HOL_Obool))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6098,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6099,tc_fun(X6098,tc_HOL_Obool)),X6100),X6097)),X6096)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6099,tc_fun(X6098,tc_HOL_Obool)),X6100),hAPP(hAPP(c_COMBC(X6099,tc_fun(X6098,tc_HOL_Obool),tc_fun(X6098,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6098,tc_HOL_Obool),tc_fun(tc_fun(X6098,tc_HOL_Obool),tc_fun(X6098,tc_HOL_Obool)),X6099),c_Groups_Ominus__class_Ominus(tc_fun(X6098,tc_HOL_Obool))),X6097)),X6096)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__extend__simps_I3_J])])])). 4.05/4.30 cnf(c_0_6221, 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_4988, c_0_4434])). 4.05/4.30 cnf(c_0_6222, 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_4989, c_0_4434])). 4.05/4.30 cnf(c_0_6223, 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_4990, c_0_4434])). 4.05/4.30 fof(c_0_6224, plain, ![X8965, X8966, X8967, X8968, X8969, X8970, X8971]:(~c_Fun_Oinj__on(X8971,X8970,X8969,c_Orderings_Otop__class_Otop(tc_fun(X8971,tc_HOL_Obool)))|(hAPP(hAPP(c_Map_Omap__of(X8971,X8968),X8967),X8966)!=hAPP(c_Option_Ooption_OSome(X8968),X8965)|hAPP(c_Option_Ooption_OSome(X8968),X8965)=hAPP(hAPP(c_Map_Omap__of(X8970,X8968),hAPP(hAPP(c_List_Omap(tc_prod(X8971,X8968),tc_prod(X8970,X8968)),hAPP(c_Product__Type_Oprod_Oprod__case(X8971,X8968,tc_prod(X8970,X8968)),hAPP(hAPP(c_COMBB(X8970,tc_fun(X8968,tc_prod(X8970,X8968)),X8971),c_Product__Type_OPair(X8970,X8968)),X8969))),X8967)),hAPP(X8969,X8966)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__mapk__SomeI])])). 4.05/4.30 cnf(c_0_6225, plain, (c_List_OtakeWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Orev(X1),hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X3)),X2))),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2)))), inference(rw,[status(thm)],[c_0_4991, c_0_4950])). 4.05/4.30 cnf(c_0_6226, 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_4992, c_0_4993]), ['final']). 4.05/4.30 cnf(c_0_6227, 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_4994])). 4.05/4.30 cnf(c_0_6228, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3))))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4995, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_6229, plain, ![X3262, X3263, X3264, X3265]:(~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X3265),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X3265))),X3264)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3263),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3265))),c_List_Otranspose(X3265,X3264))))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3262),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3265))),hAPP(c_List_Ofilter(tc_List_Olist(X3265),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X3265)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3263)),c_Nat_Osize__class_Osize(tc_List_Olist(X3265)))),X3264))))|hAPP(hAPP(c_List_Onth(X3265),hAPP(hAPP(c_List_Onth(tc_List_Olist(X3265)),c_List_Otranspose(X3265,X3264)),X3263)),X3262)=hAPP(hAPP(c_List_Onth(X3265),hAPP(hAPP(c_List_Onth(tc_List_Olist(X3265)),X3264),X3262)),X3263)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__nth__transpose__sorted])])])). 4.05/4.30 cnf(c_0_6230, 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_4931])). 4.05/4.30 cnf(c_0_6231, 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_4932])). 4.05/4.30 cnf(c_0_6232, 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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4996, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6233, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X5)),c_Groups_Ozero__class_Ozero(X4))),X3)=hAPP(X5,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_4983])). 4.05/4.30 cnf(c_0_6234, plain, (hAPP(X4,X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X5),hAPP(hAPP(c_COMBC(X1,X5,X5),hAPP(hAPP(c_COMBS(X1,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X1),c_If(X5)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))),X4)),c_Groups_Oone__class_Oone(X5))),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__mult(X5)), inference(split_conjunct,[status(thm)],[c_0_4981])). 4.05/4.30 fof(c_0_6235, plain, ![X7962, X7963, X7964, X7965, X7966, X7967, X7968, X7969, X7970]:(~c_Equiv__Relations_Oequiv(X7970,X7969,X7968)|(~c_Equiv__Relations_Oequiv(X7967,X7966,X7965)|(~c_Equiv__Relations_Ocongruent2(X7970,X7967,tc_fun(X7964,tc_HOL_Obool),X7968,X7965,X7963)|(~hBOOL(hAPP(hAPP(c_member(X7967),X7962),X7966))|c_Equiv__Relations_Ocongruent(X7970,tc_fun(X7964,tc_HOL_Obool),X7968,hAPP(hAPP(c_COMBB(tc_fun(X7967,tc_fun(X7964,tc_HOL_Obool)),tc_fun(X7964,tc_HOL_Obool),X7970),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7967,tc_fun(X7964,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7967,X7967,X7965),hAPP(hAPP(c_Set_Oinsert(X7967),X7962),c_Orderings_Obot__class_Obot(tc_fun(X7967,tc_HOL_Obool)))))),X7963)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_congruent2__implies__congruent__UN])])])). 4.05/4.30 cnf(c_0_6236, plain, (hAPP(hAPP(c_HOL_OLet(X2,X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))),hAPP(hAPP(c_COMBS(X2,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X2),c_Groups_Otimes__class_Otimes(X2)),hAPP(c_Groups_Otimes__class_Otimes(X2),X3))),c_COMBI(X2)))=hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[c_0_4997, c_0_4475])). 4.05/4.30 cnf(c_0_6237, 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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2))=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4998, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6238, 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_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))|~class_Rings_Olinordered__idom(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4999, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6239, 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,esk262_3(X2,X3,X1))),hAPP(X3,esk262_3(X2,X3,X1))))), inference(split_conjunct,[status(thm)],[c_0_5000])). 4.05/4.30 fof(c_0_6240, plain, ![X6879, X6880, X6881, X6882, X6883, X6884]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6884)),X6883)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6882)),X6881)))|c_Map_Omap__upds(X6884,X6882,X6880,hAPP(hAPP(c_List_Oappend(X6884),X6883),hAPP(hAPP(c_List_Olist_OCons(X6884),X6879),c_List_Olist_ONil(X6884))),X6881)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6884,tc_Option_Ooption(X6882)),c_Map_Omap__upds(X6884,X6882,X6880,X6883,X6881)),X6879),hAPP(c_Option_Ooption_OSome(X6882),hAPP(hAPP(c_List_Onth(X6882),X6881),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6884)),X6883))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upds__append1])])). 4.05/4.30 fof(c_0_6241, plain, ![X2839, X2840, X2841, X2842, X2843, X2844]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X2844,X2844)),hAPP(hAPP(c_Product__Type_OPair(X2844,X2844),X2843),X2842)),c_Transitive__Closure_Ortrancl(X2844,X2841)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2844),tc_List_Olist(X2844))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2844),tc_List_Olist(X2844)),X2840),X2839)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2844),c_List_Olistrel1(X2844,X2841))))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2844),tc_List_Olist(X2844))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2844),tc_List_Olist(X2844)),hAPP(hAPP(c_List_Olist_OCons(X2844),X2843),X2840)),hAPP(hAPP(c_List_Olist_OCons(X2844),X2842),X2839))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2844),c_List_Olistrel1(X2844,X2841)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__listrel1__ConsI2])])])). 4.05/4.30 cnf(c_0_6242, 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)),esk158_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),esk158_4(X2,X3,X4,X1)),X3))),X2)))), inference(split_conjunct,[status(thm)],[c_0_5001])). 4.05/4.30 cnf(c_0_6243, 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)),X2),X1)),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_4973])). 4.05/4.30 cnf(c_0_6244, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5002, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_6245, plain, ![X10764, X10765, X10766, X10767, X10768]:(~class_Groups_Oab__group__add(X10768)|hAPP(c_List_Omonoid__add__class_Olistsum(X10768),hAPP(hAPP(c_List_Omap(X10767,X10768),hAPP(hAPP(c_COMBS(X10767,X10768,X10768),hAPP(hAPP(c_COMBB(X10768,tc_fun(X10768,X10768),X10767),c_Groups_Ominus__class_Ominus(X10768)),X10766)),X10765)),X10764))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10768),hAPP(c_List_Omonoid__add__class_Olistsum(X10768),hAPP(hAPP(c_List_Omap(X10767,X10768),X10766),X10764))),hAPP(c_List_Omonoid__add__class_Olistsum(X10768),hAPP(hAPP(c_List_Omap(X10767,X10768),X10765),X10764)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__subtractf])])])). 4.05/4.30 fof(c_0_6246, plain, ![X15164, X15165, X15166, X15167, X15168]:(~class_Groups_Ocomm__monoid__add(X15168)|hAPP(c_List_Omonoid__add__class_Olistsum(X15168),hAPP(hAPP(c_List_Omap(X15167,X15168),hAPP(hAPP(c_COMBS(X15167,X15168,X15168),hAPP(hAPP(c_COMBB(X15168,tc_fun(X15168,X15168),X15167),c_Groups_Oplus__class_Oplus(X15168)),X15166)),X15165)),X15164))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15168),hAPP(c_List_Omonoid__add__class_Olistsum(X15168),hAPP(hAPP(c_List_Omap(X15167,X15168),X15166),X15164))),hAPP(c_List_Omonoid__add__class_Olistsum(X15168),hAPP(hAPP(c_List_Omap(X15167,X15168),X15165),X15164)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__addf])])])). 4.05/4.30 fof(c_0_6247, plain, ![X12727, X12728, X12729, X12730, X12731]:((hBOOL(hAPP(hAPP(c_member(X12730),esk392_5(X12727,X12728,X12729,X12730,X12731)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12730,tc_HOL_Obool)),X12729),X12728)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12730,X12731),X12727),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12730,tc_HOL_Obool)),X12729),X12728))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12731),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12730,X12731),X12727),X12729)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12730,X12731),X12727),X12728))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12730),X12728))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12730),X12729))|~class_Groups_Ocomm__monoid__mult(X12731))&(hAPP(X12727,esk392_5(X12727,X12728,X12729,X12730,X12731))!=c_Groups_Oone__class_Oone(X12731)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12730,X12731),X12727),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12730,tc_HOL_Obool)),X12729),X12728))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12731),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12730,X12731),X12727),X12729)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12730,X12731),X12727),X12728))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12730),X12728))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12730),X12729))|~class_Groups_Ocomm__monoid__mult(X12731))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod_Ounion__inter__neutral])])])])])). 4.05/4.30 fof(c_0_6248, plain, ![X10750, X10751, X10752, X10753, X10754]:((hBOOL(hAPP(hAPP(c_member(X10753),esk326_5(X10750,X10751,X10752,X10753,X10754)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10753,tc_HOL_Obool)),X10752),X10751)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10753,X10754),X10750),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10753,tc_HOL_Obool)),X10752),X10751))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10754),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10753,X10754),X10750),X10752)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10753,X10754),X10750),X10751))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10753),X10751))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10753),X10752))|~class_Groups_Ocomm__monoid__mult(X10754))&(hAPP(X10750,esk326_5(X10750,X10751,X10752,X10753,X10754))!=c_Groups_Oone__class_Oone(X10754)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10753,X10754),X10750),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10753,tc_HOL_Obool)),X10752),X10751))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10754),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10753,X10754),X10750),X10752)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10753,X10754),X10750),X10751))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10753),X10751))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10753),X10752))|~class_Groups_Ocomm__monoid__mult(X10754))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__Un__one])])])])])). 4.05/4.30 fof(c_0_6249, plain, ![X11777, X11778, X11779, X11780, X11781]:((hBOOL(hAPP(hAPP(c_member(X11780),esk366_5(X11777,X11778,X11779,X11780,X11781)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11780,tc_HOL_Obool)),X11779),X11778)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11780,X11781),X11777),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11780,tc_HOL_Obool)),X11779),X11778))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11781),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11780,X11781),X11777),X11779)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11780,X11781),X11777),X11778))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11780),X11778))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11780),X11779))|~class_Groups_Ocomm__monoid__add(X11781))&(c_Groups_Ozero__class_Ozero(X11781)!=hAPP(X11777,esk366_5(X11777,X11778,X11779,X11780,X11781))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11780,X11781),X11777),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11780,tc_HOL_Obool)),X11779),X11778))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11781),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11780,X11781),X11777),X11779)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11780,X11781),X11777),X11778))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11780),X11778))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11780),X11779))|~class_Groups_Ocomm__monoid__add(X11781))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__Un__zero])])])])])). 4.05/4.30 fof(c_0_6250, plain, ![X4896, X4897, X4898, X4899, X4900]:((hBOOL(hAPP(hAPP(c_member(X4899),esk150_5(X4896,X4897,X4898,X4899,X4900)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4899,tc_HOL_Obool)),X4898),X4897)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4899,X4900),X4896),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4899,tc_HOL_Obool)),X4898),X4897))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4900),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4899,X4900),X4896),X4898)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4899,X4900),X4896),X4897))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4899),X4897))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4899),X4898))|~class_Groups_Ocomm__monoid__add(X4900))&(c_Groups_Ozero__class_Ozero(X4900)!=hAPP(X4896,esk150_5(X4896,X4897,X4898,X4899,X4900))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4899,X4900),X4896),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4899,tc_HOL_Obool)),X4898),X4897))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4900),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4899,X4900),X4896),X4898)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4899,X4900),X4896),X4897))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4899),X4897))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4899),X4898))|~class_Groups_Ocomm__monoid__add(X4900))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum_Ounion__inter__neutral])])])])])). 4.05/4.30 cnf(c_0_6251, 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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[c_0_5003, c_0_4475])). 4.05/4.30 cnf(c_0_6252, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|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)],[c_0_5004, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_6253, plain, ![X8614, X8615, X8616, X8617, X8618, X8619, X8620, X8621]:((hBOOL(hAPP(hAPP(c_member(X8617),esk275_8(X8614,X8615,X8616,X8617,X8618,X8619,X8620,X8621)),X8616))|(~hBOOL(hAPP(hAPP(c_member(X8617),X8614),X8616))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8617,tc_fun(X8620,tc_HOL_Obool)),X8616),hAPP(hAPP(c_COMBB(tc_fun(X8621,tc_HOL_Obool),tc_fun(X8620,tc_HOL_Obool),X8617),c_Set_Oimage(X8621,X8620,X8619)),X8615))=hAPP(c_Set_Oimage(X8621,X8620,X8619),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8617,tc_fun(X8621,tc_HOL_Obool)),X8616),X8615)))|~c_Fun_Oinj__on(X8621,X8620,X8619,X8618))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8621,tc_HOL_Obool)),hAPP(X8615,esk275_8(X8614,X8615,X8616,X8617,X8618,X8619,X8620,X8621))),X8618))|(~hBOOL(hAPP(hAPP(c_member(X8617),X8614),X8616))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8617,tc_fun(X8620,tc_HOL_Obool)),X8616),hAPP(hAPP(c_COMBB(tc_fun(X8621,tc_HOL_Obool),tc_fun(X8620,tc_HOL_Obool),X8617),c_Set_Oimage(X8621,X8620,X8619)),X8615))=hAPP(c_Set_Oimage(X8621,X8620,X8619),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8617,tc_fun(X8621,tc_HOL_Obool)),X8616),X8615)))|~c_Fun_Oinj__on(X8621,X8620,X8619,X8618))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__INT])])])])])). 4.05/4.30 cnf(c_0_6254, plain, (X2=X3|c_List_Oconcat(X1,X2)!=c_List_Oconcat(X1,X3)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(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)))),esk257_3(X3,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_5005])). 4.05/4.30 cnf(c_0_6255, 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)))),esk75_3(X2,X3,X1)))|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)|c_List_Oconcat(X1,X2)!=c_List_Oconcat(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_5006])). 4.05/4.30 fof(c_0_6256, plain, ![X15582, X15583, X15584, X15585, X15586]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X15586,X15586)),hAPP(hAPP(c_Product__Type_OPair(X15586,X15586),X15585),esk469_5(X15582,X15583,X15584,X15585,X15586))),c_Transitive__Closure_Ortrancl(X15586,X15583)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X15586,X15586)),hAPP(hAPP(c_Product__Type_OPair(X15586,X15586),X15585),X15584)),c_Transitive__Closure_Ortrancl(X15586,X15583)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X15586,X15586)),hAPP(hAPP(c_Product__Type_OPair(X15586,X15586),X15585),X15584)),c_Transitive__Closure_Ortrancl(X15586,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15586,X15586),tc_HOL_Obool)),X15583),X15582)))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X15586,X15586)),hAPP(hAPP(c_Product__Type_OPair(X15586,X15586),esk469_5(X15582,X15583,X15584,X15585,X15586)),esk470_5(X15582,X15583,X15584,X15585,X15586))),X15582))|hBOOL(hAPP(hAPP(c_member(tc_prod(X15586,X15586)),hAPP(hAPP(c_Product__Type_OPair(X15586,X15586),X15585),X15584)),c_Transitive__Closure_Ortrancl(X15586,X15583)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X15586,X15586)),hAPP(hAPP(c_Product__Type_OPair(X15586,X15586),X15585),X15584)),c_Transitive__Closure_Ortrancl(X15586,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15586,X15586),tc_HOL_Obool)),X15583),X15582)))))&(esk470_5(X15582,X15583,X15584,X15585,X15586)!=esk469_5(X15582,X15583,X15584,X15585,X15586)|hBOOL(hAPP(hAPP(c_member(tc_prod(X15586,X15586)),hAPP(hAPP(c_Product__Type_OPair(X15586,X15586),X15585),X15584)),c_Transitive__Closure_Ortrancl(X15586,X15583)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X15586,X15586)),hAPP(hAPP(c_Product__Type_OPair(X15586,X15586),X15585),X15584)),c_Transitive__Closure_Ortrancl(X15586,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15586,X15586),tc_HOL_Obool)),X15583),X15582))))))), 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])])])])])). 4.05/4.30 cnf(c_0_6257, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5007, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6258, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5008, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_6259, plain, ![X7468, X7469, X7470, X7471, X7472]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X7472,X7472)),hAPP(hAPP(c_Product__Type_OPair(X7472,X7472),esk236_5(X7468,X7469,X7470,X7471,X7472)),X7470)),c_Transitive__Closure_Ortrancl(X7472,X7469)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X7472,X7472)),hAPP(hAPP(c_Product__Type_OPair(X7472,X7472),X7471),X7470)),c_Transitive__Closure_Ortrancl(X7472,X7469)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X7472,X7472)),hAPP(hAPP(c_Product__Type_OPair(X7472,X7472),X7471),X7470)),c_Transitive__Closure_Ortrancl(X7472,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7472,X7472),tc_HOL_Obool)),X7469),X7468)))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X7472,X7472)),hAPP(hAPP(c_Product__Type_OPair(X7472,X7472),esk237_5(X7468,X7469,X7470,X7471,X7472)),esk236_5(X7468,X7469,X7470,X7471,X7472))),X7468))|hBOOL(hAPP(hAPP(c_member(tc_prod(X7472,X7472)),hAPP(hAPP(c_Product__Type_OPair(X7472,X7472),X7471),X7470)),c_Transitive__Closure_Ortrancl(X7472,X7469)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X7472,X7472)),hAPP(hAPP(c_Product__Type_OPair(X7472,X7472),X7471),X7470)),c_Transitive__Closure_Ortrancl(X7472,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7472,X7472),tc_HOL_Obool)),X7469),X7468)))))&(esk236_5(X7468,X7469,X7470,X7471,X7472)!=esk237_5(X7468,X7469,X7470,X7471,X7472)|hBOOL(hAPP(hAPP(c_member(tc_prod(X7472,X7472)),hAPP(hAPP(c_Product__Type_OPair(X7472,X7472),X7471),X7470)),c_Transitive__Closure_Ortrancl(X7472,X7469)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X7472,X7472)),hAPP(hAPP(c_Product__Type_OPair(X7472,X7472),X7471),X7470)),c_Transitive__Closure_Ortrancl(X7472,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X7472,X7472),tc_HOL_Obool)),X7469),X7468))))))), 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])])])])])). 4.05/4.30 cnf(c_0_6260, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4))),X4))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),hAPP(hAPP(c_List_Otake(X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4))),X3))|hBOOL(hAPP(X5,hAPP(hAPP(c_List_Ozip(X2,X1),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_5009])). 4.05/4.30 cnf(c_0_6261, 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_5010, c_0_5011]), ['final']). 4.05/4.30 cnf(c_0_6262, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5012, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5013, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6264, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|~class_Groups_Omonoid__mult(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5014, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6265, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),X2)|~class_Groups_Omonoid__mult(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5015, c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6266, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))=hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5016, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4867]), ['final']). 4.05/4.30 cnf(c_0_6267, 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),c_Transitive__Closure_Ortrancl(X1,X4)),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),c_Transitive__Closure_Ortrancl(X1,X4)),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),c_Transitive__Closure_Ortrancl(X1,X4)),X4)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5017, c_0_5018]), c_0_5018]), c_0_5018])). 4.05/4.30 cnf(c_0_6268, 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_5019]), ['final']). 4.05/4.30 fof(c_0_6269, plain, ![X13348, X13349, X13350]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13350),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X13349))),c_List_Otranspose(X13349,X13348))))|hAPP(hAPP(c_List_Onth(tc_List_Olist(X13349)),c_List_Otranspose(X13349,X13348)),X13350)=hAPP(hAPP(c_List_Omap(tc_List_Olist(X13349),X13349),hAPP(hAPP(c_COMBC(tc_List_Olist(X13349),tc_Nat_Onat,X13349),c_List_Onth(X13349)),X13350)),hAPP(c_List_Ofilter(tc_List_Olist(X13349),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X13349)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13350)),c_Nat_Osize__class_Osize(tc_List_Olist(X13349)))),X13348))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__transpose])])])). 4.05/4.30 fof(c_0_6270, plain, ![X6657, X6658, X6659, X6660]:(((esk204_4(X6657,X6658,X6659,X6660)!=esk205_4(X6657,X6658,X6659,X6660)|(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6660),tc_List_Olist(X6660))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6660),tc_List_Olist(X6660)),X6658),X6657)),c_List_Olexord(X6660,X6659)))|X6657=X6658|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6660),tc_List_Olist(X6660))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6660),tc_List_Olist(X6660)),X6657),X6658)),c_List_Olexord(X6660,X6659)))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X6660,X6660)),hAPP(hAPP(c_Product__Type_OPair(X6660,X6660),esk205_4(X6657,X6658,X6659,X6660)),esk204_4(X6657,X6658,X6659,X6660))),X6659))|(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6660),tc_List_Olist(X6660))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6660),tc_List_Olist(X6660)),X6658),X6657)),c_List_Olexord(X6660,X6659)))|X6657=X6658|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6660),tc_List_Olist(X6660))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6660),tc_List_Olist(X6660)),X6657),X6658)),c_List_Olexord(X6660,X6659))))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X6660,X6660)),hAPP(hAPP(c_Product__Type_OPair(X6660,X6660),esk204_4(X6657,X6658,X6659,X6660)),esk205_4(X6657,X6658,X6659,X6660))),X6659))|(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6660),tc_List_Olist(X6660))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6660),tc_List_Olist(X6660)),X6658),X6657)),c_List_Olexord(X6660,X6659)))|X6657=X6658|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6660),tc_List_Olist(X6660))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6660),tc_List_Olist(X6660)),X6657),X6658)),c_List_Olexord(X6660,X6659)))))), 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])])])])])). 4.05/4.30 fof(c_0_6271, plain, ![X11545, X11546, X11547, X11548, X11549]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X11549,X11548),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X11547),X11546)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X11548))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11545),X11549),X11548),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),X11545),X11547)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11545),X11546)),X11548))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11545),X11546),X11548)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__nat__rel__mult1__eq])])])). 4.05/4.30 cnf(c_0_6272, 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_5020])). 4.05/4.30 cnf(c_0_6273, 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))), inference(split_conjunct,[status(thm)],[c_0_5021]), ['final']). 4.05/4.30 cnf(c_0_6274, 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_5022])). 4.05/4.30 fof(c_0_6275, plain, ![X6380, X6381, X6382, X6383, X6384, X6385]:(((X6382!=X6384|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6385,X6385)),hAPP(hAPP(c_Product__Type_OPair(X6385,X6385),X6383),X6381)),X6380))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6385),tc_List_Olist(X6385))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6385),tc_List_Olist(X6385)),hAPP(hAPP(c_List_Oappend(X6385),X6384),hAPP(hAPP(c_List_Olist_OCons(X6385),X6383),c_List_Olist_ONil(X6385)))),hAPP(hAPP(c_List_Oappend(X6385),X6382),hAPP(hAPP(c_List_Olist_OCons(X6385),X6381),c_List_Olist_ONil(X6385))))),c_List_Olistrel1(X6385,X6380))))&(X6383!=X6381|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6385),tc_List_Olist(X6385))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6385),tc_List_Olist(X6385)),X6384),X6382)),c_List_Olistrel1(X6385,X6380)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6385),tc_List_Olist(X6385))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6385),tc_List_Olist(X6385)),hAPP(hAPP(c_List_Oappend(X6385),X6384),hAPP(hAPP(c_List_Olist_OCons(X6385),X6383),c_List_Olist_ONil(X6385)))),hAPP(hAPP(c_List_Oappend(X6385),X6382),hAPP(hAPP(c_List_Olist_OCons(X6385),X6381),c_List_Olist_ONil(X6385))))),c_List_Olistrel1(X6385,X6380)))))&(((X6383=X6381|X6382=X6384|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6385),tc_List_Olist(X6385))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6385),tc_List_Olist(X6385)),hAPP(hAPP(c_List_Oappend(X6385),X6384),hAPP(hAPP(c_List_Olist_OCons(X6385),X6383),c_List_Olist_ONil(X6385)))),hAPP(hAPP(c_List_Oappend(X6385),X6382),hAPP(hAPP(c_List_Olist_OCons(X6385),X6381),c_List_Olist_ONil(X6385))))),c_List_Olistrel1(X6385,X6380))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6385),tc_List_Olist(X6385))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6385),tc_List_Olist(X6385)),X6384),X6382)),c_List_Olistrel1(X6385,X6380)))|X6382=X6384|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6385),tc_List_Olist(X6385))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6385),tc_List_Olist(X6385)),hAPP(hAPP(c_List_Oappend(X6385),X6384),hAPP(hAPP(c_List_Olist_OCons(X6385),X6383),c_List_Olist_ONil(X6385)))),hAPP(hAPP(c_List_Oappend(X6385),X6382),hAPP(hAPP(c_List_Olist_OCons(X6385),X6381),c_List_Olist_ONil(X6385))))),c_List_Olistrel1(X6385,X6380)))))&((X6383=X6381|hBOOL(hAPP(hAPP(c_member(tc_prod(X6385,X6385)),hAPP(hAPP(c_Product__Type_OPair(X6385,X6385),X6383),X6381)),X6380))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6385),tc_List_Olist(X6385))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6385),tc_List_Olist(X6385)),hAPP(hAPP(c_List_Oappend(X6385),X6384),hAPP(hAPP(c_List_Olist_OCons(X6385),X6383),c_List_Olist_ONil(X6385)))),hAPP(hAPP(c_List_Oappend(X6385),X6382),hAPP(hAPP(c_List_Olist_OCons(X6385),X6381),c_List_Olist_ONil(X6385))))),c_List_Olistrel1(X6385,X6380))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6385),tc_List_Olist(X6385))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6385),tc_List_Olist(X6385)),X6384),X6382)),c_List_Olistrel1(X6385,X6380)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X6385,X6385)),hAPP(hAPP(c_Product__Type_OPair(X6385,X6385),X6383),X6381)),X6380))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6385),tc_List_Olist(X6385))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6385),tc_List_Olist(X6385)),hAPP(hAPP(c_List_Oappend(X6385),X6384),hAPP(hAPP(c_List_Olist_OCons(X6385),X6383),c_List_Olist_ONil(X6385)))),hAPP(hAPP(c_List_Oappend(X6385),X6382),hAPP(hAPP(c_List_Olist_OCons(X6385),X6381),c_List_Olist_ONil(X6385))))),c_List_Olistrel1(X6385,X6380))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__listrel1__snoc__iff])])])). 4.05/4.30 fof(c_0_6276, plain, ![X15294, X15295, X15296, X15297, X15298, X15299, X15300, X15301]:((hBOOL(hAPP(hAPP(c_member(X15300),esk461_7(X15294,X15295,X15296,X15297,X15298,X15299,X15300)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15300,tc_HOL_Obool)),X15295),X15294)))|hAPP(hAPP(X15299,hAPP(X15296,X15295)),hAPP(X15296,X15294))=hAPP(X15296,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15300,tc_HOL_Obool)),X15295),X15294))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15300),X15294))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15300),X15295))|~c_Finite__Set_Ofolding__image__simple(X15301,X15300,X15299,X15298,X15297,X15296))&(X15298!=hAPP(X15297,esk461_7(X15294,X15295,X15296,X15297,X15298,X15299,X15300))|hAPP(hAPP(X15299,hAPP(X15296,X15295)),hAPP(X15296,X15294))=hAPP(X15296,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15300,tc_HOL_Obool)),X15295),X15294))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15300),X15294))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15300),X15295))|~c_Finite__Set_Ofolding__image__simple(X15301,X15300,X15299,X15298,X15297,X15296))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Ounion__inter__neutral])])])])])])])). 4.05/4.30 fof(c_0_6277, plain, ![X1901, X1902, X1903]:(~class_Orderings_Olinorder(X1903)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1903),X1902))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1903),X1901))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1903,tc_HOL_Obool)),X1902),X1901)=c_Orderings_Obot__class_Obot(tc_fun(X1903,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1903),c_Big__Operators_Olattice_OSup__fin(X1903,c_Orderings_Oord__class_Omax(X1903),X1902)),c_Big__Operators_Olattice_OSup__fin(X1903,c_Orderings_Oord__class_Omax(X1903),X1901))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1903),c_Big__Operators_Olattice_OSup__fin(X1903,c_Orderings_Oord__class_Omax(X1903),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1903,tc_HOL_Obool)),X1902),X1901))),c_Big__Operators_Olattice_OSup__fin(X1903,c_Orderings_Oord__class_Omax(X1903),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1903,tc_HOL_Obool)),X1902),X1901))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Ounion__inter])])])). 4.05/4.30 cnf(c_0_6278, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(c_fequal,X2))),X5)),c_Groups_Ozero__class_Ozero(X4))),X3)=c_Groups_Ozero__class_Ozero(X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__add(X4)), inference(split_conjunct,[status(thm)],[c_0_5023])). 4.05/4.30 cnf(c_0_6279, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|c_Groups_Oone__class_Oone(X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),hAPP(hAPP(c_COMBC(X1,X4,X4),hAPP(hAPP(c_COMBS(X1,X4,tc_fun(X4,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1),c_If(X4)),hAPP(c_fequal,X2))),X5)),c_Groups_Oone__class_Oone(X4))),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__mult(X4)), inference(split_conjunct,[status(thm)],[c_0_5024])). 4.05/4.30 fof(c_0_6280, plain, ![X10137, X10138, X10139, X10140, X10141]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X10141,X10140),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X10139),X10138)))|(X10140=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X10137),X10141),X10140),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),X10137),X10139)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X10137),X10138)),X10140))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X10137),X10138),X10140)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult1__lemma])])). 4.05/4.30 cnf(c_0_6281, plain, (hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4)=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~c_Equiv__Relations_Oequiv(X1,X5,X4)), inference(split_conjunct,[status(thm)],[c_0_5025])). 4.05/4.30 cnf(c_0_6282, 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_5026]), ['final']). 4.05/4.30 cnf(c_0_6283, 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_5026]), ['final']). 4.05/4.30 fof(c_0_6284, plain, ![X8626, X8627, X8628, X8629, X8630]:(~class_Groups_Ocomm__monoid__mult(X8630)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8629),X8628))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8629),X8627))|(c_Orderings_Obot__class_Obot(tc_fun(X8629,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8629,tc_HOL_Obool)),X8628),X8627)|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8630,X8629,c_Groups_Otimes__class_Otimes(X8630)),X8626),c_Groups_Oone__class_Oone(X8630)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8629,tc_HOL_Obool)),X8628),X8627))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8630),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8630,X8629,c_Groups_Otimes__class_Otimes(X8630)),X8626),c_Groups_Oone__class_Oone(X8630)),X8628)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8630,X8629,c_Groups_Otimes__class_Otimes(X8630)),X8626),c_Groups_Oone__class_Oone(X8630)),X8627)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__Un__disjoint])])])). 4.05/4.30 fof(c_0_6285, plain, ![X15923]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X15923))|(X15923=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))),X15923)),c_FunDef_Omax__strict)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_smax__emptyI])])])). 4.05/4.30 fof(c_0_6286, plain, ![X2208, X2209, X2210]:(~class_Orderings_Olinorder(X2210)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2210),X2209))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2210),X2208))|(c_Orderings_Obot__class_Obot(tc_fun(X2210,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2210,tc_HOL_Obool)),X2209),X2208)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X2210),c_Big__Operators_Olattice_OInf__fin(X2210,c_Orderings_Oord__class_Omin(X2210),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2210,tc_HOL_Obool)),X2209),X2208))),c_Big__Operators_Olattice_OInf__fin(X2210,c_Orderings_Oord__class_Omin(X2210),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2210,tc_HOL_Obool)),X2209),X2208)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X2210),c_Big__Operators_Olattice_OInf__fin(X2210,c_Orderings_Oord__class_Omin(X2210),X2209)),c_Big__Operators_Olattice_OInf__fin(X2210,c_Orderings_Oord__class_Omin(X2210),X2208)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Ounion__inter])])])). 4.05/4.30 fof(c_0_6287, plain, ![X8951, X8952, X8953, X8954, X8955]:(~class_Groups_Oab__group__add(X8955)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8954),X8953))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8954),X8952))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8955),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8955),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8954,X8955),X8951),X8953)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8954,X8955),X8951),X8952))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8954,X8955),X8951),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8954,tc_HOL_Obool)),X8953),X8952)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8954,X8955),X8951),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8954,tc_HOL_Obool)),X8953),X8952))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__Un])])])). 4.05/4.30 cnf(c_0_6288, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),X5))))|c_Map_Omap__upds(X1,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),X6),X2),hAPP(c_Option_Ooption_OSome(X3),X7)),X5,X4)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),c_Map_Omap__upds(X1,X3,X6,X5,X4)),X2),hAPP(c_Option_Ooption_OSome(X3),X7))), inference(split_conjunct,[status(thm)],[c_0_5027])). 4.05/4.30 cnf(c_0_6289, plain, (c_Map_Omap__upds(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)),X6,X7)=c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X6),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X7))), inference(split_conjunct,[status(thm)],[c_0_5028]), ['final']). 4.05/4.30 cnf(c_0_6290, 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_Olexord(X1,X5)))|hAPP(hAPP(c_List_Otake(X1),X2),X3)!=hAPP(hAPP(c_List_Otake(X1),X2),X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X4),X2)),hAPP(hAPP(c_List_Onth(X1),X3),X2))),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(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))))), inference(split_conjunct,[status(thm)],[c_0_5029])). 4.05/4.30 fof(c_0_6291, plain, ![X4484, X4485, X4486, X4487, X4489]:((hBOOL(hAPP(hAPP(c_member(X4487),esk140_4(X4484,X4485,X4486,X4487)),X4486))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X4487,tc_HOL_Obool),tc_fun(X4487,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4487,tc_HOL_Obool),tc_fun(X4487,tc_HOL_Obool)),X4486),X4485)),c_Wellfounded_Omax__ext(X4487,X4484)))|c_Orderings_Obot__class_Obot(tc_fun(X4487,tc_HOL_Obool))=X4485|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4487),X4485))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4487),X4486)))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4487,X4487)),hAPP(hAPP(c_Product__Type_OPair(X4487,X4487),esk140_4(X4484,X4485,X4486,X4487)),X4489)),X4484))|~hBOOL(hAPP(hAPP(c_member(X4487),X4489),X4485))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X4487,tc_HOL_Obool),tc_fun(X4487,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X4487,tc_HOL_Obool),tc_fun(X4487,tc_HOL_Obool)),X4486),X4485)),c_Wellfounded_Omax__ext(X4487,X4484)))|c_Orderings_Obot__class_Obot(tc_fun(X4487,tc_HOL_Obool))=X4485|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4487),X4485))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4487),X4486)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_max__ext_Ointros])])])])])])). 4.05/4.30 fof(c_0_6292, plain, ![X732, X733, X734, X735, X736, X737, X738]:(~hBOOL(hAPP(X738,X737))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X736,X736)),hAPP(hAPP(c_Product__Type_OPair(X736,X736),X735),X734)),hAPP(X733,X737)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X732,X736),tc_prod(X732,X736))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X732,X736),tc_prod(X732,X736)),hAPP(hAPP(c_Product__Type_OPair(X732,X736),X737),X735)),hAPP(hAPP(c_Product__Type_OPair(X732,X736),X737),X734))),c_Recdef_Osame__fst(X732,X736,X738,X733))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_same__fstI])])])). 4.05/4.30 cnf(c_0_6293, 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_5030])). 4.05/4.30 cnf(c_0_6294, 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),esk508_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_5029])). 4.05/4.30 cnf(c_0_6295, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5031, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6296, plain, (hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Otimes__class_Otimes(X1)),c_COMBI(X1)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X3)),X3)),c_Int_OMin)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5032, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.30 fof(c_0_6297, plain, ![X13398, X13399, X13400, X13401, X13402, X13403]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13403,X13403)),hAPP(hAPP(c_Product__Type_OPair(X13403,X13403),X13402),X13401)),X13400))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13403,X13403)),hAPP(hAPP(c_Product__Type_OPair(X13403,X13403),X13401),X13399)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X13403,X13403),tc_HOL_Obool),X13398),X13400)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X13403,X13403)),hAPP(hAPP(c_Product__Type_OPair(X13403,X13403),X13402),X13399)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X13403,X13403),tc_HOL_Obool),hAPP(c_Nat_OSuc,X13398)),X13400))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__I2])])])). 4.05/4.30 fof(c_0_6298, plain, ![X2294, X2295, X2296, X2297, X2298, X2299]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X2299,X2299)),hAPP(hAPP(c_Product__Type_OPair(X2299,X2299),X2298),X2297)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2299,X2299),tc_HOL_Obool),X2296),X2295)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X2299,X2299)),hAPP(hAPP(c_Product__Type_OPair(X2299,X2299),X2297),X2294)),X2295))|hBOOL(hAPP(hAPP(c_member(tc_prod(X2299,X2299)),hAPP(hAPP(c_Product__Type_OPair(X2299,X2299),X2298),X2294)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2299,X2299),tc_HOL_Obool),hAPP(c_Nat_OSuc,X2296)),X2295))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__I])])])). 4.05/4.30 cnf(c_0_6299, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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_5033])). 4.05/4.30 cnf(c_0_6300, plain, (c_Enum_Oenum__the(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))=c_Divides_Odivmod__nat(X1,X2)), inference(rw,[status(thm)],[c_0_5034, c_0_4980])). 4.05/4.30 cnf(c_0_6301, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5035, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_6302, plain, ![X7441, X7442, X7443, X7444, X7445]:(~class_Groups_Ocomm__monoid__add(X7445)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7445),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X7445,tc_Nat_Onat),X7444),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X7442))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X7443),X7441))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X7445),X7444),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7443),X7442)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7441),X7442)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__shift__bounds__nat__ivl])])])). 4.05/4.30 cnf(c_0_6303, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5036, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6304, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_5037])). 4.05/4.30 cnf(c_0_6305, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))|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)],[c_0_5038, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_6306, plain, ![X5113, X5114, X5115, X5116, X5117]:(~class_Groups_Ocomm__monoid__mult(X5117)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5116),X5115))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5116),X5114))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5117),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5116,X5117),X5113),X5115)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5116,X5117),X5113),X5114))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5117),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5116,X5117),X5113),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5116,tc_HOL_Obool)),X5115),X5114))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5116,X5117),X5113),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5116,tc_HOL_Obool)),X5115),X5114)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un__Int])])). 4.05/4.30 fof(c_0_6307, plain, ![X5912, X5913, X5914, X5915, X5916]:(~class_Groups_Ocomm__monoid__add(X5916)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5915),X5914))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5915),X5913))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5916),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5915,X5916),X5912),X5914)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5915,X5916),X5912),X5913))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5916),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5915,X5916),X5912),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5915,tc_HOL_Obool)),X5914),X5913))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5915,X5916),X5912),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5915,tc_HOL_Obool)),X5914),X5913)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__Un__Int])])])). 4.05/4.30 fof(c_0_6308, plain, ![X16613, X16614, X16615]:(~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X16615),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X16615))),X16614)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16613),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X16615))),X16614)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X16615))),hAPP(c_List_Ofilter(tc_List_Olist(X16615),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X16615)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16613)),c_Nat_Osize__class_Osize(tc_List_Olist(X16615)))),c_List_Otranspose(X16615,X16614)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16615)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X16615)),X16614),X16613)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transpose__column__length])])])). 4.05/4.30 cnf(c_0_6309, 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),X1),X5))),c_Wellfounded_Olex__prod(X7,X3,X8,X6)))|X1!=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),X6))), inference(split_conjunct,[status(thm)],[c_0_5039])). 4.05/4.30 fof(c_0_6310, plain, ![X8130, X8131, X8132, X8133]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8133),X8132))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8133),X8131))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8133,tc_Nat_Onat),X8130),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8133,tc_HOL_Obool)),X8132),X8131))=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(X8133,tc_Nat_Onat),X8130),X8132)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8133,tc_Nat_Onat),X8130),X8131))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8133,tc_Nat_Onat),X8130),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8133,tc_HOL_Obool)),X8132),X8131))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__Un__nat])])])). 4.05/4.30 cnf(c_0_6311, 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),c_Transitive__Closure_Ortrancl(X1,X4)),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),c_Transitive__Closure_Ortrancl(X1,X4)),X4)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5040, c_0_5018]), c_0_5018])). 4.05/4.30 cnf(c_0_6312, 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),c_Transitive__Closure_Ortrancl(X1,X4)),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),c_Transitive__Closure_Ortrancl(X1,X4)),X4)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5041, c_0_5018]), c_0_5018])). 4.05/4.30 fof(c_0_6313, plain, ![X17466, X17467, X17468, X17469, X17470, X17471, X17472, X17473]:((hBOOL(hAPP(hAPP(c_member(X17473),esk523_8(X17466,X17467,X17468,X17469,X17470,X17471,X17472,X17473)),hAPP(c_List_Oset(X17473),X17472)))|hAPP(X17468,hAPP(c_List_Ofoldl(X17470,X17473,hAPP(c_COMBC(X17473,X17470,X17470),X17467),X17466),X17472))=hAPP(c_List_Ofoldl(X17471,X17473,hAPP(c_COMBC(X17473,X17471,X17471),X17469),hAPP(X17468,X17466)),X17472))&(hAPP(c_Fun_Ocomp(X17471,X17471,X17470,hAPP(X17469,esk523_8(X17466,X17467,X17468,X17469,X17470,X17471,X17472,X17473))),X17468)!=hAPP(c_Fun_Ocomp(X17470,X17471,X17470,X17468),hAPP(X17467,esk523_8(X17466,X17467,X17468,X17469,X17470,X17471,X17472,X17473)))|hAPP(X17468,hAPP(c_List_Ofoldl(X17470,X17473,hAPP(c_COMBC(X17473,X17470,X17470),X17467),X17466),X17472))=hAPP(c_List_Ofoldl(X17471,X17473,hAPP(c_COMBC(X17473,X17471,X17471),X17469),hAPP(X17468,X17466)),X17472))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_foldl__apply])])])])])). 4.05/4.30 fof(c_0_6314, plain, ![X14444, X14445, X14446, X14447, X14448, X14449]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X14449,X14449)),hAPP(hAPP(c_Product__Type_OPair(X14449,X14449),X14448),X14447)),X14446))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14449),tc_List_Olist(X14449))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14449),tc_List_Olist(X14449)),X14445),X14444)),c_List_Olistrel(X14449,X14446)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14449),tc_List_Olist(X14449))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14449),tc_List_Olist(X14449)),hAPP(hAPP(c_List_Olist_OCons(X14449),X14448),X14445)),hAPP(hAPP(c_List_Olist_OCons(X14449),X14447),X14444))),c_List_Olistrel(X14449,X14446))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel_OCons])])])). 4.05/4.30 cnf(c_0_6315, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Osemiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5042, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6316, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Osemiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5043, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6317, 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_5044, c_0_4655]), c_0_4655])). 4.05/4.30 cnf(c_0_6318, plain, (X2=X3|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk257_3(X3,X2,X1)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3))))|c_List_Oconcat(X1,X2)!=c_List_Oconcat(X1,X3)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)), inference(split_conjunct,[status(thm)],[c_0_5005])). 4.05/4.30 cnf(c_0_6319, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk75_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))),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)|c_List_Oconcat(X1,X2)!=c_List_Oconcat(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_5006])). 4.05/4.30 cnf(c_0_6320, 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_4961])). 4.05/4.30 fof(c_0_6321, plain, ![X6106, X6107, X6108, X6109, X6110]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6110),tc_List_Olist(X6110))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6110),tc_List_Olist(X6110)),X6109),X6108)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X6110),c_List_Olistrel1(X6110,X6107))))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6110),tc_List_Olist(X6110))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6110),tc_List_Olist(X6110)),hAPP(hAPP(c_List_Olist_OCons(X6110),X6106),X6109)),hAPP(hAPP(c_List_Olist_OCons(X6110),X6106),X6108))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X6110),c_List_Olistrel1(X6110,X6107))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__listrel1__ConsI1])])])). 4.05/4.30 fof(c_0_6322, plain, ![X12206, X12207, X12208, X12209, X12210]:(~c_Equiv__Relations_Oequiv(X12210,X12209,X12208)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X12210,X12210)),hAPP(hAPP(c_Product__Type_OPair(X12210,X12210),X12207),X12206)),X12208))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12210,tc_HOL_Obool)),hAPP(c_Relation_OImage(X12210,X12210,X12208),hAPP(hAPP(c_Set_Oinsert(X12210),X12207),c_Orderings_Obot__class_Obot(tc_fun(X12210,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X12210,X12210,X12208),hAPP(hAPP(c_Set_Oinsert(X12210),X12206),c_Orderings_Obot__class_Obot(tc_fun(X12210,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equiv__class__subset])])])). 4.05/4.30 cnf(c_0_6323, 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),esk508_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_5029])). 4.05/4.30 fof(c_0_6324, plain, ![X8037, X8038, X8039, X8040, X8041]:(~class_Groups_Ocomm__monoid__add(X8041)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X8041),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X8041,tc_Nat_Onat),X8040),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X8038))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X8039,X8037))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X8041),X8040),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8039),X8038),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8037),X8038)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__nat__ivl])])). 4.05/4.30 cnf(c_0_6325, 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),c_Transitive__Closure_Ortrancl(X1,X4)),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),c_Transitive__Closure_Ortrancl(X1,X4)),X4)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5045, c_0_5018]), c_0_5018])). 4.05/4.30 cnf(c_0_6326, 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),c_Transitive__Closure_Ortrancl(X1,X4)),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),c_Transitive__Closure_Ortrancl(X1,X4)),X4)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5046, c_0_5018]), c_0_5018])). 4.05/4.30 fof(c_0_6327, plain, ![X5628, X5629, X5630, X5631, X5632]:(((hAPP(c_Nat_OSuc,esk176_5(X5628,X5629,X5630,X5631,X5632))=X5629|X5629=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5632,X5632)),hAPP(hAPP(c_Product__Type_OPair(X5632,X5632),X5631),X5630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5632,X5632),tc_HOL_Obool),X5629),X5628))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X5632,X5632)),hAPP(hAPP(c_Product__Type_OPair(X5632,X5632),X5631),esk175_5(X5628,X5629,X5630,X5631,X5632))),X5628))|X5629=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5632,X5632)),hAPP(hAPP(c_Product__Type_OPair(X5632,X5632),X5631),X5630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5632,X5632),tc_HOL_Obool),X5629),X5628))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X5632,X5632)),hAPP(hAPP(c_Product__Type_OPair(X5632,X5632),esk175_5(X5628,X5629,X5630,X5631,X5632)),X5630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5632,X5632),tc_HOL_Obool),esk176_5(X5628,X5629,X5630,X5631,X5632)),X5628)))|X5629=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5632,X5632)),hAPP(hAPP(c_Product__Type_OPair(X5632,X5632),X5631),X5630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5632,X5632),tc_HOL_Obool),X5629),X5628))))))&((hAPP(c_Nat_OSuc,esk176_5(X5628,X5629,X5630,X5631,X5632))=X5629|X5631=X5630|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5632,X5632)),hAPP(hAPP(c_Product__Type_OPair(X5632,X5632),X5631),X5630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5632,X5632),tc_HOL_Obool),X5629),X5628))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X5632,X5632)),hAPP(hAPP(c_Product__Type_OPair(X5632,X5632),X5631),esk175_5(X5628,X5629,X5630,X5631,X5632))),X5628))|X5631=X5630|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5632,X5632)),hAPP(hAPP(c_Product__Type_OPair(X5632,X5632),X5631),X5630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5632,X5632),tc_HOL_Obool),X5629),X5628))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X5632,X5632)),hAPP(hAPP(c_Product__Type_OPair(X5632,X5632),esk175_5(X5628,X5629,X5630,X5631,X5632)),X5630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5632,X5632),tc_HOL_Obool),esk176_5(X5628,X5629,X5630,X5631,X5632)),X5628)))|X5631=X5630|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5632,X5632)),hAPP(hAPP(c_Product__Type_OPair(X5632,X5632),X5631),X5630)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5632,X5632),tc_HOL_Obool),X5629),X5628))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__E2])])])])])). 4.05/4.30 fof(c_0_6328, plain, ![X13234, X13235, X13236, X13237, X13238, X13239, X13240]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13240,X13240)),hAPP(hAPP(c_Product__Type_OPair(X13240,X13240),X13239),X13238)),X13237))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X13240),tc_List_Olist(X13240))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X13240),tc_List_Olist(X13240)),hAPP(hAPP(c_List_Oappend(X13240),X13236),hAPP(hAPP(c_List_Olist_OCons(X13240),X13239),X13235))),hAPP(hAPP(c_List_Oappend(X13240),X13236),hAPP(hAPP(c_List_Olist_OCons(X13240),X13238),X13234)))),c_List_Olexord(X13240,X13237)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__left__rightI])])). 4.05/4.30 cnf(c_0_6329, plain, (hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2),c_fNot),hAPP(c_fequal,hAPP(X3,X4)))),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))=hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X4))),X5))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5047, c_0_4655]), c_0_4655])). 4.05/4.30 fof(c_0_6330, plain, ![X12627, X12628, X12629, X12630, X12631]:(((hAPP(c_Nat_OSuc,esk389_5(X12627,X12628,X12629,X12630,X12631))=X12628|X12628=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X12631,X12631)),hAPP(hAPP(c_Product__Type_OPair(X12631,X12631),X12630),X12629)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X12631,X12631),tc_HOL_Obool),X12628),X12627))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X12631,X12631)),hAPP(hAPP(c_Product__Type_OPair(X12631,X12631),X12630),esk388_5(X12627,X12628,X12629,X12630,X12631))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X12631,X12631),tc_HOL_Obool),esk389_5(X12627,X12628,X12629,X12630,X12631)),X12627)))|X12628=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X12631,X12631)),hAPP(hAPP(c_Product__Type_OPair(X12631,X12631),X12630),X12629)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X12631,X12631),tc_HOL_Obool),X12628),X12627))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X12631,X12631)),hAPP(hAPP(c_Product__Type_OPair(X12631,X12631),esk388_5(X12627,X12628,X12629,X12630,X12631)),X12629)),X12627))|X12628=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X12631,X12631)),hAPP(hAPP(c_Product__Type_OPair(X12631,X12631),X12630),X12629)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X12631,X12631),tc_HOL_Obool),X12628),X12627))))))&((hAPP(c_Nat_OSuc,esk389_5(X12627,X12628,X12629,X12630,X12631))=X12628|X12629=X12630|~hBOOL(hAPP(hAPP(c_member(tc_prod(X12631,X12631)),hAPP(hAPP(c_Product__Type_OPair(X12631,X12631),X12630),X12629)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X12631,X12631),tc_HOL_Obool),X12628),X12627))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X12631,X12631)),hAPP(hAPP(c_Product__Type_OPair(X12631,X12631),X12630),esk388_5(X12627,X12628,X12629,X12630,X12631))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X12631,X12631),tc_HOL_Obool),esk389_5(X12627,X12628,X12629,X12630,X12631)),X12627)))|X12629=X12630|~hBOOL(hAPP(hAPP(c_member(tc_prod(X12631,X12631)),hAPP(hAPP(c_Product__Type_OPair(X12631,X12631),X12630),X12629)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X12631,X12631),tc_HOL_Obool),X12628),X12627))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X12631,X12631)),hAPP(hAPP(c_Product__Type_OPair(X12631,X12631),esk388_5(X12627,X12628,X12629,X12630,X12631)),X12629)),X12627))|X12629=X12630|~hBOOL(hAPP(hAPP(c_member(tc_prod(X12631,X12631)),hAPP(hAPP(c_Product__Type_OPair(X12631,X12631),X12630),X12629)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X12631,X12631),tc_HOL_Obool),X12628),X12627))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__E])])])])])). 4.05/4.30 fof(c_0_6331, plain, ![X8857, X8858, X8859]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8859),X8858))|(~c_Fun_Oinj__on(X8859,tc_fun(tc_fun(X8859,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X8859,tc_fun(tc_prod(X8859,X8859),tc_HOL_Obool),tc_fun(tc_fun(X8859,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8859,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X8859,X8859),tc_HOL_Obool),tc_fun(tc_fun(X8859,tc_HOL_Obool),tc_HOL_Obool)),X8859),c_Equiv__Relations_Oquotient(X8859)),hAPP(hAPP(c_COMBC(X8859,tc_fun(X8859,tc_HOL_Obool),tc_fun(X8859,tc_HOL_Obool)),c_Set_Oinsert(X8859)),c_Orderings_Obot__class_Obot(tc_fun(X8859,tc_HOL_Obool))))),X8857),X8858)|hAPP(c_Finite__Set_Ocard(X8859),X8858)=hAPP(c_Finite__Set_Ocard(tc_fun(X8859,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X8859),X8858),X8857)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__quotient__disjoint])])])). 4.05/4.30 fof(c_0_6332, plain, ![X12394, X12395, X12396, X12397]:((~hBOOL(hAPP(hAPP(c_member(X12396),X12394),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12397,tc_fun(X12396,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12397,tc_HOL_Obool))),X12395)))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12397,tc_fun(X12396,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12397,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X12396,tc_HOL_Obool),tc_fun(X12396,tc_HOL_Obool),X12397),hAPP(c_COMBC(X12396,tc_fun(X12396,tc_HOL_Obool),tc_HOL_Obool),c_member(X12396))),X12395)),X12394)))&(~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12397,tc_fun(X12396,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12397,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X12396,tc_HOL_Obool),tc_fun(X12396,tc_HOL_Obool),X12397),hAPP(c_COMBC(X12396,tc_fun(X12396,tc_HOL_Obool),tc_HOL_Obool),c_member(X12396))),X12395)),X12394))|hBOOL(hAPP(hAPP(c_member(X12396),X12394),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12397,tc_fun(X12396,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12397,tc_HOL_Obool))),X12395))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq])])). 4.05/4.30 fof(c_0_6333, plain, ![X6089, X6090, X6091, X6092]:((~hBOOL(hAPP(hAPP(c_member(X6091),X6089),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6092,tc_fun(X6091,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X6092,tc_HOL_Obool))),X6090)))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6092,tc_fun(X6091,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X6092,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X6091,tc_HOL_Obool),tc_fun(X6091,tc_HOL_Obool),X6092),hAPP(c_COMBC(X6091,tc_fun(X6091,tc_HOL_Obool),tc_HOL_Obool),c_member(X6091))),X6090)),X6089)))&(~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6092,tc_fun(X6091,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X6092,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X6091,tc_HOL_Obool),tc_fun(X6091,tc_HOL_Obool),X6092),hAPP(c_COMBC(X6091,tc_fun(X6091,tc_HOL_Obool),tc_HOL_Obool),c_member(X6091))),X6090)),X6089))|hBOOL(hAPP(hAPP(c_member(X6091),X6089),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6092,tc_fun(X6091,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X6092,tc_HOL_Obool))),X6090))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq])])). 4.05/4.30 fof(c_0_6334, plain, ![X16796, X16797, X16798, X16799, X16800]:(~class_Fields_Ofield__inverse__zero(X16800)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16799),X16798))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16799,X16800),hAPP(hAPP(c_COMBS(X16799,X16800,X16800),hAPP(hAPP(c_COMBB(X16800,tc_fun(X16800,X16800),X16799),c_Rings_Oinverse__class_Odivide(X16800)),X16797)),X16796)),X16798)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16800),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16799,X16800),X16797),X16798)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16799,X16800),X16796),X16798)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__dividef])])])). 4.05/4.30 fof(c_0_6335, plain, ![X335, X336, X337]:(~class_Lattices_Olattice(X337)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X337),X336))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X337),X335))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X337,tc_HOL_Obool)),X336),X335)=c_Orderings_Obot__class_Obot(tc_fun(X337,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X337),c_Big__Operators_Olattice__class_OSup__fin(X337,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X337,tc_HOL_Obool)),X336),X335))),c_Big__Operators_Olattice__class_OSup__fin(X337,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X337,tc_HOL_Obool)),X336),X335)))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X337),c_Big__Operators_Olattice__class_OSup__fin(X337,X336)),c_Big__Operators_Olattice__class_OSup__fin(X337,X335)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Ounion__inter])])])). 4.05/4.30 fof(c_0_6336, plain, ![X11231, X11232, X11233]:(~class_Orderings_Olinorder(X11233)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11233),X11232))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11233),X11231))|(c_Orderings_Obot__class_Obot(tc_fun(X11233,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11233,tc_HOL_Obool)),X11232),X11231)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X11233),c_Big__Operators_Olinorder__class_OMin(X11233,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11233,tc_HOL_Obool)),X11232),X11231))),c_Big__Operators_Olinorder__class_OMin(X11233,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11233,tc_HOL_Obool)),X11232),X11231)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X11233),c_Big__Operators_Olinorder__class_OMin(X11233,X11232)),c_Big__Operators_Olinorder__class_OMin(X11233,X11231)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Ounion__inter])])])). 4.05/4.30 fof(c_0_6337, plain, ![X16975, X16976, X16977]:(~class_Orderings_Olinorder(X16977)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16977),X16976))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16977),X16975))|(c_Orderings_Obot__class_Obot(tc_fun(X16977,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16977,tc_HOL_Obool)),X16976),X16975)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X16977),c_Big__Operators_Olinorder__class_OMax(X16977,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16977,tc_HOL_Obool)),X16976),X16975))),c_Big__Operators_Olinorder__class_OMax(X16977,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16977,tc_HOL_Obool)),X16976),X16975)))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X16977),c_Big__Operators_Olinorder__class_OMax(X16977,X16976)),c_Big__Operators_Olinorder__class_OMax(X16977,X16975)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Ounion__inter])])])). 4.05/4.30 fof(c_0_6338, plain, ![X12862, X12863, X12864]:(~class_Lattices_Olattice(X12864)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12864),X12863))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12864),X12862))|(c_Orderings_Obot__class_Obot(tc_fun(X12864,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12864,tc_HOL_Obool)),X12863),X12862)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12864),c_Big__Operators_Olattice__class_OInf__fin(X12864,X12863)),c_Big__Operators_Olattice__class_OInf__fin(X12864,X12862))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12864),c_Big__Operators_Olattice__class_OInf__fin(X12864,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12864,tc_HOL_Obool)),X12863),X12862))),c_Big__Operators_Olattice__class_OInf__fin(X12864,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12864,tc_HOL_Obool)),X12863),X12862))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Ounion__inter])])])). 4.05/4.30 cnf(c_0_6339, 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_5048, c_0_5049]), c_0_5050])). 4.05/4.30 cnf(c_0_6340, plain, (hAPP(X1,hAPP(X2,X3))=hAPP(hAPP(c_Fun_Ocomp(X4,X5,X6,X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_5051]), ['final']). 4.05/4.30 cnf(c_0_6341, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X8)),c_List_Olistrel1(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|X5!=hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X7))|X8!=hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X7))), inference(split_conjunct,[status(thm)],[c_0_5052])). 4.05/4.30 fof(c_0_6342, plain, ![X1220, X1221, X1222, X1223, X1224]:((hBOOL(hAPP(hAPP(c_member(X1223),esk34_5(X1220,X1221,X1222,X1223,X1224)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1223,tc_HOL_Obool)),X1222),X1221)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1224),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1223,X1224),X1220),X1221)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1223,X1224),X1220),X1222)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1223,tc_HOL_Obool)),X1221),X1222))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1223),X1222))|(~class_Groups_Oordered__ab__semigroup__add(X1224)|~class_Groups_Ocomm__monoid__add(X1224)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1224),c_Groups_Ozero__class_Ozero(X1224)),hAPP(X1220,esk34_5(X1220,X1221,X1222,X1223,X1224))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1224),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1223,X1224),X1220),X1221)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1223,X1224),X1220),X1222)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1223,tc_HOL_Obool)),X1221),X1222))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1223),X1222))|(~class_Groups_Oordered__ab__semigroup__add(X1224)|~class_Groups_Ocomm__monoid__add(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_setsum__mono3])])])])])). 4.05/4.30 cnf(c_0_6343, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk279_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_5053])). 4.05/4.30 cnf(c_0_6344, 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_5054, c_0_4434])). 4.05/4.30 cnf(c_0_6345, 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_5055, c_0_4434])). 4.05/4.30 fof(c_0_6346, plain, ![X637, X638, X639]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X638),hAPP(hAPP(c_COMBB(tc_fun(X639,tc_HOL_Obool),tc_HOL_Obool,X638),c_Enum_Oenum__class_Oenum__all(X639)),hAPP(hAPP(c_COMBB(tc_fun(X639,tc_prod(X638,X639)),tc_fun(X639,tc_HOL_Obool),X638),hAPP(c_COMBB(tc_prod(X638,X639),tc_HOL_Obool,X639),X637)),c_Product__Type_OPair(X638,X639)))))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X638,X639)),X637))|(~class_Enum_Oenum(X638)|~class_Enum_Oenum(X639)))&(~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X638,X639)),X637))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X638),hAPP(hAPP(c_COMBB(tc_fun(X639,tc_HOL_Obool),tc_HOL_Obool,X638),c_Enum_Oenum__class_Oenum__all(X639)),hAPP(hAPP(c_COMBB(tc_fun(X639,tc_prod(X638,X639)),tc_fun(X639,tc_HOL_Obool),X638),hAPP(c_COMBB(tc_prod(X638,X639),tc_HOL_Obool,X639),X637)),c_Product__Type_OPair(X638,X639)))))|(~class_Enum_Oenum(X638)|~class_Enum_Oenum(X639)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_enum__all__prod__def])])])])). 4.05/4.30 fof(c_0_6347, plain, ![X12654, X12655, X12656]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12656,tc_HOL_Obool)),X12655),hAPP(hAPP(c_Set_Oinsert(X12656),X12654),c_Orderings_Obot__class_Obot(tc_fun(X12656,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X12656,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X12656),X12654),c_Big__Operators_Olattice_OInf__fin(X12656,c_Orderings_Oord__class_Omin(X12656),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12656,tc_HOL_Obool)),X12655),hAPP(hAPP(c_Set_Oinsert(X12656),X12654),c_Orderings_Obot__class_Obot(tc_fun(X12656,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OInf__fin(X12656,c_Orderings_Oord__class_Omin(X12656),X12655)|~hBOOL(hAPP(hAPP(c_member(X12656),X12654),X12655))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12656),X12655))|~class_Orderings_Olinorder(X12656))&(c_Orderings_Obot__class_Obot(tc_fun(X12656,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12656,tc_HOL_Obool)),X12655),hAPP(hAPP(c_Set_Oinsert(X12656),X12654),c_Orderings_Obot__class_Obot(tc_fun(X12656,tc_HOL_Obool))))|c_Big__Operators_Olattice_OInf__fin(X12656,c_Orderings_Oord__class_Omin(X12656),X12655)=X12654|~hBOOL(hAPP(hAPP(c_member(X12656),X12654),X12655))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12656),X12655))|~class_Orderings_Olinorder(X12656))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oremove])])])])). 4.05/4.30 fof(c_0_6348, plain, ![X3897, X3898, X3899, X3900, X3901]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3901,X3900),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3899),X3898)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3900))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3897))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3901,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3900),X3897)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3899),X3897)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3900),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3899,X3897))),X3898))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult2__eq])])). 4.05/4.30 fof(c_0_6349, plain, ![X15800, X15801, X15802, X15803, X15804, X15805]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15802,tc_HOL_Obool)),X15801),X15800))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15802,X15805),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X15802,X15805),X15801),hAPP(c_COMBK(tc_fun(X15805,tc_HOL_Obool),X15802),X15803))),hAPP(hAPP(c_Product__Type_OSigma(X15802,X15805),X15800),hAPP(c_COMBK(tc_fun(X15805,tc_HOL_Obool),X15802),X15803))))|~hBOOL(hAPP(hAPP(c_member(X15805),X15804),X15803)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15802,X15805),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X15802,X15805),X15801),hAPP(c_COMBK(tc_fun(X15805,tc_HOL_Obool),X15802),X15803))),hAPP(hAPP(c_Product__Type_OSigma(X15802,X15805),X15800),hAPP(c_COMBK(tc_fun(X15805,tc_HOL_Obool),X15802),X15803))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15802,tc_HOL_Obool)),X15801),X15800))|~hBOOL(hAPP(hAPP(c_member(X15805),X15804),X15803)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Times__subset__cancel2])])])])). 4.05/4.30 fof(c_0_6350, plain, ![X6682, X6683, X6684]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X6683),hAPP(hAPP(c_COMBB(tc_fun(X6684,tc_HOL_Obool),tc_HOL_Obool,X6683),c_Enum_Oenum__class_Oenum__ex(X6684)),hAPP(hAPP(c_COMBB(tc_fun(X6684,tc_prod(X6683,X6684)),tc_fun(X6684,tc_HOL_Obool),X6683),hAPP(c_COMBB(tc_prod(X6683,X6684),tc_HOL_Obool,X6684),X6682)),c_Product__Type_OPair(X6683,X6684)))))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X6683,X6684)),X6682))|(~class_Enum_Oenum(X6683)|~class_Enum_Oenum(X6684)))&(~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X6683,X6684)),X6682))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X6683),hAPP(hAPP(c_COMBB(tc_fun(X6684,tc_HOL_Obool),tc_HOL_Obool,X6683),c_Enum_Oenum__class_Oenum__ex(X6684)),hAPP(hAPP(c_COMBB(tc_fun(X6684,tc_prod(X6683,X6684)),tc_fun(X6684,tc_HOL_Obool),X6683),hAPP(c_COMBB(tc_prod(X6683,X6684),tc_HOL_Obool,X6684),X6682)),c_Product__Type_OPair(X6683,X6684)))))|(~class_Enum_Oenum(X6683)|~class_Enum_Oenum(X6684)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_enum__ex__prod__def])])])])). 4.05/4.30 fof(c_0_6351, plain, ![X10066, X10067, X10068, X10069, X10070, X10071, X10072, X10073, X10074, X10075, X10076, X10077, X10078, X10079, X10080, X10081]:(((hAPP(hAPP(X10070,X10073),X10074)!=hAPP(hAPP(X10070,X10067),X10066)|~c_Nitpick_Ofold__graph_H(X10072,X10071,X10070,X10069,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10072,tc_HOL_Obool)),X10068),hAPP(hAPP(c_Set_Oinsert(X10072),X10073),c_Orderings_Obot__class_Obot(tc_fun(X10072,tc_HOL_Obool)))),X10074)|~hBOOL(hAPP(hAPP(c_member(X10072),X10073),X10068))|c_Nitpick_Ofold__graph_H(X10072,X10071,X10070,X10069,X10068,hAPP(hAPP(X10070,X10067),X10066)))&(X10068!=c_Orderings_Obot__class_Obot(tc_fun(X10072,tc_HOL_Obool))|hAPP(hAPP(X10070,X10067),X10066)!=X10069|c_Nitpick_Ofold__graph_H(X10072,X10071,X10070,X10069,X10068,hAPP(hAPP(X10070,X10067),X10066))))&((((X10077=c_Orderings_Obot__class_Obot(tc_fun(X10081,tc_HOL_Obool))|hAPP(hAPP(X10079,esk307_7(X10075,X10076,X10077,X10078,X10079,X10080,X10081)),esk308_7(X10075,X10076,X10077,X10078,X10079,X10080,X10081))=hAPP(hAPP(X10079,X10076),X10075)|~c_Nitpick_Ofold__graph_H(X10081,X10080,X10079,X10078,X10077,hAPP(hAPP(X10079,X10076),X10075)))&(hAPP(hAPP(X10079,X10076),X10075)=X10078|hAPP(hAPP(X10079,esk307_7(X10075,X10076,X10077,X10078,X10079,X10080,X10081)),esk308_7(X10075,X10076,X10077,X10078,X10079,X10080,X10081))=hAPP(hAPP(X10079,X10076),X10075)|~c_Nitpick_Ofold__graph_H(X10081,X10080,X10079,X10078,X10077,hAPP(hAPP(X10079,X10076),X10075))))&((X10077=c_Orderings_Obot__class_Obot(tc_fun(X10081,tc_HOL_Obool))|c_Nitpick_Ofold__graph_H(X10081,X10080,X10079,X10078,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10081,tc_HOL_Obool)),X10077),hAPP(hAPP(c_Set_Oinsert(X10081),esk307_7(X10075,X10076,X10077,X10078,X10079,X10080,X10081)),c_Orderings_Obot__class_Obot(tc_fun(X10081,tc_HOL_Obool)))),esk308_7(X10075,X10076,X10077,X10078,X10079,X10080,X10081))|~c_Nitpick_Ofold__graph_H(X10081,X10080,X10079,X10078,X10077,hAPP(hAPP(X10079,X10076),X10075)))&(hAPP(hAPP(X10079,X10076),X10075)=X10078|c_Nitpick_Ofold__graph_H(X10081,X10080,X10079,X10078,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10081,tc_HOL_Obool)),X10077),hAPP(hAPP(c_Set_Oinsert(X10081),esk307_7(X10075,X10076,X10077,X10078,X10079,X10080,X10081)),c_Orderings_Obot__class_Obot(tc_fun(X10081,tc_HOL_Obool)))),esk308_7(X10075,X10076,X10077,X10078,X10079,X10080,X10081))|~c_Nitpick_Ofold__graph_H(X10081,X10080,X10079,X10078,X10077,hAPP(hAPP(X10079,X10076),X10075)))))&((X10077=c_Orderings_Obot__class_Obot(tc_fun(X10081,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X10081),esk307_7(X10075,X10076,X10077,X10078,X10079,X10080,X10081)),X10077))|~c_Nitpick_Ofold__graph_H(X10081,X10080,X10079,X10078,X10077,hAPP(hAPP(X10079,X10076),X10075)))&(hAPP(hAPP(X10079,X10076),X10075)=X10078|hBOOL(hAPP(hAPP(c_member(X10081),esk307_7(X10075,X10076,X10077,X10078,X10079,X10080,X10081)),X10077))|~c_Nitpick_Ofold__graph_H(X10081,X10080,X10079,X10078,X10077,hAPP(hAPP(X10079,X10076),X10075)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Oequations_I2_J])])])])])])). 4.05/4.30 fof(c_0_6352, plain, ![X9791, X9792, X9793]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9793,tc_HOL_Obool)),X9792),hAPP(hAPP(c_Set_Oinsert(X9793),X9791),c_Orderings_Obot__class_Obot(tc_fun(X9793,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X9793,tc_HOL_Obool))|c_Big__Operators_Olattice_OSup__fin(X9793,c_Orderings_Oord__class_Omax(X9793),X9792)=X9791|~hBOOL(hAPP(hAPP(c_member(X9793),X9791),X9792))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9793),X9792))|~class_Orderings_Olinorder(X9793))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9793,tc_HOL_Obool)),X9792),hAPP(hAPP(c_Set_Oinsert(X9793),X9791),c_Orderings_Obot__class_Obot(tc_fun(X9793,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X9793,tc_HOL_Obool))|c_Big__Operators_Olattice_OSup__fin(X9793,c_Orderings_Oord__class_Omax(X9793),X9792)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X9793),X9791),c_Big__Operators_Olattice_OSup__fin(X9793,c_Orderings_Oord__class_Omax(X9793),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9793,tc_HOL_Obool)),X9792),hAPP(hAPP(c_Set_Oinsert(X9793),X9791),c_Orderings_Obot__class_Obot(tc_fun(X9793,tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(c_member(X9793),X9791),X9792))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9793),X9792))|~class_Orderings_Olinorder(X9793))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oremove])])])])). 4.05/4.30 fof(c_0_6353, plain, ![X10607, X10608, X10609, X10610, X10611]:((hBOOL(hAPP(hAPP(c_member(X10610),esk324_5(X10607,X10608,X10609,X10610,X10611)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10610,tc_HOL_Obool)),X10609),X10608)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10611),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10610,X10611),X10607),X10608)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10610,X10611),X10607),X10609)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10610,tc_HOL_Obool)),X10608),X10609))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10610),X10609))|~class_Groups_Oordered__comm__monoid__add(X10611))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10611),c_Groups_Ozero__class_Ozero(X10611)),hAPP(X10607,esk324_5(X10607,X10608,X10609,X10610,X10611))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10611),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10610,X10611),X10607),X10608)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10610,X10611),X10607),X10609)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10610,tc_HOL_Obool)),X10608),X10609))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10610),X10609))|~class_Groups_Oordered__comm__monoid__add(X10611))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__mono2])])])])])). 4.05/4.30 cnf(c_0_6354, 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_5056])). 4.05/4.30 fof(c_0_6355, plain, ![X10693]:(X10693=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)),X10693),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_smin__emptyI])])])). 4.05/4.30 cnf(c_0_6356, plain, (hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[c_0_5057, c_0_4475])). 4.05/4.30 fof(c_0_6357, plain, ![X4305, X4306, X4307, X4308, X4309]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4309,X4308),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4307),X4306)))|(X4308=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)),X4305))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4309,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4308),X4305)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4307),X4305)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4308),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4307,X4305))),X4306))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult2__lemma])])])). 4.05/4.30 fof(c_0_6358, plain, ![X2570, X2571, X2572, X2573, X2574]:(~class_Groups_Oab__semigroup__mult(X2574)|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X2574,X2574,c_Groups_Otimes__class_Otimes(X2574),X2573,X2572),X2571))|(~hBOOL(hAPP(hAPP(c_member(X2574),X2570),X2572))|(hBOOL(hAPP(hAPP(c_member(X2574),X2573),X2572))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X2574,X2574,c_Groups_Otimes__class_Otimes(X2574),X2570,hAPP(hAPP(c_Set_Oinsert(X2574),X2573),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2574,tc_HOL_Obool)),X2572),hAPP(hAPP(c_Set_Oinsert(X2574),X2570),c_Orderings_Obot__class_Obot(tc_fun(X2574,tc_HOL_Obool)))))),X2571)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__graph__permute__diff])])])). 4.05/4.30 cnf(c_0_6359, 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_5058])). 4.05/4.30 fof(c_0_6360, plain, ![X12505]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X12505))|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))),X12505)),c_FunDef_Omax__weak))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmax__emptyI])])). 4.05/4.30 fof(c_0_6361, plain, ![X10012, X10013, X10014]:((c_Orderings_Obot__class_Obot(tc_fun(X10014,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10014,tc_HOL_Obool)),X10013),hAPP(hAPP(c_Set_Oinsert(X10014),X10012),c_Orderings_Obot__class_Obot(tc_fun(X10014,tc_HOL_Obool))))|c_Big__Operators_Olattice_OInf__fin(X10014,c_Orderings_Oord__class_Omin(X10014),hAPP(hAPP(c_Set_Oinsert(X10014),X10012),X10013))=X10012|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10014),X10013))|~class_Orderings_Olinorder(X10014))&(c_Orderings_Obot__class_Obot(tc_fun(X10014,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10014,tc_HOL_Obool)),X10013),hAPP(hAPP(c_Set_Oinsert(X10014),X10012),c_Orderings_Obot__class_Obot(tc_fun(X10014,tc_HOL_Obool))))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X10014),X10012),c_Big__Operators_Olattice_OInf__fin(X10014,c_Orderings_Oord__class_Omin(X10014),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10014,tc_HOL_Obool)),X10013),hAPP(hAPP(c_Set_Oinsert(X10014),X10012),c_Orderings_Obot__class_Obot(tc_fun(X10014,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OInf__fin(X10014,c_Orderings_Oord__class_Omin(X10014),hAPP(hAPP(c_Set_Oinsert(X10014),X10012),X10013))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10014),X10013))|~class_Orderings_Olinorder(X10014))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oinsert__remove])])])])). 4.05/4.30 cnf(c_0_6362, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk319_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)),esk317_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_5059])). 4.05/4.30 fof(c_0_6363, plain, ![X5664, X5665, X5666, X5667, X5668, X5669]:((((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5669),tc_List_Olist(X5669))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5669),tc_List_Olist(X5669)),X5667),X5665)),c_List_Olistrel1(X5669,X5664)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5669,X5669)),hAPP(hAPP(c_Product__Type_OPair(X5669,X5669),X5668),X5666)),X5664))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5669),tc_List_Olist(X5669))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5669),tc_List_Olist(X5669)),hAPP(hAPP(c_List_Olist_OCons(X5669),X5668),X5667)),hAPP(hAPP(c_List_Olist_OCons(X5669),X5666),X5665))),c_List_Olistrel1(X5669,X5664))))&(X5666=X5668|hBOOL(hAPP(hAPP(c_member(tc_prod(X5669,X5669)),hAPP(hAPP(c_Product__Type_OPair(X5669,X5669),X5668),X5666)),X5664))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5669),tc_List_Olist(X5669))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5669),tc_List_Olist(X5669)),hAPP(hAPP(c_List_Olist_OCons(X5669),X5668),X5667)),hAPP(hAPP(c_List_Olist_OCons(X5669),X5666),X5665))),c_List_Olistrel1(X5669,X5664)))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5669),tc_List_Olist(X5669))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5669),tc_List_Olist(X5669)),X5667),X5665)),c_List_Olistrel1(X5669,X5664)))|X5665=X5667|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5669),tc_List_Olist(X5669))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5669),tc_List_Olist(X5669)),hAPP(hAPP(c_List_Olist_OCons(X5669),X5668),X5667)),hAPP(hAPP(c_List_Olist_OCons(X5669),X5666),X5665))),c_List_Olistrel1(X5669,X5664))))&(X5666=X5668|X5665=X5667|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5669),tc_List_Olist(X5669))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5669),tc_List_Olist(X5669)),hAPP(hAPP(c_List_Olist_OCons(X5669),X5668),X5667)),hAPP(hAPP(c_List_Olist_OCons(X5669),X5666),X5665))),c_List_Olistrel1(X5669,X5664))))))&((~hBOOL(hAPP(hAPP(c_member(tc_prod(X5669,X5669)),hAPP(hAPP(c_Product__Type_OPair(X5669,X5669),X5668),X5666)),X5664))|X5665!=X5667|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5669),tc_List_Olist(X5669))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5669),tc_List_Olist(X5669)),hAPP(hAPP(c_List_Olist_OCons(X5669),X5668),X5667)),hAPP(hAPP(c_List_Olist_OCons(X5669),X5666),X5665))),c_List_Olistrel1(X5669,X5664))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5669),tc_List_Olist(X5669))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5669),tc_List_Olist(X5669)),X5667),X5665)),c_List_Olistrel1(X5669,X5664)))|X5666!=X5668|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5669),tc_List_Olist(X5669))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5669),tc_List_Olist(X5669)),hAPP(hAPP(c_List_Olist_OCons(X5669),X5668),X5667)),hAPP(hAPP(c_List_Olist_OCons(X5669),X5666),X5665))),c_List_Olistrel1(X5669,X5664)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__listrel1__Cons])])])). 4.05/4.30 cnf(c_0_6364, 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))),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),esk375_4(X2,X3,X4,X1)),X3))),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)),esk375_4(X2,X3,X4,X1))),X4)), inference(split_conjunct,[status(thm)],[c_0_5060])). 4.05/4.30 fof(c_0_6365, plain, ![X7085, X7086, X7087, X7088, X7089]:(~class_Groups_Ocomm__monoid__mult(X7089)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7088,X7089),hAPP(hAPP(c_COMBS(X7088,X7089,X7089),hAPP(hAPP(c_COMBB(X7089,tc_fun(X7089,X7089),X7088),c_Groups_Otimes__class_Otimes(X7089)),X7087)),X7086)),X7085)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7089),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7088,X7089),X7087),X7085)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7088,X7089),X7086),X7085))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__timesf])])])). 4.05/4.30 fof(c_0_6366, plain, ![X9803, X9804, X9805]:((c_Orderings_Obot__class_Obot(tc_fun(X9805,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9805,tc_HOL_Obool)),X9804),hAPP(hAPP(c_Set_Oinsert(X9805),X9803),c_Orderings_Obot__class_Obot(tc_fun(X9805,tc_HOL_Obool))))|c_Big__Operators_Olattice_OSup__fin(X9805,c_Orderings_Oord__class_Omax(X9805),hAPP(hAPP(c_Set_Oinsert(X9805),X9803),X9804))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X9805),X9803),c_Big__Operators_Olattice_OSup__fin(X9805,c_Orderings_Oord__class_Omax(X9805),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9805,tc_HOL_Obool)),X9804),hAPP(hAPP(c_Set_Oinsert(X9805),X9803),c_Orderings_Obot__class_Obot(tc_fun(X9805,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9805),X9804))|~class_Orderings_Olinorder(X9805))&(c_Orderings_Obot__class_Obot(tc_fun(X9805,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9805,tc_HOL_Obool)),X9804),hAPP(hAPP(c_Set_Oinsert(X9805),X9803),c_Orderings_Obot__class_Obot(tc_fun(X9805,tc_HOL_Obool))))|c_Big__Operators_Olattice_OSup__fin(X9805,c_Orderings_Oord__class_Omax(X9805),hAPP(hAPP(c_Set_Oinsert(X9805),X9803),X9804))=X9803|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9805),X9804))|~class_Orderings_Olinorder(X9805))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oinsert__remove])])])])). 4.05/4.30 cnf(c_0_6367, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk318_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)),esk317_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_5059])). 4.05/4.30 fof(c_0_6368, plain, ![X14907, X14908, X14909, X14910, X14911, X14912]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14912),X14911)),X14910)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X14909),X14908)),X14907)|(~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),X14909),X14908)),X14907)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14910),X14912))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14907))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14909))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14909),X14912))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14908),X14911)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono2__neg__lemma])])])). 4.05/4.30 fof(c_0_6369, plain, ![X15905, X15906, X15907, X15908, X15909, X15910]:(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15910),X15909)),X15908)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X15907),X15906)),X15905)|(~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),X15907),X15906)),X15905)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15905),X15907))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15908))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15907))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15907),X15910))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15909),X15906)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono2__lemma])])])). 4.05/4.30 fof(c_0_6370, plain, ![X16978, X16979, X16980, X16981, X16982, X16983, X16984, X16985, X16986]:(((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16981)),X16979)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16981)),X16980)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16981),tc_List_Olist(X16981))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16981),tc_List_Olist(X16981)),X16980),X16979)),c_List_Olistrel(X16981,X16978))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16982),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16981)),X16980)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X16981,X16981)),hAPP(hAPP(c_Product__Type_OPair(X16981,X16981),hAPP(hAPP(c_List_Onth(X16981),X16980),X16982)),hAPP(hAPP(c_List_Onth(X16981),X16979),X16982))),X16978))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16981),tc_List_Olist(X16981))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16981),tc_List_Olist(X16981)),X16980),X16979)),c_List_Olistrel(X16981,X16978)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk510_4(X16983,X16984,X16985,X16986)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16986)),X16985)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16986)),X16984)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16986)),X16985)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16986),tc_List_Olist(X16986))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16986),tc_List_Olist(X16986)),X16985),X16984)),c_List_Olistrel(X16986,X16983))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16986,X16986)),hAPP(hAPP(c_Product__Type_OPair(X16986,X16986),hAPP(hAPP(c_List_Onth(X16986),X16985),esk510_4(X16983,X16984,X16985,X16986))),hAPP(hAPP(c_List_Onth(X16986),X16984),esk510_4(X16983,X16984,X16985,X16986)))),X16983))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16986)),X16984)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16986)),X16985)|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X16986),tc_List_Olist(X16986))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X16986),tc_List_Olist(X16986)),X16985),X16984)),c_List_Olistrel(X16986,X16983)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__iff__nth])])])])])])). 4.05/4.30 fof(c_0_6371, plain, ![X17701, X17702, X17703, X17704, X17705]:(~class_Groups_Oab__group__add(X17705)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17704,X17705),hAPP(hAPP(c_COMBS(X17704,X17705,X17705),hAPP(hAPP(c_COMBB(X17705,tc_fun(X17705,X17705),X17704),c_Groups_Ominus__class_Ominus(X17705)),X17703)),X17702)),X17701)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17705),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17704,X17705),X17703),X17701)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17704,X17705),X17702),X17701))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__subtractf])])). 4.05/4.30 cnf(c_0_6372, 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),c_Transitive__Closure_Ortrancl(X1,X2)),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_5061, c_0_5018])). 4.05/4.30 fof(c_0_6373, plain, ![X17015, X17016, X17017, X17018, X17019, X17020, X17021, X17022]:((X17020=hAPP(hAPP(c_Product__Type_OPair(X17022,X17021),hAPP(X17017,esk511_8(X17015,X17016,X17017,X17018,X17019,X17020,X17021,X17022))),hAPP(X17016,esk512_8(X17015,X17016,X17017,X17018,X17019,X17020,X17021,X17022)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X17022,X17021)),X17020),hAPP(c_Set_Oimage(tc_prod(X17019,X17018),tc_prod(X17022,X17021),c_Product__Type_Omap__pair(X17019,X17022,X17018,X17021,X17017,X17016)),X17015))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X17019,X17018)),hAPP(hAPP(c_Product__Type_OPair(X17019,X17018),esk511_8(X17015,X17016,X17017,X17018,X17019,X17020,X17021,X17022)),esk512_8(X17015,X17016,X17017,X17018,X17019,X17020,X17021,X17022))),X17015))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X17022,X17021)),X17020),hAPP(c_Set_Oimage(tc_prod(X17019,X17018),tc_prod(X17022,X17021),c_Product__Type_Omap__pair(X17019,X17022,X17018,X17021,X17017,X17016)),X17015))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_prod__fun__imageE])])])])])). 4.05/4.30 fof(c_0_6374, plain, ![X14322, X14323, X14324, X14325]:((hBOOL(hAPP(hAPP(c_member(X14325),esk438_4(X14322,X14323,X14324,X14325)),hAPP(c_List_Oset(X14325),hAPP(hAPP(c_List_Omap(tc_prod(X14325,X14324),X14325),c_Product__Type_Ofst(X14325,X14324)),X14323))))|hAPP(c_Map_Omap__of(X14325,X14324),X14323)=hAPP(c_Map_Omap__of(X14325,X14324),X14322)|hAPP(c_List_Oset(X14325),hAPP(hAPP(c_List_Omap(tc_prod(X14325,X14324),X14325),c_Product__Type_Ofst(X14325,X14324)),X14322))!=hAPP(c_List_Oset(X14325),hAPP(hAPP(c_List_Omap(tc_prod(X14325,X14324),X14325),c_Product__Type_Ofst(X14325,X14324)),X14323)))&(hAPP(hAPP(c_Map_Omap__of(X14325,X14324),X14322),esk438_4(X14322,X14323,X14324,X14325))!=hAPP(hAPP(c_Map_Omap__of(X14325,X14324),X14323),esk438_4(X14322,X14323,X14324,X14325))|hAPP(c_Map_Omap__of(X14325,X14324),X14323)=hAPP(c_Map_Omap__of(X14325,X14324),X14322)|hAPP(c_List_Oset(X14325),hAPP(hAPP(c_List_Omap(tc_prod(X14325,X14324),X14325),c_Product__Type_Ofst(X14325,X14324)),X14322))!=hAPP(c_List_Oset(X14325),hAPP(hAPP(c_List_Omap(tc_prod(X14325,X14324),X14325),c_Product__Type_Ofst(X14325,X14324)),X14323)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__eqI])])])])])). 4.05/4.30 fof(c_0_6375, plain, ![X5437, X5438, X5439, X5440, X5441]:(~class_Groups_Ocomm__monoid__add(X5441)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5440,X5441),hAPP(hAPP(c_COMBS(X5440,X5441,X5441),hAPP(hAPP(c_COMBB(X5441,tc_fun(X5441,X5441),X5440),c_Groups_Oplus__class_Oplus(X5441)),X5439)),X5438)),X5437)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5441),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5440,X5441),X5439),X5437)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5440,X5441),X5438),X5437))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__addf])])])). 4.05/4.30 fof(c_0_6376, plain, ![X11655, X11656, X11657, X11658, X11659]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11659,tc_HOL_Obool)),X11656),hAPP(hAPP(c_Set_Oinsert(X11659),X11655),c_Orderings_Obot__class_Obot(tc_fun(X11659,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X11659,tc_HOL_Obool))|X11655=hAPP(X11657,X11656)|~hBOOL(hAPP(hAPP(c_member(X11659),X11655),X11656))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11659),X11656))|~c_Finite__Set_Ofolding__one(X11659,X11658,X11657))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11659,tc_HOL_Obool)),X11656),hAPP(hAPP(c_Set_Oinsert(X11659),X11655),c_Orderings_Obot__class_Obot(tc_fun(X11659,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X11659,tc_HOL_Obool))|hAPP(hAPP(X11658,X11655),hAPP(X11657,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11659,tc_HOL_Obool)),X11656),hAPP(hAPP(c_Set_Oinsert(X11659),X11655),c_Orderings_Obot__class_Obot(tc_fun(X11659,tc_HOL_Obool))))))=hAPP(X11657,X11656)|~hBOOL(hAPP(hAPP(c_member(X11659),X11655),X11656))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11659),X11656))|~c_Finite__Set_Ofolding__one(X11659,X11658,X11657))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Oremove])])])])). 4.05/4.30 cnf(c_0_6377, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk106_3(X2,X3,X1)),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),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk104_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_5062])). 4.05/4.30 cnf(c_0_6378, 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_5063]), ['final']). 4.05/4.30 cnf(c_0_6379, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk105_3(X2,X3,X1)),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),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk104_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_5062])). 4.05/4.30 cnf(c_0_6380, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X3)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5064, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6381, 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))|hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)!=X6|~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_5065])). 4.05/4.30 cnf(c_0_6382, plain, (c_Enum_Oenum__the(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)|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_5066, c_0_4980])). 4.05/4.30 cnf(c_0_6383, 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),c_Transitive__Closure_Ortrancl(X1,X4)),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_5067, c_0_5018])). 4.05/4.30 fof(c_0_6384, plain, ![X5160, X5161, X5162, X5163, X5164, X5165, X5166, X5167]:(~c_Finite__Set_Ofolding(X5167,X5166,X5165,X5164)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5167),X5163))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5167),X5162))|hAPP(c_Fun_Ocomp(X5166,X5166,X5161,hAPP(X5164,X5162)),hAPP(c_Fun_Ocomp(X5166,X5166,X5161,hAPP(X5164,X5163)),X5160))=hAPP(c_Fun_Ocomp(X5166,X5166,X5161,hAPP(X5164,X5163)),hAPP(c_Fun_Ocomp(X5166,X5166,X5161,hAPP(X5164,X5162)),X5160))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ocommute__left__comp_H_H])])])). 4.05/4.30 fof(c_0_6385, plain, ![X9102, X9103, X9104, X9105, X9106]:((c_Orderings_Obot__class_Obot(tc_fun(X9106,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9106,tc_HOL_Obool)),X9103),hAPP(hAPP(c_Set_Oinsert(X9106),X9102),c_Orderings_Obot__class_Obot(tc_fun(X9106,tc_HOL_Obool))))|hAPP(hAPP(X9105,X9102),hAPP(X9104,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9106,tc_HOL_Obool)),X9103),hAPP(hAPP(c_Set_Oinsert(X9106),X9102),c_Orderings_Obot__class_Obot(tc_fun(X9106,tc_HOL_Obool))))))=hAPP(X9104,hAPP(hAPP(c_Set_Oinsert(X9106),X9102),X9103))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9106),X9103))|~c_Finite__Set_Ofolding__one(X9106,X9105,X9104))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9106,tc_HOL_Obool)),X9103),hAPP(hAPP(c_Set_Oinsert(X9106),X9102),c_Orderings_Obot__class_Obot(tc_fun(X9106,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X9106,tc_HOL_Obool))|hAPP(X9104,hAPP(hAPP(c_Set_Oinsert(X9106),X9102),X9103))=X9102|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9106),X9103))|~c_Finite__Set_Ofolding__one(X9106,X9105,X9104))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert__remove])])])). 4.05/4.30 fof(c_0_6386, plain, ![X12912, X12913, X12914, X12915, X12916]:((((c_Fun_Oinj__on(X12916,X12915,X12914,X12913)|~c_Fun_Oinj__on(X12916,X12915,X12914,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12916,tc_HOL_Obool)),X12913),X12912)))&(c_Fun_Oinj__on(X12916,X12915,X12914,X12912)|~c_Fun_Oinj__on(X12916,X12915,X12914,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12916,tc_HOL_Obool)),X12913),X12912))))&(c_Orderings_Obot__class_Obot(tc_fun(X12915,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12915,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12916,X12915,X12914),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12916,tc_HOL_Obool)),X12913),X12912))),hAPP(c_Set_Oimage(X12916,X12915,X12914),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12916,tc_HOL_Obool)),X12912),X12913)))|~c_Fun_Oinj__on(X12916,X12915,X12914,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12916,tc_HOL_Obool)),X12913),X12912))))&(~c_Fun_Oinj__on(X12916,X12915,X12914,X12913)|~c_Fun_Oinj__on(X12916,X12915,X12914,X12912)|c_Orderings_Obot__class_Obot(tc_fun(X12915,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12915,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12916,X12915,X12914),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12916,tc_HOL_Obool)),X12913),X12912))),hAPP(c_Set_Oimage(X12916,X12915,X12914),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12916,tc_HOL_Obool)),X12912),X12913)))|c_Fun_Oinj__on(X12916,X12915,X12914,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12916,tc_HOL_Obool)),X12913),X12912)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Un])])])). 4.05/4.30 fof(c_0_6387, plain, ![X6796, X6797, X6798, X6799, X6800, X6801, X6802]:((hBOOL(hAPP(hAPP(c_member(X6802),esk209_7(X6796,X6797,X6798,X6799,X6800,X6801,X6802)),X6801))|X6796=X6797|~hBOOL(hAPP(hAPP(c_member(tc_fun(X6802,tc_HOL_Obool)),X6796),hAPP(hAPP(c_Equiv__Relations_Oquotient(X6802),X6801),X6800)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X6802,tc_HOL_Obool)),X6797),hAPP(hAPP(c_Equiv__Relations_Oquotient(X6802),X6801),X6800)))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6802,tc_fun(X6799,tc_HOL_Obool)),X6797),X6798)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6802,tc_fun(X6799,tc_HOL_Obool)),X6796),X6798)|~c_Equiv__Relations_Ocongruent(X6802,tc_fun(X6799,tc_HOL_Obool),X6800,X6798)|~c_Equiv__Relations_Oequiv(X6802,X6801,X6800))&((hBOOL(hAPP(hAPP(c_member(X6802),esk210_7(X6796,X6797,X6798,X6799,X6800,X6801,X6802)),X6801))|X6796=X6797|~hBOOL(hAPP(hAPP(c_member(tc_fun(X6802,tc_HOL_Obool)),X6796),hAPP(hAPP(c_Equiv__Relations_Oquotient(X6802),X6801),X6800)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X6802,tc_HOL_Obool)),X6797),hAPP(hAPP(c_Equiv__Relations_Oquotient(X6802),X6801),X6800)))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6802,tc_fun(X6799,tc_HOL_Obool)),X6797),X6798)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6802,tc_fun(X6799,tc_HOL_Obool)),X6796),X6798)|~c_Equiv__Relations_Ocongruent(X6802,tc_fun(X6799,tc_HOL_Obool),X6800,X6798)|~c_Equiv__Relations_Oequiv(X6802,X6801,X6800))&((hAPP(X6798,esk210_7(X6796,X6797,X6798,X6799,X6800,X6801,X6802))=hAPP(X6798,esk209_7(X6796,X6797,X6798,X6799,X6800,X6801,X6802))|X6796=X6797|~hBOOL(hAPP(hAPP(c_member(tc_fun(X6802,tc_HOL_Obool)),X6796),hAPP(hAPP(c_Equiv__Relations_Oquotient(X6802),X6801),X6800)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X6802,tc_HOL_Obool)),X6797),hAPP(hAPP(c_Equiv__Relations_Oquotient(X6802),X6801),X6800)))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6802,tc_fun(X6799,tc_HOL_Obool)),X6797),X6798)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6802,tc_fun(X6799,tc_HOL_Obool)),X6796),X6798)|~c_Equiv__Relations_Ocongruent(X6802,tc_fun(X6799,tc_HOL_Obool),X6800,X6798)|~c_Equiv__Relations_Oequiv(X6802,X6801,X6800))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X6802,X6802)),hAPP(hAPP(c_Product__Type_OPair(X6802,X6802),esk209_7(X6796,X6797,X6798,X6799,X6800,X6801,X6802)),esk210_7(X6796,X6797,X6798,X6799,X6800,X6801,X6802))),X6800))|X6796=X6797|~hBOOL(hAPP(hAPP(c_member(tc_fun(X6802,tc_HOL_Obool)),X6796),hAPP(hAPP(c_Equiv__Relations_Oquotient(X6802),X6801),X6800)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X6802,tc_HOL_Obool)),X6797),hAPP(hAPP(c_Equiv__Relations_Oquotient(X6802),X6801),X6800)))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6802,tc_fun(X6799,tc_HOL_Obool)),X6797),X6798)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6802,tc_fun(X6799,tc_HOL_Obool)),X6796),X6798)|~c_Equiv__Relations_Ocongruent(X6802,tc_fun(X6799,tc_HOL_Obool),X6800,X6798)|~c_Equiv__Relations_Oequiv(X6802,X6801,X6800))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__equiv__class__inject])])])])])). 4.05/4.30 cnf(c_0_6388, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Orestrict__map(X1,X4,X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),X2),X6)=c_Map_Orestrict__map(X1,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),X5),X2),X6),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5068])). 4.05/4.30 cnf(c_0_6389, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X4)),X5),X6)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),X5),X6)), inference(split_conjunct,[status(thm)],[c_0_5069]), ['final']). 4.05/4.30 cnf(c_0_6390, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))=X2|c_Groups_Oone__class_Oone(X1)=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))!=c_Groups_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5070, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865])). 4.05/4.30 cnf(c_0_6391, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))), inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5071, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865])])). 4.05/4.30 cnf(c_0_6392, 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_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5072, c_0_4867]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865])). 4.05/4.30 cnf(c_0_6393, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Ozero__class_Ozero(X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5073, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865])). 4.05/4.30 cnf(c_0_6394, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_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_5074])). 4.05/4.30 cnf(c_0_6395, 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))), inference(split_conjunct,[status(thm)],[c_0_5075]), ['final']). 4.05/4.30 cnf(c_0_6396, 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_5076]), ['final']). 4.05/4.30 fof(c_0_6397, plain, ![X13949, X13950, X13951]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13951,tc_HOL_Obool)),X13950),hAPP(hAPP(c_Set_Oinsert(X13951),X13949),c_Orderings_Obot__class_Obot(tc_fun(X13951,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X13951,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X13951),X13949),c_Big__Operators_Olinorder__class_OMax(X13951,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13951,tc_HOL_Obool)),X13950),hAPP(hAPP(c_Set_Oinsert(X13951),X13949),c_Orderings_Obot__class_Obot(tc_fun(X13951,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMax(X13951,X13950)|~hBOOL(hAPP(hAPP(c_member(X13951),X13949),X13950))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13951),X13950))|~class_Orderings_Olinorder(X13951))&(c_Orderings_Obot__class_Obot(tc_fun(X13951,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13951,tc_HOL_Obool)),X13950),hAPP(hAPP(c_Set_Oinsert(X13951),X13949),c_Orderings_Obot__class_Obot(tc_fun(X13951,tc_HOL_Obool))))|X13949=c_Big__Operators_Olinorder__class_OMax(X13951,X13950)|~hBOOL(hAPP(hAPP(c_member(X13951),X13949),X13950))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13951),X13950))|~class_Orderings_Olinorder(X13951))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Oremove])])])])). 4.05/4.30 cnf(c_0_6398, 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_5077])). 4.05/4.30 fof(c_0_6399, plain, ![X3391, X3392, X3393, X3394, X3395, X3396, X3397]:((hBOOL(hAPP(hAPP(c_member(X3397),esk111_7(X3391,X3392,X3393,X3394,X3395,X3396,X3397)),X3396))|hBOOL(hAPP(hAPP(c_member(tc_fun(X3394,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3397,tc_fun(X3394,tc_HOL_Obool)),X3392),X3393)),X3391))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3397,tc_HOL_Obool)),X3392),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3397),X3396),X3395)))|~c_Equiv__Relations_Ocongruent(X3397,tc_fun(X3394,tc_HOL_Obool),X3395,X3393)|~c_Equiv__Relations_Oequiv(X3397,X3396,X3395))&(~hBOOL(hAPP(hAPP(c_member(tc_fun(X3394,tc_HOL_Obool)),hAPP(X3393,esk111_7(X3391,X3392,X3393,X3394,X3395,X3396,X3397))),X3391))|hBOOL(hAPP(hAPP(c_member(tc_fun(X3394,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3397,tc_fun(X3394,tc_HOL_Obool)),X3392),X3393)),X3391))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3397,tc_HOL_Obool)),X3392),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3397),X3396),X3395)))|~c_Equiv__Relations_Ocongruent(X3397,tc_fun(X3394,tc_HOL_Obool),X3395,X3393)|~c_Equiv__Relations_Oequiv(X3397,X3396,X3395))), 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])])])])])). 4.05/4.30 fof(c_0_6400, plain, ![X16682, X16683, X16684, X16685, X16686, X16687]:((hBOOL(hAPP(hAPP(c_member(X16686),esk497_6(X16682,X16683,X16684,X16685,X16686,X16687)),X16685))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16686,X16687),hAPP(c_Fun_Ocomp(X16682,X16687,X16686,X16683),X16684)),X16685)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16682,X16687),X16683),hAPP(c_Set_Oimage(X16686,X16682,X16684),X16685))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16686),X16685))|~class_Groups_Ocomm__monoid__add(X16687))&((hBOOL(hAPP(hAPP(c_member(X16686),esk498_6(X16682,X16683,X16684,X16685,X16686,X16687)),X16685))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16686,X16687),hAPP(c_Fun_Ocomp(X16682,X16687,X16686,X16683),X16684)),X16685)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16682,X16687),X16683),hAPP(c_Set_Oimage(X16686,X16682,X16684),X16685))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16686),X16685))|~class_Groups_Ocomm__monoid__add(X16687))&((esk498_6(X16682,X16683,X16684,X16685,X16686,X16687)!=esk497_6(X16682,X16683,X16684,X16685,X16686,X16687)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16686,X16687),hAPP(c_Fun_Ocomp(X16682,X16687,X16686,X16683),X16684)),X16685)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16682,X16687),X16683),hAPP(c_Set_Oimage(X16686,X16682,X16684),X16685))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16686),X16685))|~class_Groups_Ocomm__monoid__add(X16687))&((hAPP(X16684,esk498_6(X16682,X16683,X16684,X16685,X16686,X16687))=hAPP(X16684,esk497_6(X16682,X16683,X16684,X16685,X16686,X16687))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16686,X16687),hAPP(c_Fun_Ocomp(X16682,X16687,X16686,X16683),X16684)),X16685)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16682,X16687),X16683),hAPP(c_Set_Oimage(X16686,X16682,X16684),X16685))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16686),X16685))|~class_Groups_Ocomm__monoid__add(X16687))&(hAPP(X16683,hAPP(X16684,esk497_6(X16682,X16683,X16684,X16685,X16686,X16687)))!=c_Groups_Ozero__class_Ozero(X16687)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16686,X16687),hAPP(c_Fun_Ocomp(X16682,X16687,X16686,X16683),X16684)),X16685)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16682,X16687),X16683),hAPP(c_Set_Oimage(X16686,X16682,X16684),X16685))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16686),X16685))|~class_Groups_Ocomm__monoid__add(X16687)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__reindex__nonzero])])])])])). 4.05/4.30 cnf(c_0_6401, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),X6))|X1!=X2|~hBOOL(hAPP(hAPP(c_member(X3),X5),X2))|~hBOOL(hAPP(hAPP(c_member(X3),X4),X1))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))|~c_Equiv__Relations_Oequiv(X3,X7,X6)), inference(split_conjunct,[status(thm)],[c_0_5078])). 4.05/4.30 fof(c_0_6402, plain, ![X12140, X12141, X12142]:((c_Orderings_Obot__class_Obot(tc_fun(X12142,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12142,tc_HOL_Obool)),X12141),hAPP(hAPP(c_Set_Oinsert(X12142),X12140),c_Orderings_Obot__class_Obot(tc_fun(X12142,tc_HOL_Obool))))|c_Big__Operators_Olinorder__class_OMin(X12142,X12141)=X12140|~hBOOL(hAPP(hAPP(c_member(X12142),X12140),X12141))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12142),X12141))|~class_Orderings_Olinorder(X12142))&(c_Orderings_Obot__class_Obot(tc_fun(X12142,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12142,tc_HOL_Obool)),X12141),hAPP(hAPP(c_Set_Oinsert(X12142),X12140),c_Orderings_Obot__class_Obot(tc_fun(X12142,tc_HOL_Obool))))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X12142),X12140),c_Big__Operators_Olinorder__class_OMin(X12142,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12142,tc_HOL_Obool)),X12141),hAPP(hAPP(c_Set_Oinsert(X12142),X12140),c_Orderings_Obot__class_Obot(tc_fun(X12142,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMin(X12142,X12141)|~hBOOL(hAPP(hAPP(c_member(X12142),X12140),X12141))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X12142),X12141))|~class_Orderings_Olinorder(X12142))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Oremove])])])])). 4.05/4.30 cnf(c_0_6403, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X4),X1)),hAPP(hAPP(c_List_Oappend(X3),X5),X2))),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_5077])). 4.05/4.30 cnf(c_0_6404, 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),X1),X4)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),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_5079])). 4.05/4.30 fof(c_0_6405, plain, ![X16454, X16455, X16456]:((c_Orderings_Obot__class_Obot(tc_fun(X16456,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16456,tc_HOL_Obool)),X16455),hAPP(hAPP(c_Set_Oinsert(X16456),X16454),c_Orderings_Obot__class_Obot(tc_fun(X16456,tc_HOL_Obool))))|c_Big__Operators_Olattice__class_OInf__fin(X16456,X16455)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16456),X16454),c_Big__Operators_Olattice__class_OInf__fin(X16456,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16456,tc_HOL_Obool)),X16455),hAPP(hAPP(c_Set_Oinsert(X16456),X16454),c_Orderings_Obot__class_Obot(tc_fun(X16456,tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(c_member(X16456),X16454),X16455))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16456),X16455))|~class_Lattices_Olattice(X16456))&(c_Orderings_Obot__class_Obot(tc_fun(X16456,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16456,tc_HOL_Obool)),X16455),hAPP(hAPP(c_Set_Oinsert(X16456),X16454),c_Orderings_Obot__class_Obot(tc_fun(X16456,tc_HOL_Obool))))|c_Big__Operators_Olattice__class_OInf__fin(X16456,X16455)=X16454|~hBOOL(hAPP(hAPP(c_member(X16456),X16454),X16455))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16456),X16455))|~class_Lattices_Olattice(X16456))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oremove])])])])). 4.05/4.30 cnf(c_0_6406, 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),X1),X4)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))),c_List_Olexord(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_Olexord(X3,X6)))), inference(split_conjunct,[status(thm)],[c_0_5080])). 4.05/4.30 cnf(c_0_6407, 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),c_Transitive__Closure_Ortrancl(X1,X4)),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_5081, c_0_5018])). 4.05/4.30 fof(c_0_6408, plain, ![X16399, X16400, X16401]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16401,tc_HOL_Obool)),X16400),hAPP(hAPP(c_Set_Oinsert(X16401),X16399),c_Orderings_Obot__class_Obot(tc_fun(X16401,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X16401,tc_HOL_Obool))|X16399=c_Big__Operators_Olattice__class_OSup__fin(X16401,X16400)|~hBOOL(hAPP(hAPP(c_member(X16401),X16399),X16400))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16401),X16400))|~class_Lattices_Olattice(X16401))&(c_Orderings_Obot__class_Obot(tc_fun(X16401,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16401,tc_HOL_Obool)),X16400),hAPP(hAPP(c_Set_Oinsert(X16401),X16399),c_Orderings_Obot__class_Obot(tc_fun(X16401,tc_HOL_Obool))))|c_Big__Operators_Olattice__class_OSup__fin(X16401,X16400)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X16401),X16399),c_Big__Operators_Olattice__class_OSup__fin(X16401,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16401,tc_HOL_Obool)),X16400),hAPP(hAPP(c_Set_Oinsert(X16401),X16399),c_Orderings_Obot__class_Obot(tc_fun(X16401,tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(c_member(X16401),X16399),X16400))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16401),X16400))|~class_Lattices_Olattice(X16401))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oremove])])])). 4.05/4.30 cnf(c_0_6409, plain, (hBOOL(hAPP(X1,esk279_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_5053])). 4.05/4.30 fof(c_0_6410, plain, ![X13386, X13387, X13388, X13389, X13390, X13391, X13392, X13393]:((~c_Relation_Ototal__on(X13388,X13387,X13386)|(~hBOOL(hAPP(hAPP(c_member(X13388),X13389),X13387))|(~hBOOL(hAPP(hAPP(c_member(X13388),X13390),X13387))|(X13389=X13390|(hBOOL(hAPP(hAPP(c_member(tc_prod(X13388,X13388)),hAPP(hAPP(c_Product__Type_OPair(X13388,X13388),X13389),X13390)),X13386))|hBOOL(hAPP(hAPP(c_member(tc_prod(X13388,X13388)),hAPP(hAPP(c_Product__Type_OPair(X13388,X13388),X13390),X13389)),X13386)))))))&((hBOOL(hAPP(hAPP(c_member(X13393),esk416_3(X13391,X13392,X13393)),X13392))|c_Relation_Ototal__on(X13393,X13392,X13391))&((hBOOL(hAPP(hAPP(c_member(X13393),esk417_3(X13391,X13392,X13393)),X13392))|c_Relation_Ototal__on(X13393,X13392,X13391))&((esk416_3(X13391,X13392,X13393)!=esk417_3(X13391,X13392,X13393)|c_Relation_Ototal__on(X13393,X13392,X13391))&((~hBOOL(hAPP(hAPP(c_member(tc_prod(X13393,X13393)),hAPP(hAPP(c_Product__Type_OPair(X13393,X13393),esk416_3(X13391,X13392,X13393)),esk417_3(X13391,X13392,X13393))),X13391))|c_Relation_Ototal__on(X13393,X13392,X13391))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13393,X13393)),hAPP(hAPP(c_Product__Type_OPair(X13393,X13393),esk417_3(X13391,X13392,X13393)),esk416_3(X13391,X13392,X13393))),X13391))|c_Relation_Ototal__on(X13393,X13392,X13391))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_total__on__def])])])])])])])). 4.05/4.30 fof(c_0_6411, plain, ![X7931, X7932, X7933, X7934, X7935]:(~c_Finite__Set_Ofolding__one(X7935,X7934,X7933)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7935),X7932))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7935),X7931))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7935,tc_HOL_Obool)),X7932),X7931)=c_Orderings_Obot__class_Obot(tc_fun(X7935,tc_HOL_Obool))|hAPP(hAPP(X7934,hAPP(X7933,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7935,tc_HOL_Obool)),X7932),X7931))),hAPP(X7933,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7935,tc_HOL_Obool)),X7932),X7931)))=hAPP(hAPP(X7934,hAPP(X7933,X7932)),hAPP(X7933,X7931)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Ounion__inter])])])). 4.05/4.30 fof(c_0_6412, plain, ![X3993, X3994, X3995, X3996]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3996),X3995))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3994),X3993))|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),X3996),X3994)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3995),X3993))),c_FunDef_Opair__leq)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pair__leqI2])])])). 4.05/4.30 fof(c_0_6413, plain, ![X14272, X14273, X14274, X14275, X14276, X14277, X14278]:((~c_List_Olist__all2(X14278,X14277,X14276,X14275,hAPP(hAPP(c_List_Omap(X14274,X14277),X14273),X14272))|c_List_Olist__all2(X14278,X14274,hAPP(hAPP(c_COMBC(X14278,tc_fun(X14274,X14277),tc_fun(X14274,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14277,tc_HOL_Obool),tc_fun(tc_fun(X14274,X14277),tc_fun(X14274,tc_HOL_Obool)),X14278),c_COMBB(X14277,tc_HOL_Obool,X14274)),X14276)),X14273),X14275,X14272))&(~c_List_Olist__all2(X14278,X14274,hAPP(hAPP(c_COMBC(X14278,tc_fun(X14274,X14277),tc_fun(X14274,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14277,tc_HOL_Obool),tc_fun(tc_fun(X14274,X14277),tc_fun(X14274,tc_HOL_Obool)),X14278),c_COMBB(X14277,tc_HOL_Obool,X14274)),X14276)),X14273),X14275,X14272)|c_List_Olist__all2(X14278,X14277,X14276,X14275,hAPP(hAPP(c_List_Omap(X14274,X14277),X14273),X14272)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__map2])])). 4.05/4.30 fof(c_0_6414, plain, ![X1660, X1661, X1662, X1663, X1664, X1665]:(~c_Relation_Osingle__valued(X1665,X1664,hAPP(c_Relation_Oconverse(X1664,X1665),X1663))|(c_Orderings_Obot__class_Obot(tc_fun(X1661,tc_HOL_Obool))=X1662|hAPP(c_Relation_OImage(X1664,X1665,X1663),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1661,tc_fun(X1664,tc_HOL_Obool)),X1662),X1660))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1661,tc_fun(X1665,tc_HOL_Obool)),X1662),hAPP(hAPP(c_COMBB(tc_fun(X1664,tc_HOL_Obool),tc_fun(X1665,tc_HOL_Obool),X1661),c_Relation_OImage(X1664,X1665,X1663)),X1660)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Image__INT__eq])])])). 4.05/4.30 fof(c_0_6415, plain, ![X4378, X4379, X4380]:((c_Orderings_Obot__class_Obot(tc_fun(X4380,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4380,tc_HOL_Obool)),X4379),hAPP(hAPP(c_Set_Oinsert(X4380),X4378),c_Orderings_Obot__class_Obot(tc_fun(X4380,tc_HOL_Obool))))|c_Big__Operators_Olattice__class_OInf__fin(X4380,hAPP(hAPP(c_Set_Oinsert(X4380),X4378),X4379))=X4378|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4380),X4379))|~class_Lattices_Olattice(X4380))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4380,tc_HOL_Obool)),X4379),hAPP(hAPP(c_Set_Oinsert(X4380),X4378),c_Orderings_Obot__class_Obot(tc_fun(X4380,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X4380,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X4380),X4378),c_Big__Operators_Olattice__class_OInf__fin(X4380,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4380,tc_HOL_Obool)),X4379),hAPP(hAPP(c_Set_Oinsert(X4380),X4378),c_Orderings_Obot__class_Obot(tc_fun(X4380,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OInf__fin(X4380,hAPP(hAPP(c_Set_Oinsert(X4380),X4378),X4379))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4380),X4379))|~class_Lattices_Olattice(X4380))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oinsert__remove])])])])). 4.05/4.30 fof(c_0_6416, plain, ![X2679, X2680, X2681, X2682]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2682),X2681))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2680),X2679))|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),X2682),X2680)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2681),X2679))),c_FunDef_Opair__less)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pair__lessI2])])])). 4.05/4.30 fof(c_0_6417, plain, ![X11953, X11954, X11955, X11956, X11957]:(~class_Groups_Oordered__ab__group__add__abs(X11957)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11957),hAPP(c_Groups_Oabs__class_Oabs(X11957),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X11957),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11957),X11956),X11955)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11957),X11954),X11953)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11957),hAPP(c_Groups_Oabs__class_Oabs(X11957),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X11957),X11956),X11954))),hAPP(c_Groups_Oabs__class_Oabs(X11957),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X11957),X11955),X11953)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__diff__triangle__ineq])])])). 4.05/4.30 fof(c_0_6418, plain, ![X17688, X17689, X17690, X17691]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17691),X17688)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17689),X17690)|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),X17691),X17690)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X17689),X17688))),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),X17691),X17690)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X17689),X17688))),c_Int_Ointrel))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17691),X17688)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17689),X17690))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_intrel__iff])])). 4.05/4.30 fof(c_0_6419, plain, ![X6982, X6983, X6984, X6985, X6986]:((c_Orderings_Obot__class_Obot(tc_fun(X6985,tc_HOL_Obool))=X6986|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6984,tc_HOL_Obool)),X6983),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6985,tc_fun(X6984,tc_HOL_Obool)),X6986),X6982))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6985,tc_fun(X6984,tc_HOL_Obool)),X6986),hAPP(hAPP(c_COMBB(tc_fun(X6984,tc_HOL_Obool),tc_fun(X6984,tc_HOL_Obool),X6985),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6984,tc_HOL_Obool)),X6983)),X6982)))&(X6986!=c_Orderings_Obot__class_Obot(tc_fun(X6985,tc_HOL_Obool))|c_Orderings_Otop__class_Otop(tc_fun(X6984,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6985,tc_fun(X6984,tc_HOL_Obool)),X6986),hAPP(hAPP(c_COMBB(tc_fun(X6984,tc_HOL_Obool),tc_fun(X6984,tc_HOL_Obool),X6985),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6984,tc_HOL_Obool)),X6983)),X6982)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__simps_I2_J])])])). 4.05/4.30 fof(c_0_6420, plain, ![X8188, X8189, X8190, X8191, X8192, X8193]:((hBOOL(hAPP(hAPP(c_member(X8193),esk259_6(X8188,X8189,X8190,X8191,X8192,X8193)),X8192))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X8193,X8190),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X8193,X8190),X8192),X8189)),hAPP(hAPP(c_Product__Type_OSigma(X8193,X8190),X8191),X8188)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8193,tc_HOL_Obool)),X8192),X8191)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8190,tc_HOL_Obool)),hAPP(X8189,esk259_6(X8188,X8189,X8190,X8191,X8192,X8193))),hAPP(X8188,esk259_6(X8188,X8189,X8190,X8191,X8192,X8193))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X8193,X8190),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X8193,X8190),X8192),X8189)),hAPP(hAPP(c_Product__Type_OSigma(X8193,X8190),X8191),X8188)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8193,tc_HOL_Obool)),X8192),X8191)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sigma__mono])])])])). 4.05/4.30 fof(c_0_6421, plain, ![X13113, X13114, X13115, X13116, X13117]:(~c_Equiv__Relations_Oequiv(X13117,X13116,X13115)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13117,X13117)),hAPP(hAPP(c_Product__Type_OPair(X13117,X13117),X13114),X13113)),X13115))|hAPP(c_Relation_OImage(X13117,X13117,X13115),hAPP(hAPP(c_Set_Oinsert(X13117),X13114),c_Orderings_Obot__class_Obot(tc_fun(X13117,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X13117,X13117,X13115),hAPP(hAPP(c_Set_Oinsert(X13117),X13113),c_Orderings_Obot__class_Obot(tc_fun(X13117,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equiv__class__eq])])])). 4.05/4.30 fof(c_0_6422, plain, ![X1306, X1307, X1308]:((c_Orderings_Obot__class_Obot(tc_fun(X1308,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1308,tc_HOL_Obool)),X1307),hAPP(hAPP(c_Set_Oinsert(X1308),X1306),c_Orderings_Obot__class_Obot(tc_fun(X1308,tc_HOL_Obool))))|X1306=c_Big__Operators_Olattice__class_OSup__fin(X1308,hAPP(hAPP(c_Set_Oinsert(X1308),X1306),X1307))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1308),X1307))|~class_Lattices_Olattice(X1308))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1308,tc_HOL_Obool)),X1307),hAPP(hAPP(c_Set_Oinsert(X1308),X1306),c_Orderings_Obot__class_Obot(tc_fun(X1308,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1308,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1308),X1306),c_Big__Operators_Olattice__class_OSup__fin(X1308,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1308,tc_HOL_Obool)),X1307),hAPP(hAPP(c_Set_Oinsert(X1308),X1306),c_Orderings_Obot__class_Obot(tc_fun(X1308,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OSup__fin(X1308,hAPP(hAPP(c_Set_Oinsert(X1308),X1306),X1307))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1308),X1307))|~class_Lattices_Olattice(X1308))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oinsert__remove])])])])). 4.05/4.30 cnf(c_0_6423, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk230_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),X4)))|c_List_OdropWhile(X1,X3,X2)=c_List_OdropWhile(X1,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_5082])). 4.05/4.30 fof(c_0_6424, plain, ![X13491, X13492, X13493, X13494, X13495]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X13495),tc_List_Olist(X13495))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X13495),tc_List_Olist(X13495)),X13494),X13493)),c_List_Olexord(X13495,X13492)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X13495),tc_List_Olist(X13495))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X13495),tc_List_Olist(X13495)),hAPP(hAPP(c_List_Oappend(X13495),X13491),X13494)),hAPP(hAPP(c_List_Oappend(X13495),X13491),X13493))),c_List_Olexord(X13495,X13492)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__leftI])])). 4.05/4.30 fof(c_0_6425, plain, ![X14479, X14480, X14481, X14482, X14483]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14483),tc_List_Olist(X14483))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14483),tc_List_Olist(X14483)),X14482),X14481)),c_List_Olistrel1(X14483,X14480)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X14483),tc_List_Olist(X14483))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X14483),tc_List_Olist(X14483)),hAPP(hAPP(c_List_Olist_OCons(X14483),X14479),X14482)),hAPP(hAPP(c_List_Olist_OCons(X14483),X14479),X14481))),c_List_Olistrel1(X14483,X14480)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel1I2])])])). 4.05/4.30 fof(c_0_6426, plain, ![X15290, X15291, X15292, X15293]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15293),X15292))|(~hBOOL(hAPP(hAPP(c_member(X15293),X15291),X15292))|(hBOOL(hAPP(hAPP(c_member(X15293),X15291),X15290))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X15293),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15293,tc_HOL_Obool)),X15292),X15290))),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Finite__Set_Ocard(X15293),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15293,tc_HOL_Obool)),X15292),hAPP(hAPP(c_Set_Oinsert(X15293),X15291),X15290)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff__insert])])])). 4.05/4.30 fof(c_0_6427, plain, ![X2558, X2559, X2560, X2561]:(~c_FunDef_Oreduction__pair(X2561,X2560)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2561,X2561),tc_HOL_Obool)),X2559),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X2561,X2561),tc_HOL_Obool),tc_fun(tc_prod(X2561,X2561),tc_HOL_Obool)),X2560)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2561,X2561),tc_HOL_Obool)),X2558),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X2561,X2561),tc_HOL_Obool),tc_fun(tc_prod(X2561,X2561),tc_HOL_Obool)),X2560)))|(~c_Wellfounded_Owf(X2561,X2558)|c_Wellfounded_Owf(X2561,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2561,X2561),tc_HOL_Obool)),X2559),X2558)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_reduction__pair__lemma])])])). 4.05/4.30 fof(c_0_6428, plain, ![X1884, X1885, X1886, X1887, X1888]:((hBOOL(hAPP(hAPP(c_member(X1888),X1887),X1886))|c_Map_Orestrict__map(X1888,X1885,X1884,X1886)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1888,tc_Option_Ooption(X1885)),c_Map_Orestrict__map(X1888,X1885,X1884,X1886)),X1887),c_Option_Ooption_ONone(X1885)))&(~hBOOL(hAPP(hAPP(c_member(X1888),X1887),X1886))|c_Map_Orestrict__map(X1888,X1885,X1884,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1888,tc_HOL_Obool)),X1886),hAPP(hAPP(c_Set_Oinsert(X1888),X1887),c_Orderings_Obot__class_Obot(tc_fun(X1888,tc_HOL_Obool)))))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1888,tc_Option_Ooption(X1885)),c_Map_Orestrict__map(X1888,X1885,X1884,X1886)),X1887),c_Option_Ooption_ONone(X1885)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__upd__None__restrict])])])). 4.05/4.30 fof(c_0_6429, plain, ![X6610, X6611, X6612]:((c_Orderings_Obot__class_Obot(tc_fun(X6612,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6612,tc_HOL_Obool)),X6611),hAPP(hAPP(c_Set_Oinsert(X6612),X6610),c_Orderings_Obot__class_Obot(tc_fun(X6612,tc_HOL_Obool))))|X6610=c_Big__Operators_Olinorder__class_OMax(X6612,hAPP(hAPP(c_Set_Oinsert(X6612),X6610),X6611))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6612),X6611))|~class_Orderings_Olinorder(X6612))&(c_Orderings_Obot__class_Obot(tc_fun(X6612,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6612,tc_HOL_Obool)),X6611),hAPP(hAPP(c_Set_Oinsert(X6612),X6610),c_Orderings_Obot__class_Obot(tc_fun(X6612,tc_HOL_Obool))))|c_Big__Operators_Olinorder__class_OMax(X6612,hAPP(hAPP(c_Set_Oinsert(X6612),X6610),X6611))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X6612),X6610),c_Big__Operators_Olinorder__class_OMax(X6612,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6612,tc_HOL_Obool)),X6611),hAPP(hAPP(c_Set_Oinsert(X6612),X6610),c_Orderings_Obot__class_Obot(tc_fun(X6612,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6612),X6611))|~class_Orderings_Olinorder(X6612))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Oinsert__remove])])])])). 4.05/4.30 fof(c_0_6430, plain, ![X4348, X4349, X4350, X4351, X4352]:((hBOOL(hAPP(hAPP(c_member(X4351),esk134_5(X4348,X4349,X4350,X4351,X4352)),hAPP(c_List_Oset(X4351),X4350)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4352),hAPP(c_List_Omonoid__add__class_Olistsum(X4352),hAPP(hAPP(c_List_Omap(X4351,X4352),X4349),X4350))),hAPP(c_List_Omonoid__add__class_Olistsum(X4352),hAPP(hAPP(c_List_Omap(X4351,X4352),X4348),X4350))))|(~class_Groups_Oordered__ab__semigroup__add(X4352)|~class_Groups_Omonoid__add(X4352)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4352),hAPP(X4349,esk134_5(X4348,X4349,X4350,X4351,X4352))),hAPP(X4348,esk134_5(X4348,X4349,X4350,X4351,X4352))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4352),hAPP(c_List_Omonoid__add__class_Olistsum(X4352),hAPP(hAPP(c_List_Omap(X4351,X4352),X4349),X4350))),hAPP(c_List_Omonoid__add__class_Olistsum(X4352),hAPP(hAPP(c_List_Omap(X4351,X4352),X4348),X4350))))|(~class_Groups_Oordered__ab__semigroup__add(X4352)|~class_Groups_Omonoid__add(X4352)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__mono])])])])])). 4.05/4.30 cnf(c_0_6431, 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_5083])). 4.05/4.30 cnf(c_0_6432, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Product__Type_Osnd(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)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Product__Type_Ofst(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_5084])). 4.05/4.30 cnf(c_0_6433, 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_5085]), ['final']). 4.05/4.30 fof(c_0_6434, plain, ![X6625, X6626, X6627, X6628, X6629, X6630, X6631, X6632, X6633]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X6633,X6632)),hAPP(hAPP(c_Product__Type_OPair(X6633,X6632),X6631),X6630)),X6629))|hBOOL(hAPP(hAPP(c_member(tc_prod(X6628,X6627)),hAPP(hAPP(c_Product__Type_OPair(X6628,X6627),hAPP(X6626,X6631)),hAPP(X6625,X6630))),hAPP(c_Set_Oimage(tc_prod(X6633,X6632),tc_prod(X6628,X6627),c_Product__Type_Omap__pair(X6633,X6628,X6632,X6627,X6626,X6625)),X6629)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__pair__imageI])])])). 4.05/4.30 cnf(c_0_6435, 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_5079])). 4.05/4.30 cnf(c_0_6436, 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_5086]), ['final']). 4.05/4.30 cnf(c_0_6437, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),X5)=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)),X2)),X3)),X4)!=X5|X2!=hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),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)),X5)|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)!=X3), inference(split_conjunct,[status(thm)],[c_0_5087])). 4.05/4.30 fof(c_0_6438, plain, ![X2123, X2124, X2125]:(~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,X2125),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X2125)),X2124))))|hBOOL(hAPP(hAPP(c_member(X2125),hAPP(c_Product__Type_Ofst(X2125,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X2125,X2124),X2123))),hAPP(c_List_Oset(X2125),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X2125),X2125),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X2125)),X2124))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_select__weight__member])])])). 4.05/4.30 fof(c_0_6439, plain, ![X772, X773, X774, X775, X776, X777, X778, X779]:(~c_Finite__Set_Ofolding(X779,X778,X777,X776)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X779),X775))|hAPP(c_Fun_Ocomp(X778,X778,X774,hAPP(X777,X773)),hAPP(c_Fun_Ocomp(X778,X778,X774,hAPP(X776,X775)),X772))=hAPP(c_Fun_Ocomp(X778,X778,X774,hAPP(X776,X775)),hAPP(c_Fun_Ocomp(X778,X778,X774,hAPP(X777,X773)),X772)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ocommute__left__comp_H])])])). 4.05/4.30 fof(c_0_6440, plain, ![X12677, X12678, X12679, X12680, X12681, X12682, X12683]:((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X12683,X12682,X12681,X12680,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12683,tc_HOL_Obool)),X12679),hAPP(hAPP(c_Set_Oinsert(X12683),X12677),c_Orderings_Obot__class_Obot(tc_fun(X12683,tc_HOL_Obool))))),esk390_7(X12677,X12678,X12679,X12680,X12681,X12682,X12683)))|~hBOOL(hAPP(hAPP(c_member(X12683),X12677),X12679))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X12683,X12682,X12681,X12680,X12679),X12678))|~c_Finite__Set_Ofun__left__comm(X12683,X12682,X12681))&(hAPP(hAPP(X12681,X12677),esk390_7(X12677,X12678,X12679,X12680,X12681,X12682,X12683))=X12678|~hBOOL(hAPP(hAPP(c_member(X12683),X12677),X12679))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X12683,X12682,X12681,X12680,X12679),X12678))|~c_Finite__Set_Ofun__left__comm(X12683,X12682,X12681))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE__aux])])])])])). 4.05/4.30 fof(c_0_6441, plain, ![X13941, X13942, X13943, X13944, X13945, X13946, X13947, X13948]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13948,X13947)),hAPP(hAPP(c_Product__Type_OPair(X13948,X13947),X13946),X13945)),X13944))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13947,X13943)),hAPP(hAPP(c_Product__Type_OPair(X13947,X13943),X13945),X13942)),X13941))|hBOOL(hAPP(hAPP(c_member(tc_prod(X13948,X13943)),hAPP(hAPP(c_Product__Type_OPair(X13948,X13943),X13946),X13942)),hAPP(hAPP(c_Relation_Orel__comp(X13948,X13947,X13943),X13944),X13941))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__compI])])])). 4.05/4.30 fof(c_0_6442, plain, ![X839, X840, X841]:((c_Orderings_Obot__class_Obot(tc_fun(X841,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X841,tc_HOL_Obool)),X840),hAPP(hAPP(c_Set_Oinsert(X841),X839),c_Orderings_Obot__class_Obot(tc_fun(X841,tc_HOL_Obool))))|c_Big__Operators_Olinorder__class_OMin(X841,hAPP(hAPP(c_Set_Oinsert(X841),X839),X840))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X841),X839),c_Big__Operators_Olinorder__class_OMin(X841,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X841,tc_HOL_Obool)),X840),hAPP(hAPP(c_Set_Oinsert(X841),X839),c_Orderings_Obot__class_Obot(tc_fun(X841,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X841),X840))|~class_Orderings_Olinorder(X841))&(c_Orderings_Obot__class_Obot(tc_fun(X841,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X841,tc_HOL_Obool)),X840),hAPP(hAPP(c_Set_Oinsert(X841),X839),c_Orderings_Obot__class_Obot(tc_fun(X841,tc_HOL_Obool))))|X839=c_Big__Operators_Olinorder__class_OMin(X841,hAPP(hAPP(c_Set_Oinsert(X841),X839),X840))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X841),X840))|~class_Orderings_Olinorder(X841))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Oinsert__remove])])])])). 4.05/4.30 cnf(c_0_6443, 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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5088, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_6444, plain, ![X17085, X17086, X17087, X17088, X17089, X17090]:(~class_Groups_Oab__semigroup__mult(X17090)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17089),X17088))|(hBOOL(hAPP(hAPP(c_member(X17089),X17087),X17088))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17090),hAPP(X17086,X17087)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17090,X17089,c_Groups_Otimes__class_Otimes(X17090)),X17086),X17085),X17088))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X17090,X17089,c_Groups_Otimes__class_Otimes(X17090)),X17086),X17085),hAPP(hAPP(c_Set_Oinsert(X17089),X17087),X17088))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__insert])])])). 4.05/4.30 cnf(c_0_6445, plain, (hAPP(c_Fun_Othe__inv__into(X4,X2,X6,hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X7)=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)|~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_5089])). 4.05/4.30 fof(c_0_6446, plain, ![X362, X363, X364, X365]:((hBOOL(hAPP(hAPP(c_member(X365),esk1_4(X362,X363,X364,X365)),X364))|hAPP(c_Finite__Set_Ocard(tc_prod(X365,X363)),hAPP(hAPP(c_Product__Type_OSigma(X365,X363),X364),X362))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X365,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X363,tc_HOL_Obool),tc_Nat_Onat,X365),c_Finite__Set_Ocard(X363)),X362)),X364)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X365),X364)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X363),hAPP(X362,esk1_4(X362,X363,X364,X365))))|hAPP(c_Finite__Set_Ocard(tc_prod(X365,X363)),hAPP(hAPP(c_Product__Type_OSigma(X365,X363),X364),X362))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X365,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X363,tc_HOL_Obool),tc_Nat_Onat,X365),c_Finite__Set_Ocard(X363)),X362)),X364)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X365),X364)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__SigmaI])])])])])). 4.05/4.30 fof(c_0_6447, plain, ![X12363, X12364, X12365, X12366, X12367, X12368]:(~c_Finite__Set_Ofolding(X12368,X12367,X12366,X12365)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12368),X12364))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12368),X12363))|hAPP(c_Fun_Ocomp(X12367,X12367,X12367,hAPP(X12365,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12368,tc_HOL_Obool)),X12364),X12363))),hAPP(X12365,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12368,tc_HOL_Obool)),X12364),X12363)))=hAPP(c_Fun_Ocomp(X12367,X12367,X12367,hAPP(X12365,X12364)),hAPP(X12365,X12363))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ounion__inter])])). 4.05/4.30 fof(c_0_6448, plain, ![X4263, X4264, X4265, X4266, X4267]:(~class_Fields_Ofield(X4267)|(c_Groups_Ozero__class_Ozero(X4267)=X4266|(c_Groups_Ozero__class_Ozero(X4267)=X4265|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4267),X4264),X4266)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4267),X4263),X4265))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4267),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4267),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4267),X4264),X4265)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4267),X4263),X4266))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4267),X4266),X4265))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__frac__eq])])])). 4.05/4.30 fof(c_0_6449, plain, ![X10284, X10285, X10286, X10287, X10288, X10289]:((hBOOL(hAPP(hAPP(c_member(X10288),esk313_6(X10284,X10285,X10286,X10287,X10288,X10289)),X10287))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10289,X10288,c_Groups_Otimes__class_Otimes(X10289)),X10285),X10284),X10287)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10289,X10288,c_Groups_Otimes__class_Otimes(X10289)),X10286),X10284),X10287)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10288),X10287))|~class_Groups_Oab__semigroup__mult(X10289))&(hAPP(X10285,esk313_6(X10284,X10285,X10286,X10287,X10288,X10289))!=hAPP(X10286,esk313_6(X10284,X10285,X10286,X10287,X10288,X10289))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10289,X10288,c_Groups_Otimes__class_Otimes(X10289)),X10285),X10284),X10287)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10289,X10288,c_Groups_Otimes__class_Otimes(X10289)),X10286),X10284),X10287)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10288),X10287))|~class_Groups_Oab__semigroup__mult(X10289))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__cong])])])])])). 4.05/4.30 fof(c_0_6450, plain, ![X9424, X9425, X9426, X9427, X9428, X9429]:(~c_Finite__Set_Ofun__left__comm(X9429,X9428,X9427)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9429),X9426))|hAPP(hAPP(c_Finite__Set_Ofold(X9429,X9428,X9427),X9425),hAPP(hAPP(c_Set_Oinsert(X9429),X9424),X9426))=hAPP(hAPP(X9427,X9424),hAPP(hAPP(c_Finite__Set_Ofold(X9429,X9428,X9427),X9425),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9429,tc_HOL_Obool)),X9426),hAPP(hAPP(c_Set_Oinsert(X9429),X9424),c_Orderings_Obot__class_Obot(tc_fun(X9429,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])])])). 4.05/4.30 fof(c_0_6451, plain, ![X15273, X15274, X15275, X15276, X15277, X15278]:(~c_Finite__Set_Ofun__left__comm(X15278,X15277,X15276)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15278),X15275))|(~hBOOL(hAPP(hAPP(c_member(X15278),X15274),X15275))|hAPP(hAPP(c_Finite__Set_Ofold(X15278,X15277,X15276),X15273),X15275)=hAPP(hAPP(X15276,X15274),hAPP(hAPP(c_Finite__Set_Ofold(X15278,X15277,X15276),X15273),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15278,tc_HOL_Obool)),X15275),hAPP(hAPP(c_Set_Oinsert(X15278),X15274),c_Orderings_Obot__class_Obot(tc_fun(X15278,tc_HOL_Obool))))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__rec])])])). 4.05/4.30 fof(c_0_6452, plain, ![X4394, X4395, X4396, X4397, X4398]:(~class_Fields_Ofield(X4398)|(c_Groups_Ozero__class_Ozero(X4398)=X4397|(X4396=c_Groups_Ozero__class_Ozero(X4398)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4398),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4398),X4395),X4397)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4398),X4394),X4396))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4398),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4398),X4395),X4396)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4398),X4394),X4397))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4398),X4397),X4396))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__frac__eq])])])). 4.05/4.30 fof(c_0_6453, plain, ![X17583, X17584, X17585, X17586]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17586),X17585))|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),X17586),X17584)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X17585),X17583))),c_FunDef_Opair__leq))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__leqI1])])). 4.05/4.30 fof(c_0_6454, plain, ![X6375, X6376, X6377, X6378]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6378),X6377))|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),X6378),X6376)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6377),X6375))),c_FunDef_Opair__less))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__lessI1])])). 4.05/4.30 fof(c_0_6455, plain, ![X1879, X1880, X1881, X1882, X1883]:(~class_Groups_Ocomm__monoid__mult(X1883)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1882),X1881))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1883),hAPP(X1880,X1879)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1882,X1883),X1880),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1882,tc_HOL_Obool)),X1881),hAPP(hAPP(c_Set_Oinsert(X1882),X1879),c_Orderings_Obot__class_Obot(tc_fun(X1882,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1882,X1883),X1880),hAPP(hAPP(c_Set_Oinsert(X1882),X1879),X1881)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod_Oinsert__remove])])])). 4.05/4.30 fof(c_0_6456, plain, ![X2535, X2536, X2537, X2538, X2539, X2540]:(~c_Fun_Oinj__on(X2540,X2539,X2538,X2537)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2540,tc_HOL_Obool)),X2536),X2537))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2540,tc_HOL_Obool)),X2535),X2537))|hAPP(c_Set_Oimage(X2540,X2539,X2538),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2540,tc_HOL_Obool)),X2536),X2535))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2539,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2540,X2539,X2538),X2536)),hAPP(c_Set_Oimage(X2540,X2539,X2538),X2535))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__image__set__diff])])])). 4.05/4.30 fof(c_0_6457, plain, ![X11168, X11169, X11170, X11171, X11172, X11173]:(~c_Fun_Oinj__on(X11173,X11172,X11171,X11170)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11173,tc_HOL_Obool)),X11169),X11170))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11173,tc_HOL_Obool)),X11168),X11170))|hAPP(c_Set_Oimage(X11173,X11172,X11171),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11173,tc_HOL_Obool)),X11169),X11168))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11172,tc_HOL_Obool)),hAPP(c_Set_Oimage(X11173,X11172,X11171),X11169)),hAPP(c_Set_Oimage(X11173,X11172,X11171),X11168))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__image__Int])])])). 4.05/4.30 fof(c_0_6458, plain, ![X14720, X14721, X14722, X14723, X14724]:(~class_Groups_Ocomm__monoid__add(X14724)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14723),X14722))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14723,X14724),X14721),hAPP(hAPP(c_Set_Oinsert(X14723),X14720),X14722))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14724),hAPP(X14721,X14720)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14723,X14724),X14721),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14723,tc_HOL_Obool)),X14722),hAPP(hAPP(c_Set_Oinsert(X14723),X14720),c_Orderings_Obot__class_Obot(tc_fun(X14723,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum_Oinsert__remove])])])). 4.05/4.30 fof(c_0_6459, plain, ![X2811, X2812, X2813, X2814, X2815]:((hBOOL(hAPP(hAPP(c_member(X2814),esk95_5(X2811,X2812,X2813,X2814,X2815)),X2813))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2815),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2814,X2815),X2812),X2813)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2814,X2815),X2811),X2813)))|c_Orderings_Obot__class_Obot(tc_fun(X2814,tc_HOL_Obool))=X2813|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2814),X2813))|(~class_Groups_Ocomm__monoid__add(X2815)|~class_Groups_Oordered__cancel__ab__semigroup__add(X2815)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2815),hAPP(X2812,esk95_5(X2811,X2812,X2813,X2814,X2815))),hAPP(X2811,esk95_5(X2811,X2812,X2813,X2814,X2815))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2815),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2814,X2815),X2812),X2813)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2814,X2815),X2811),X2813)))|c_Orderings_Obot__class_Obot(tc_fun(X2814,tc_HOL_Obool))=X2813|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2814),X2813))|(~class_Groups_Ocomm__monoid__add(X2815)|~class_Groups_Oordered__cancel__ab__semigroup__add(X2815)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__strict__mono])])])])])). 4.05/4.30 fof(c_0_6460, plain, ![X2958, X2959, X2960, X2961, X2962]:((~c_Fun_Oinj__on(X2962,X2961,X2960,X2958)|hBOOL(hAPP(hAPP(c_member(X2961),hAPP(X2960,X2959)),hAPP(c_Set_Oimage(X2962,X2961,X2960),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2962,tc_HOL_Obool)),X2958),hAPP(hAPP(c_Set_Oinsert(X2962),X2959),c_Orderings_Obot__class_Obot(tc_fun(X2962,tc_HOL_Obool)))))))|c_Fun_Oinj__on(X2962,X2961,X2960,hAPP(hAPP(c_Set_Oinsert(X2962),X2959),X2958)))&((c_Fun_Oinj__on(X2962,X2961,X2960,X2958)|~c_Fun_Oinj__on(X2962,X2961,X2960,hAPP(hAPP(c_Set_Oinsert(X2962),X2959),X2958)))&(~hBOOL(hAPP(hAPP(c_member(X2961),hAPP(X2960,X2959)),hAPP(c_Set_Oimage(X2962,X2961,X2960),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2962,tc_HOL_Obool)),X2958),hAPP(hAPP(c_Set_Oinsert(X2962),X2959),c_Orderings_Obot__class_Obot(tc_fun(X2962,tc_HOL_Obool)))))))|~c_Fun_Oinj__on(X2962,X2961,X2960,hAPP(hAPP(c_Set_Oinsert(X2962),X2959),X2958))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__insert])])])])). 4.05/4.30 fof(c_0_6461, plain, ![X3313, X3314, X3315, X3316, X3317, X3318, X3319, X3320]:(~c_Finite__Set_Ofolding__image(X3320,X3319,X3318,X3317,X3316)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3319),X3315))|hAPP(hAPP(X3316,hAPP(hAPP(c_COMBS(X3319,X3320,X3320),hAPP(hAPP(c_COMBB(X3320,tc_fun(X3320,X3320),X3319),X3318),X3314)),X3313)),X3315)=hAPP(hAPP(X3318,hAPP(hAPP(X3316,X3314),X3315)),hAPP(hAPP(X3316,X3313),X3315)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image_Odistrib])])])). 4.05/4.30 fof(c_0_6462, plain, ![X11381, X11382, X11383, X11384, X11385]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X11385,X11385)),hAPP(hAPP(c_Product__Type_OPair(X11385,X11385),X11384),esk348_5(X11381,X11382,X11383,X11384,X11385))),X11381))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X11385,X11385)),hAPP(hAPP(c_Product__Type_OPair(X11385,X11385),X11384),X11383)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X11385,X11385),tc_HOL_Obool),hAPP(c_Nat_OSuc,X11382)),X11381))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X11385,X11385)),hAPP(hAPP(c_Product__Type_OPair(X11385,X11385),esk348_5(X11381,X11382,X11383,X11384,X11385)),X11383)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X11385,X11385),tc_HOL_Obool),X11382),X11381)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X11385,X11385)),hAPP(hAPP(c_Product__Type_OPair(X11385,X11385),X11384),X11383)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X11385,X11385),tc_HOL_Obool),hAPP(c_Nat_OSuc,X11382)),X11381))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__E2])])])])])). 4.05/4.30 fof(c_0_6463, plain, ![X6704, X6705, X6706, X6707, X6708]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X6708,X6708)),hAPP(hAPP(c_Product__Type_OPair(X6708,X6708),X6707),esk207_5(X6704,X6705,X6706,X6707,X6708))),X6704))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6708,X6708)),hAPP(hAPP(c_Product__Type_OPair(X6708,X6708),X6707),X6706)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X6708,X6708),tc_HOL_Obool),hAPP(c_Nat_OSuc,X6705)),X6704))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X6708,X6708)),hAPP(hAPP(c_Product__Type_OPair(X6708,X6708),esk207_5(X6704,X6705,X6706,X6707,X6708)),X6706)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X6708,X6708),tc_HOL_Obool),X6705),X6704)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6708,X6708)),hAPP(hAPP(c_Product__Type_OPair(X6708,X6708),X6707),X6706)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X6708,X6708),tc_HOL_Obool),hAPP(c_Nat_OSuc,X6705)),X6704))))), 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])])])])])). 4.05/4.30 fof(c_0_6464, plain, ![X16437, X16438, X16439, X16440, X16441]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X16441,X16441)),hAPP(hAPP(c_Product__Type_OPair(X16441,X16441),X16440),esk492_5(X16437,X16438,X16439,X16440,X16441))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X16441,X16441),tc_HOL_Obool),X16438),X16437)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16441,X16441)),hAPP(hAPP(c_Product__Type_OPair(X16441,X16441),X16440),X16439)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X16441,X16441),tc_HOL_Obool),hAPP(c_Nat_OSuc,X16438)),X16437))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X16441,X16441)),hAPP(hAPP(c_Product__Type_OPair(X16441,X16441),esk492_5(X16437,X16438,X16439,X16440,X16441)),X16439)),X16437))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16441,X16441)),hAPP(hAPP(c_Product__Type_OPair(X16441,X16441),X16440),X16439)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X16441,X16441),tc_HOL_Obool),hAPP(c_Nat_OSuc,X16438)),X16437))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__E])])])])])). 4.05/4.30 fof(c_0_6465, plain, ![X15425, X15426, X15427, X15428, X15429]:(~class_Groups_Ocomm__monoid__mult(X15429)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15428),X15427))|(~hBOOL(hAPP(hAPP(c_member(X15428),X15426),X15427))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X15428,X15429),X15425),X15427)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15429),hAPP(X15425,X15426)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X15428,X15429),X15425),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15428,tc_HOL_Obool)),X15427),hAPP(hAPP(c_Set_Oinsert(X15428),X15426),c_Orderings_Obot__class_Obot(tc_fun(X15428,tc_HOL_Obool))))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod_Oremove])])])). 4.05/4.30 fof(c_0_6466, plain, ![X11625, X11626, X11627, X11628, X11629]:(~class_Groups_Ocomm__monoid__add(X11629)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11628),X11627))|(~hBOOL(hAPP(hAPP(c_member(X11628),X11626),X11627))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11628,X11629),X11625),X11627)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11629),hAPP(X11625,X11626)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11628,X11629),X11625),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11628,tc_HOL_Obool)),X11627),hAPP(hAPP(c_Set_Oinsert(X11628),X11626),c_Orderings_Obot__class_Obot(tc_fun(X11628,tc_HOL_Obool))))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__diff1_H])])])). 4.05/4.30 cnf(c_0_6467, 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,esk279_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_5053])). 4.05/4.30 cnf(c_0_6468, 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,esk172_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_5090])). 4.05/4.30 cnf(c_0_6469, plain, (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))))=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)|~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_5091, c_0_4950]), c_0_4950])). 4.05/4.30 cnf(c_0_6470, 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_5092]), ['final']). 4.05/4.30 fof(c_0_6471, plain, ![X6085, X6086, X6087, X6088]:(hAPP(c_List_Oset(X6088),X6087)!=c_Map_Odom(X6088,X6086,X6085)|X6085=hAPP(c_Map_Omap__of(X6088,X6086),hAPP(hAPP(c_List_Omap(X6088,tc_prod(X6088,X6086)),hAPP(hAPP(c_COMBS(X6088,X6086,tc_prod(X6088,X6086)),c_Product__Type_OPair(X6088,X6086)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X6086),X6086,X6088),c_Option_Othe(X6086)),X6085))),X6087))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__map__keys])])). 4.05/4.30 fof(c_0_6472, plain, ![X13706, X13707, X13708, X13709, X13710, X13711, X13712]:(~class_Groups_Oab__semigroup__mult(X13712)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13711),X13710))|(~c_Fun_Oinj__on(X13711,X13709,X13708,X13710)|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13712,X13711,c_Groups_Otimes__class_Otimes(X13712)),hAPP(c_Fun_Ocomp(X13709,X13712,X13711,X13707),X13708)),X13706),X13710)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X13712,X13709,c_Groups_Otimes__class_Otimes(X13712)),X13707),X13706),hAPP(c_Set_Oimage(X13711,X13709,X13708),X13710))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__reindex])])])). 4.05/4.30 fof(c_0_6473, plain, ![X15231, X15232, X15233, X15234, X15235, X15236]:((hBOOL(hAPP(hAPP(c_member(X15236),X15235),X15234))|hAPP(c_Set_Oimage(X15236,X15233,X15232),X15234)=hAPP(c_Set_Oimage(X15236,X15233,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X15236,X15233),X15232),X15235),X15231)),X15234))&(~hBOOL(hAPP(hAPP(c_member(X15236),X15235),X15234))|hAPP(c_Set_Oimage(X15236,X15233,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X15236,X15233),X15232),X15235),X15231)),X15234)=hAPP(hAPP(c_Set_Oinsert(X15233),X15231),hAPP(c_Set_Oimage(X15236,X15233,X15232),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15236,tc_HOL_Obool)),X15234),hAPP(hAPP(c_Set_Oinsert(X15236),X15235),c_Orderings_Obot__class_Obot(tc_fun(X15236,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__upd__image])])])). 4.05/4.30 cnf(c_0_6474, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk363_3(X3,X2,X1))),esk364_3(X3,X2,X1))|X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk361_3(X3,X2,X1))),esk362_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_5093])). 4.05/4.30 cnf(c_0_6475, plain, (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),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk104_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)),esk105_3(X2,X3,X1)),esk106_3(X2,X3,X1))|~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_5062])). 4.05/4.30 cnf(c_0_6476, 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),esk363_3(X1,X2,X3))),esk364_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),esk361_3(X1,X2,X3))),esk362_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_5093])). 4.05/4.30 cnf(c_0_6477, 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_5094, c_0_4655]), c_0_4655])). 4.05/4.30 fof(c_0_6478, plain, ![X17293, X17294, X17295, X17296, X17297]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17297),X17296))|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),X17296),X17297)),X17295)),X17294)),X17293)=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),X17296),X17295)),X17294)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17297),X17295)),X17293))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__diff__add__eq1])])])). 4.05/4.30 fof(c_0_6479, plain, ![X8587, X8588, X8589, X8590, X8591]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8591),X8590))|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),X8591),X8589)),X8588)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8590),X8589)),X8587))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8588),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),X8590),X8591)),X8589)),X8587))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__diff__add__eq2])])])). 4.05/4.30 cnf(c_0_6480, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk106_3(X2,X3,X1)),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),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))|hAPP(c_Finite__Set_Ocard(X1),esk104_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_5062])). 4.05/4.30 cnf(c_0_6481, 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),c_Transitive__Closure_Ortrancl(X1,X2)),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),c_Transitive__Closure_Ortrancl(X1,X2)),X2)),X3)),X2)),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5095, c_0_5018]), c_0_5018])). 4.05/4.30 cnf(c_0_6482, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk105_3(X2,X3,X1)),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),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))|hAPP(c_Finite__Set_Ocard(X1),esk104_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_5062])). 4.05/4.30 fof(c_0_6483, plain, ![X11030, X11031, X11032, X11033, X11034]:(~class_Rings_Osemiring__0(X11034)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11034),hAPP(c_List_Omonoid__add__class_Olistsum(X11034),hAPP(hAPP(c_List_Omap(X11033,X11034),X11032),X11030))),X11031)=hAPP(c_List_Omonoid__add__class_Olistsum(X11034),hAPP(hAPP(c_List_Omap(X11033,X11034),hAPP(hAPP(c_COMBC(X11033,X11034,X11034),hAPP(hAPP(c_COMBB(X11034,tc_fun(X11034,X11034),X11033),c_Groups_Otimes__class_Otimes(X11034)),X11032)),X11031)),X11030))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__mult__const])])). 4.05/4.30 fof(c_0_6484, plain, ![X13292, X13293, X13294, X13295, X13296]:((X13295=hAPP(hAPP(c_List_Olist_OCons(X13296),esk414_5(X13292,X13293,X13294,X13295,X13296)),esk415_5(X13292,X13293,X13294,X13295,X13296))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X13296),tc_List_Olist(X13296))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X13296),tc_List_Olist(X13296)),X13295),hAPP(hAPP(c_List_Olist_OCons(X13296),X13294),X13293))),c_List_Olistrel(X13296,X13292))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X13296,X13296)),hAPP(hAPP(c_Product__Type_OPair(X13296,X13296),esk414_5(X13292,X13293,X13294,X13295,X13296)),X13294)),X13292))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X13296),tc_List_Olist(X13296))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X13296),tc_List_Olist(X13296)),X13295),hAPP(hAPP(c_List_Olist_OCons(X13296),X13294),X13293))),c_List_Olistrel(X13296,X13292))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X13296),tc_List_Olist(X13296))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X13296),tc_List_Olist(X13296)),esk415_5(X13292,X13293,X13294,X13295,X13296)),X13293)),c_List_Olistrel(X13296,X13292)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X13296),tc_List_Olist(X13296))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X13296),tc_List_Olist(X13296)),X13295),hAPP(hAPP(c_List_Olist_OCons(X13296),X13294),X13293))),c_List_Olistrel(X13296,X13292)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel__Cons2])])])])])). 4.05/4.30 fof(c_0_6485, plain, ![X3030, X3031, X3032, X3033, X3034]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3034),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3033)),X3032)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3034),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3031)),X3030)))|hAPP(hAPP(c_Product__Type_OPair(X3033,X3031),hAPP(hAPP(c_List_Onth(X3033),X3032),X3034)),hAPP(hAPP(c_List_Onth(X3031),X3030),X3034))=hAPP(hAPP(c_List_Onth(tc_prod(X3033,X3031)),hAPP(hAPP(c_List_Ozip(X3033,X3031),X3032),X3030)),X3034))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__zip])])])). 4.05/4.30 cnf(c_0_6486, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3))),esk355_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),esk352_3(X1,X2,X3))),esk353_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5096])). 4.05/4.30 cnf(c_0_6487, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3))),esk355_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),esk352_3(X1,X2,X3))),esk353_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(split_conjunct,[status(thm)],[c_0_5096])). 4.05/4.30 fof(c_0_6488, plain, ![X1832, X1833, X1834, X1835, X1836]:((X1833=hAPP(hAPP(c_List_Olist_OCons(X1836),esk63_5(X1832,X1833,X1834,X1835,X1836)),esk64_5(X1832,X1833,X1834,X1835,X1836))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1836),tc_List_Olist(X1836))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1836),tc_List_Olist(X1836)),hAPP(hAPP(c_List_Olist_OCons(X1836),X1835),X1834)),X1833)),c_List_Olistrel(X1836,X1832))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X1836,X1836)),hAPP(hAPP(c_Product__Type_OPair(X1836,X1836),X1835),esk63_5(X1832,X1833,X1834,X1835,X1836))),X1832))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1836),tc_List_Olist(X1836))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1836),tc_List_Olist(X1836)),hAPP(hAPP(c_List_Olist_OCons(X1836),X1835),X1834)),X1833)),c_List_Olistrel(X1836,X1832))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1836),tc_List_Olist(X1836))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1836),tc_List_Olist(X1836)),X1834),esk64_5(X1832,X1833,X1834,X1835,X1836))),c_List_Olistrel(X1836,X1832)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1836),tc_List_Olist(X1836))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1836),tc_List_Olist(X1836)),hAPP(hAPP(c_List_Olist_OCons(X1836),X1835),X1834)),X1833)),c_List_Olistrel(X1836,X1832)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel__Cons1])])])])])). 4.05/4.30 fof(c_0_6489, plain, ![X2165, X2166, X2167, X2168, X2169, X2170]:(~class_Complete__Lattice_Ocomplete__lattice(X2170)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2169,X2170),X2168),hAPP(hAPP(c_COMBB(tc_fun(X2167,X2170),X2170,X2169),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2167,X2170),X2166)),X2165))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2167,X2170),X2166),hAPP(hAPP(c_COMBB(tc_fun(X2169,X2170),X2170,X2167),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2169,X2170),X2168)),hAPP(c_COMBC(X2169,X2167,X2170),X2165)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF__commute])])])). 4.05/4.30 fof(c_0_6490, plain, ![X7532, X7533, X7534, X7535, X7536, X7537]:(~class_Complete__Lattice_Ocomplete__lattice(X7537)|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7536,X7537),X7535),hAPP(hAPP(c_COMBB(tc_fun(X7534,X7537),X7537,X7536),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7534,X7537),X7533)),X7532))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7534,X7537),X7533),hAPP(hAPP(c_COMBB(tc_fun(X7536,X7537),X7537,X7534),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7536,X7537),X7535)),hAPP(c_COMBC(X7536,X7534,X7537),X7532)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__commute])])). 4.05/4.30 cnf(c_0_6491, plain, (hBOOL(hAPP(X3,esk72_2(X3,X2)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk71_2(X3,X2)),X2))))|hBOOL(hAPP(X3,esk70_2(X3,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(X3,X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5097])). 4.05/4.30 cnf(c_0_6492, 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_5098]), ['final']). 4.05/4.30 fof(c_0_6493, plain, ![X11335, X11336, X11337, X11338, X11339]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X11339,X11338)),hAPP(X11339,X11337)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X11336,X11336)),hAPP(hAPP(c_Product__Type_OPair(X11336,X11336),X11338),X11337)),c_List_Omeasures(X11336,X11335)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X11336,X11336)),hAPP(hAPP(c_Product__Type_OPair(X11336,X11336),X11338),X11337)),c_List_Omeasures(X11336,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X11336,tc_Nat_Onat)),X11339),X11335)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_measures__lesseq])])])). 4.05/4.30 fof(c_0_6494, plain, ![X6493, X6494, X6495, X6496, X6497]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X6497,X6497)),hAPP(hAPP(c_Product__Type_OPair(X6497,X6497),X6496),X6495)),X6494))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6497),tc_List_Olist(X6497))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6497),tc_List_Olist(X6497)),hAPP(hAPP(c_List_Olist_OCons(X6497),X6496),X6493)),hAPP(hAPP(c_List_Olist_OCons(X6497),X6495),X6493))),c_List_Olistrel1(X6497,X6494)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I1])])). 4.05/4.30 fof(c_0_6495, plain, ![X5488, X5489, X5490, X5491, X5492, X5493]:(~hBOOL(hAPP(hAPP(c_member(X5493),X5492),X5491))|hAPP(hAPP(c_Set_Oinsert(X5490),X5489),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5493,tc_fun(X5490,tc_HOL_Obool)),X5491),X5488))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5493,tc_fun(X5490,tc_HOL_Obool)),X5491),hAPP(hAPP(c_COMBB(tc_fun(X5490,tc_HOL_Obool),tc_fun(X5490,tc_HOL_Obool),X5493),hAPP(c_Set_Oinsert(X5490),X5489)),X5488))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__insert__distrib])])). 4.05/4.30 fof(c_0_6496, plain, ![X16356, X16357, X16358]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X16358),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X16357),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X16357)),X16356))))|hBOOL(hAPP(hAPP(c_member(X16357),hAPP(c_Random_Opick(X16357,X16356),X16358)),hAPP(c_List_Oset(X16357),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X16357),X16357),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X16357)),X16356))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pick__member])])). 4.05/4.30 cnf(c_0_6497, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5099, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6498, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5100, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_6499, plain, ![X17639, X17640, X17641, X17642, X17643]:(hAPP(c_Relation_OImage(X17643,X17643,X17642),hAPP(hAPP(c_Set_Oinsert(X17643),X17641),c_Orderings_Obot__class_Obot(tc_fun(X17643,tc_HOL_Obool))))!=hAPP(c_Relation_OImage(X17643,X17643,X17642),hAPP(hAPP(c_Set_Oinsert(X17643),X17640),c_Orderings_Obot__class_Obot(tc_fun(X17643,tc_HOL_Obool))))|(~c_Equiv__Relations_Oequiv(X17643,X17639,X17642)|(~hBOOL(hAPP(hAPP(c_member(X17643),X17640),X17639))|hBOOL(hAPP(hAPP(c_member(tc_prod(X17643,X17643)),hAPP(hAPP(c_Product__Type_OPair(X17643,X17643),X17641),X17640)),X17642))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__equiv__class])])])). 4.05/4.30 fof(c_0_6500, plain, ![X7779, X7780, X7781, X7782, X7783]:((hBOOL(hAPP(hAPP(c_member(X7782),esk250_5(X7779,X7780,X7781,X7782,X7783)),hAPP(c_List_Oset(X7782),X7781)))|hAPP(c_List_Omonoid__add__class_Olistsum(X7783),hAPP(hAPP(c_List_Omap(X7782,X7783),X7779),X7781))=hAPP(c_List_Omonoid__add__class_Olistsum(X7783),hAPP(hAPP(c_List_Omap(X7782,X7783),X7779),hAPP(c_List_Ofilter(X7782,X7780),X7781)))|~class_Groups_Omonoid__add(X7783))&((~hBOOL(hAPP(X7780,esk250_5(X7779,X7780,X7781,X7782,X7783)))|hAPP(c_List_Omonoid__add__class_Olistsum(X7783),hAPP(hAPP(c_List_Omap(X7782,X7783),X7779),X7781))=hAPP(c_List_Omonoid__add__class_Olistsum(X7783),hAPP(hAPP(c_List_Omap(X7782,X7783),X7779),hAPP(c_List_Ofilter(X7782,X7780),X7781)))|~class_Groups_Omonoid__add(X7783))&(hAPP(X7779,esk250_5(X7779,X7780,X7781,X7782,X7783))!=c_Groups_Ozero__class_Ozero(X7783)|hAPP(c_List_Omonoid__add__class_Olistsum(X7783),hAPP(hAPP(c_List_Omap(X7782,X7783),X7779),X7781))=hAPP(c_List_Omonoid__add__class_Olistsum(X7783),hAPP(hAPP(c_List_Omap(X7782,X7783),X7779),hAPP(c_List_Ofilter(X7782,X7780),X7781)))|~class_Groups_Omonoid__add(X7783)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__map__filter])])])])])). 4.05/4.30 fof(c_0_6501, plain, ![X8483, X8484, X8485, X8486, X8487]:((hBOOL(hAPP(hAPP(c_member(X8486),X8483),X8485))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8486,X8487),X8484),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8486,tc_HOL_Obool)),X8485),hAPP(hAPP(c_Set_Oinsert(X8486),X8483),c_Orderings_Obot__class_Obot(tc_fun(X8486,tc_HOL_Obool)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8486,X8487),X8484),X8485)|hAPP(X8484,X8483)=c_Groups_Ozero__class_Ozero(X8487)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8486),X8485))|~class_Fields_Ofield(X8487))&(~hBOOL(hAPP(hAPP(c_member(X8486),X8483),X8485))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8486,X8487),X8484),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8486,tc_HOL_Obool)),X8485),hAPP(hAPP(c_Set_Oinsert(X8486),X8483),c_Orderings_Obot__class_Obot(tc_fun(X8486,tc_HOL_Obool)))))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8487),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8486,X8487),X8484),X8485)),hAPP(X8484,X8483))|hAPP(X8484,X8483)=c_Groups_Ozero__class_Ozero(X8487)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8486),X8485))|~class_Fields_Ofield(X8487))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__diff1])])])])). 4.05/4.30 cnf(c_0_6502, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5101, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_6503, plain, ![X2437, X2438, X2439, X2440]:(~hBOOL(hAPP(c_List_Odistinct(X2440),X2439))|(hBOOL(hAPP(hAPP(c_member(X2440),X2438),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2440,tc_HOL_Obool)),hAPP(c_List_Oset(X2440),X2439)),hAPP(hAPP(c_Set_Oinsert(X2440),hAPP(hAPP(c_List_Onth(X2440),X2439),X2437)),c_Orderings_Obot__class_Obot(tc_fun(X2440,tc_HOL_Obool))))))|hBOOL(hAPP(c_List_Odistinct(X2440),hAPP(hAPP(c_List_Olist__update(X2440,X2439),X2437),X2438))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__list__update])])])). 4.05/4.30 cnf(c_0_6504, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk38_3(X1,X2,X3)),esk39_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(X1,esk38_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk39_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_5102])). 4.05/4.30 cnf(c_0_6505, 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,esk419_8(X2,X1,X3,X4,X5,X6,X7,X8))!=hAPP(X2,esk419_8(X2,X1,X3,X4,X5,X6,X7,X8))|X4!=X3|X6!=X5|~class_Orderings_Oord(X7)|~class_Groups_Ocomm__monoid__add(X8)), inference(split_conjunct,[status(thm)],[c_0_5103])). 4.05/4.30 cnf(c_0_6506, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk232_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),esk231_4(X1,X2,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk231_4(X1,X2,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5104])). 4.05/4.30 cnf(c_0_6507, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk232_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),esk231_4(X2,X3,X4,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X3,esk231_4(X2,X3,X4,X1))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5104])). 4.05/4.30 fof(c_0_6508, plain, ![X5496, X5497, X5498, X5499, X5500]:(~class_Rings_Oring(X5500)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5499),X5498))|(~hBOOL(hAPP(hAPP(c_member(X5499),X5497),X5498))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5499,X5500),X5496),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5499,tc_HOL_Obool)),X5498),hAPP(hAPP(c_Set_Oinsert(X5499),X5497),c_Orderings_Obot__class_Obot(tc_fun(X5499,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5500),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5499,X5500),X5496),X5498)),hAPP(X5496,X5497))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__diff1__ring])])])). 4.05/4.30 fof(c_0_6509, plain, ![X4647, X4648, X4649]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4649),X4648))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4649),X4647))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4649),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4649,tc_HOL_Obool)),X4648),X4647))),hAPP(c_Finite__Set_Ocard(X4649),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4649,tc_HOL_Obool)),X4648),X4647)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4649),X4648)),hAPP(c_Finite__Set_Ocard(X4649),X4647)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Un__Int])])])). 4.05/4.30 cnf(c_0_6510, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin))=hAPP(hAPP(c_Groups_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))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5105, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.30 fof(c_0_6511, plain, ![X11724, X11725, X11726, X11727, X11728, X11729, X11730, X11731]:(~c_Finite__Set_Ofolding(X11731,X11730,X11729,X11728)|hAPP(c_Fun_Ocomp(X11730,X11730,X11727,hAPP(X11729,X11725)),hAPP(c_Fun_Ocomp(X11730,X11730,X11727,hAPP(X11729,X11726)),X11724))=hAPP(c_Fun_Ocomp(X11730,X11730,X11727,hAPP(X11729,X11726)),hAPP(c_Fun_Ocomp(X11730,X11730,X11727,hAPP(X11729,X11725)),X11724))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp])])). 4.05/4.30 cnf(c_0_6512, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,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),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2))!=X3), inference(split_conjunct,[status(thm)],[c_0_5084])). 4.05/4.30 cnf(c_0_6513, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk319_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),esk317_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_5059])). 4.05/4.30 cnf(c_0_6514, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk318_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),esk317_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_5059])). 4.05/4.30 fof(c_0_6515, plain, ![X2420, X2421, X2422, X2423, X2424, X2425, X2426, X2427]:(~c_Finite__Set_Ofolding__image__simple(X2427,X2426,X2425,X2424,X2423,X2422)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2426),X2421))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2426),X2420))|hAPP(hAPP(X2425,hAPP(X2422,X2421)),hAPP(X2422,X2420))=hAPP(hAPP(X2425,hAPP(X2422,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2426,tc_HOL_Obool)),X2421),X2420))),hAPP(X2422,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2426,tc_HOL_Obool)),X2421),X2420)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Ounion__inter])])])). 4.05/4.30 cnf(c_0_6516, plain, (c_List_OdropWhile(X4,X1,X2)=c_List_OdropWhile(X4,X1,hAPP(hAPP(c_List_Oappend(X4),X3),X2))|~hBOOL(hAPP(X1,esk230_4(X2,X1,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_5082])). 4.05/4.30 fof(c_0_6517, plain, ![X13715, X13716, X13717, X13718, X13719]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13719,X13719)),hAPP(hAPP(c_Product__Type_OPair(X13719,X13719),X13718),X13717)),c_Transitive__Closure_Ortrancl(X13719,X13716)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13719,X13719)),hAPP(hAPP(c_Product__Type_OPair(X13719,X13719),X13717),X13715)),c_Transitive__Closure_Ortrancl(X13719,X13716)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X13719,X13719)),hAPP(hAPP(c_Product__Type_OPair(X13719,X13719),X13718),X13715)),c_Transitive__Closure_Ortrancl(X13719,X13716))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__trans])])])). 4.05/4.30 fof(c_0_6518, plain, ![X3059, X3060, X3061, X3062, X3063]:((hBOOL(hAPP(hAPP(c_member(X3062),X3060),X3061))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3062,X3063),X3059),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3062,tc_HOL_Obool)),X3061),hAPP(hAPP(c_Set_Oinsert(X3062),X3060),c_Orderings_Obot__class_Obot(tc_fun(X3062,tc_HOL_Obool)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3062,X3063),X3059),X3061)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3062),X3061))|~class_Groups_Oab__group__add(X3063))&(~hBOOL(hAPP(hAPP(c_member(X3062),X3060),X3061))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3063),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3062,X3063),X3059),X3061)),hAPP(X3059,X3060))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3062,X3063),X3059),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3062,tc_HOL_Obool)),X3061),hAPP(hAPP(c_Set_Oinsert(X3062),X3060),c_Orderings_Obot__class_Obot(tc_fun(X3062,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3062),X3061))|~class_Groups_Oab__group__add(X3063))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__diff1])])])])). 4.05/4.30 cnf(c_0_6519, 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_4652])). 4.05/4.30 cnf(c_0_6520, 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_5106, c_0_4523]), c_0_4523]), c_0_4523]), ['final']). 4.05/4.30 fof(c_0_6521, plain, ![X11182, X11183, X11184, X11185, X11186, X11187]:(~c_Finite__Set_Ofolding(X11187,X11186,X11185,X11184)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11187),X11183))|hAPP(X11184,hAPP(hAPP(c_Set_Oinsert(X11187),X11182),X11183))=hAPP(c_Fun_Ocomp(X11186,X11186,X11186,hAPP(X11184,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11187,tc_HOL_Obool)),X11183),hAPP(hAPP(c_Set_Oinsert(X11187),X11182),c_Orderings_Obot__class_Obot(tc_fun(X11187,tc_HOL_Obool)))))),hAPP(X11185,X11182)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oinsert__remove])])). 4.05/4.30 fof(c_0_6522, plain, ![X10351, X10352, X10353, X10354]:(hAPP(c_Set_Oimage(X10354,X10353,X10352),c_Orderings_Otop__class_Otop(tc_fun(X10354,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X10353,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10353,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10353,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10354,X10353,X10352),X10351))),hAPP(c_Set_Oimage(X10354,X10353,X10352),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10354,tc_HOL_Obool)),X10351))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__Compl__image__subset])])). 4.05/4.30 fof(c_0_6523, plain, ![X6077, X6078, X6079]:(~class_Fields_Ofield(X6079)|(c_Groups_Oone__class_Oone(X6079)=X6078|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6079),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X6079),hAPP(hAPP(c_Power_Opower__class_Opower(X6079),X6078),X6077)),c_Groups_Oone__class_Oone(X6079))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X6079),X6078),c_Groups_Oone__class_Oone(X6079)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6079),hAPP(c_Power_Opower__class_Opower(X6079),X6078)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6077)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_geometric__sum])])). 4.05/4.30 fof(c_0_6524, plain, ![X12717, X12718, X12719, X12720, X12721]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X12721,X12721)),hAPP(hAPP(c_Product__Type_OPair(X12721,X12721),X12720),X12719)),c_List_Omeasures(X12721,X12717)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X12718,X12720)),hAPP(X12718,X12719)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X12721,X12721)),hAPP(hAPP(c_Product__Type_OPair(X12721,X12721),X12720),X12719)),c_List_Omeasures(X12721,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X12721,tc_Nat_Onat)),X12718),X12717)))))&(hAPP(X12718,X12720)=hAPP(X12718,X12719)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X12718,X12720)),hAPP(X12718,X12719)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X12721,X12721)),hAPP(hAPP(c_Product__Type_OPair(X12721,X12721),X12720),X12719)),c_List_Omeasures(X12721,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X12721,tc_Nat_Onat)),X12718),X12717))))))&((~hBOOL(hAPP(hAPP(c_member(tc_prod(X12721,X12721)),hAPP(hAPP(c_Product__Type_OPair(X12721,X12721),X12720),X12719)),c_List_Omeasures(X12721,X12717)))|hAPP(X12718,X12720)!=hAPP(X12718,X12719)|hBOOL(hAPP(hAPP(c_member(tc_prod(X12721,X12721)),hAPP(hAPP(c_Product__Type_OPair(X12721,X12721),X12720),X12719)),c_List_Omeasures(X12721,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X12721,tc_Nat_Onat)),X12718),X12717)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X12718,X12720)),hAPP(X12718,X12719)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X12721,X12721)),hAPP(hAPP(c_Product__Type_OPair(X12721,X12721),X12720),X12719)),c_List_Omeasures(X12721,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X12721,tc_Nat_Onat)),X12718),X12717))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measures_I2_J])])])). 4.05/4.30 fof(c_0_6525, plain, ![X940, X941, X942, X943, X944, X945]:(~class_Rings_Olinordered__semiring__1__strict(X945)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X945),X944),X943))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X945),X942),X943))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X945),c_Groups_Ozero__class_Ozero(X945)),X941))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X945),c_Groups_Ozero__class_Ozero(X945)),X940))|(c_Groups_Oone__class_Oone(X945)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X945),X941),X940)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X945),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X945),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X945),X941),X944)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X945),X940),X942))),X943)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_convex__bound__lt])])])). 4.05/4.30 fof(c_0_6526, plain, ![X7663, X7664, X7665, X7666, X7667, X7668]:(~class_Rings_Olinordered__semiring__1(X7668)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7668),X7667),X7666))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7668),X7665),X7666))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7668),c_Groups_Ozero__class_Ozero(X7668)),X7664))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7668),c_Groups_Ozero__class_Ozero(X7668)),X7663))|(c_Groups_Oone__class_Oone(X7668)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7668),X7664),X7663)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7668),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7668),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7668),X7664),X7667)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7668),X7663),X7665))),X7666)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__le])])). 4.05/4.30 fof(c_0_6527, plain, ![X1018, X1019, X1020, X1021, X1022, X1023]:(~c_Finite__Set_Ofolding(X1023,X1022,X1021,X1020)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1023),X1019))|(~hBOOL(hAPP(hAPP(c_member(X1023),X1018),X1019))|hAPP(c_Fun_Ocomp(X1022,X1022,X1022,hAPP(X1020,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1023,tc_HOL_Obool)),X1019),hAPP(hAPP(c_Set_Oinsert(X1023),X1018),c_Orderings_Obot__class_Obot(tc_fun(X1023,tc_HOL_Obool)))))),hAPP(X1021,X1018))=hAPP(X1020,X1019)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Oremove])])])). 4.05/4.30 fof(c_0_6528, plain, ![X6911, X6912, X6913, X6914]:(~class_Orderings_Olinorder(X6914)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X6914,X6914,c_COMBI(X6914)),X6912),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X6914,X6914,c_COMBI(X6914)),X6913),X6911))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X6914,X6914,c_COMBI(X6914)),X6913),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X6914,X6914,c_COMBI(X6914)),X6912),X6911))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__left__comm])])). 4.05/4.30 cnf(c_0_6529, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hAPP(hAPP(c_List_Oappend(X1),X2),X5)=hAPP(hAPP(c_List_Oappend(X1),X3),X4)|hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4)!=X5|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_5087])). 4.05/4.30 fof(c_0_6530, plain, ![X16448, X16449, X16450, X16451, X16452]:((hBOOL(hAPP(hAPP(c_member(X16451),esk493_5(X16448,X16449,X16450,X16451,X16452)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16451,tc_HOL_Obool)),X16450),X16449)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16451,X16452),X16448),X16449)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16451,X16452),X16448),X16450)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16451,tc_HOL_Obool)),X16449),X16450))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16451),X16450))|~class_Groups_Ocomm__monoid__mult(X16452))&(hAPP(X16448,esk493_5(X16448,X16449,X16450,X16451,X16452))!=c_Groups_Oone__class_Oone(X16452)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16451,X16452),X16448),X16449)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16451,X16452),X16448),X16450)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16451,tc_HOL_Obool)),X16449),X16450))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16451),X16450))|~class_Groups_Ocomm__monoid__mult(X16452))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__mono__one__right])])])])])). 4.05/4.30 fof(c_0_6531, plain, ![X7487, X7488, X7489, X7490, X7491]:((hBOOL(hAPP(hAPP(c_member(X7490),esk238_5(X7487,X7488,X7489,X7490,X7491)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7490,tc_HOL_Obool)),X7489),X7488)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7490,X7491),X7487),X7489)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7490,X7491),X7487),X7488)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7490,tc_HOL_Obool)),X7488),X7489))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7490),X7489))|~class_Groups_Ocomm__monoid__mult(X7491))&(c_Groups_Oone__class_Oone(X7491)!=hAPP(X7487,esk238_5(X7487,X7488,X7489,X7490,X7491))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7490,X7491),X7487),X7489)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7490,X7491),X7487),X7488)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7490,tc_HOL_Obool)),X7488),X7489))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7490),X7489))|~class_Groups_Ocomm__monoid__mult(X7491))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__mono__one__left])])])])])). 4.05/4.30 fof(c_0_6532, plain, ![X17275, X17276, X17277, X17278, X17279]:((hBOOL(hAPP(hAPP(c_member(X17278),esk518_5(X17275,X17276,X17277,X17278,X17279)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17278,tc_HOL_Obool)),X17277),X17276)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17278,X17279),X17275),X17277)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17278,X17279),X17275),X17276)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17278,tc_HOL_Obool)),X17276),X17277))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X17278),X17277))|~class_Groups_Ocomm__monoid__add(X17279))&(hAPP(X17275,esk518_5(X17275,X17276,X17277,X17278,X17279))!=c_Groups_Ozero__class_Ozero(X17279)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17278,X17279),X17275),X17277)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17278,X17279),X17275),X17276)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17278,tc_HOL_Obool)),X17276),X17277))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X17278),X17277))|~class_Groups_Ocomm__monoid__add(X17279))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__mono__zero__left])])])])])). 4.05/4.30 fof(c_0_6533, plain, ![X5699, X5700, X5701, X5702, X5703]:((hBOOL(hAPP(hAPP(c_member(X5702),esk178_5(X5699,X5700,X5701,X5702,X5703)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5702,tc_HOL_Obool)),X5701),X5700)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5702,X5703),X5699),X5701)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5702,X5703),X5699),X5700)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5702,tc_HOL_Obool)),X5700),X5701))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5702),X5701))|~class_Groups_Ocomm__monoid__add(X5703))&(c_Groups_Ozero__class_Ozero(X5703)!=hAPP(X5699,esk178_5(X5699,X5700,X5701,X5702,X5703))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5702,X5703),X5699),X5701)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5702,X5703),X5699),X5700)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5702,tc_HOL_Obool)),X5700),X5701))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5702),X5701))|~class_Groups_Ocomm__monoid__add(X5703))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__mono__zero__right])])])])])). 4.05/4.30 fof(c_0_6534, plain, ![X5219, X5220, X5221]:(~class_Orderings_Olinorder(X5221)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5221),X5220))|c_List_Olinorder__class_Osorted__list__of__set(X5221,hAPP(hAPP(c_Set_Oinsert(X5221),X5219),X5220))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5221,X5221,c_COMBI(X5221)),X5219),c_List_Olinorder__class_Osorted__list__of__set(X5221,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5221,tc_HOL_Obool)),X5220),hAPP(hAPP(c_Set_Oinsert(X5221),X5219),c_Orderings_Obot__class_Obot(tc_fun(X5221,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__insert])])). 4.05/4.30 cnf(c_0_6535, plain, (hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oconcat(X2,X1)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),esk317_2(X1,X2)),hAPP(c_List_Oset(tc_List_Olist(X2)),X1)))|esk318_2(X1,X2)!=esk319_2(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1))), inference(split_conjunct,[status(thm)],[c_0_5059])). 4.05/4.30 cnf(c_0_6536, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X3,tc_HOL_Obool)),X2))=hAPP(c_Finite__Set_Ocard(X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2))|hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),esk104_3(X1,X2,X3)),X2))|esk106_3(X1,X2,X3)!=esk105_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_5062])). 4.05/4.30 fof(c_0_6537, plain, ![X5831, X5832, X5833, X5834, X5835]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5835,X5835)),hAPP(hAPP(c_Product__Type_OPair(X5835,X5835),hAPP(X5834,hAPP(c_Nat_OSuc,esk182_5(X5831,X5832,X5833,X5834,X5835)))),hAPP(X5834,esk182_5(X5831,X5832,X5833,X5834,X5835)))),c_Transitive__Closure_Ortrancl(X5835,X5833)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5835,X5835)),hAPP(hAPP(c_Product__Type_OPair(X5835,X5835),hAPP(X5834,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5832),X5831))),hAPP(X5834,X5832))),c_Transitive__Closure_Ortrancl(X5835,X5833)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sequence__trans])])])])). 4.05/4.30 cnf(c_0_6538, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk165_6(X2,X3,X4,X5,X1,X6)),hAPP(c_List_Oset(X1),X6)))|hAPP(c_List_Ofilter(X1,X5),X4)=hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)|X4!=hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X7))|~hBOOL(hAPP(X5,X3))|hAPP(c_List_Ofilter(X1,X5),X7)!=X2), inference(split_conjunct,[status(thm)],[c_0_5107])). 4.05/4.30 fof(c_0_6539, plain, ![X4988, X4989, X4990, X4991, X4992, X4993, X4994, X4995]:(~c_Finite__Set_Ofolding__image__simple(X4995,X4994,X4993,X4992,X4991,X4990)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4994),X4989))|hAPP(X4990,hAPP(hAPP(c_Set_Oinsert(X4994),X4988),X4989))=hAPP(hAPP(X4993,hAPP(X4991,X4988)),hAPP(X4990,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4994,tc_HOL_Obool)),X4989),hAPP(hAPP(c_Set_Oinsert(X4994),X4988),c_Orderings_Obot__class_Obot(tc_fun(X4994,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert__remove])])])). 4.05/4.30 fof(c_0_6540, plain, ![X592, X593, X594, X595, X596]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X596,tc_HOL_Obool)),hAPP(c_Relation_OImage(X595,X596,X594),X593)),X592))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X595,tc_HOL_Obool)),X593),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X595,tc_HOL_Obool)),hAPP(c_Relation_OImage(X596,X595,hAPP(c_Relation_Oconverse(X595,X596),X594)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X596,tc_HOL_Obool)),X592))))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X595,tc_HOL_Obool)),X593),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X595,tc_HOL_Obool)),hAPP(c_Relation_OImage(X596,X595,hAPP(c_Relation_Oconverse(X595,X596),X594)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X596,tc_HOL_Obool)),X592)))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X596,tc_HOL_Obool)),hAPP(c_Relation_OImage(X595,X596,X594),X593)),X592)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__subset__eq])])). 4.05/4.30 fof(c_0_6541, plain, ![X13190, X13191, X13192]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X13192,tc_HOL_Obool)),esk407_3(X13190,X13191,X13192)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X13192,tc_HOL_Obool)),X13191),X13190)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13192,tc_HOL_Obool)),X13191),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13192,tc_HOL_Obool),X13190))=c_Orderings_Obot__class_Obot(tc_fun(X13192,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_fun(X13192,tc_HOL_Obool)),X13191),X13190)))&((hBOOL(hAPP(hAPP(c_member(tc_fun(X13192,tc_HOL_Obool)),esk408_3(X13190,X13191,X13192)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X13192,tc_HOL_Obool)),X13191),X13190)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13192,tc_HOL_Obool)),X13191),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13192,tc_HOL_Obool),X13190))=c_Orderings_Obot__class_Obot(tc_fun(X13192,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_fun(X13192,tc_HOL_Obool)),X13191),X13190)))&((esk407_3(X13190,X13191,X13192)!=esk408_3(X13190,X13191,X13192)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13192,tc_HOL_Obool)),X13191),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13192,tc_HOL_Obool),X13190))=c_Orderings_Obot__class_Obot(tc_fun(X13192,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_fun(X13192,tc_HOL_Obool)),X13191),X13190)))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13192,tc_HOL_Obool)),esk407_3(X13190,X13191,X13192)),esk408_3(X13190,X13191,X13192))!=c_Orderings_Obot__class_Obot(tc_fun(X13192,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13192,tc_HOL_Obool)),X13191),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13192,tc_HOL_Obool),X13190))=c_Orderings_Obot__class_Obot(tc_fun(X13192,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_fun(X13192,tc_HOL_Obool)),X13191),X13190)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__partition])])])])])). 4.05/4.30 cnf(c_0_6542, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|c_Map_Omap__upds(X1,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),X5),X2),hAPP(c_Option_Ooption_OSome(X4),X6)),X3,X7)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Omap__upds(X1,X4,X5,X3,X7)),X2),hAPP(c_Option_Ooption_OSome(X4),X6))), inference(split_conjunct,[status(thm)],[c_0_5108])). 4.05/4.30 fof(c_0_6543, plain, ![X6251, X6252, X6253, X6254, X6255]:(~class_Groups_Oab__group__add(X6255)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6254),X6253))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6253),X6252))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X6255),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6255),X6251),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6254),X6252))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6255),X6251),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6254),X6253)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6255),X6251),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6253),X6252))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat__ivl])])). 4.05/4.30 cnf(c_0_6544, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk73_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),esk70_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk71_2(X1,X2)),X2))))|hBOOL(hAPP(X1,esk70_2(X1,X2)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5097])). 4.05/4.30 fof(c_0_6545, plain, ![X8336, X8337, X8338, X8339, X8340, X8341, X8342, X8343]:(~c_Finite__Set_Ofolding__image__simple(X8343,X8342,X8341,X8340,X8339,X8338)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8342),X8337))|(~hBOOL(hAPP(hAPP(c_member(X8342),X8336),X8337))|hAPP(hAPP(X8341,hAPP(X8339,X8336)),hAPP(X8338,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8342,tc_HOL_Obool)),X8337),hAPP(hAPP(c_Set_Oinsert(X8342),X8336),c_Orderings_Obot__class_Obot(tc_fun(X8342,tc_HOL_Obool))))))=hAPP(X8338,X8337)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oremove])])). 4.05/4.30 cnf(c_0_6546, plain, (hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))=hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),hAPP(hAPP(c_COMBC(X3,X3,tc_HOL_Obool),c_fequal),X2))),X1))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5109])). 4.05/4.30 fof(c_0_6547, plain, ![X1492, X1493, X1494, X1495, X1496]:(~c_Equiv__Relations_Oequiv(X1496,X1495,X1494)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1496,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1496,X1496,X1494),hAPP(hAPP(c_Set_Oinsert(X1496),X1493),c_Orderings_Obot__class_Obot(tc_fun(X1496,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X1496,X1496,X1494),hAPP(hAPP(c_Set_Oinsert(X1496),X1492),c_Orderings_Obot__class_Obot(tc_fun(X1496,tc_HOL_Obool))))))|(~hBOOL(hAPP(hAPP(c_member(X1496),X1493),X1495))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1496,X1496)),hAPP(hAPP(c_Product__Type_OPair(X1496,X1496),X1492),X1493)),X1494))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__equiv__class])])])). 4.05/4.30 cnf(c_0_6548, 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_5110])). 4.05/4.30 fof(c_0_6549, plain, ![X5007, X5008, X5009, X5010, X5011]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5011,X5011)),hAPP(hAPP(c_Product__Type_OPair(X5011,X5011),X5010),X5009)),X5008))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5011,X5011)),hAPP(hAPP(c_Product__Type_OPair(X5011,X5011),X5009),X5007)),c_Transitive__Closure_Ortrancl(X5011,X5008)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5011,X5011)),hAPP(hAPP(c_Product__Type_OPair(X5011,X5011),X5010),X5007)),c_Transitive__Closure_Ortrancl(X5011,X5008))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_converse__rtrancl__into__rtrancl])])])). 4.05/4.30 fof(c_0_6550, plain, ![X9417, X9418, X9419, X9420, X9421]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9421,X9421)),hAPP(hAPP(c_Product__Type_OPair(X9421,X9421),X9420),X9419)),c_Transitive__Closure_Ortrancl(X9421,X9418)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9421,X9421)),hAPP(hAPP(c_Product__Type_OPair(X9421,X9421),X9419),X9417)),X9418))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9421,X9421)),hAPP(hAPP(c_Product__Type_OPair(X9421,X9421),X9420),X9417)),c_Transitive__Closure_Ortrancl(X9421,X9418))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl])])). 4.05/4.30 fof(c_0_6551, plain, ![X6815, X6816, X6817, X6818, X6819]:(~class_Groups_Ocomm__monoid__add(X6819)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6818),X6817))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6817),X6816))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6819),X6815),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6818),X6816))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6819),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6819),X6815),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6818),X6817))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X6819),X6815),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6817),X6816)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__add__nat__ivl])])])). 4.05/4.30 fof(c_0_6552, plain, ![X12846, X12847, X12848, X12849, X12850]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X12850)),hAPP(c_Set_Oimage(X12849,tc_Option_Ooption(X12850),X12848),c_Orderings_Otop__class_Otop(tc_fun(X12849,tc_HOL_Obool)))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X12850)),hAPP(c_Set_Oimage(X12849,tc_Option_Ooption(X12850),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X12849,tc_Option_Ooption(X12850)),X12848),X12847),hAPP(c_Option_Ooption_OSome(X12850),X12846))),c_Orderings_Otop__class_Otop(tc_fun(X12849,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__updI])])). 4.05/4.30 cnf(c_0_6553, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5111, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.30 fof(c_0_6554, plain, ![X13561, X13562, X13563, X13564, X13565, X13566]:(~class_Orderings_Olinorder(X13566)|(hAPP(X13565,X13564)=hAPP(X13565,X13563)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13562,X13566,X13565),X13564),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13562,X13566,X13565),X13563),X13561))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13562,X13566,X13565),X13563),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13562,X13566,X13565),X13564),X13561)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__key__left__comm])])])). 4.05/4.30 fof(c_0_6555, plain, ![X1436, X1437, X1438, X1439]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk44_4(X1436,X1437,X1438,X1439)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1438)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1439),X1437))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1439),X1438)),X1437)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1437),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1436))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1438)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk45_4(X1436,X1437,X1438,X1439)),X1436))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1439),X1437))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1439),X1438)),X1437)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1437),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1436))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1438)))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk45_4(X1436,X1437,X1438,X1439)),esk44_4(X1436,X1437,X1438,X1439))=X1439|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1439),X1437))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1439),X1438)),X1437)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1437),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1436))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1438))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_aset_I6_J])])])])])])). 4.05/4.30 cnf(c_0_6556, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk240_4(X1,X2,X3,X4)),esk239_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_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_5112])). 4.05/4.30 cnf(c_0_6557, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk317_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),esk318_2(X2,X1))),hAPP(c_List_Oset(X1),esk319_2(X2,X1)))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_5059])). 4.05/4.30 fof(c_0_6558, plain, ![X15045, X15046, X15047]:(~class_Lattices_Oab__semigroup__idem__mult(X15047)|(hAPP(X15046,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15047),esk450_3(X15045,X15046,X15047)),esk451_3(X15045,X15046,X15047)))!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15047),hAPP(X15046,esk450_3(X15045,X15046,X15047))),hAPP(X15046,esk451_3(X15045,X15046,X15047)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15047),X15045))|(X15045=c_Orderings_Obot__class_Obot(tc_fun(X15047,tc_HOL_Obool))|hAPP(X15046,hAPP(c_Finite__Set_Ofold1(X15047,c_Groups_Otimes__class_Otimes(X15047)),X15045))=hAPP(c_Finite__Set_Ofold1(X15047,c_Groups_Otimes__class_Otimes(X15047)),hAPP(c_Set_Oimage(X15047,X15047,X15046),X15045)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hom__fold1__commute])])])). 4.05/4.30 fof(c_0_6559, plain, ![X2791, X2792, X2793, X2794, X2795]:(~class_Groups_Ocomm__monoid__mult(X2795)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2794),X2793))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2794),X2792))|(c_Orderings_Obot__class_Obot(tc_fun(X2794,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2794,tc_HOL_Obool)),X2793),X2792)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2795),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2794,X2795),X2791),X2793)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2794,X2795),X2791),X2792))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2794,X2795),X2791),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2794,tc_HOL_Obool)),X2793),X2792)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod_Ounion__disjoint])])])). 4.05/4.30 cnf(c_0_6560, plain, (hAPP(c_List_Orev(X2),hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4))=hAPP(hAPP(c_List_Olist__update(X2,hAPP(c_List_Orev(X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_5113])). 4.05/4.30 cnf(c_0_6561, 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))), inference(split_conjunct,[status(thm)],[c_0_5114]), ['final']). 4.05/4.30 fof(c_0_6562, plain, ![X13154, X13155, X13156, X13157]:(~c_Fun_Oinj__on(X13157,X13156,X13155,c_Orderings_Otop__class_Otop(tc_fun(X13157,tc_HOL_Obool)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13156,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13157,X13156,X13155),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X13157,tc_HOL_Obool)),X13154))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X13156,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13157,X13156,X13155),X13154))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__Compl__subset])])). 4.05/4.30 fof(c_0_6563, plain, ![X12587, X12588, X12589, X12590, X12591]:(~class_Groups_Ocomm__monoid__add(X12591)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12590),X12589))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12590),X12588))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12590,tc_HOL_Obool)),X12589),X12588)!=c_Orderings_Obot__class_Obot(tc_fun(X12590,tc_HOL_Obool))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12590,X12591),X12587),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12590,tc_HOL_Obool)),X12589),X12588))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12591),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12590,X12591),X12587),X12589)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12590,X12591),X12587),X12588)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__Un__disjoint])])])). 4.05/4.30 cnf(c_0_6564, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk239_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_5112])). 4.05/4.30 cnf(c_0_6565, 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_5115])). 4.05/4.30 fof(c_0_6566, plain, ![X14639, X14640, X14641, X14642, X14643, X14644]:(~c_Equiv__Relations_Oequiv(X14644,X14643,X14642)|(~hBOOL(hAPP(hAPP(c_member(X14644),X14641),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14644,tc_HOL_Obool)),hAPP(c_Relation_OImage(X14644,X14644,X14642),hAPP(hAPP(c_Set_Oinsert(X14644),X14640),c_Orderings_Obot__class_Obot(tc_fun(X14644,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X14644,X14644,X14642),hAPP(hAPP(c_Set_Oinsert(X14644),X14639),c_Orderings_Obot__class_Obot(tc_fun(X14644,tc_HOL_Obool)))))))|hBOOL(hAPP(hAPP(c_member(tc_prod(X14644,X14644)),hAPP(hAPP(c_Product__Type_OPair(X14644,X14644),X14640),X14639)),X14642)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__nondisjoint])])). 4.05/4.30 fof(c_0_6567, plain, ![X3759, X3760, X3761, X3762]:((hBOOL(hAPP(hAPP(c_member(X3762),X3761),X3760))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3762,tc_Nat_Onat),X3759),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3762,tc_HOL_Obool)),X3760),hAPP(hAPP(c_Set_Oinsert(X3762),X3761),c_Orderings_Obot__class_Obot(tc_fun(X3762,tc_HOL_Obool)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3762,tc_Nat_Onat),X3759),X3760))&(~hBOOL(hAPP(hAPP(c_member(X3762),X3761),X3760))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3762,tc_Nat_Onat),X3759),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3762,tc_HOL_Obool)),X3760),hAPP(hAPP(c_Set_Oinsert(X3762),X3761),c_Orderings_Obot__class_Obot(tc_fun(X3762,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3762,tc_Nat_Onat),X3759),X3760)),hAPP(X3759,X3761)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__diff1__nat])])])). 4.05/4.30 fof(c_0_6568, plain, ![X13118, X13119, X13120, X13121, X13124, X13125, X13126, X13127, X13128, X13130, X13131]:((((hBOOL(hAPP(hAPP(c_member(X13121),esk404_4(X13118,X13119,X13120,X13121)),X13119))|hBOOL(hAPP(hAPP(c_member(X13121),esk403_4(X13118,X13119,X13120,X13121)),X13120))|(~hBOOL(hAPP(hAPP(c_member(X13121),X13124),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13121,tc_HOL_Obool)),X13120),X13119)))|hBOOL(hAPP(X13118,X13124))))&(~hBOOL(hAPP(X13118,esk404_4(X13118,X13119,X13120,X13121)))|hBOOL(hAPP(hAPP(c_member(X13121),esk403_4(X13118,X13119,X13120,X13121)),X13120))|(~hBOOL(hAPP(hAPP(c_member(X13121),X13124),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13121,tc_HOL_Obool)),X13120),X13119)))|hBOOL(hAPP(X13118,X13124)))))&((hBOOL(hAPP(hAPP(c_member(X13121),esk404_4(X13118,X13119,X13120,X13121)),X13119))|~hBOOL(hAPP(X13118,esk403_4(X13118,X13119,X13120,X13121)))|(~hBOOL(hAPP(hAPP(c_member(X13121),X13124),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13121,tc_HOL_Obool)),X13120),X13119)))|hBOOL(hAPP(X13118,X13124))))&(~hBOOL(hAPP(X13118,esk404_4(X13118,X13119,X13120,X13121)))|~hBOOL(hAPP(X13118,esk403_4(X13118,X13119,X13120,X13121)))|(~hBOOL(hAPP(hAPP(c_member(X13121),X13124),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13121,tc_HOL_Obool)),X13120),X13119)))|hBOOL(hAPP(X13118,X13124))))))&(((~hBOOL(hAPP(hAPP(c_member(X13128),X13130),X13127))|hBOOL(hAPP(X13125,X13130))|hBOOL(hAPP(hAPP(c_member(X13128),esk405_4(X13125,X13126,X13127,X13128)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13128,tc_HOL_Obool)),X13127),X13126))))&(~hBOOL(hAPP(hAPP(c_member(X13128),X13131),X13126))|hBOOL(hAPP(X13125,X13131))|hBOOL(hAPP(hAPP(c_member(X13128),esk405_4(X13125,X13126,X13127,X13128)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13128,tc_HOL_Obool)),X13127),X13126)))))&((~hBOOL(hAPP(hAPP(c_member(X13128),X13130),X13127))|hBOOL(hAPP(X13125,X13130))|~hBOOL(hAPP(X13125,esk405_4(X13125,X13126,X13127,X13128))))&(~hBOOL(hAPP(hAPP(c_member(X13128),X13131),X13126))|hBOOL(hAPP(X13125,X13131))|~hBOOL(hAPP(X13125,esk405_4(X13125,X13126,X13127,X13128))))))), 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])])])])])])). 4.05/4.30 fof(c_0_6569, plain, ![X16573, X16574, X16575, X16576, X16577]:((~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),X16576),X16577)),X16575)),X16574)),X16573))|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),X16576),X16575)),X16574)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16577),X16575)),X16573)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16577),X16576)))&(~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),X16576),X16575)),X16574)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16577),X16575)),X16573)))|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),X16576),X16577)),X16575)),X16574)),X16573))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16577),X16576)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__less__add__iff1])])])])). 4.05/4.30 fof(c_0_6570, plain, ![X9826, X9827, X9828, X9829, X9830]:((~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),X9829),X9828)),X9827)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9830),X9828)),X9826)))|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),X9829),X9830)),X9828)),X9827)),X9826))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9830),X9829)))&(~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),X9829),X9830)),X9828)),X9827)),X9826))|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),X9829),X9828)),X9827)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9830),X9828)),X9826)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9830),X9829)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__le__add__iff1])])])])). 4.05/4.30 fof(c_0_6571, plain, ![X5098, X5099, X5100, X5101, X5102]:((~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),X5102),X5100)),X5099)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5101),X5100)),X5098)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5099),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),X5101),X5102)),X5100)),X5098)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5102),X5101)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5099),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),X5101),X5102)),X5100)),X5098)))|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),X5102),X5100)),X5099)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5101),X5100)),X5098)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5102),X5101)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2])])])). 4.05/4.30 fof(c_0_6572, plain, ![X10144, X10145, X10146, X10147, X10148, X10149, X10150]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10150,X10149),tc_HOL_Obool)),X10148),X10147))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10149,X10146),tc_HOL_Obool)),X10145),X10144))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10150,X10146),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10150,X10149,X10146),X10148),X10145)),hAPP(hAPP(c_Relation_Orel__comp(X10150,X10149,X10146),X10147),X10144))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__comp__mono])])])). 4.05/4.30 cnf(c_0_6573, plain, (c_List_Oupt(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X1,X2)),c_List_Oupt(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5116])). 4.05/4.30 fof(c_0_6574, plain, ![X12712, X12713, X12714, X12715, X12716]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12713),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),X12715),X12716)),X12714)),X12712)))|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),X12716),X12714)),X12713)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12715),X12714)),X12712)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12716),X12715)))&(~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),X12716),X12714)),X12713)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12715),X12714)),X12712)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12713),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),X12715),X12716)),X12714)),X12712)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12716),X12715)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__le__add__iff2])])])])). 4.05/4.30 fof(c_0_6575, plain, ![X2896, X2897, X2898, X2899, X2900]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2900),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2899)),X2898)))|hAPP(hAPP(c_List_Olist__update(X2899,hAPP(hAPP(c_List_Oappend(X2899),X2898),X2897)),X2900),X2896)=hAPP(hAPP(c_List_Oappend(X2899),X2898),hAPP(hAPP(c_List_Olist__update(X2899,X2897),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2900),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2899)),X2898))),X2896)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2900),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2899)),X2898)))|hAPP(hAPP(c_List_Olist__update(X2899,hAPP(hAPP(c_List_Oappend(X2899),X2898),X2897)),X2900),X2896)=hAPP(hAPP(c_List_Oappend(X2899),hAPP(hAPP(c_List_Olist__update(X2899,X2898),X2900),X2896)),X2897))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__update__append])])])). 4.05/4.30 fof(c_0_6576, plain, ![X4774, X4775, X4776, X4777, X4778]:((hBOOL(hAPP(hAPP(c_member(X4777),esk147_5(X4774,X4775,X4776,X4777,X4778)),X4776))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4778),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4777,X4778),X4775),X4776)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4778),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4778),hAPP(c_Finite__Set_Ocard(X4777),X4776))),X4774)))|(~class_Groups_Oordered__ab__semigroup__add(X4778)|~class_Rings_Osemiring__1(X4778)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4778),hAPP(X4775,esk147_5(X4774,X4775,X4776,X4777,X4778))),X4774))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4778),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4777,X4778),X4775),X4776)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4778),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4778),hAPP(c_Finite__Set_Ocard(X4777),X4776))),X4774)))|(~class_Groups_Oordered__ab__semigroup__add(X4778)|~class_Rings_Osemiring__1(X4778)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__bounded])])])])). 4.05/4.30 cnf(c_0_6577, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk187_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),c_Transitive__Closure_Ortrancl(X1,X2)),X2)))), inference(rw,[status(thm)],[c_0_5117, c_0_5018])). 4.05/4.30 cnf(c_0_6578, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk185_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),c_Transitive__Closure_Ortrancl(X1,X3)),X3)))), inference(rw,[status(thm)],[c_0_5118, c_0_5018])). 4.05/4.30 fof(c_0_6579, plain, ![X14687, X14688, X14689, X14690, X14691, X14692]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14692)),X14691)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14690)),X14689)|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14692)),X14688)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14690)),X14687)|hAPP(hAPP(c_List_Ozip(X14692,X14690),hAPP(hAPP(c_List_Oappend(X14692),X14691),X14688)),hAPP(hAPP(c_List_Oappend(X14690),X14689),X14687))=hAPP(hAPP(c_List_Oappend(tc_prod(X14692,X14690)),hAPP(hAPP(c_List_Ozip(X14692,X14690),X14691),X14689)),hAPP(hAPP(c_List_Ozip(X14692,X14690),X14688),X14687)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zip__append])])])). 4.05/4.30 fof(c_0_6580, plain, ![X2996, X2997, X2998]:((hBOOL(hAPP(hAPP(c_member(X2998),esk102_3(X2996,X2997,X2998)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2998,tc_HOL_Obool)),X2997),X2996)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2998),X2997)),hAPP(c_Finite__Set_Ocard(X2998),X2996))=hAPP(c_Finite__Set_Ocard(X2998),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2998,tc_HOL_Obool)),X2997),X2996))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2998),X2996))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2998),X2997)))&(c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2998),X2997)),hAPP(c_Finite__Set_Ocard(X2998),X2996))=hAPP(c_Finite__Set_Ocard(X2998),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2998,tc_HOL_Obool)),X2997),X2996))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2998),X2996))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2998),X2997)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card_Ounion__inter__neutral])])])])])). 4.05/4.30 fof(c_0_6581, plain, ![X13827, X13828, X13829, X13830, X13831, X13832]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13832),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13832),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13832),X13831),X13830)),X13829)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13832),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13832),X13828),X13830)),X13827)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13832),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13832),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13832),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13832),X13831),X13828)),X13830)),X13829)),X13827))|~class_Rings_Oordered__ring(X13832))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13832),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13832),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13832),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13832),X13831),X13828)),X13830)),X13829)),X13827))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13832),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13832),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13832),X13831),X13830)),X13829)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13832),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13832),X13828),X13830)),X13827)))|~class_Rings_Oordered__ring(X13832))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__add__iff1])])])])). 4.05/4.30 fof(c_0_6582, plain, ![X4563, X4564, X4565, X4566, X4567, X4568]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4568),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4568),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4568),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4568),X4567),X4564)),X4566)),X4565)),X4563))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4568),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4568),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4568),X4567),X4566)),X4565)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4568),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4568),X4564),X4566)),X4563)))|~class_Rings_Oordered__ring(X4568))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4568),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4568),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4568),X4567),X4566)),X4565)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4568),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4568),X4564),X4566)),X4563)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4568),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4568),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4568),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4568),X4567),X4564)),X4566)),X4565)),X4563))|~class_Rings_Oordered__ring(X4568))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__add__iff1])])])])). 4.05/4.30 fof(c_0_6583, plain, ![X8791, X8792, X8793, X8794, X8795, X8796]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8796),X8793),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8796),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8796),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8796),X8792),X8795)),X8794)),X8791)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8796),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8796),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8796),X8795),X8794)),X8793)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8796),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8796),X8792),X8794)),X8791)))|~class_Rings_Oordered__ring(X8796))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8796),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8796),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8796),X8795),X8794)),X8793)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8796),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8796),X8792),X8794)),X8791)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8796),X8793),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8796),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8796),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8796),X8792),X8795)),X8794)),X8791)))|~class_Rings_Oordered__ring(X8796))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff2])])])). 4.05/4.30 cnf(c_0_6584, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X4)),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),c_Transitive__Closure_Ortrancl(X1,X3)),X3)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5119, c_0_5018]), c_0_5018])). 4.05/4.30 fof(c_0_6585, plain, ![X2135, X2136, X2137, X2138]:(~c_Finite__Set_Ofolding__one(X2138,X2137,X2136)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2138),X2135))|(X2135=c_Orderings_Obot__class_Obot(tc_fun(X2138,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_member(X2138),hAPP(hAPP(X2137,esk76_4(X2135,X2136,X2137,X2138)),esk77_4(X2135,X2136,X2137,X2138))),hAPP(hAPP(c_Set_Oinsert(X2138),esk76_4(X2135,X2136,X2137,X2138)),hAPP(hAPP(c_Set_Oinsert(X2138),esk77_4(X2135,X2136,X2137,X2138)),c_Orderings_Obot__class_Obot(tc_fun(X2138,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X2138),hAPP(X2136,X2135)),X2135)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Oclosed])])])])). 4.05/4.30 cnf(c_0_6586, 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_5120])). 4.05/4.30 cnf(c_0_6587, plain, (c_Lazy__Sequence_Ohb__bind(X1,X2,X3,X4)=c_Lazy__Sequence_Ohb__flat(X2,c_Lazy__Sequence_Ohb__map(X1,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)),X4,X3))), inference(split_conjunct,[status(thm)],[c_0_5121])). 4.05/4.30 fof(c_0_6588, plain, ![X8945, X8946, X8947, X8948, X8949, X8950]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8950),X8947),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8950),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8950),X8946),X8949)),X8948)),X8945)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8950),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8950),X8949),X8948)),X8947)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8950),X8946),X8948)),X8945)))|~class_Rings_Oordered__ring(X8950))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8950),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8950),X8949),X8948)),X8947)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8950),X8946),X8948)),X8945)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8950),X8947),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8950),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8950),X8946),X8949)),X8948)),X8945)))|~class_Rings_Oordered__ring(X8950))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__add__iff2])])])])). 4.05/4.30 cnf(c_0_6589, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk363_3(X3,X2,X1))),esk364_3(X3,X2,X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_3(X3,X2,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|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_5093])). 4.05/4.30 cnf(c_0_6590, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk364_3(X2,X3,X1)))|X3=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk361_3(X2,X3,X1))),esk362_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_5093])). 4.05/4.30 cnf(c_0_6591, 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_5122])). 4.05/4.30 fof(c_0_6592, plain, ![X10296, X10297, X10298, X10299, X10300, X10301]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10299)),X10298)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10301)),X10300)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10301,tc_HOL_Obool)),hAPP(c_List_Oset(X10301),X10300)),X10297))|c_Map_Omap__upds(X10301,X10299,c_Map_Orestrict__map(X10301,X10299,X10296,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10301,tc_HOL_Obool)),X10297),hAPP(c_List_Oset(X10301),X10300))),X10300,X10298)=c_Map_Orestrict__map(X10301,X10299,c_Map_Omap__upds(X10301,X10299,X10296,X10300,X10298),X10297))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_restrict__map__upds])])])). 4.05/4.30 fof(c_0_6593, plain, ![X14454, X14455, X14456, X14457, X14458, X14459, X14460]:(X14460=X14459|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X14458,X14457),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X14458,X14457),X14456),X14460),X14455)),X14459),X14454)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X14458,X14457),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X14458,X14457),X14456),X14459),X14454)),X14460),X14455)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__upd__twist])])])). 4.05/4.30 fof(c_0_6594, plain, ![X6953, X6954, X6955, X6956]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6956),tc_List_Olist(X6956))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6956),tc_List_Olist(X6956)),X6955),X6954)),c_List_Olistrel(X6956,X6953)))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6956),tc_List_Olist(X6956))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6956),tc_List_Olist(X6956)),X6955),X6954)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X6956),c_List_Olistrel1(X6956,X6953))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__listrel1__if__listrel])])])). 4.05/4.30 cnf(c_0_6595, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk516_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk517_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk516_3(X1,X2,X3)),esk517_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_5123])). 4.05/4.30 fof(c_0_6596, plain, ![X7674, X7675, X7676, X7677, X7678, X7679]:(hBOOL(hAPP(hAPP(c_member(X7679),X7678),c_Map_Odom(X7679,X7677,X7676)))|c_Map_Omap__add(X7679,X7677,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7679,tc_Option_Ooption(X7677)),X7675),X7678),hAPP(c_Option_Ooption_OSome(X7677),X7674)),X7676)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7679,tc_Option_Ooption(X7677)),c_Map_Omap__add(X7679,X7677,X7675,X7676)),X7678),hAPP(c_Option_Ooption_OSome(X7677),X7674))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__add__upd__left])])])). 4.05/4.30 fof(c_0_6597, plain, ![X9024, X9025, X9026, X9027, X9028, X9029]:(~c_Equiv__Relations_Oequiv(X9029,X9028,X9027)|(~c_Equiv__Relations_Ocongruent(X9029,tc_fun(X9026,tc_HOL_Obool),X9027,X9025)|(~hBOOL(hAPP(hAPP(c_member(X9029),X9024),X9028))|hAPP(X9025,X9024)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9029,tc_fun(X9026,tc_HOL_Obool)),hAPP(c_Relation_OImage(X9029,X9029,X9027),hAPP(hAPP(c_Set_Oinsert(X9029),X9024),c_Orderings_Obot__class_Obot(tc_fun(X9029,tc_HOL_Obool))))),X9025)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__equiv__class])])])). 4.05/4.30 fof(c_0_6598, plain, ![X8055, X8056, X8057, X8058]:((hBOOL(hAPP(hAPP(c_member(X8058),esk255_4(X8055,X8056,X8057,X8058)),X8057))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8058),hAPP(hAPP(c_Finite__Set_Ofold(X8058,X8058,c_Lattices_Osemilattice__sup__class_Osup(X8058)),X8055),X8057)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8058),X8056),X8055)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8058),X8057))|~class_Lattices_Osemilattice__sup(X8058))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8058),esk255_4(X8055,X8056,X8057,X8058)),X8056))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8058),hAPP(hAPP(c_Finite__Set_Ofold(X8058,X8058,c_Lattices_Osemilattice__sup__class_Osup(X8058)),X8055),X8057)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8058),X8056),X8055)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8058),X8057))|~class_Lattices_Osemilattice__sup(X8058))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__sup__le__sup])])])])])). 4.05/4.30 fof(c_0_6599, plain, ![X520, X521, X522, X523]:((hBOOL(hAPP(hAPP(c_member(X523),esk9_4(X520,X521,X522,X523)),X522))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X523),hAPP(hAPP(c_Finite__Set_Ofold(X523,X523,c_Orderings_Oord__class_Omax(X523)),X520),X522)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X523),X521),X520)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X523),X522))|~class_Orderings_Olinorder(X523))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X523),esk9_4(X520,X521,X522,X523)),X521))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X523),hAPP(hAPP(c_Finite__Set_Ofold(X523,X523,c_Orderings_Oord__class_Omax(X523)),X520),X522)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X523),X521),X520)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X523),X522))|~class_Orderings_Olinorder(X523))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ofold__sup__le__sup])])])])])). 4.05/4.30 fof(c_0_6600, plain, ![X10091, X10092, X10093, X10094]:((hBOOL(hAPP(hAPP(c_member(X10094),esk309_4(X10091,X10092,X10093,X10094)),X10093))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10094),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10094),X10092),X10091)),hAPP(hAPP(c_Finite__Set_Ofold(X10094,X10094,c_Orderings_Oord__class_Omin(X10094)),X10091),X10093)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10094),X10093))|~class_Orderings_Olinorder(X10094))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10094),X10092),esk309_4(X10091,X10092,X10093,X10094)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10094),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10094),X10092),X10091)),hAPP(hAPP(c_Finite__Set_Ofold(X10094,X10094,c_Orderings_Oord__class_Omin(X10094)),X10091),X10093)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10094),X10093))|~class_Orderings_Olinorder(X10094))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__le__fold__inf])])])])])). 4.05/4.30 fof(c_0_6601, plain, ![X3456, X3457, X3458, X3459]:((hBOOL(hAPP(hAPP(c_member(X3459),esk112_4(X3456,X3457,X3458,X3459)),X3458))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3459),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3459),X3457),X3456)),hAPP(hAPP(c_Finite__Set_Ofold(X3459,X3459,c_Lattices_Osemilattice__inf__class_Oinf(X3459)),X3456),X3458)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3459),X3458))|~class_Lattices_Osemilattice__inf(X3459))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3459),X3457),esk112_4(X3456,X3457,X3458,X3459)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3459),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3459),X3457),X3456)),hAPP(hAPP(c_Finite__Set_Ofold(X3459,X3459,c_Lattices_Osemilattice__inf__class_Oinf(X3459)),X3456),X3458)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3459),X3458))|~class_Lattices_Osemilattice__inf(X3459))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__le__fold__inf])])])])])). 4.05/4.30 fof(c_0_6602, plain, ![X2028, X2029]:(~c_Nat__Transfer_Onat__set(X2029)|(~c_Nat__Transfer_Onat__set(X2028)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X2029),X2028)=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),X2029)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2028))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J])])])). 4.05/4.30 cnf(c_0_6603, plain, (X1=hAPP(X2,esk232_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),esk231_4(X1,X2,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk231_4(X1,X2,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5104])). 4.05/4.30 cnf(c_0_6604, 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_5124])). 4.05/4.30 cnf(c_0_6605, 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_5125]), ['final']). 4.05/4.30 cnf(c_0_6606, 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_5126]), ['final']). 4.05/4.30 fof(c_0_6607, plain, ![X13084, X13085, X13086, X13087, X13088, X13089]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13089),hAPP(X13088,X13087)),hAPP(X13088,X13086)))|hAPP(hAPP(c_List_Olist_OCons(X13085),X13086),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13085,X13089,X13088),X13087),X13084))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13085,X13089,X13088),X13087),hAPP(hAPP(c_List_Olist_OCons(X13085),X13086),X13084))|~class_Orderings_Olinorder(X13089))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13089),hAPP(X13088,X13087)),hAPP(X13088,X13086)))|hAPP(hAPP(c_List_Olist_OCons(X13085),X13087),hAPP(hAPP(c_List_Olist_OCons(X13085),X13086),X13084))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X13085,X13089,X13088),X13087),hAPP(hAPP(c_List_Olist_OCons(X13085),X13086),X13084))|~class_Orderings_Olinorder(X13089))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__key_Osimps_I2_J])])])])). 4.05/4.30 cnf(c_0_6608, 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_5127])). 4.05/4.30 cnf(c_0_6609, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_5128]), ['final']). 4.05/4.30 cnf(c_0_6610, 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_5129, c_0_5130]), c_0_5131]), ['final']). 4.05/4.30 cnf(c_0_6611, 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),esk363_3(X1,X2,X3))),esk364_3(X1,X2,X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_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(split_conjunct,[status(thm)],[c_0_5093])). 4.05/4.30 fof(c_0_6612, plain, ![X1973, X1974, X1975, X1976, X1977, X1978]:(hAPP(c_Set_Oimage(X1978,X1977,X1976),c_Orderings_Otop__class_Otop(tc_fun(X1978,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X1977,tc_HOL_Obool))|(hAPP(c_Set_Oimage(X1975,X1974,X1973),c_Orderings_Otop__class_Otop(tc_fun(X1975,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X1974,tc_HOL_Obool))|c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1977,X1974),tc_HOL_Obool))=hAPP(c_Set_Oimage(tc_prod(X1978,X1975),tc_prod(X1977,X1974),c_Product__Type_Omap__pair(X1978,X1977,X1975,X1974,X1976,X1973)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1978,X1975),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__pair__surj])])])). 4.05/4.30 fof(c_0_6613, plain, ![X13252, X13253, X13254, X13255, X13256, X13259, X13260, X13261, X13262, X13263, X13264, X13266, X13267]:(((hBOOL(hAPP(hAPP(c_member(X13255),esk409_5(X13252,X13253,X13254,X13255,X13256)),X13254))|(~hBOOL(hAPP(hAPP(c_member(X13256),X13259),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13255,tc_fun(X13256,tc_HOL_Obool)),X13254),X13253)))|hBOOL(hAPP(X13252,X13259))))&((hBOOL(hAPP(hAPP(c_member(X13256),esk410_5(X13252,X13253,X13254,X13255,X13256)),hAPP(X13253,esk409_5(X13252,X13253,X13254,X13255,X13256))))|(~hBOOL(hAPP(hAPP(c_member(X13256),X13259),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13255,tc_fun(X13256,tc_HOL_Obool)),X13254),X13253)))|hBOOL(hAPP(X13252,X13259))))&(~hBOOL(hAPP(X13252,esk410_5(X13252,X13253,X13254,X13255,X13256)))|(~hBOOL(hAPP(hAPP(c_member(X13256),X13259),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13255,tc_fun(X13256,tc_HOL_Obool)),X13254),X13253)))|hBOOL(hAPP(X13252,X13259))))))&((hBOOL(hAPP(hAPP(c_member(X13264),esk411_5(X13260,X13261,X13262,X13263,X13264)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13263,tc_fun(X13264,tc_HOL_Obool)),X13262),X13261)))|(~hBOOL(hAPP(hAPP(c_member(X13263),X13266),X13262))|(~hBOOL(hAPP(hAPP(c_member(X13264),X13267),hAPP(X13261,X13266)))|hBOOL(hAPP(X13260,X13267)))))&(~hBOOL(hAPP(X13260,esk411_5(X13260,X13261,X13262,X13263,X13264)))|(~hBOOL(hAPP(hAPP(c_member(X13263),X13266),X13262))|(~hBOOL(hAPP(hAPP(c_member(X13264),X13267),hAPP(X13261,X13266)))|hBOOL(hAPP(X13260,X13267))))))), 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])])])])])])). 4.05/4.30 cnf(c_0_6614, 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_5132])). 4.05/4.30 cnf(c_0_6615, 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)),esk364_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),esk361_3(X1,X2,X3))),esk362_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_5093])). 4.05/4.30 fof(c_0_6616, plain, ![X13607, X13608, X13609, X13610]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X13609)),X13608))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X13610),X13607),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X13608,hAPP(c_Nat_OSuc,X13609)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13610),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X13610),X13607),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X13608,X13609))),hAPP(X13607,hAPP(c_Nat_OSuc,X13609)))|~class_Groups_Ocomm__monoid__add(X13610))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X13609)),X13608))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X13610),X13607),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X13608,hAPP(c_Nat_OSuc,X13609)))=c_Groups_Ozero__class_Ozero(X13610)|~class_Groups_Ocomm__monoid__add(X13610))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__cl__ivl__Suc])])])])). 4.05/4.30 cnf(c_0_6617, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5133, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_6618, plain, ![X7766, X7767, X7768, X7769, X7770]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X7770,X7769)),esk249_5(X7766,X7767,X7768,X7769,X7770)),hAPP(c_List_Oset(tc_prod(X7770,X7769)),hAPP(hAPP(c_List_Ozip(X7770,X7769),X7768),X7767))))|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7770)),X7768)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7769)),X7767)|c_List_Olist__all2(X7770,X7769,X7766,X7768,X7767)))&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7770,X7769,tc_HOL_Obool),X7766),esk249_5(X7766,X7767,X7768,X7769,X7770)))|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7770)),X7768)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7769)),X7767)|c_List_Olist__all2(X7770,X7769,X7766,X7768,X7767)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2I])])])])])). 4.05/4.30 fof(c_0_6619, plain, ![X13588, X13589, X13590, X13591, X13592, X13593, X13594, X13595, X13596, X13597, X13598]:(((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13591)),X13588)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13592)),X13589)|~c_List_Olist__all2(X13592,X13591,X13590,X13589,X13588))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X13592,X13591)),X13593),hAPP(c_List_Oset(tc_prod(X13592,X13591)),hAPP(hAPP(c_List_Ozip(X13592,X13591),X13589),X13588))))|hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13592,X13591,tc_HOL_Obool),X13590),X13593))|~c_List_Olist__all2(X13592,X13591,X13590,X13589,X13588)))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X13598,X13597)),esk420_5(X13594,X13595,X13596,X13597,X13598)),hAPP(c_List_Oset(tc_prod(X13598,X13597)),hAPP(hAPP(c_List_Ozip(X13598,X13597),X13595),X13594))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13597)),X13594)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13598)),X13595)|c_List_Olist__all2(X13598,X13597,X13596,X13595,X13594))&(~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13598,X13597,tc_HOL_Obool),X13596),esk420_5(X13594,X13595,X13596,X13597,X13598)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13597)),X13594)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13598)),X13595)|c_List_Olist__all2(X13598,X13597,X13596,X13595,X13594)))), 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])])])])])])])). 4.05/4.30 fof(c_0_6620, plain, ![X8148, X8149, X8150, X8151, X8152]:(~class_Orderings_Olinorder(X8152)|c_List_Olinorder__class_Osorted(X8152,hAPP(hAPP(c_List_Omap(X8151,X8152),X8150),hAPP(c_List_Ofilter(X8151,hAPP(hAPP(c_COMBC(X8151,X8152,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X8152,tc_fun(X8152,tc_HOL_Obool),X8151),c_fequal),X8150)),hAPP(X8149,X8148))),X8148)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__map__same])])). 4.05/4.30 cnf(c_0_6621, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Product__Type_Ofst(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_5084])). 4.05/4.30 cnf(c_0_6622, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5134, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6623, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|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_5084])). 4.05/4.30 cnf(c_0_6624, 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_5135]), ['final']). 4.05/4.30 cnf(c_0_6625, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5136, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6626, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5137, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_6627, plain, ![X1129, X1130, X1131]:((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),esk29_3(X1129,X1130,X1131)),esk30_3(X1129,X1130,X1131))))|hBOOL(hAPP(hAPP(X1129,X1131),X1130))|~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),X1131),X1130))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk30_3(X1129,X1130,X1131)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X1129,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk29_3(X1129,X1130,X1131))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk30_3(X1129,X1130,X1131))))|hBOOL(hAPP(hAPP(X1129,X1131),X1130))|~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),X1131),X1130))))&(~hBOOL(hAPP(hAPP(X1129,esk29_3(X1129,X1130,X1131)),esk30_3(X1129,X1130,X1131)))|hBOOL(hAPP(hAPP(X1129,X1131),X1130))|~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),X1131),X1130)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_norm__frac_Opinduct])])])])])). 4.05/4.30 fof(c_0_6628, plain, ![X17508, X17509, X17510]:(~class_Groups_Oab__semigroup__mult(X17510)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17510),X17509))|(X17509=c_Orderings_Obot__class_Obot(tc_fun(X17510,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17510),X17508))|(X17508=c_Orderings_Obot__class_Obot(tc_fun(X17510,tc_HOL_Obool))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17510,tc_HOL_Obool)),X17509),X17508)!=c_Orderings_Obot__class_Obot(tc_fun(X17510,tc_HOL_Obool))|hAPP(c_Finite__Set_Ofold1(X17510,c_Groups_Otimes__class_Otimes(X17510)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17510,tc_HOL_Obool)),X17509),X17508))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17510),hAPP(c_Finite__Set_Ofold1(X17510,c_Groups_Otimes__class_Otimes(X17510)),X17509)),hAPP(c_Finite__Set_Ofold1(X17510,c_Groups_Otimes__class_Otimes(X17510)),X17508)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__Un])])])). 4.05/4.30 cnf(c_0_6629, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3))),esk355_3(X1,X2,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_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(split_conjunct,[status(thm)],[c_0_5096])). 4.05/4.30 cnf(c_0_6630, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_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),esk352_3(X1,X2,X3))),esk353_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5096])). 4.05/4.30 fof(c_0_6631, plain, ![X10347, X10348]:(~class_Groups_Oab__semigroup__mult(X10348)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10348),X10347))|(X10347=c_Orderings_Obot__class_Obot(tc_fun(X10348,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_member(X10348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10348),esk314_2(X10347,X10348)),esk315_2(X10347,X10348))),hAPP(hAPP(c_Set_Oinsert(X10348),esk314_2(X10347,X10348)),hAPP(hAPP(c_Set_Oinsert(X10348),esk315_2(X10347,X10348)),c_Orderings_Obot__class_Obot(tc_fun(X10348,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X10348),hAPP(c_Finite__Set_Ofold1(X10348,c_Groups_Otimes__class_Otimes(X10348)),X10347)),X10347)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__in])])])])). 4.05/4.30 fof(c_0_6632, plain, ![X15536, X15537, X15538, X15539, X15540]:(~class_Groups_Oab__group__add(X15540)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15539),X15538))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15539,tc_HOL_Obool)),X15537),X15538))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15539,X15540),X15536),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15539,tc_HOL_Obool)),X15538),X15537))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15540),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15539,X15540),X15536),X15538)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15539,X15540),X15536),X15537))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__diff])])])). 4.05/4.30 fof(c_0_6633, plain, ![X6759, X6760, X6761, X6762]:((hAPP(c_List_Oset(tc_prod(X6762,X6761)),X6759)!=hAPP(c_List_Oset(tc_prod(X6762,X6761)),X6760)|hAPP(c_Map_Omap__of(X6762,X6761),X6759)=hAPP(c_Map_Omap__of(X6762,X6761),X6760)|~hBOOL(hAPP(c_List_Odistinct(X6762),hAPP(hAPP(c_List_Omap(tc_prod(X6762,X6761),X6762),c_Product__Type_Ofst(X6762,X6761)),X6759)))|~hBOOL(hAPP(c_List_Odistinct(X6762),hAPP(hAPP(c_List_Omap(tc_prod(X6762,X6761),X6762),c_Product__Type_Ofst(X6762,X6761)),X6760))))&(hAPP(c_Map_Omap__of(X6762,X6761),X6759)!=hAPP(c_Map_Omap__of(X6762,X6761),X6760)|hAPP(c_List_Oset(tc_prod(X6762,X6761)),X6759)=hAPP(c_List_Oset(tc_prod(X6762,X6761)),X6760)|~hBOOL(hAPP(c_List_Odistinct(X6762),hAPP(hAPP(c_List_Omap(tc_prod(X6762,X6761),X6762),c_Product__Type_Ofst(X6762,X6761)),X6759)))|~hBOOL(hAPP(c_List_Odistinct(X6762),hAPP(hAPP(c_List_Omap(tc_prod(X6762,X6761),X6762),c_Product__Type_Ofst(X6762,X6761)),X6760))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__inject__set])])])])). 4.05/4.30 fof(c_0_6634, plain, ![X14862, X14863, X14864, X14865, X14866, X14867]:(~c_Finite__Set_Ofun__left__comm(X14867,X14866,X14865)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14867),X14864))|(hBOOL(hAPP(hAPP(c_member(X14867),X14863),X14864))|hAPP(hAPP(X14865,X14863),hAPP(hAPP(c_Finite__Set_Ofold(X14867,X14866,X14865),X14862),X14864))=hAPP(hAPP(c_Finite__Set_Ofold(X14867,X14866,X14865),X14862),hAPP(hAPP(c_Set_Oinsert(X14867),X14863),X14864))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert])])])). 4.05/4.30 cnf(c_0_6635, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk419_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_Orderings_Oord(X1)|~class_Groups_Ocomm__monoid__add(X8)), inference(split_conjunct,[status(thm)],[c_0_5103])). 4.05/4.30 cnf(c_0_6636, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk419_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_Orderings_Oord(X1)|~class_Groups_Ocomm__monoid__add(X8)), inference(split_conjunct,[status(thm)],[c_0_5103])). 4.05/4.30 cnf(c_0_6637, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk421_7(X2,X3,X4,X5,X1,X6,X7)),hAPP(c_List_Oset(X1),X6)))|hAPP(c_List_Ofilter(X1,X3),X2)=hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)|X2!=hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X7))|~hBOOL(hAPP(X3,X5))|hAPP(c_List_Ofilter(X1,X3),X7)!=X4), inference(split_conjunct,[status(thm)],[c_0_5138])). 4.05/4.30 cnf(c_0_6638, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X2,X3,X1)),X2))|X3=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk361_3(X2,X3,X1))),esk362_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_5093])). 4.05/4.30 cnf(c_0_6639, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk363_3(X3,X2,X1))),esk364_3(X3,X2,X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),esk362_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_5093])). 4.05/4.30 cnf(c_0_6640, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5139, c_0_4475])). 4.05/4.30 cnf(c_0_6641, 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']). 4.05/4.30 cnf(c_0_6642, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3))),esk355_3(X1,X2,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_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)))), inference(split_conjunct,[status(thm)],[c_0_5096])). 4.05/4.30 fof(c_0_6643, plain, ![X17025, X17026]:(~class_Rings_Ocomm__semiring__1(X17026)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17026),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X17026),X17025)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17026),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X17026),X17025)),c_Groups_Oone__class_Oone(X17026)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17026),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17026),c_Groups_Oone__class_Oone(X17026)),c_Groups_Oone__class_Oone(X17026))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X17026),c_Nat_Osemiring__1__class_Oof__nat(X17026)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X17025)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_gauss__sum])])])). 4.05/4.30 cnf(c_0_6644, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5140, c_0_4475])). 4.05/4.30 fof(c_0_6645, plain, ![X5805, X5806, X5807, X5808]:((((hBOOL(hAPP(hAPP(c_member(X5808),X5806),X5807))|~hBOOL(hAPP(hAPP(c_member(X5808),X5806),X5807))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5808,tc_HOL_Obool)),X5807),hAPP(hAPP(c_Set_Oinsert(X5808),X5806),X5805))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5808,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5808,tc_HOL_Obool)),X5807),hAPP(hAPP(c_Set_Oinsert(X5808),X5806),c_Orderings_Obot__class_Obot(tc_fun(X5808,tc_HOL_Obool))))),X5805))|~hBOOL(hAPP(hAPP(c_member(X5808),X5806),X5807))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5808,tc_HOL_Obool)),X5807),hAPP(hAPP(c_Set_Oinsert(X5808),X5806),X5805)))))&((hBOOL(hAPP(hAPP(c_member(X5808),X5806),X5807))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5808,tc_HOL_Obool)),X5807),X5805))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5808,tc_HOL_Obool)),X5807),hAPP(hAPP(c_Set_Oinsert(X5808),X5806),X5805))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5808,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5808,tc_HOL_Obool)),X5807),hAPP(hAPP(c_Set_Oinsert(X5808),X5806),c_Orderings_Obot__class_Obot(tc_fun(X5808,tc_HOL_Obool))))),X5805))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5808,tc_HOL_Obool)),X5807),X5805))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5808,tc_HOL_Obool)),X5807),hAPP(hAPP(c_Set_Oinsert(X5808),X5806),X5805))))))&((hBOOL(hAPP(hAPP(c_member(X5808),X5806),X5807))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5808,tc_HOL_Obool)),X5807),X5805))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5808,tc_HOL_Obool)),X5807),hAPP(hAPP(c_Set_Oinsert(X5808),X5806),X5805))))&(~hBOOL(hAPP(hAPP(c_member(X5808),X5806),X5807))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5808,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5808,tc_HOL_Obool)),X5807),hAPP(hAPP(c_Set_Oinsert(X5808),X5806),c_Orderings_Obot__class_Obot(tc_fun(X5808,tc_HOL_Obool))))),X5805))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5808,tc_HOL_Obool)),X5807),hAPP(hAPP(c_Set_Oinsert(X5808),X5806),X5805)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__insert__iff])])])])). 4.05/4.30 cnf(c_0_6646, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X1,X2,X3)),X1))|X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_3(X1,X2,X3))),esk362_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_5093])). 4.05/4.30 fof(c_0_6647, plain, ![X11219, X11220, X11221, X11222]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk342_4(X11219,X11220,X11221,X11222)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X11221)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11222),X11220))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11222),X11221)),X11220)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X11220),X11219))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11221)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk343_4(X11219,X11220,X11221,X11222)),X11219))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11222),X11220))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11222),X11221)),X11220)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X11220),X11219))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11221)))&(X11222=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk343_4(X11219,X11220,X11221,X11222)),esk342_4(X11219,X11220,X11221,X11222))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11222),X11220))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11222),X11221)),X11220)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X11220),X11219))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11221))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_aset_I5_J])])])])])])). 4.05/4.30 fof(c_0_6648, plain, ![X10588, X10589, X10590, X10591]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk322_4(X10588,X10589,X10590,X10591)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10590)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10589),X10591))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10589),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10591),X10590))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X10589),X10588))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10590)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk323_4(X10588,X10589,X10590,X10591)),X10588))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10589),X10591))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10589),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10591),X10590))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X10589),X10588))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10590)))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk323_4(X10588,X10589,X10590,X10591)),esk322_4(X10588,X10589,X10590,X10591))=X10591|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10589),X10591))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10589),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10591),X10590))))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X10589),X10588))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10590))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bset_I7_J])])])])])])). 4.05/4.30 cnf(c_0_6649, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk296_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),esk295_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk295_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5141])). 4.05/4.30 cnf(c_0_6650, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk97_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),esk96_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk96_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5142])). 4.05/4.30 cnf(c_0_6651, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_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),esk352_3(X1,X2,X3))),esk353_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(split_conjunct,[status(thm)],[c_0_5096])). 4.05/4.30 cnf(c_0_6652, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X5)),X6)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X5)),X1)|X1!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X3),X4)),X5)),X6)|~class_Rings_Oring(X2)), inference(split_conjunct,[status(thm)],[c_0_5143])). 4.05/4.30 cnf(c_0_6653, 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),esk363_3(X1,X2,X3))),esk364_3(X1,X2,X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk362_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_5093])). 4.05/4.30 fof(c_0_6654, plain, ![X13277, X13278, X13279]:(~class_Orderings_Olinorder(X13279)|(hAPP(hAPP(c_Orderings_Oord__class_Omax(X13279),hAPP(X13278,esk412_3(X13277,X13278,X13279))),hAPP(X13278,esk413_3(X13277,X13278,X13279)))!=hAPP(X13278,hAPP(hAPP(c_Orderings_Oord__class_Omax(X13279),esk412_3(X13277,X13278,X13279)),esk413_3(X13277,X13278,X13279)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13279),X13277))|(c_Orderings_Obot__class_Obot(tc_fun(X13279,tc_HOL_Obool))=X13277|c_Big__Operators_Olattice_OSup__fin(X13279,c_Orderings_Oord__class_Omax(X13279),hAPP(c_Set_Oimage(X13279,X13279,X13278),X13277))=hAPP(X13278,c_Big__Operators_Olattice_OSup__fin(X13279,c_Orderings_Oord__class_Omax(X13279),X13277)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Ohom__commute])])])])). 4.05/4.30 fof(c_0_6655, plain, ![X11214, X11215, X11216]:(~class_Orderings_Olinorder(X11216)|(hAPP(hAPP(c_Orderings_Oord__class_Omin(X11216),hAPP(X11215,esk340_3(X11214,X11215,X11216))),hAPP(X11215,esk341_3(X11214,X11215,X11216)))!=hAPP(X11215,hAPP(hAPP(c_Orderings_Oord__class_Omin(X11216),esk340_3(X11214,X11215,X11216)),esk341_3(X11214,X11215,X11216)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11216),X11214))|(X11214=c_Orderings_Obot__class_Obot(tc_fun(X11216,tc_HOL_Obool))|c_Big__Operators_Olattice_OInf__fin(X11216,c_Orderings_Oord__class_Omin(X11216),hAPP(c_Set_Oimage(X11216,X11216,X11215),X11214))=hAPP(X11215,c_Big__Operators_Olattice_OInf__fin(X11216,c_Orderings_Oord__class_Omin(X11216),X11214)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Ohom__commute])])])])). 4.05/4.30 cnf(c_0_6656, plain, (hBOOL(hAPP(X1,X2))|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))=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5109])). 4.05/4.30 fof(c_0_6657, plain, ![X2643, X2644, X2645, X2646]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2646),X2645))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2646,tc_HOL_Obool)),X2645),X2644))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2646,tc_Nat_Onat),X2643),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2646,tc_HOL_Obool)),X2644),X2645))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2646,tc_Nat_Onat),X2643),X2644)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2646,tc_Nat_Onat),X2643),X2645)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__diff__nat])])])). 4.05/4.30 cnf(c_0_6658, 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_5144])). 4.05/4.30 fof(c_0_6659, plain, ![X3491, X3492, X3493, X3494, X3495, X3496]:(hAPP(c_Option_Ooption_OSome(X3495),X3492)!=hAPP(hAPP(c_Map_Omap__of(X3496,X3495),X3494),X3493)|(~hBOOL(hAPP(hAPP(X3491,X3493),X3492))|hAPP(c_Option_Ooption_OSome(X3495),X3492)=hAPP(hAPP(c_Map_Omap__of(X3496,X3495),hAPP(c_List_Ofilter(tc_prod(X3496,X3495),hAPP(c_Product__Type_Oprod_Oprod__case(X3496,X3495,tc_HOL_Obool),X3491)),X3494)),X3493))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__filter__in])])])). 4.05/4.30 cnf(c_0_6660, 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_5009])). 4.05/4.30 cnf(c_0_6661, 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_5145]), ['final']). 4.05/4.30 fof(c_0_6662, plain, ![X17657, X17658, X17659, X17660]:(~class_Enum_Oenum(X17660)|~class_Enum_Oenum(X17659)|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17660)),c_Enum_Oenum__class_Oenum(X17660))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17659)),X17658)|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17660)),c_Enum_Oenum__class_Oenum(X17660))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17659)),X17657)|(hAPP(c_Fun_Ocomp(tc_Option_Ooption(X17659),X17659,X17660,c_Option_Othe(X17659)),hAPP(c_Map_Omap__of(X17660,X17659),hAPP(hAPP(c_List_Ozip(X17660,X17659),c_Enum_Oenum__class_Oenum(X17660)),X17658)))!=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X17659),X17659,X17660,c_Option_Othe(X17659)),hAPP(c_Map_Omap__of(X17660,X17659),hAPP(hAPP(c_List_Ozip(X17660,X17659),c_Enum_Oenum__class_Oenum(X17660)),X17657)))|X17658=X17657)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__zip__enum__inject])])])). 4.05/4.30 fof(c_0_6663, plain, ![X17498, X17499, X17500]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17500),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17499)),X17498)))|hAPP(hAPP(c_List_Oappend(X17499),hAPP(hAPP(c_List_Otake(X17499),X17500),X17498)),hAPP(hAPP(c_List_Olist_OCons(X17499),hAPP(c_List_Ohd(X17499),hAPP(hAPP(c_List_Odrop(X17499),X17500),X17498))),c_List_Olist_ONil(X17499)))=hAPP(hAPP(c_List_Otake(X17499),hAPP(c_Nat_OSuc,X17500)),X17498)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_take__hd__drop])])])). 4.05/4.30 fof(c_0_6664, plain, ![X8694, X8695, X8696, X8697]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8697))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8696))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8696),X8695))|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),X8695),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8694,X8697))),X8696)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8695),X8697)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult2__lemma__aux4])])])). 4.05/4.30 fof(c_0_6665, plain, ![X4559, X4560, X4561, X4562]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4562))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4561),X4560))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4560),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),X4561),X4562)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4561),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4559,X4562))),X4560)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult2__lemma__aux1])])])). 4.05/4.30 fof(c_0_6666, plain, ![X4219, X4220, X4221, X4222, X4223]:(~class_Rings_Osemiring__0(X4223)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4222,X4223),hAPP(hAPP(c_COMBC(X4222,X4223,X4223),hAPP(hAPP(c_COMBB(X4223,tc_fun(X4223,X4223),X4222),c_Groups_Otimes__class_Otimes(X4223)),X4221)),X4219)),X4220)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4223),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4222,X4223),X4221),X4220)),X4219)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__left__distrib])])])). 4.05/4.30 cnf(c_0_6667, 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),c_Transitive__Closure_Ortrancl(X1,X4)),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_5146, c_0_5018])). 4.05/4.30 cnf(c_0_6668, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X1,X2,X3)),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_3(X1,X2,X3))),esk353_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(split_conjunct,[status(thm)],[c_0_5096])). 4.05/4.30 cnf(c_0_6669, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X1,X2,X3)),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_3(X1,X2,X3))),esk353_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5096])). 4.05/4.30 cnf(c_0_6670, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3))),esk355_3(X1,X2,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk353_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_5096])). 4.05/4.30 cnf(c_0_6671, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3))),esk355_3(X1,X2,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk353_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_5096])). 4.05/4.30 fof(c_0_6672, plain, ![X9712, X9713, X9714, X9715]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9715),X9714)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9713)),X9712)))|hAPP(hAPP(c_List_Otake(X9713),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9715),X9714)),X9712)=hAPP(hAPP(c_List_Oappend(X9713),hAPP(hAPP(c_List_Otake(X9713),X9715),X9712)),hAPP(hAPP(c_List_Otake(X9713),X9714),hAPP(hAPP(c_List_Odrop(X9713),X9715),X9712)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_take__add])])])). 4.05/4.30 fof(c_0_6673, plain, ![X16874, X16875, X16876, X16877, X16878, X16879, X16881, X16882, X16883, X16884, X16885]:((((hBOOL(hAPP(hAPP(c_member(X16877),esk503_4(X16874,X16875,X16876,X16877)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16877,tc_HOL_Obool)),X16876),X16875)))|(~hBOOL(hAPP(hAPP(c_member(X16877),X16878),X16876))|~hBOOL(hAPP(X16874,X16878))))&(hBOOL(hAPP(X16874,esk503_4(X16874,X16875,X16876,X16877)))|(~hBOOL(hAPP(hAPP(c_member(X16877),X16878),X16876))|~hBOOL(hAPP(X16874,X16878)))))&((hBOOL(hAPP(hAPP(c_member(X16877),esk503_4(X16874,X16875,X16876,X16877)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16877,tc_HOL_Obool)),X16876),X16875)))|(~hBOOL(hAPP(hAPP(c_member(X16877),X16879),X16875))|~hBOOL(hAPP(X16874,X16879))))&(hBOOL(hAPP(X16874,esk503_4(X16874,X16875,X16876,X16877)))|(~hBOOL(hAPP(hAPP(c_member(X16877),X16879),X16875))|~hBOOL(hAPP(X16874,X16879))))))&(((hBOOL(hAPP(hAPP(c_member(X16884),esk505_4(X16881,X16882,X16883,X16884)),X16882))|hBOOL(hAPP(hAPP(c_member(X16884),esk504_4(X16881,X16882,X16883,X16884)),X16883))|(~hBOOL(hAPP(hAPP(c_member(X16884),X16885),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16884,tc_HOL_Obool)),X16883),X16882)))|~hBOOL(hAPP(X16881,X16885))))&(hBOOL(hAPP(X16881,esk505_4(X16881,X16882,X16883,X16884)))|hBOOL(hAPP(hAPP(c_member(X16884),esk504_4(X16881,X16882,X16883,X16884)),X16883))|(~hBOOL(hAPP(hAPP(c_member(X16884),X16885),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16884,tc_HOL_Obool)),X16883),X16882)))|~hBOOL(hAPP(X16881,X16885)))))&((hBOOL(hAPP(hAPP(c_member(X16884),esk505_4(X16881,X16882,X16883,X16884)),X16882))|hBOOL(hAPP(X16881,esk504_4(X16881,X16882,X16883,X16884)))|(~hBOOL(hAPP(hAPP(c_member(X16884),X16885),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16884,tc_HOL_Obool)),X16883),X16882)))|~hBOOL(hAPP(X16881,X16885))))&(hBOOL(hAPP(X16881,esk505_4(X16881,X16882,X16883,X16884)))|hBOOL(hAPP(X16881,esk504_4(X16881,X16882,X16883,X16884)))|(~hBOOL(hAPP(hAPP(c_member(X16884),X16885),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16884,tc_HOL_Obool)),X16883),X16882)))|~hBOOL(hAPP(X16881,X16885))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bex__Un])])])])])])). 4.05/4.30 fof(c_0_6674, plain, ![X16131, X16132, X16133, X16134, X16135, X16136]:((hAPP(hAPP(c_Product__Type_OPair(X16136,X16135),esk483_6(X16131,X16132,X16133,X16134,X16135,X16136)),esk485_6(X16131,X16132,X16133,X16134,X16135,X16136))=X16134|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16136,X16135)),X16134),hAPP(hAPP(c_Relation_Orel__comp(X16136,X16133,X16135),X16132),X16131))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X16136,X16133)),hAPP(hAPP(c_Product__Type_OPair(X16136,X16133),esk483_6(X16131,X16132,X16133,X16134,X16135,X16136)),esk484_6(X16131,X16132,X16133,X16134,X16135,X16136))),X16132))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16136,X16135)),X16134),hAPP(hAPP(c_Relation_Orel__comp(X16136,X16133,X16135),X16132),X16131))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X16133,X16135)),hAPP(hAPP(c_Product__Type_OPair(X16133,X16135),esk484_6(X16131,X16132,X16133,X16134,X16135,X16136)),esk485_6(X16131,X16132,X16133,X16134,X16135,X16136))),X16131))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16136,X16135)),X16134),hAPP(hAPP(c_Relation_Orel__comp(X16136,X16133,X16135),X16132),X16131)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__compE])])])])])). 4.05/4.30 fof(c_0_6675, plain, ![X17556, X17557]:(~class_Orderings_Olinorder(X17557)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17557),X17556))|(c_Orderings_Obot__class_Obot(tc_fun(X17557,tc_HOL_Obool))=X17556|(~hBOOL(hAPP(hAPP(c_member(X17557),hAPP(hAPP(c_Orderings_Oord__class_Omin(X17557),esk525_2(X17556,X17557)),esk526_2(X17556,X17557))),hAPP(hAPP(c_Set_Oinsert(X17557),esk525_2(X17556,X17557)),hAPP(hAPP(c_Set_Oinsert(X17557),esk526_2(X17556,X17557)),c_Orderings_Obot__class_Obot(tc_fun(X17557,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X17557),c_Big__Operators_Olattice_OInf__fin(X17557,c_Orderings_Oord__class_Omin(X17557),X17556)),X17556)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oclosed])])])])). 4.05/4.30 fof(c_0_6676, plain, ![X7402, X7403]:(~class_Orderings_Olinorder(X7403)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7403),X7402))|(c_Orderings_Obot__class_Obot(tc_fun(X7403,tc_HOL_Obool))=X7402|(~hBOOL(hAPP(hAPP(c_member(X7403),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7403),esk234_2(X7402,X7403)),esk235_2(X7402,X7403))),hAPP(hAPP(c_Set_Oinsert(X7403),esk234_2(X7402,X7403)),hAPP(hAPP(c_Set_Oinsert(X7403),esk235_2(X7402,X7403)),c_Orderings_Obot__class_Obot(tc_fun(X7403,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X7403),c_Big__Operators_Olattice_OSup__fin(X7403,c_Orderings_Oord__class_Omax(X7403),X7402)),X7402)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oclosed])])])])). 4.05/4.30 fof(c_0_6677, plain, ![X626, X627, X628]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X628,tc_HOL_Obool)),X627),X626))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X628),X626))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X628,tc_HOL_Obool),tc_fun(X628,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X628,tc_HOL_Obool),tc_fun(X628,tc_HOL_Obool)),X627),X626)),c_Wellfounded_Ofinite__psubset(X628))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X628,tc_HOL_Obool)),X627),X626))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X628,tc_HOL_Obool),tc_fun(X628,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X628,tc_HOL_Obool),tc_fun(X628,tc_HOL_Obool)),X627),X626)),c_Wellfounded_Ofinite__psubset(X628))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X628),X626))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X628,tc_HOL_Obool),tc_fun(X628,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X628,tc_HOL_Obool),tc_fun(X628,tc_HOL_Obool)),X627),X626)),c_Wellfounded_Ofinite__psubset(X628)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__finite__psubset])])])). 4.05/4.30 fof(c_0_6678, plain, ![X7433, X7434, X7435, X7436]:(~class_Rings_Oring(X7436)|~class_Int_Onumber(X7436)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7436),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7436),hAPP(c_Int_Onumber__class_Onumber__of(X7436),X7435)),X7434)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7436),hAPP(c_Int_Onumber__class_Onumber__of(X7436),X7435)),X7433))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7436),hAPP(c_Int_Onumber__class_Onumber__of(X7436),X7435)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7436),X7434),X7433))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_right__diff__distrib__number__of])])])). 4.05/4.30 fof(c_0_6679, plain, ![X8235, X8236, X8237]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8237),X8236))|(~hBOOL(hAPP(hAPP(c_member(X8237),X8235),X8236))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X8237),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8237,tc_HOL_Obool)),X8236),hAPP(hAPP(c_Set_Oinsert(X8237),X8235),c_Orderings_Obot__class_Obot(tc_fun(X8237,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X8237),X8236))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff1__less])])])). 4.05/4.30 cnf(c_0_6680, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X1))), inference(rw,[status(thm)],[c_0_5147, c_0_4475])). 4.05/4.30 cnf(c_0_6681, 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_5148, c_0_5149]), ['final']). 4.05/4.30 cnf(c_0_6682, 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_5150, c_0_4427]), ['final']). 4.05/4.30 fof(c_0_6683, plain, ![X4932, X4933, X4934, X4935]:(~class_Int_Onumber(X4935)|~class_Rings_Osemiring(X4935)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4935),hAPP(c_Int_Onumber__class_Onumber__of(X4935),X4934)),X4933)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4935),hAPP(c_Int_Onumber__class_Onumber__of(X4935),X4934)),X4932))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4935),hAPP(c_Int_Onumber__class_Onumber__of(X4935),X4934)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4935),X4933),X4932))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_right__distrib__number__of])])])). 4.05/4.30 fof(c_0_6684, plain, ![X2190, X2191, X2192]:((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),esk81_3(X2190,X2191,X2192)),esk82_3(X2190,X2191,X2192))))|hBOOL(hAPP(hAPP(X2190,X2192),X2191))|~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),X2192),X2191))))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=esk82_3(X2190,X2191,X2192)|hBOOL(hAPP(hAPP(X2190,esk82_3(X2190,X2191,X2192)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk81_3(X2190,X2191,X2192),esk82_3(X2190,X2191,X2192))))|hBOOL(hAPP(hAPP(X2190,X2192),X2191))|~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),X2192),X2191))))&(~hBOOL(hAPP(hAPP(X2190,esk81_3(X2190,X2191,X2192)),esk82_3(X2190,X2191,X2192)))|hBOOL(hAPP(hAPP(X2190,X2192),X2191))|~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),X2192),X2191)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__gcd_Opinduct])])])])])). 4.05/4.30 fof(c_0_6685, plain, ![X11860, X11861, X11862, X11863, X11864]:(~class_Fields_Ofield(X11864)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11863,X11864),hAPP(hAPP(c_COMBC(X11863,X11864,X11864),hAPP(hAPP(c_COMBB(X11864,tc_fun(X11864,X11864),X11863),c_Rings_Oinverse__class_Odivide(X11864)),X11862)),X11860)),X11861)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11864),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11863,X11864),X11862),X11861)),X11860)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__divide__distrib])])])). 4.05/4.30 cnf(c_0_6686, 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_5151])). 4.05/4.30 cnf(c_0_6687, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk185_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),c_Transitive__Closure_Ortrancl(X1,X2)),X2)))), inference(rw,[status(thm)],[c_0_5152, c_0_5018])). 4.05/4.30 cnf(c_0_6688, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk187_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),c_Transitive__Closure_Ortrancl(X1,X3)),X3)))), inference(rw,[status(thm)],[c_0_5153, c_0_5018])). 4.05/4.30 cnf(c_0_6689, plain, (c_Map_Omap__upds(X1,X3,X6,X5,X4)=c_Map_Omap__upds(X1,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),X6),X2),hAPP(c_Option_Ooption_OSome(X3),X7)),X5,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),X5))))), inference(split_conjunct,[status(thm)],[c_0_5027])). 4.05/4.30 fof(c_0_6690, plain, ![X4871, X4872, X4873]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4873),X4872))|c_Smallcheck_Osmall_H(X4871,X4873,X4872)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X4871,X4873,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4872),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X4871,X4872)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4873),X4872))|c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))=c_Smallcheck_Osmall_H(X4871,X4873,X4872))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_small_H_Osimps])])])). 4.05/4.30 fof(c_0_6691, plain, ![X5971, X5972, X5973, X5974, X5975, X5976]:(~c_Finite__Set_Ofun__left__comm(X5976,X5975,X5974)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5976),X5973))|(hBOOL(hAPP(hAPP(c_member(X5976),X5972),X5973))|hAPP(hAPP(c_Finite__Set_Ofold(X5976,X5975,X5974),hAPP(hAPP(X5974,X5972),X5971)),X5973)=hAPP(hAPP(c_Finite__Set_Ofold(X5976,X5975,X5974),X5971),hAPP(hAPP(c_Set_Oinsert(X5976),X5972),X5973))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert2])])])). 4.05/4.30 fof(c_0_6692, plain, ![X3534, X3535, X3536]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3536),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3536,tc_HOL_Obool)),X3535),X3534)))|hAPP(c_Finite__Set_Ocard(X3536),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3536,tc_HOL_Obool)),X3535),X3534))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X3536),X3535)),hAPP(c_Finite__Set_Ocard(X3536),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3536,tc_HOL_Obool)),X3535),X3534)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff__subset__Int])])])). 4.05/4.30 fof(c_0_6693, plain, ![X10933, X10934, X10935, X10936, X10937, X10938]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X10938,X10938)),hAPP(hAPP(c_Product__Type_OPair(X10938,X10938),X10937),X10936)),hAPP(hAPP(c_Relation_Oinv__image(X10935,X10938),X10934),X10933)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X10935,X10935)),hAPP(hAPP(c_Product__Type_OPair(X10935,X10935),hAPP(X10933,X10937)),hAPP(X10933,X10936))),X10934)))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10935,X10935)),hAPP(hAPP(c_Product__Type_OPair(X10935,X10935),hAPP(X10933,X10937)),hAPP(X10933,X10936))),X10934))|hBOOL(hAPP(hAPP(c_member(tc_prod(X10938,X10938)),hAPP(hAPP(c_Product__Type_OPair(X10938,X10938),X10937),X10936)),hAPP(hAPP(c_Relation_Oinv__image(X10935,X10938),X10934),X10933))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__inv__image])])). 4.05/4.30 fof(c_0_6694, plain, ![X3151, X3152, X3153, X3154, X3155, X3156]:(~c_Finite__Set_Ofolding(X3156,X3155,X3154,X3153)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3156),X3152))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3156),X3151))|(c_Orderings_Obot__class_Obot(tc_fun(X3156,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3156,tc_HOL_Obool)),X3152),X3151)|hAPP(X3153,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3156,tc_HOL_Obool)),X3152),X3151))=hAPP(c_Fun_Ocomp(X3155,X3155,X3155,hAPP(X3153,X3152)),hAPP(X3153,X3151)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ounion])])])). 4.05/4.30 cnf(c_0_6695, plain, (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),c_Complete__Lattice_OSup__class_OSup(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)),esk105_3(X2,X3,X1)),esk106_3(X2,X3,X1))|hAPP(c_Finite__Set_Ocard(X1),esk104_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_5062])). 4.05/4.30 cnf(c_0_6696, 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_5154])). 4.05/4.30 cnf(c_0_6697, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk197_3(X2,X3,X1))),esk198_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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5155])). 4.05/4.30 cnf(c_0_6698, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk376_3(X1,X3,X2))),esk377_3(X1,X3,X2))|hBOOL(hAPP(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5156])). 4.05/4.30 fof(c_0_6699, plain, ![X16839, X16840, X16841]:((hBOOL(hAPP(hAPP(c_member(X16841),X16839),X16840))|hAPP(c_Finite__Set_Ocard(X16841),X16840)=hAPP(c_Finite__Set_Ocard(X16841),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16841,tc_HOL_Obool)),X16840),hAPP(hAPP(c_Set_Oinsert(X16841),X16839),c_Orderings_Obot__class_Obot(tc_fun(X16841,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16841),X16840)))&(~hBOOL(hAPP(hAPP(c_member(X16841),X16839),X16840))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X16841),X16840)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Finite__Set_Ocard(X16841),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16841,tc_HOL_Obool)),X16840),hAPP(hAPP(c_Set_Oinsert(X16841),X16839),c_Orderings_Obot__class_Obot(tc_fun(X16841,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16841),X16840)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff__singleton__if])])])])). 4.05/4.30 fof(c_0_6700, plain, ![X2550, X2551, X2552, X2553, X2554]:((hBOOL(hAPP(hAPP(c_member(X2554),esk90_5(X2550,X2551,X2552,X2553,X2554)),X2553))|c_Relation_Orefl__on(X2552,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2554,tc_fun(X2552,tc_HOL_Obool)),X2553),X2551),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2554,tc_fun(tc_prod(X2552,X2552),tc_HOL_Obool)),X2553),X2550)))&(~c_Relation_Orefl__on(X2552,hAPP(X2551,esk90_5(X2550,X2551,X2552,X2553,X2554)),hAPP(X2550,esk90_5(X2550,X2551,X2552,X2553,X2554)))|c_Relation_Orefl__on(X2552,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2554,tc_fun(X2552,tc_HOL_Obool)),X2553),X2551),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2554,tc_fun(tc_prod(X2552,X2552),tc_HOL_Obool)),X2553),X2550)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__on__INTER])])])])])). 4.05/4.30 cnf(c_0_6701, plain, (c_Map_Oran(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3))=hAPP(c_Set_Oimage(tc_prod(X1,X2),X2,c_Product__Type_Osnd(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_5157])). 4.05/4.30 cnf(c_0_6702, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),X2,c_Product__Type_Osnd(X1,X2)),X3)=hAPP(c_Relation_ORange(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_5158]), ['final']). 4.05/4.30 cnf(c_0_6703, plain, (hAPP(hAPP(c_List_Oappend(X1),X3),X5)=hAPP(hAPP(c_List_Oappend(X1),X2),X4)|~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)))|X4!=hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X5)|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)!=X2), inference(split_conjunct,[status(thm)],[c_0_5087])). 4.05/4.30 cnf(c_0_6704, plain, (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),esk361_3(X2,X3,X1))),esk362_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_5093])). 4.05/4.30 cnf(c_0_6705, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk363_3(X3,X2,X1))),esk364_3(X3,X2,X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|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_5093])). 4.05/4.30 fof(c_0_6706, plain, ![X7229, X7230, X7231]:((hBOOL(hAPP(hAPP(c_member(X7231),esk226_3(X7229,X7230,X7231)),X7230))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7231,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X7231),c_Int_Onat),X7229)),X7230))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7231,tc_Int_Oint),X7229),X7230))&(~c_Nat__Transfer_Ois__nat(hAPP(X7229,esk226_3(X7229,X7230,X7231)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7231,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X7231),c_Int_Onat),X7229)),X7230))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7231,tc_Int_Oint),X7229),X7230))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod2_I2_J])])])])). 4.05/4.30 cnf(c_0_6707, 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_5159])). 4.05/4.30 cnf(c_0_6708, 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),X5)!=hAPP(c_List_Oset(X2),X4)), inference(split_conjunct,[status(thm)],[c_0_5160])). 4.05/4.30 cnf(c_0_6709, 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_5161]), ['final']). 4.05/4.30 fof(c_0_6710, plain, ![X12557, X12558, X12559]:((hBOOL(hAPP(hAPP(c_member(X12559),esk384_3(X12557,X12558,X12559)),X12558))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12559,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X12559),c_Int_Onat),X12557)),X12558))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12559,tc_Int_Oint),X12557),X12558))&(~c_Nat__Transfer_Ois__nat(hAPP(X12557,esk384_3(X12557,X12558,X12559)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12559,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X12559),c_Int_Onat),X12557)),X12558))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X12559,tc_Int_Oint),X12557),X12558))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__int__nat__sum__prod2_I1_J])])])])])). 4.05/4.30 cnf(c_0_6711, 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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1))),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)))), inference(split_conjunct,[status(thm)],[c_0_5162])). 4.05/4.30 fof(c_0_6712, plain, ![X10801, X10802, X10803, X10804]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X10804,X10804)),hAPP(hAPP(c_Product__Type_OPair(X10804,X10804),esk327_4(X10801,X10802,X10803,X10804)),esk328_4(X10801,X10802,X10803,X10804))),X10801))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10804),tc_List_Olist(X10804))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10804),tc_List_Olist(X10804)),X10803),X10802)),c_List_Olistrel1(X10804,X10801))))&((hAPP(hAPP(c_List_Oappend(X10804),esk329_4(X10801,X10802,X10803,X10804)),hAPP(hAPP(c_List_Olist_OCons(X10804),esk327_4(X10801,X10802,X10803,X10804)),esk330_4(X10801,X10802,X10803,X10804)))=X10803|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10804),tc_List_Olist(X10804))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10804),tc_List_Olist(X10804)),X10803),X10802)),c_List_Olistrel1(X10804,X10801))))&(X10802=hAPP(hAPP(c_List_Oappend(X10804),esk329_4(X10801,X10802,X10803,X10804)),hAPP(hAPP(c_List_Olist_OCons(X10804),esk328_4(X10801,X10802,X10803,X10804)),esk330_4(X10801,X10802,X10803,X10804)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10804),tc_List_Olist(X10804))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10804),tc_List_Olist(X10804)),X10803),X10802)),c_List_Olistrel1(X10804,X10801)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel1E])])])])])). 4.05/4.30 fof(c_0_6713, plain, ![X14802, X14803, X14804, X14805, X14806]:(~c_Finite__Set_Ofolding__one(X14806,X14805,X14804)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14806),X14803))|(X14803=c_Orderings_Obot__class_Obot(tc_fun(X14806,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14806),X14802))|(c_Orderings_Obot__class_Obot(tc_fun(X14806,tc_HOL_Obool))=X14802|(c_Orderings_Obot__class_Obot(tc_fun(X14806,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14806,tc_HOL_Obool)),X14803),X14802)|hAPP(X14804,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14806,tc_HOL_Obool)),X14803),X14802))=hAPP(hAPP(X14805,hAPP(X14804,X14803)),hAPP(X14804,X14802)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Ounion__disjoint])])])). 4.05/4.30 fof(c_0_6714, plain, ![X12037, X12038, X12039, X12040, X12041]:(~class_Orderings_Olinorder(X12041)|(~hBOOL(hAPP(hAPP(c_member(X12040),X12039),hAPP(c_List_Oset(X12040),X12038)))|(~c_List_Olinorder__class_Osorted(X12041,hAPP(hAPP(c_List_Omap(X12040,X12041),X12037),X12038))|(X12039!=hAPP(c_List_Ohd(X12040),hAPP(c_List_Ofilter(X12040,hAPP(hAPP(c_COMBB(X12041,tc_HOL_Obool,X12040),hAPP(c_fequal,hAPP(X12037,X12039))),X12037)),X12038))|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12040,X12041,X12037),X12039),c_List_Oremove1(X12040,X12039,X12038))=X12038)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__key__remove1])])])). 4.05/4.30 fof(c_0_6715, plain, ![X17344, X17345, X17346, X17347, X17348, X17349]:(~class_Orderings_Olinorder(X17349)|(~c_List_Olinorder__class_Osorted(X17349,hAPP(hAPP(c_List_Omap(X17348,X17349),X17347),X17346))|(~hBOOL(hAPP(X17345,X17344))|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17348,X17349,X17347),X17344),hAPP(c_List_Ofilter(X17348,X17345),X17346))=hAPP(c_List_Ofilter(X17348,X17345),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X17348,X17349,X17347),X17344),X17346))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__insort])])). 4.05/4.30 fof(c_0_6716, plain, ![X2640, X2641, X2642]:(~class_Orderings_Olinorder(X2642)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2642),X2641))|(c_Orderings_Obot__class_Obot(tc_fun(X2642,tc_HOL_Obool))=X2641|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2642),X2640))|(c_Orderings_Obot__class_Obot(tc_fun(X2642,tc_HOL_Obool))=X2640|c_Big__Operators_Olattice_OSup__fin(X2642,c_Orderings_Oord__class_Omax(X2642),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2642,tc_HOL_Obool)),X2641),X2640))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X2642),c_Big__Operators_Olattice_OSup__fin(X2642,c_Orderings_Oord__class_Omax(X2642),X2641)),c_Big__Operators_Olattice_OSup__fin(X2642,c_Orderings_Oord__class_Omax(X2642),X2640))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Ounion__idem])])])). 4.05/4.30 cnf(c_0_6717, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5163])). 4.05/4.30 cnf(c_0_6718, 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_5164, c_0_4635]), c_0_4635]), c_0_5165]), ['final']). 4.05/4.30 cnf(c_0_6719, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5166]), ['final']). 4.05/4.30 cnf(c_0_6720, 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_5167]), ['final']). 4.05/4.30 cnf(c_0_6721, 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_5168])). 4.05/4.30 cnf(c_0_6722, 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))|X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_3(X1,X2,X3))),esk362_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_5093])). 4.05/4.30 fof(c_0_6723, plain, ![X4812, X4813, X4814, X4815, X4816, X4817, X4818, X4819]:(~c_Finite__Set_Ofolding__image__simple(X4819,X4818,X4817,X4816,X4815,X4814)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4818),X4813))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4818),X4812))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4818,tc_HOL_Obool)),X4813),X4812)!=c_Orderings_Obot__class_Obot(tc_fun(X4818,tc_HOL_Obool))|hAPP(hAPP(X4817,hAPP(X4814,X4813)),hAPP(X4814,X4812))=hAPP(X4814,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4818,tc_HOL_Obool)),X4813),X4812)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Ounion__disjoint])])])). 4.05/4.30 cnf(c_0_6724, plain, (hBOOL(hAPP(X3,X4))|c_List_OdropWhile(X2,X3,X1)=hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)|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_5169])). 4.05/4.30 cnf(c_0_6725, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X3),hAPP(hAPP(c_Relation_Orel__comp(X2,X2,X2),c_Transitive__Closure_Ortrancl(X2,X4)),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_5170, c_0_5018])). 4.05/4.30 cnf(c_0_6726, 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),esk363_3(X1,X2,X3))),esk364_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)))), inference(split_conjunct,[status(thm)],[c_0_5093])). 4.05/4.30 fof(c_0_6727, plain, ![X12804, X12805, X12806]:(~class_Orderings_Olinorder(X12806)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12806),X12805))|(X12805=c_Orderings_Obot__class_Obot(tc_fun(X12806,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12806),X12804))|(X12804=c_Orderings_Obot__class_Obot(tc_fun(X12806,tc_HOL_Obool))|c_Big__Operators_Olattice_OInf__fin(X12806,c_Orderings_Oord__class_Omin(X12806),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12806,tc_HOL_Obool)),X12805),X12804))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X12806),c_Big__Operators_Olattice_OInf__fin(X12806,c_Orderings_Oord__class_Omin(X12806),X12805)),c_Big__Operators_Olattice_OInf__fin(X12806,c_Orderings_Oord__class_Omin(X12806),X12804))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Ounion__idem])])])). 4.05/4.30 cnf(c_0_6728, 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_5171])). 4.05/4.30 cnf(c_0_6729, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),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),X1),hAPP(c_List_Oset(X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_5172])). 4.05/4.30 cnf(c_0_6730, plain, (c_Wellfounded_Oacyclic(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk125_2(X2,X1)),esk125_2(X2,X1))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2)))), inference(rw,[status(thm)],[c_0_5173, c_0_5018])). 4.05/4.30 fof(c_0_6731, plain, ![X6864, X6865, X6866, X6867, X6868]:(~class_Groups_Ocomm__monoid__add(X6868)|(~hBOOL(hAPP(hAPP(c_member(X6867),X6866),hAPP(c_List_Oset(X6867),X6865)))|hAPP(c_List_Omonoid__add__class_Olistsum(X6868),hAPP(hAPP(c_List_Omap(X6867,X6868),X6864),X6865))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6868),hAPP(X6864,X6866)),hAPP(c_List_Omonoid__add__class_Olistsum(X6868),hAPP(hAPP(c_List_Omap(X6867,X6868),X6864),c_List_Oremove1(X6867,X6866,X6865)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__map__remove1])])])). 4.05/4.30 cnf(c_0_6732, plain, (c_Wellfounded_Oacyclic(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk124_2(X2,X1)),esk124_2(X2,X1))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2)))), inference(rw,[status(thm)],[c_0_5174, c_0_5018])). 4.05/4.30 cnf(c_0_6733, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5175])). 4.05/4.30 cnf(c_0_6734, 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_5176]), ['final']). 4.05/4.30 fof(c_0_6735, plain, ![X9468, X9469]:(~class_Lattices_Olattice(X9469)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9469),X9468))|(c_Orderings_Obot__class_Obot(tc_fun(X9469,tc_HOL_Obool))=X9468|(~hBOOL(hAPP(hAPP(c_member(X9469),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9469),esk289_2(X9468,X9469)),esk290_2(X9468,X9469))),hAPP(hAPP(c_Set_Oinsert(X9469),esk289_2(X9468,X9469)),hAPP(hAPP(c_Set_Oinsert(X9469),esk290_2(X9468,X9469)),c_Orderings_Obot__class_Obot(tc_fun(X9469,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X9469),c_Big__Operators_Olattice__class_OInf__fin(X9469,X9468)),X9468)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oclosed])])])])). 4.05/4.30 fof(c_0_6736, plain, ![X14123, X14124]:(~class_Lattices_Olattice(X14124)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14124),X14123))|(X14123=c_Orderings_Obot__class_Obot(tc_fun(X14124,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_member(X14124),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X14124),esk431_2(X14123,X14124)),esk432_2(X14123,X14124))),hAPP(hAPP(c_Set_Oinsert(X14124),esk431_2(X14123,X14124)),hAPP(hAPP(c_Set_Oinsert(X14124),esk432_2(X14123,X14124)),c_Orderings_Obot__class_Obot(tc_fun(X14124,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(X14124),c_Big__Operators_Olattice__class_OSup__fin(X14124,X14123)),X14123)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oclosed])])])])). 4.05/4.30 cnf(c_0_6737, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk23_3(X3,X2,X1)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X3)),X3)))), inference(rw,[status(thm)],[c_0_5177, c_0_5018])). 4.05/4.30 cnf(c_0_6738, 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_5178])). 4.05/4.30 fof(c_0_6739, plain, ![X10825, X10826, X10827, X10828, X10829]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10829,tc_HOL_Obool)),X10828),X10827))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10829,tc_HOL_Obool)),X10826),X10825))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10829,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10829,tc_HOL_Obool)),X10828),X10825)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10829,tc_HOL_Obool)),X10827),X10826))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Diff__mono])])])). 4.05/4.30 fof(c_0_6740, plain, ![X15371, X15372, X15373, X15374, X15375]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15375,X15375)),hAPP(hAPP(c_Product__Type_OPair(X15375,X15375),X15374),X15373)),c_Transitive__Closure_Ortrancl(X15375,X15372)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15375,X15375),tc_HOL_Obool)),X15372),hAPP(hAPP(c_Product__Type_OSigma(X15375,X15375),X15371),hAPP(c_COMBK(tc_fun(X15375,tc_HOL_Obool),X15375),X15371))))|(hBOOL(hAPP(hAPP(c_member(X15375),X15374),X15371))|X15373=X15374))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trancl__subset__Sigma__aux])])])). 4.05/4.30 fof(c_0_6741, plain, ![X9725, X9726, X9727, X9728, X9729, X9730]:((hAPP(hAPP(c_Product__Type_OPair(X9729,X9728),esk297_6(X9725,X9726,X9727,X9728,X9729,X9730)),esk298_6(X9725,X9726,X9727,X9728,X9729,X9730))=X9730|hBOOL(hAPP(hAPP(c_member(X9727),X9726),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X9729,X9728,tc_fun(X9727,tc_HOL_Obool)),X9725),X9730))))&(~hBOOL(hAPP(hAPP(c_member(X9727),X9726),hAPP(hAPP(X9725,esk297_6(X9725,X9726,X9727,X9728,X9729,X9730)),esk298_6(X9725,X9726,X9727,X9728,X9729,X9730))))|hBOOL(hAPP(hAPP(c_member(X9727),X9726),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X9729,X9728,tc_fun(X9727,tc_HOL_Obool)),X9725),X9730))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI2])])])])). 4.05/4.30 fof(c_0_6742, plain, ![X1928, X1929, X1930, X1931]:(~class_Rings_Osemiring(X1931)|~class_Int_Onumber(X1931)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1931),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1931),X1930),hAPP(c_Int_Onumber__class_Onumber__of(X1931),X1928))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1931),X1929),hAPP(c_Int_Onumber__class_Onumber__of(X1931),X1928)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1931),X1930),X1929)),hAPP(c_Int_Onumber__class_Onumber__of(X1931),X1928))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of])])). 4.05/4.30 fof(c_0_6743, plain, ![X8360, X8361, X8362, X8363, X8364]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8364,tc_HOL_Obool)),X8363),X8362))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8364,tc_HOL_Obool)),X8361),X8360))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8364,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8364,tc_HOL_Obool)),X8363),X8361)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8364,tc_HOL_Obool)),X8362),X8360))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__mono])])])). 4.05/4.30 fof(c_0_6744, plain, ![X13870, X13871, X13872, X13873, X13874]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13874,tc_HOL_Obool)),X13873),X13872))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13874,tc_HOL_Obool)),X13871),X13870))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13874,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13874,tc_HOL_Obool)),X13873),X13871)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13874,tc_HOL_Obool)),X13872),X13870))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__mono])])). 4.05/4.30 cnf(c_0_6745, plain, (hBOOL(hAPP(X1,esk73_2(X1,X2)))|hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk71_2(X1,X2)),X2))))|hBOOL(hAPP(X1,esk70_2(X1,X2)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5097])). 4.05/4.30 fof(c_0_6746, plain, ![X1166, X1167, X1168, X1169, X1170]:(~class_Rings_Osemiring(X1170)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1170),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1170),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1170),X1169),X1167)),X1168)),X1166)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1170),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1170),X1169),X1168)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1170),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1170),X1167),X1168)),X1166))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_combine__common__factor])])])). 4.05/4.30 fof(c_0_6747, plain, ![X2381, X2382, X2383, X2384, X2385, X2386]:((hBOOL(hAPP(hAPP(c_member(X2385),esk85_6(X2381,X2382,X2383,X2384,X2385,X2386)),X2386))|c_Fun_Oinj__on(X2384,X2383,X2382,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2385,tc_fun(X2384,tc_HOL_Obool)),X2386),X2381))|c_Orderings_Obot__class_Obot(tc_fun(X2385,tc_HOL_Obool))=X2386)&(~c_Fun_Oinj__on(X2384,X2383,X2382,hAPP(X2381,esk85_6(X2381,X2382,X2383,X2384,X2385,X2386)))|c_Fun_Oinj__on(X2384,X2383,X2382,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2385,tc_fun(X2384,tc_HOL_Obool)),X2386),X2381))|c_Orderings_Obot__class_Obot(tc_fun(X2385,tc_HOL_Obool))=X2386)), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__INTER])])])])])). 4.05/4.30 cnf(c_0_6748, 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_5179, c_0_5049])). 4.05/4.30 fof(c_0_6749, plain, ![X7304, X7305, X7306, X7307]:(~class_Rings_Oring(X7307)|~class_Int_Onumber(X7307)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7307),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7307),X7306),X7305)),hAPP(c_Int_Onumber__class_Onumber__of(X7307),X7304))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7307),X7306),hAPP(c_Int_Onumber__class_Onumber__of(X7307),X7304))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7307),X7305),hAPP(c_Int_Onumber__class_Onumber__of(X7307),X7304)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__diff__distrib__number__of])])). 4.05/4.30 fof(c_0_6750, plain, ![X1171, X1172, X1173, X1174]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk31_4(X1171,X1172,X1173,X1174)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1173)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1174),X1171))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1174),X1173)),X1171)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1173)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk32_4(X1171,X1172,X1173,X1174)),X1172))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1174),X1171))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1174),X1173)),X1171)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1173)))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk32_4(X1171,X1172,X1173,X1174)),esk31_4(X1171,X1172,X1173,X1174))=X1174|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1174),X1171))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1174),X1173)),X1171)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1173))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bset_I6_J])])])])])])). 4.05/4.30 fof(c_0_6751, plain, ![X14682, X14683, X14684, X14685]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk445_4(X14682,X14683,X14684,X14685)),X14685))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14685),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14683)),X14682)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14685),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14683)),c_List_OtakeWhile(X14683,X14684,X14682))))))&(~hBOOL(hAPP(X14684,hAPP(hAPP(c_List_Onth(X14683),X14682),esk445_4(X14682,X14683,X14684,X14685))))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14685),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14683)),X14682)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14685),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14683)),c_List_OtakeWhile(X14683,X14684,X14682))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_length__takeWhile__less__P__nth])])])])])). 4.05/4.30 fof(c_0_6752, plain, ![X10897, X10898, X10899, X10900, X10901]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X10901,X10900)),hAPP(X10901,X10899)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X10898,X10898)),hAPP(hAPP(c_Product__Type_OPair(X10898,X10898),X10900),X10899)),c_List_Omeasures(X10898,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X10898,tc_Nat_Onat)),X10901),X10897))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__less])])). 4.05/4.30 cnf(c_0_6753, 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_5180, c_0_5049])). 4.05/4.30 fof(c_0_6754, plain, ![X9135, X9136, X9137, X9138]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk283_4(X9135,X9136,X9137,X9138)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X9137)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9138),X9135))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9138),X9137)),X9135)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9137)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk284_4(X9135,X9136,X9137,X9138)),X9136))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9138),X9135))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9138),X9137)),X9135)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9137)))&(X9138=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk284_4(X9135,X9136,X9137,X9138)),esk283_4(X9135,X9136,X9137,X9138))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9138),X9135))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9138),X9137)),X9135)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9137))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bset_I5_J])])])])])])). 4.05/4.30 fof(c_0_6755, plain, ![X13668, X13669, X13670, X13671]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk425_4(X13668,X13669,X13670,X13671)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X13670)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13668),X13671))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13668),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13671),X13670))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13670)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk426_4(X13668,X13669,X13670,X13671)),X13669))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13668),X13671))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13668),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13671),X13670))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13670)))&(X13671=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk426_4(X13668,X13669,X13670,X13671)),esk425_4(X13668,X13669,X13670,X13671))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13668),X13671))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13668),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13671),X13670))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13670))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_aset_I8_J])])])])])])). 4.05/4.30 fof(c_0_6756, plain, ![X11989, X11990, X11991, X11992]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk371_4(X11989,X11990,X11991,X11992)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X11991)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11989),X11992))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11989),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11992),X11991))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11991)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk372_4(X11989,X11990,X11991,X11992)),X11990))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11989),X11992))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11989),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11992),X11991))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11991)))&(X11992=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk372_4(X11989,X11990,X11991,X11992)),esk371_4(X11989,X11990,X11991,X11992))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11989),X11992))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11989),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11992),X11991))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11991))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_aset_I7_J])])])])])])). 4.05/4.30 fof(c_0_6757, plain, ![X9148, X9149, X9150, X9151, X9152]:(~c_Relation_Osingle__valued(X9152,X9151,hAPP(c_Relation_Oconverse(X9151,X9152),X9150))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9152,tc_HOL_Obool)),hAPP(c_Relation_OImage(X9151,X9152,X9150),X9149)),hAPP(c_Relation_OImage(X9151,X9152,X9150),X9148))=hAPP(c_Relation_OImage(X9151,X9152,X9150),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9151,tc_HOL_Obool)),X9149),X9148))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Image__Int__eq])])])). 4.05/4.30 cnf(c_0_6758, 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_5181])). 4.05/4.30 cnf(c_0_6759, plain, (hAPP(X1,esk296_3(X2,X1,X3))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),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(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk295_3(X2,X1,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk295_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5141])). 4.05/4.30 cnf(c_0_6760, plain, (hAPP(X1,esk97_3(X2,X1,X3))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),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(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk96_3(X2,X1,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk96_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5142])). 4.05/4.30 fof(c_0_6761, plain, ![X11826, X11827, X11828, X11829, X11830, X11831, X11832, X11833]:(~c_Fun_Oinj__on(X11833,X11832,X11831,X11830)|(~c_Fun_Oinj__on(X11829,X11828,X11827,X11826)|c_Fun_Oinj__on(tc_prod(X11833,X11829),tc_prod(X11832,X11828),c_Product__Type_Omap__pair(X11833,X11832,X11829,X11828,X11831,X11827),hAPP(hAPP(c_Product__Type_OSigma(X11833,X11829),X11830),hAPP(c_COMBK(tc_fun(X11829,tc_HOL_Obool),X11833),X11826))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__inj__on])])). 4.05/4.30 fof(c_0_6762, plain, ![X17081, X17082, X17083, X17084]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X17084)),hAPP(c_Set_Oimage(X17083,tc_Option_Ooption(X17084),X17082),c_Orderings_Otop__class_Otop(tc_fun(X17083,tc_HOL_Obool)))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X17084)),hAPP(c_Set_Oimage(X17083,tc_Option_Ooption(X17084),c_Map_Omap__add(X17083,X17084,X17082,hAPP(c_Map_Omap__of(X17083,X17084),X17081))),c_Orderings_Otop__class_Otop(tc_fun(X17083,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__range__map__of__map__add])])])). 4.05/4.30 fof(c_0_6763, plain, ![X5458, X5459, X5460, X5461]:(~class_Groups_Ocomm__monoid__add(X5461)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5460),X5459))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5461),hAPP(X5458,X5460)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5461),X5458),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X5460)),X5459)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5461),X5458),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5460),X5459)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__head__upt__Suc])])])). 4.05/4.30 fof(c_0_6764, plain, ![X5320, X5321, X5322]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5322),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5321)),X5320)))|hAPP(hAPP(c_List_Oappend(X5321),hAPP(hAPP(c_List_Otake(X5321),X5322),X5320)),hAPP(hAPP(c_List_Olist_OCons(X5321),hAPP(hAPP(c_List_Onth(X5321),X5320),X5322)),hAPP(hAPP(c_List_Odrop(X5321),hAPP(c_Nat_OSuc,X5322)),X5320)))=X5320), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_id__take__nth__drop])])])). 4.05/4.30 cnf(c_0_6765, 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),esk363_3(X1,X2,X3))),esk364_3(X1,X2,X3))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk361_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_5093])). 4.05/4.30 cnf(c_0_6766, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X3=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_3(X1,X3,X2))),esk362_3(X1,X3,X2))|hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1)))|~hBOOL(hAPP(X2,esk363_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_5093])). 4.05/4.30 fof(c_0_6767, plain, ![X6902, X6903, X6904, X6905, X6906, X6907]:((hAPP(c_Option_Ooption_OSome(X6904),X6907)!=hAPP(hAPP(c_Map_Omap__of(X6906,X6904),hAPP(hAPP(c_List_Ozip(X6906,X6904),X6905),X6903)),X6902)|hBOOL(hAPP(hAPP(c_member(X6906),X6902),hAPP(c_List_Oset(X6906),X6905)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6906)),X6905)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6904)),X6903))&(~hBOOL(hAPP(hAPP(c_member(X6906),X6902),hAPP(c_List_Oset(X6906),X6905)))|hAPP(c_Option_Ooption_OSome(X6904),esk216_5(X6902,X6903,X6904,X6905,X6906))=hAPP(hAPP(c_Map_Omap__of(X6906,X6904),hAPP(hAPP(c_List_Ozip(X6906,X6904),X6905),X6903)),X6902)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6906)),X6905)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6904)),X6903))), 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_map__of__zip__is__Some])])])])])])). 4.05/4.30 fof(c_0_6768, plain, ![X15841, X15842, X15843, X15844, X15845]:(~class_Rings_Osemiring__0(X15845)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15845),X15843),hAPP(c_List_Omonoid__add__class_Olistsum(X15845),hAPP(hAPP(c_List_Omap(X15844,X15845),X15842),X15841)))=hAPP(c_List_Omonoid__add__class_Olistsum(X15845),hAPP(hAPP(c_List_Omap(X15844,X15845),hAPP(hAPP(c_COMBB(X15845,X15845,X15844),hAPP(c_Groups_Otimes__class_Otimes(X15845),X15843)),X15842)),X15841))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__const__mult])])])). 4.05/4.30 fof(c_0_6769, plain, ![X12247, X12248, X12249, X12250, X12251]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X12251,X12250)),hAPP(X12251,X12249)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X12248,X12248)),hAPP(hAPP(c_Product__Type_OPair(X12248,X12248),X12250),X12249)),X12247))|hBOOL(hAPP(hAPP(c_member(tc_prod(X12248,X12248)),hAPP(hAPP(c_Product__Type_OPair(X12248,X12248),X12250),X12249)),c_Wellfounded_Omlex__prod(X12248,X12251,X12247))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mlex__leq])])])). 4.05/4.30 cnf(c_0_6770, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_3(X1,X2,X3))),esk353_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5096])). 4.05/4.30 cnf(c_0_6771, plain, (hBOOL(hAPP(hAPP(X1,X4),X5))|~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)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X4)),X5)!=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))|~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_5155])). 4.05/4.30 fof(c_0_6772, plain, ![X3224, X3225, X3226, X3227]:(~class_Groups_Oordered__ab__group__add__abs(X3227)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3227),hAPP(c_Groups_Oabs__class_Oabs(X3227),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3226,X3227),X3225),X3224))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3226,X3227),hAPP(hAPP(c_COMBB(X3227,X3227,X3226),c_Groups_Oabs__class_Oabs(X3227)),X3225)),X3224)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__abs])])). 4.05/4.30 cnf(c_0_6773, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3))),esk355_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(split_conjunct,[status(thm)],[c_0_5096])). 4.05/4.30 fof(c_0_6774, plain, ![X10291, X10292, X10293, X10294, X10295]:(~class_Orderings_Olinorder(X10295)|(~c_List_Olinorder__class_Osorted(X10295,hAPP(c_List_Orev(X10295),hAPP(hAPP(c_List_Omap(X10294,X10295),X10293),X10292)))|hAPP(c_List_Ofilter(X10294,hAPP(hAPP(c_COMBB(X10295,tc_HOL_Obool,X10294),hAPP(c_Orderings_Oord__class_Oless(X10295),X10291)),X10293)),X10292)=c_List_OtakeWhile(X10294,hAPP(hAPP(c_COMBB(X10295,tc_HOL_Obool,X10294),hAPP(c_Orderings_Oord__class_Oless(X10295),X10291)),X10293),X10292))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__equals__takeWhile__sorted__rev])])])). 4.05/4.30 fof(c_0_6775, plain, ![X17267, X17268, X17269, X17270, X17271, X17272]:(~c_Finite__Set_Ofolding(X17272,X17271,X17270,X17269)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17272),X17268))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17272),X17267))|hAPP(c_Fun_Ocomp(X17271,X17271,X17271,hAPP(X17269,X17267)),hAPP(X17269,X17268))=hAPP(c_Fun_Ocomp(X17271,X17271,X17271,hAPP(X17269,X17268)),hAPP(X17269,X17267))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ocommute__comp_H_H])])])). 4.05/4.30 cnf(c_0_6776, 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(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_4658])). 4.05/4.30 cnf(c_0_6777, plain, (hBOOL(hAPP(hAPP(X1,X5),X4))|~hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),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),X3),X5)),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X4))|~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_5156])). 4.05/4.30 cnf(c_0_6778, 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_5182])). 4.05/4.30 cnf(c_0_6779, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),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(rw,[status(thm)],[c_0_5183, c_0_4475])). 4.05/4.30 cnf(c_0_6780, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk488_3(X2,X3,X1)),hAPP(c_List_Oset(X1),c_List_OdropWhile(X1,X3,X2))))|c_List_OtakeWhile(X1,X3,X2)=hAPP(c_List_Ofilter(X1,X3),X2)), inference(split_conjunct,[status(thm)],[c_0_5184])). 4.05/4.30 fof(c_0_6781, plain, ![X4805, X4806, X4807, X4808, X4809]:(~class_Groups_Oab__semigroup__mult(X4809)|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4809,X4809,c_Groups_Otimes__class_Otimes(X4809),X4808,X4807),X4806))|(hBOOL(hAPP(hAPP(c_member(X4809),X4808),X4807))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4809,X4809,c_Groups_Otimes__class_Otimes(X4809),X4805,hAPP(hAPP(c_Set_Oinsert(X4809),X4808),X4807)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4809),X4805),X4806)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__graph__insert__swap])])])). 4.05/4.30 cnf(c_0_6782, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))=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)],[c_0_5185, c_0_4475])). 4.05/4.30 fof(c_0_6783, plain, ![X10036, X10037, X10038, X10039]:(~class_Complete__Lattice_Ocomplete__lattice(X10039)|hAPP(c_List_Ofoldl(X10039,X10038,hAPP(c_COMBC(X10038,X10039,X10039),hAPP(hAPP(c_COMBB(X10039,tc_fun(X10039,X10039),X10038),c_Lattices_Osemilattice__inf__class_Oinf(X10039)),X10036)),c_Orderings_Otop__class_Otop(X10039)),X10037)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10038,X10039),hAPP(c_List_Oset(X10038),X10037)),X10036)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__set__fold])])). 4.05/4.30 fof(c_0_6784, plain, ![X12213, X12214, X12215, X12216]:(~class_Complete__Lattice_Ocomplete__lattice(X12216)|hAPP(c_List_Ofoldl(X12216,X12215,hAPP(c_COMBC(X12215,X12216,X12216),hAPP(hAPP(c_COMBB(X12216,tc_fun(X12216,X12216),X12215),c_Lattices_Osemilattice__sup__class_Osup(X12216)),X12213)),c_Orderings_Obot__class_Obot(X12216)),X12214)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12215,X12216),hAPP(c_List_Oset(X12215),X12214)),X12213)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUPR__set__fold])])])). 4.05/4.30 fof(c_0_6785, plain, ![X17044, X17045, X17046, X17047, X17048]:(~c_Equiv__Relations_Oequiv(X17048,X17047,X17046)|(~hBOOL(hAPP(hAPP(c_member(tc_fun(X17048,tc_HOL_Obool)),X17045),hAPP(hAPP(c_Equiv__Relations_Oquotient(X17048),X17047),X17046)))|(~hBOOL(hAPP(hAPP(c_member(tc_fun(X17048,tc_HOL_Obool)),X17044),hAPP(hAPP(c_Equiv__Relations_Oquotient(X17048),X17047),X17046)))|(X17044=X17045|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17048,tc_HOL_Obool)),X17045),X17044)=c_Orderings_Obot__class_Obot(tc_fun(X17048,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__disj])])). 4.05/4.30 fof(c_0_6786, plain, ![X3007, X3008, X3009, X3010, X3011, X3012]:(~c_Map_Omap__le(X3012,X3011,X3010,X3009)|c_Map_Omap__le(X3012,X3011,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3012,tc_Option_Ooption(X3011)),X3010),X3008),c_Option_Ooption_ONone(X3011)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3012,tc_Option_Ooption(X3011)),X3009),X3008),hAPP(c_Option_Ooption_OSome(X3011),X3007)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__le__imp__upd__le])])])). 4.05/4.30 fof(c_0_6787, plain, ![X5873, X5874, X5875, X5876]:(~hBOOL(hAPP(hAPP(c_member(X5876),X5875),X5874))|hBOOL(hAPP(hAPP(c_member(tc_fun(X5876,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5876,X5876,X5873),hAPP(hAPP(c_Set_Oinsert(X5876),X5875),c_Orderings_Obot__class_Obot(tc_fun(X5876,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5876),X5874),X5873)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_quotientI])])])). 4.05/4.30 fof(c_0_6788, plain, ![X17316, X17317, X17318, X17319]:(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X17319,X17319),tc_HOL_Obool))!=hAPP(hAPP(c_Relation_Orel__comp(X17319,X17319,X17319),X17318),X17317)|(hAPP(hAPP(c_Relation_Orel__comp(X17319,X17319,X17319),X17316),X17317)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X17319,X17319),tc_HOL_Obool))|hAPP(hAPP(c_Relation_Orel__comp(X17319,X17319,X17319),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X17319,X17319),tc_HOL_Obool)),X17318),X17316)),X17317)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X17319,X17319),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_union__comp__emptyL])])])). 4.05/4.30 fof(c_0_6789, plain, ![X4667, X4668, X4669, X4670]:(hAPP(hAPP(c_Relation_Orel__comp(X4670,X4670,X4670),X4669),X4668)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4670,X4670),tc_HOL_Obool))|(hAPP(hAPP(c_Relation_Orel__comp(X4670,X4670,X4670),X4669),X4667)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4670,X4670),tc_HOL_Obool))|hAPP(hAPP(c_Relation_Orel__comp(X4670,X4670,X4670),X4669),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X4670,X4670),tc_HOL_Obool)),X4668),X4667))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4670,X4670),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_union__comp__emptyR])])])). 4.05/4.30 fof(c_0_6790, plain, ![X13907, X13908, X13909]:(~class_Lattices_Oab__semigroup__idem__mult(X13909)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13909),X13908))|(c_Orderings_Obot__class_Obot(tc_fun(X13909,tc_HOL_Obool))=X13908|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13909),X13907))|(X13907=c_Orderings_Obot__class_Obot(tc_fun(X13909,tc_HOL_Obool))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13909),hAPP(c_Finite__Set_Ofold1(X13909,c_Groups_Otimes__class_Otimes(X13909)),X13908)),hAPP(c_Finite__Set_Ofold1(X13909,c_Groups_Otimes__class_Otimes(X13909)),X13907))=hAPP(c_Finite__Set_Ofold1(X13909,c_Groups_Otimes__class_Otimes(X13909)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13909,tc_HOL_Obool)),X13908),X13907))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__Un2])])])). 4.05/4.30 cnf(c_0_6791, 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_5186])). 4.05/4.30 fof(c_0_6792, plain, ![X13659, X13660, X13661]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13661,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X13661,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk424_3(X13659,X13660,X13661))),X13660)),X13659))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13661,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X13661,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X13660)),X13659))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__finite__subset])])])])). 4.05/4.30 fof(c_0_6793, plain, ![X14024, X14025, X14026, X14027, X14028, X14029]:(~c_Finite__Set_Ofun__left__comm__idem(X14029,X14028,X14027)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14029),X14026))|hAPP(hAPP(X14027,X14024),hAPP(hAPP(c_Finite__Set_Ofold(X14029,X14028,X14027),X14025),X14026))=hAPP(hAPP(c_Finite__Set_Ofold(X14029,X14028,X14027),X14025),hAPP(hAPP(c_Set_Oinsert(X14029),X14024),X14026)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem])])])). 4.05/4.30 fof(c_0_6794, plain, ![X6041, X6042, X6043, X6044, X6045, X6046]:(~c_Finite__Set_Ofun__left__comm__idem(X6046,X6045,X6044)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6046),X6043))|hAPP(hAPP(c_Finite__Set_Ofold(X6046,X6045,X6044),X6042),hAPP(hAPP(c_Set_Oinsert(X6046),X6041),X6043))=hAPP(hAPP(c_Finite__Set_Ofold(X6046,X6045,X6044),hAPP(hAPP(X6044,X6041),X6042)),X6043))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem2])])])). 4.05/4.30 cnf(c_0_6795, 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_4647])). 4.05/4.30 cnf(c_0_6796, 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_5187, c_0_5188]), ['final']). 4.05/4.30 cnf(c_0_6797, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X4))=hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))|hAPP(c_Map_Omap__of(X1,X2),X3)!=hAPP(c_Map_Omap__of(X1,X2),X4)), inference(split_conjunct,[status(thm)],[c_0_5189])). 4.05/4.30 cnf(c_0_6798, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_3(X1,X2,X3))),esk353_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(split_conjunct,[status(thm)],[c_0_5096])). 4.05/4.30 fof(c_0_6799, plain, ![X707, X708, X709, X710, X711, X712, X713, X714, X715, X716]:(~c_Equiv__Relations_Ocongruent2(X716,X715,X714,X713,X712,X711)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X716,X716)),hAPP(hAPP(c_Product__Type_OPair(X716,X716),X710),X709)),X713))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X715,X715)),hAPP(hAPP(c_Product__Type_OPair(X715,X715),X708),X707)),X712))|hAPP(hAPP(X711,X710),X708)=hAPP(hAPP(X711,X709),X707)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_congruent2D])])])). 4.05/4.30 fof(c_0_6800, plain, ![X11497, X11498, X11499, X11500]:((~c_Wellfounded_Oacyclic(X11500,X11497)|hBOOL(hAPP(hAPP(c_member(tc_prod(X11500,X11500)),hAPP(hAPP(c_Product__Type_OPair(X11500,X11500),X11498),X11499)),c_Transitive__Closure_Ortrancl(X11500,X11497)))|c_Wellfounded_Oacyclic(X11500,hAPP(hAPP(c_Set_Oinsert(tc_prod(X11500,X11500)),hAPP(hAPP(c_Product__Type_OPair(X11500,X11500),X11499),X11498)),X11497)))&((c_Wellfounded_Oacyclic(X11500,X11497)|~c_Wellfounded_Oacyclic(X11500,hAPP(hAPP(c_Set_Oinsert(tc_prod(X11500,X11500)),hAPP(hAPP(c_Product__Type_OPair(X11500,X11500),X11499),X11498)),X11497)))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X11500,X11500)),hAPP(hAPP(c_Product__Type_OPair(X11500,X11500),X11498),X11499)),c_Transitive__Closure_Ortrancl(X11500,X11497)))|~c_Wellfounded_Oacyclic(X11500,hAPP(hAPP(c_Set_Oinsert(tc_prod(X11500,X11500)),hAPP(hAPP(c_Product__Type_OPair(X11500,X11500),X11499),X11498)),X11497))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acyclic__insert])])])])). 4.05/4.30 fof(c_0_6801, plain, ![X3195, X3196, X3197, X3198]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X3198,X3198)),hAPP(hAPP(c_Product__Type_OPair(X3198,X3198),X3196),X3197)),c_Transitive__Closure_Ortrancl(X3198,X3195)))|~c_Wellfounded_Owf(X3198,X3195)|c_Wellfounded_Owf(X3198,hAPP(hAPP(c_Set_Oinsert(tc_prod(X3198,X3198)),hAPP(hAPP(c_Product__Type_OPair(X3198,X3198),X3197),X3196)),X3195)))&((~hBOOL(hAPP(hAPP(c_member(tc_prod(X3198,X3198)),hAPP(hAPP(c_Product__Type_OPair(X3198,X3198),X3196),X3197)),c_Transitive__Closure_Ortrancl(X3198,X3195)))|~c_Wellfounded_Owf(X3198,hAPP(hAPP(c_Set_Oinsert(tc_prod(X3198,X3198)),hAPP(hAPP(c_Product__Type_OPair(X3198,X3198),X3197),X3196)),X3195)))&(c_Wellfounded_Owf(X3198,X3195)|~c_Wellfounded_Owf(X3198,hAPP(hAPP(c_Set_Oinsert(tc_prod(X3198,X3198)),hAPP(hAPP(c_Product__Type_OPair(X3198,X3198),X3197),X3196)),X3195))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__insert])])])])). 4.05/4.30 cnf(c_0_6802, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3))),esk355_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)))|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_5096])). 4.05/4.30 fof(c_0_6803, plain, ![X5344, X5345, X5346]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5346),X5345))|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,X5346),X5345)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5345),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5345),X5344)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5346),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5345),X5344))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__add__Un])])])). 4.05/4.30 fof(c_0_6804, plain, ![X485, X486, X487, X488]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X488),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X487)),X486)))|hAPP(hAPP(c_List_Oappend(X487),hAPP(hAPP(c_List_Otake(X487),X488),X486)),hAPP(hAPP(c_List_Olist_OCons(X487),X485),hAPP(hAPP(c_List_Odrop(X487),hAPP(c_Nat_OSuc,X488)),X486)))=hAPP(hAPP(c_List_Olist__update(X487,X486),X488),X485)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upd__conv__take__nth__drop])])])). 4.05/4.30 cnf(c_0_6805, plain, (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))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),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_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5190])). 4.05/4.30 fof(c_0_6806, plain, ![X1587, X1588, X1589]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1589),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1588)),X1587)))|hAPP(hAPP(c_List_Otake(X1588),hAPP(c_Nat_OSuc,X1589)),X1587)=hAPP(hAPP(c_List_Oappend(X1588),hAPP(hAPP(c_List_Otake(X1588),X1589),X1587)),hAPP(hAPP(c_List_Olist_OCons(X1588),hAPP(hAPP(c_List_Onth(X1588),X1587),X1589)),c_List_Olist_ONil(X1588)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Suc__conv__app__nth])])). 4.05/4.30 fof(c_0_6807, plain, ![X12417, X12418, X12419, X12420, X12421]:(~class_Rings_Olinordered__idom(X12421)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12421),hAPP(c_Groups_Oabs__class_Oabs(X12421),X12420)),X12419))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12421),hAPP(c_Groups_Oabs__class_Oabs(X12421),X12418)),X12417))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12421),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12421),hAPP(c_Groups_Oabs__class_Oabs(X12421),X12420)),hAPP(c_Groups_Oabs__class_Oabs(X12421),X12418))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12421),X12419),X12417)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__mult__less])])])). 4.05/4.30 fof(c_0_6808, plain, ![X10162, X10163, X10164]:(~class_Groups_Ocomm__monoid__mult(X10164)|~class_Groups_Ocomm__monoid__add(X10164)|(~c_Nat__Transfer_Onat__set(X10163)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X10164),hAPP(hAPP(c_COMBB(tc_Int_Oint,X10164,tc_Nat_Onat),X10162),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X10163))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X10164),X10162),X10163))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__int__nat__sum__prod_I2_J])])])). 4.05/4.30 cnf(c_0_6809, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk245_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)|hAPP(c_Set_Oimage(X1,X7,X6),X5)!=X4|~c_Fun_Oinj__on(X1,X7,X6,X5)|~class_Groups_Ocomm__monoid__add(X8)), inference(split_conjunct,[status(thm)],[c_0_5191])). 4.05/4.30 cnf(c_0_6810, 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_5192])). 4.05/4.30 cnf(c_0_6811, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk240_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_5112])). 4.05/4.30 fof(c_0_6812, plain, ![X10360, X10361, X10362, X10363]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10362),X10360),hAPP(c_Finite__Set_Ofold1(X10362,c_Orderings_Oord__class_Omin(X10362)),X10361)))|(~hBOOL(hAPP(hAPP(c_member(X10362),X10363),X10361))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10362),X10360),X10363)))|c_Orderings_Obot__class_Obot(tc_fun(X10362,tc_HOL_Obool))=X10361|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10362),X10361))|~class_Orderings_Olinorder(X10362))&((hBOOL(hAPP(hAPP(c_member(X10362),esk316_3(X10360,X10361,X10362)),X10361))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10362),X10360),hAPP(c_Finite__Set_Ofold1(X10362,c_Orderings_Oord__class_Omin(X10362)),X10361)))|c_Orderings_Obot__class_Obot(tc_fun(X10362,tc_HOL_Obool))=X10361|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10362),X10361))|~class_Orderings_Olinorder(X10362))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10362),X10360),esk316_3(X10360,X10361,X10362)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10362),X10360),hAPP(c_Finite__Set_Ofold1(X10362,c_Orderings_Oord__class_Omin(X10362)),X10361)))|c_Orderings_Obot__class_Obot(tc_fun(X10362,tc_HOL_Obool))=X10361|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10362),X10361))|~class_Orderings_Olinorder(X10362)))), 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])])])])])])). 4.05/4.30 fof(c_0_6813, plain, ![X12516, X12517, X12518]:(~class_Groups_Ocomm__monoid__add(X12518)|~class_Groups_Ocomm__monoid__mult(X12518)|(~c_Nat__Transfer_Onat__set(X12517)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X12518),X12516),X12517)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X12518),hAPP(hAPP(c_COMBB(tc_Int_Oint,X12518,tc_Nat_Onat),X12516),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X12517)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I1_J])])). 4.05/4.30 cnf(c_0_6814, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3))),esk355_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,esk353_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_5096])). 4.05/4.30 cnf(c_0_6815, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk352_3(X2,X3,X1))),esk353_3(X2,X3,X1))=X3|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,esk355_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5096])). 4.05/4.30 cnf(c_0_6816, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk286_8(X2,X3,X4,X5,X6,X7,X1,X8)),X5))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X7,X8),X2),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X8),X3),X5)|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_5193])). 4.05/4.30 fof(c_0_6817, plain, ![X7602, X7603, X7604, X7605]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7604),X7602),hAPP(c_Finite__Set_Ofold1(X7604,c_Lattices_Osemilattice__inf__class_Oinf(X7604)),X7603)))|(~hBOOL(hAPP(hAPP(c_member(X7604),X7605),X7603))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7604),X7602),X7605)))|c_Orderings_Obot__class_Obot(tc_fun(X7604,tc_HOL_Obool))=X7603|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7604),X7603))|~class_Lattices_Osemilattice__inf(X7604))&((hBOOL(hAPP(hAPP(c_member(X7604),esk242_3(X7602,X7603,X7604)),X7603))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7604),X7602),hAPP(c_Finite__Set_Ofold1(X7604,c_Lattices_Osemilattice__inf__class_Oinf(X7604)),X7603)))|c_Orderings_Obot__class_Obot(tc_fun(X7604,tc_HOL_Obool))=X7603|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7604),X7603))|~class_Lattices_Osemilattice__inf(X7604))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7604),X7602),esk242_3(X7602,X7603,X7604)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7604),X7602),hAPP(c_Finite__Set_Ofold1(X7604,c_Lattices_Osemilattice__inf__class_Oinf(X7604)),X7603)))|c_Orderings_Obot__class_Obot(tc_fun(X7604,tc_HOL_Obool))=X7603|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7604),X7603))|~class_Lattices_Osemilattice__inf(X7604)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_below__fold1__iff])])])])])])). 4.05/4.30 fof(c_0_6818, plain, ![X13173, X13174, X13175, X13177]:(((hBOOL(hAPP(hAPP(c_member(X13175),esk406_3(X13173,X13174,X13175)),X13174))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13175),X13173),hAPP(c_Finite__Set_Ofold1(X13175,c_Orderings_Oord__class_Omin(X13175)),X13174)))|X13174=c_Orderings_Obot__class_Obot(tc_fun(X13175,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13175),X13174))|~class_Orderings_Olinorder(X13175))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13175),X13173),esk406_3(X13173,X13174,X13175)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13175),X13173),hAPP(c_Finite__Set_Ofold1(X13175,c_Orderings_Oord__class_Omin(X13175)),X13174)))|X13174=c_Orderings_Obot__class_Obot(tc_fun(X13175,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13175),X13174))|~class_Orderings_Olinorder(X13175)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13175),X13173),hAPP(c_Finite__Set_Ofold1(X13175,c_Orderings_Oord__class_Omin(X13175)),X13174)))|(~hBOOL(hAPP(hAPP(c_member(X13175),X13177),X13174))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13175),X13173),X13177)))|X13174=c_Orderings_Obot__class_Obot(tc_fun(X13175,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X13175),X13174))|~class_Orderings_Olinorder(X13175))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Obelow__fold1__iff])])])])])])). 4.05/4.30 cnf(c_0_6819, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk363_3(X3,X2,X1))),esk364_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,esk361_3(X3,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_5093])). 4.05/4.30 cnf(c_0_6820, plain, (X3=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk361_3(X2,X3,X1))),esk362_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,esk363_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5093])). 4.05/4.30 fof(c_0_6821, plain, ![X1791, X1792, X1793]:(hBOOL(hAPP(hAPP(c_member(tc_prod(X1793,X1793)),hAPP(hAPP(c_Product__Type_OPair(X1793,X1793),esk61_3(X1791,X1792,X1793)),esk61_3(X1791,X1792,X1793))),X1792))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1793),tc_List_Olist(X1793))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1793),tc_List_Olist(X1793)),X1791),X1791)),c_List_Olexord(X1793,X1792)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lexord__irreflexive])])])])). 4.05/4.30 cnf(c_0_6822, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|X3=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|~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))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X1)!=X4), inference(split_conjunct,[status(thm)],[c_0_5194])). 4.05/4.30 fof(c_0_6823, plain, ![X5045, X5046, X5047, X5048]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5048))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5047),X5046))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5046),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),X5047),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5045,X5048))),X5046)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult2__lemma__aux2])])])). 4.05/4.30 fof(c_0_6824, plain, ![X946, X947, X948, X949]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X949))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X948))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X948),X947))|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),X947),c_Divides_Odiv__class_Omod(tc_Int_Oint,X946,X949))),X948)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult2__lemma__aux3])])])). 4.05/4.30 fof(c_0_6825, plain, ![X3824, X3825, X3826, X3827, X3828, X3829, X3830]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X3830,X3829)),hAPP(hAPP(c_Product__Type_OPair(X3830,X3829),X3828),X3827)),X3826))|hBOOL(hAPP(hAPP(c_member(X3825),hAPP(hAPP(X3824,X3828),X3827)),hAPP(c_Set_Oimage(tc_prod(X3830,X3829),X3825,hAPP(c_Product__Type_Oprod_Oprod__case(X3830,X3829,X3825),X3824)),X3826)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pair__imageI])])])). 4.05/4.30 fof(c_0_6826, plain, ![X13309, X13310, X13311, X13312, X13313]:(~c_Fun_Oinj__on(X13313,X13312,X13311,c_Orderings_Otop__class_Otop(tc_fun(X13313,tc_HOL_Obool)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13312,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13313,X13312,X13311),X13310)),hAPP(c_Set_Oimage(X13313,X13312,X13311),X13309))=hAPP(c_Set_Oimage(X13313,X13312,X13311),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13313,tc_HOL_Obool)),X13310),X13309))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Int])])). 4.05/4.30 fof(c_0_6827, plain, ![X12755, X12756, X12757, X12758, X12759]:(~c_Fun_Oinj__on(X12759,X12758,X12757,c_Orderings_Otop__class_Otop(tc_fun(X12759,tc_HOL_Obool)))|hAPP(c_Set_Oimage(X12759,X12758,X12757),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12759,tc_HOL_Obool)),X12756),X12755))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12758,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12759,X12758,X12757),X12756)),hAPP(c_Set_Oimage(X12759,X12758,X12757),X12755))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__set__diff])])])). 4.05/4.30 fof(c_0_6828, plain, ![X5564, X5565, X5566]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5566),X5565))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5566),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5566,tc_HOL_Obool)),X5565),hAPP(hAPP(c_Set_Oinsert(X5566),X5564),c_Orderings_Obot__class_Obot(tc_fun(X5566,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X5566),X5565)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Diff1__le])])])). 4.05/4.30 fof(c_0_6829, plain, ![X10442, X10443, X10444, X10445]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10445))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10444),X10443))|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),X10443),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10442,X10445))),X10444)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10443),X10445))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__lemma])])])). 4.05/4.30 cnf(c_0_6830, plain, (hBOOL(hAPP(X1,esk165_6(X2,X3,X4,X1,X5,X6)))|hAPP(c_List_Ofilter(X5,X1),X4)=hAPP(hAPP(c_List_Olist_OCons(X5),X3),X2)|X4!=hAPP(hAPP(c_List_Oappend(X5),X6),hAPP(hAPP(c_List_Olist_OCons(X5),X3),X7))|~hBOOL(hAPP(X1,X3))|hAPP(c_List_Ofilter(X5,X1),X7)!=X2), inference(split_conjunct,[status(thm)],[c_0_5107])). 4.05/4.30 fof(c_0_6831, plain, ![X5660, X5661, X5662, X5663]:(~class_Orderings_Olinorder(X5663)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5663),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5663),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5663),X5662),X5661)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5663),X5662),X5660))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5663),X5662),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5663),X5661),X5660))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Odistrib__inf__le])])])). 4.05/4.30 fof(c_0_6832, plain, ![X13982, X13983, X13984, X13985]:(~class_Lattices_Olattice(X13985)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13985),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13985),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13985),X13984),X13983)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13985),X13984),X13982))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13985),X13984),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13985),X13983),X13982))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distrib__inf__le])])])). 4.05/4.30 fof(c_0_6833, plain, ![X13364, X13365, X13366, X13367]:(~class_Orderings_Olinorder(X13367)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13367),hAPP(hAPP(c_Orderings_Oord__class_Omax(X13367),X13366),hAPP(hAPP(c_Orderings_Oord__class_Omin(X13367),X13365),X13364))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X13367),hAPP(hAPP(c_Orderings_Oord__class_Omax(X13367),X13366),X13365)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X13367),X13366),X13364))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Odistrib__sup__le])])])). 4.05/4.30 fof(c_0_6834, plain, ![X2582, X2583, X2584, X2585]:(~class_Lattices_Olattice(X2585)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2585),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2585),X2584),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2585),X2583),X2582))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2585),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2585),X2584),X2583)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2585),X2584),X2582))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distrib__sup__le])])])). 4.05/4.30 fof(c_0_6835, plain, ![X9435, X9436, X9437, X9438]:((hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9438,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9438,tc_HOL_Obool)),X9437),X9436)),X9435)!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9438,tc_HOL_Obool)),X9437),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9438,tc_HOL_Obool)),X9436),X9435))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9438,tc_HOL_Obool)),X9435),X9437)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9438,tc_HOL_Obool)),X9435),X9437))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9438,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9438,tc_HOL_Obool)),X9437),X9436)),X9435)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9438,tc_HOL_Obool)),X9437),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9438,tc_HOL_Obool)),X9436),X9435)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__Int__assoc__eq])])). 4.05/4.30 fof(c_0_6836, plain, ![X8623, X8624, X8625]:(~class_Orderings_Olinorder(X8625)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8625),X8624))|c_List_Olinorder__class_Osorted__list__of__set(X8625,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8625,tc_HOL_Obool)),X8624),hAPP(hAPP(c_Set_Oinsert(X8625),X8623),c_Orderings_Obot__class_Obot(tc_fun(X8625,tc_HOL_Obool)))))=c_List_Oremove1(X8625,X8623,c_List_Olinorder__class_Osorted__list__of__set(X8625,X8624)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__list__of__set__remove])])])). 4.05/4.30 fof(c_0_6837, plain, ![X1489, X1490, X1491]:(~c_Wellfounded_Owf(X1491,X1490)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1491,X1491),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1491,X1491,X1491),X1490),X1489)),X1490))|c_FunDef_Oreduction__pair(X1491,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X1491,X1491),tc_HOL_Obool),tc_fun(tc_prod(X1491,X1491),tc_HOL_Obool)),X1490),X1489)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_reduction__pairI])])])). 4.05/4.30 fof(c_0_6838, plain, ![X11000, X11001, X11002, X11003, X11004, X11005]:(~c_Finite__Set_Ofolding(X11005,X11004,X11003,X11002)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11005),X11001))|(hBOOL(hAPP(hAPP(c_member(X11005),X11000),X11001))|hAPP(c_Fun_Ocomp(X11004,X11004,X11004,hAPP(X11002,X11001)),hAPP(X11003,X11000))=hAPP(X11002,hAPP(hAPP(c_Set_Oinsert(X11005),X11000),X11001))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Oinsert])])])). 4.05/4.30 fof(c_0_6839, plain, ![X4201, X4202, X4203]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4203),X4202))|hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X4203),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4203,tc_HOL_Obool)),X4202),hAPP(hAPP(c_Set_Oinsert(X4203),X4201),c_Orderings_Obot__class_Obot(tc_fun(X4203,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X4203),hAPP(hAPP(c_Set_Oinsert(X4203),X4201),X4202))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert])])). 4.05/4.30 cnf(c_0_6840, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5195, c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6841, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5196, c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_6842, plain, ![X11557, X11558, X11559, X11560, X11561, X11563, X11564, X11565, X11566, X11567, X11568]:(((hBOOL(hAPP(hAPP(c_member(X11560),esk357_5(X11557,X11558,X11559,X11560,X11561)),X11559))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11561,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11560,tc_fun(X11561,tc_HOL_Obool)),X11559),X11558)),X11557)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11561,tc_HOL_Obool)),hAPP(X11558,esk357_5(X11557,X11558,X11559,X11560,X11561))),X11557))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11561,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11560,tc_fun(X11561,tc_HOL_Obool)),X11559),X11558)),X11557))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11567,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11566,tc_fun(X11567,tc_HOL_Obool)),X11565),X11564)),X11563))|(~hBOOL(hAPP(hAPP(c_member(X11566),X11568),X11565))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11567,tc_HOL_Obool)),hAPP(X11564,X11568)),X11563))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UN__subset__iff])])])])])])])). 4.05/4.30 fof(c_0_6843, plain, ![X9821, X9822, X9823, X9824, X9825]:(c_Orderings_Otop__class_Otop(tc_fun(X9824,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X9825,X9824,X9823),c_Orderings_Otop__class_Otop(tc_fun(X9825,tc_HOL_Obool)))|(c_Orderings_Otop__class_Otop(tc_fun(X9822,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X9824,X9822,X9821),c_Orderings_Otop__class_Otop(tc_fun(X9824,tc_HOL_Obool)))|hAPP(c_Set_Oimage(X9825,X9822,hAPP(c_Fun_Ocomp(X9824,X9822,X9825,X9821),X9823)),c_Orderings_Otop__class_Otop(tc_fun(X9825,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X9822,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comp__surj])])])). 4.05/4.30 fof(c_0_6844, plain, ![X2001, X2002, X2003, X2004, X2005, X2006, X2007, X2008, X2009, X2010, X2011]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2005,tc_HOL_Obool)),X2004),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2003,tc_fun(X2005,tc_HOL_Obool)),X2002),X2001)))|(~hBOOL(hAPP(hAPP(c_member(X2003),X2006),X2002))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2005,tc_HOL_Obool)),X2004),hAPP(X2001,X2006)))))&((hBOOL(hAPP(hAPP(c_member(X2009),esk74_5(X2007,X2008,X2009,X2010,X2011)),X2008))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2011,tc_HOL_Obool)),X2010),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2009,tc_fun(X2011,tc_HOL_Obool)),X2008),X2007))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2011,tc_HOL_Obool)),X2010),hAPP(X2007,esk74_5(X2007,X2008,X2009,X2010,X2011))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2011,tc_HOL_Obool)),X2010),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2009,tc_fun(X2011,tc_HOL_Obool)),X2008),X2007)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__subset__iff])])])])])])])). 4.05/4.30 cnf(c_0_6845, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5197, c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_6846, plain, ![X14555, X14556, X14557]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14557),X14556))|(~hBOOL(hAPP(hAPP(c_member(X14557),X14555),X14556))|hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X14557),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14557,tc_HOL_Obool)),X14556),hAPP(hAPP(c_Set_Oinsert(X14557),X14555),c_Orderings_Obot__class_Obot(tc_fun(X14557,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X14557),X14556))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Suc__Diff1])])])). 4.05/4.30 cnf(c_0_6847, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))=c_Groups_Oone__class_Oone(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|~class_Int_Onumber__ring(X2)), inference(rw,[status(thm)],[c_0_5198, c_0_4475])). 4.05/4.30 fof(c_0_6848, plain, ![X651, X652, X653, X654]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X654),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X653)),X652)))|hAPP(hAPP(c_List_Otake(X653),X654),X652)=c_List_OtakeWhile(X653,X651,X652)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk12_4(X651,X652,X653,X654)),X654)))&(hBOOL(hAPP(X651,hAPP(hAPP(c_List_Onth(X653),X652),X654)))|hAPP(hAPP(c_List_Otake(X653),X654),X652)=c_List_OtakeWhile(X653,X651,X652)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk12_4(X651,X652,X653,X654)),X654))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X654),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X653)),X652)))|hAPP(hAPP(c_List_Otake(X653),X654),X652)=c_List_OtakeWhile(X653,X651,X652)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk12_4(X651,X652,X653,X654)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X653)),X652))))&(hBOOL(hAPP(X651,hAPP(hAPP(c_List_Onth(X653),X652),X654)))|hAPP(hAPP(c_List_Otake(X653),X654),X652)=c_List_OtakeWhile(X653,X651,X652)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk12_4(X651,X652,X653,X654)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X653)),X652)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X654),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X653)),X652)))|hAPP(hAPP(c_List_Otake(X653),X654),X652)=c_List_OtakeWhile(X653,X651,X652)|~hBOOL(hAPP(X651,hAPP(hAPP(c_List_Onth(X653),X652),esk12_4(X651,X652,X653,X654)))))&(hBOOL(hAPP(X651,hAPP(hAPP(c_List_Onth(X653),X652),X654)))|hAPP(hAPP(c_List_Otake(X653),X654),X652)=c_List_OtakeWhile(X653,X651,X652)|~hBOOL(hAPP(X651,hAPP(hAPP(c_List_Onth(X653),X652),esk12_4(X651,X652,X653,X654)))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile__eq__take__P__nth])])])])])). 4.05/4.30 cnf(c_0_6849, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),hAPP(hAPP(c_List_Onth(X2),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3)=c_List_Ofoldr(X2,X2,c_Orderings_Oord__class_Omax(X2),X1,X3)|~c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Orev(X2),X1))|~class_Orderings_Olinorder(X2)), inference(split_conjunct,[status(thm)],[c_0_5199])). 4.05/4.30 fof(c_0_6850, plain, ![X14851, X14852, X14853, X14854, X14855]:(~class_Orderings_Olinorder(X14855)|(hBOOL(hAPP(hAPP(c_member(X14855),hAPP(X14854,X14853)),hAPP(c_Set_Oimage(X14852,X14855,X14854),hAPP(c_List_Oset(X14852),X14851))))|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X14852,X14855,X14854),X14853),X14851)=c_List_Olinorder__class_Oinsort__insert__key(X14852,X14855,X14854,X14853,X14851))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__insert__insort__key])])])). 4.05/4.30 cnf(c_0_6851, plain, (hBOOL(hAPP(X1,esk421_7(X2,X1,X3,X4,X5,X6,X7)))|hAPP(c_List_Ofilter(X5,X1),X2)=hAPP(hAPP(c_List_Olist_OCons(X5),X4),X3)|X2!=hAPP(hAPP(c_List_Oappend(X5),X6),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X7))|~hBOOL(hAPP(X1,X4))|hAPP(c_List_Ofilter(X5,X1),X7)!=X3), inference(split_conjunct,[status(thm)],[c_0_5138])). 4.05/4.30 fof(c_0_6852, plain, ![X15693, X15694, X15695]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15695),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X15694)))|hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X15694),X15695),X15693))=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),X15694)),X15693)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X15694),X15695))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__update__nat])])). 4.05/4.30 cnf(c_0_6853, 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_5200, c_0_5201])). 4.05/4.30 cnf(c_0_6854, 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_5202, c_0_5201])). 4.05/4.30 fof(c_0_6855, plain, ![X16805, X16806, X16807, X16808, X16809, X16812, X16813, X16814, X16815, X16816, X16817, X16818]:((((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X16809,X16809,X16808,esk501_5(X16805,X16806,X16807,X16808,X16809),esk502_5(X16805,X16806,X16807,X16808,X16809)),X16805))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X16809,X16808,hAPP(hAPP(c_Set_Oinsert(X16809),X16807),X16806)),X16805)))&(~hBOOL(hAPP(hAPP(c_member(X16809),esk501_5(X16805,X16806,X16807,X16808,X16809)),esk502_5(X16805,X16806,X16807,X16808,X16809)))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X16809,X16808,hAPP(hAPP(c_Set_Oinsert(X16809),X16807),X16806)),X16805))))&(hAPP(hAPP(c_Set_Oinsert(X16809),X16807),X16806)=hAPP(hAPP(c_Set_Oinsert(X16809),esk501_5(X16805,X16806,X16807,X16808,X16809)),esk502_5(X16805,X16806,X16807,X16808,X16809))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X16809,X16808,hAPP(hAPP(c_Set_Oinsert(X16809),X16807),X16806)),X16805))))&(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X16816,X16816,X16815,X16817,X16818),X16812))|hBOOL(hAPP(hAPP(c_member(X16816),X16817),X16818))|hAPP(hAPP(c_Set_Oinsert(X16816),X16814),X16813)!=hAPP(hAPP(c_Set_Oinsert(X16816),X16817),X16818)|hBOOL(hAPP(c_Finite__Set_Ofold1Set(X16816,X16815,hAPP(hAPP(c_Set_Oinsert(X16816),X16814),X16813)),X16812)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1Set_Oequations])])])])])])])). 4.05/4.30 cnf(c_0_6856, 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_5203, c_0_5201])). 4.05/4.30 cnf(c_0_6857, 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_5204, c_0_5205]), ['final']). 4.05/4.30 cnf(c_0_6858, 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_5206, c_0_4523])). 4.05/4.30 fof(c_0_6859, plain, ![X3480, X3481, X3482, X3483, X3484, X3485, X3486]:(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X3486,X3485,X3484,X3483,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3486,tc_HOL_Obool)),X3482),hAPP(hAPP(c_Set_Oinsert(X3486),X3481),c_Orderings_Obot__class_Obot(tc_fun(X3486,tc_HOL_Obool))))),X3480))|(~hBOOL(hAPP(hAPP(c_member(X3486),X3481),X3482))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X3486,X3485,X3484,X3483,X3482),hAPP(hAPP(X3484,X3481),X3480))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff1__fold__graph])])). 4.05/4.30 fof(c_0_6860, plain, ![X16240, X16241, X16242, X16243]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16242,X16243)),X16241),X16240))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X16242),hAPP(hAPP(c_COMBS(X16242,X16243,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X16243,tc_fun(X16243,tc_HOL_Obool),X16242),c_Orderings_Oord__class_Oless__eq(X16243)),X16241)),X16240)))|(~class_Orderings_Oorder(X16243)|~class_Enum_Oenum(X16242)))&(~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X16242),hAPP(hAPP(c_COMBS(X16242,X16243,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X16243,tc_fun(X16243,tc_HOL_Obool),X16242),c_Orderings_Oord__class_Oless__eq(X16243)),X16241)),X16240)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16242,X16243)),X16241),X16240))|(~class_Orderings_Oorder(X16243)|~class_Enum_Oenum(X16242)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__fun_I1_J])])])). 4.05/4.30 fof(c_0_6861, plain, ![X3325, X3326, X3327, X3328, X3329]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3329),hAPP(c_Set_Oimage(X3328,X3329,X3327),c_Orderings_Otop__class_Otop(tc_fun(X3328,tc_HOL_Obool)))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X3326),hAPP(c_Set_Oimage(X3328,X3326,hAPP(hAPP(c_COMBB(X3329,X3326,X3328),X3325),X3327)),c_Orderings_Otop__class_Otop(tc_fun(X3328,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__imageI])])). 4.05/4.30 cnf(c_0_6862, 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_5207])). 4.05/4.30 cnf(c_0_6863, 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_5208])). 4.05/4.30 cnf(c_0_6864, 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_5208])). 4.05/4.30 fof(c_0_6865, plain, ![X8368, X8369, X8370, X8371, X8372, X8373]:((hAPP(hAPP(c_Product__Type_OPair(X8371,X8370),esk263_6(X8368,X8369,X8370,X8371,X8372,X8373)),esk264_6(X8368,X8369,X8370,X8371,X8372,X8373))=X8368|~hBOOL(hAPP(hAPP(c_member(X8373),X8372),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X8371,X8370,tc_fun(X8373,tc_HOL_Obool)),X8369),X8368))))&(hBOOL(hAPP(hAPP(c_member(X8373),X8372),hAPP(hAPP(X8369,esk263_6(X8368,X8369,X8370,X8371,X8372,X8373)),esk264_6(X8368,X8369,X8370,X8371,X8372,X8373))))|~hBOOL(hAPP(hAPP(c_member(X8373),X8372),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X8371,X8370,tc_fun(X8373,tc_HOL_Obool)),X8369),X8368))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mem__splitE])])])])])). 4.05/4.30 cnf(c_0_6866, 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_5209])). 4.05/4.30 fof(c_0_6867, plain, ![X14461, X14462, X14463, X14464, X14465, X14466]:(~c_Finite__Set_Ofolding__idem(X14466,X14465,X14464,X14463)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14466),X14462))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14466),X14461))|hAPP(c_Fun_Ocomp(X14465,X14465,X14465,hAPP(X14463,X14462)),hAPP(X14463,X14461))=hAPP(X14463,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14466,tc_HOL_Obool)),X14462),X14461))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Ounion__idem])])). 4.05/4.30 cnf(c_0_6868, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4))|X1!=X2|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)), inference(split_conjunct,[status(thm)],[c_0_5210])). 4.05/4.30 cnf(c_0_6869, 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_5211])). 4.05/4.30 fof(c_0_6870, plain, ![X9531, X9532, X9533]:(~class_Orderings_Olinorder(X9533)|(c_Orderings_Obot__class_Obot(tc_fun(X9533,tc_HOL_Obool))=X9532|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9533,tc_HOL_Obool)),X9532),X9531))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9533),X9531))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9533),hAPP(c_Finite__Set_Ofold1(X9533,c_Orderings_Oord__class_Omin(X9533)),X9531)),hAPP(c_Finite__Set_Ofold1(X9533,c_Orderings_Oord__class_Omin(X9533)),X9532))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__antimono])])])). 4.05/4.30 fof(c_0_6871, plain, ![X604, X605, X606, X607, X608, X609, X610, X611, X612, X613, X614, X615]:(((hAPP(hAPP(c_List_Oappend(X608),X607),X609)!=X605|X606!=hAPP(hAPP(c_List_Oappend(X608),X609),X604)|hAPP(hAPP(c_List_Oappend(X608),X605),X604)=hAPP(hAPP(c_List_Oappend(X608),X607),X606))&(hAPP(hAPP(c_List_Oappend(X608),X605),X610)!=X607|X604!=hAPP(hAPP(c_List_Oappend(X608),X610),X606)|hAPP(hAPP(c_List_Oappend(X608),X605),X604)=hAPP(hAPP(c_List_Oappend(X608),X607),X606)))&(((hAPP(hAPP(c_List_Oappend(X615),X612),esk11_5(X611,X612,X613,X614,X615))=X614|hAPP(hAPP(c_List_Oappend(X615),X614),esk10_5(X611,X612,X613,X614,X615))=X612|hAPP(hAPP(c_List_Oappend(X615),X612),X611)!=hAPP(hAPP(c_List_Oappend(X615),X614),X613))&(X611=hAPP(hAPP(c_List_Oappend(X615),esk11_5(X611,X612,X613,X614,X615)),X613)|hAPP(hAPP(c_List_Oappend(X615),X614),esk10_5(X611,X612,X613,X614,X615))=X612|hAPP(hAPP(c_List_Oappend(X615),X612),X611)!=hAPP(hAPP(c_List_Oappend(X615),X614),X613)))&((hAPP(hAPP(c_List_Oappend(X615),X612),esk11_5(X611,X612,X613,X614,X615))=X614|X613=hAPP(hAPP(c_List_Oappend(X615),esk10_5(X611,X612,X613,X614,X615)),X611)|hAPP(hAPP(c_List_Oappend(X615),X612),X611)!=hAPP(hAPP(c_List_Oappend(X615),X614),X613))&(X611=hAPP(hAPP(c_List_Oappend(X615),esk11_5(X611,X612,X613,X614,X615)),X613)|X613=hAPP(hAPP(c_List_Oappend(X615),esk10_5(X611,X612,X613,X614,X615)),X611)|hAPP(hAPP(c_List_Oappend(X615),X612),X611)!=hAPP(hAPP(c_List_Oappend(X615),X614),X613))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__append__conv2])])])])])])). 4.05/4.30 cnf(c_0_6872, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk247_3(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|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),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_5212])). 4.05/4.30 fof(c_0_6873, plain, ![X6645, X6646, X6647]:((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk202_3(X6645,X6646,X6647)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X6647)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6646),X6647)=X6646|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6646),c_Groups_Oone__class_Oone(tc_Int_Oint))),X6645))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6647)))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk203_3(X6645,X6646,X6647)),X6645))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6646),X6647)=X6646|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6646),c_Groups_Oone__class_Oone(tc_Int_Oint))),X6645))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6647)))&(X6646=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk203_3(X6645,X6646,X6647)),esk202_3(X6645,X6646,X6647))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6646),X6647)=X6646|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6646),c_Groups_Oone__class_Oone(tc_Int_Oint))),X6645))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6647))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_aset_I3_J])])])])])). 4.05/4.30 cnf(c_0_6874, 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_5213])). 4.05/4.30 fof(c_0_6875, plain, ![X7669, X7670, X7671, X7672, X7673]:(~class_Rings_Ocomm__semiring__1(X7673)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7673),X7672),X7670)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7673),X7671),X7669))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7673),X7672),X7671)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7673),X7670),X7669))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])])])). 4.05/4.30 fof(c_0_6876, plain, ![X8724, X8725, X8726, X8727, X8728]:(~class_Fields_Olinordered__field(X8728)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8728),c_Groups_Ozero__class_Ozero(X8728)),X8727))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8728),X8727),X8726))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8728),c_Groups_Ozero__class_Ozero(X8728)),X8725))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8728),X8725),X8724))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8728),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8728),X8727),X8724)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8728),X8726),X8725)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_frac__less2])])])). 4.05/4.30 fof(c_0_6877, plain, ![X3117, X3118, X3119, X3120, X3121]:(~class_Fields_Olinordered__field(X3121)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3121),c_Groups_Ozero__class_Ozero(X3121)),X3120))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3121),X3120),X3119))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3121),c_Groups_Ozero__class_Ozero(X3121)),X3118))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3121),X3118),X3117))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3121),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3121),X3120),X3117)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3121),X3119),X3118)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less])])). 4.05/4.30 fof(c_0_6878, plain, ![X1242, X1243, X1244, X1245, X1246]:(~class_Rings_Olinordered__semiring__strict(X1246)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1246),X1245),X1244))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1246),X1243),X1242))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1246),c_Groups_Ozero__class_Ozero(X1246)),X1244))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1246),c_Groups_Ozero__class_Ozero(X1246)),X1243))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1246),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1246),X1245),X1243)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1246),X1244),X1242)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__mono])])])). 4.05/4.30 fof(c_0_6879, plain, ![X477, X478, X479, X480, X481]:(~class_Rings_Olinordered__semiring__strict(X481)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X481),X480),X479))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X481),X478),X477))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X481),c_Groups_Ozero__class_Ozero(X481)),X480))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X481),c_Groups_Ozero__class_Ozero(X481)),X478))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X481),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X481),X480),X478)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X481),X479),X477)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__mono_H])])])). 4.05/4.30 cnf(c_0_6880, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3))),esk355_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk353_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5096])). 4.05/4.30 cnf(c_0_6881, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk352_3(X2,X3,X1))),esk353_3(X2,X3,X1))=X3|hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,esk355_3(X2,X3,X1)))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_5096])). 4.05/4.30 fof(c_0_6882, plain, ![X9895, X9896, X9897]:((hAPP(X9896,esk304_3(X9895,X9896,X9897))!=hAPP(X9896,esk305_3(X9895,X9896,X9897))|c_Wellfounded_OwfP(X9897,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9895,tc_fun(X9897,tc_fun(X9897,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X9895,tc_HOL_Obool))),X9896))|~c_Wellfounded_OwfP(X9897,hAPP(X9896,esk303_3(X9895,X9896,X9897))))&(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9897,tc_HOL_Obool)),c_Predicate_ODomainP(X9897,X9897,hAPP(X9896,esk304_3(X9895,X9896,X9897)))),c_Predicate_ORangeP(X9897,X9897,hAPP(X9896,esk305_3(X9895,X9896,X9897))))!=c_Orderings_Obot__class_Obot(tc_fun(X9897,tc_HOL_Obool))|c_Wellfounded_OwfP(X9897,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9895,tc_fun(X9897,tc_fun(X9897,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X9895,tc_HOL_Obool))),X9896))|~c_Wellfounded_OwfP(X9897,hAPP(X9896,esk303_3(X9895,X9896,X9897))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wfP__SUP])])])])])). 4.05/4.30 fof(c_0_6883, plain, ![X8157, X8158, X8159, X8160, X8161]:(~class_Rings_Ocomm__semiring__1(X8161)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8161),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8161),X8160),X8158)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8161),X8159),X8157))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8161),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8161),X8160),X8159)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8161),X8158),X8157))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])])])). 4.05/4.30 fof(c_0_6884, plain, ![X17566, X17567, X17568, X17569, X17570]:(~class_Rings_Olinordered__semiring__strict(X17570)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17570),X17569),X17568))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17570),X17567),X17566))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17570),c_Groups_Ozero__class_Ozero(X17570)),X17569))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17570),c_Groups_Ozero__class_Ozero(X17570)),X17567))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17570),X17569),X17567)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17570),X17568),X17566)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__less__imp__less])])])). 4.05/4.30 fof(c_0_6885, plain, ![X12810, X12811, X12812, X12813, X12814]:(~class_Rings_Olinordered__semiring__strict(X12814)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12814),X12813),X12812))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12814),X12811),X12810))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12814),c_Groups_Ozero__class_Ozero(X12814)),X12813))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12814),c_Groups_Ozero__class_Ozero(X12814)),X12811))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12814),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12814),X12813),X12811)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12814),X12812),X12810)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__le__imp__less])])])). 4.05/4.30 fof(c_0_6886, plain, ![X16307, X16308, X16309, X16310, X16311]:(~class_Fields_Olinordered__field(X16311)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16311),c_Groups_Ozero__class_Ozero(X16311)),X16310))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16311),X16310),X16309))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16311),c_Groups_Ozero__class_Ozero(X16311)),X16308))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16311),X16308),X16307))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16311),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16311),X16310),X16307)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16311),X16309),X16308)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_frac__le])])])). 4.05/4.30 fof(c_0_6887, plain, ![X16424, X16425, X16426, X16427, X16428]:(~class_Rings_Oordered__semiring(X16428)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16428),X16427),X16426))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16428),X16425),X16424))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16428),c_Groups_Ozero__class_Ozero(X16428)),X16427))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16428),c_Groups_Ozero__class_Ozero(X16428)),X16425))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16428),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16428),X16427),X16425)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16428),X16426),X16424)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__mono_H])])])). 4.05/4.30 fof(c_0_6888, plain, ![X5019, X5020, X5021, X5022, X5023]:(~c_Finite__Set_Ofolding__one__idem(X5023,X5022,X5021)|(hAPP(X5020,hAPP(hAPP(X5022,esk153_5(X5019,X5020,X5021,X5022,X5023)),esk154_5(X5019,X5020,X5021,X5022,X5023)))!=hAPP(hAPP(X5022,hAPP(X5020,esk153_5(X5019,X5020,X5021,X5022,X5023))),hAPP(X5020,esk154_5(X5019,X5020,X5021,X5022,X5023)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5023),X5019))|(c_Orderings_Obot__class_Obot(tc_fun(X5023,tc_HOL_Obool))=X5019|hAPP(X5020,hAPP(X5021,X5019))=hAPP(X5021,hAPP(c_Set_Oimage(X5023,X5023,X5020),X5019)))))), 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])])])])). 4.05/4.30 cnf(c_0_6889, plain, (hBOOL(hAPP(X3,esk72_2(X3,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(X3,X1))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk71_2(X3,X2)),X2))))|~hBOOL(hAPP(X3,esk70_2(X3,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5097])). 4.05/4.30 fof(c_0_6890, plain, ![X11943, X11944, X11945, X11946]:((hAPP(hAPP(c_Product__Type_OPair(X11946,X11945),esk368_4(X11943,X11944,X11945,X11946)),esk367_4(X11943,X11944,X11945,X11946))=X11944|~hBOOL(hAPP(hAPP(c_member(tc_prod(X11946,X11945)),X11944),hAPP(c_Relation_Oconverse(X11945,X11946),X11943))))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X11945,X11946)),hAPP(hAPP(c_Product__Type_OPair(X11945,X11946),esk367_4(X11943,X11944,X11945,X11946)),esk368_4(X11943,X11944,X11945,X11946))),X11943))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X11946,X11945)),X11944),hAPP(c_Relation_Oconverse(X11945,X11946),X11943))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_converseE])])])])])). 4.05/4.30 cnf(c_0_6891, 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_5214])). 4.05/4.30 fof(c_0_6892, plain, ![X14707, X14708, X14709, X14710, X14711]:(~class_Rings_Oordered__semiring(X14711)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14711),X14710),X14709))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14711),X14708),X14707))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14711),c_Groups_Ozero__class_Ozero(X14711)),X14709))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14711),c_Groups_Ozero__class_Ozero(X14711)),X14708))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14711),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14711),X14710),X14708)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14711),X14709),X14707)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__mono])])])). 4.05/4.30 cnf(c_0_6893, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))|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_5215, c_0_4475])). 4.05/4.30 cnf(c_0_6894, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5216, c_0_4475])). 4.05/4.30 fof(c_0_6895, plain, ![X3975, X3976, X3977, X3978]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X3978),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X3977),X3976)))|hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X3977),X3976)=hAPP(c_Random_Opick(X3977,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X3977)),X3976),X3975)),X3978))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X3978),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X3977),X3976)))|hAPP(c_Random_Opick(X3977,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X3977)),X3976),X3975)),X3978)=hAPP(c_Random_Opick(X3977,X3975),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X3978),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X3977),X3976))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pick_Osimps])])])). 4.05/4.30 fof(c_0_6896, plain, ![X1392, X1393, X1394, X1395]:((hBOOL(hAPP(hAPP(c_member(X1394),esk40_4(X1392,X1393,X1394,X1395)),X1393))|c_Groups_Oone__class_Oone(X1395)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1395,X1394,c_Groups_Otimes__class_Otimes(X1395)),X1392),c_Groups_Oone__class_Oone(X1395)),X1393)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1394),X1393))|~class_Groups_Ocomm__monoid__mult(X1395))&(hAPP(X1392,esk40_4(X1392,X1393,X1394,X1395))!=c_Groups_Oone__class_Oone(X1395)|c_Groups_Oone__class_Oone(X1395)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1395,X1394,c_Groups_Otimes__class_Otimes(X1395)),X1392),c_Groups_Oone__class_Oone(X1395)),X1393)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1394),X1393))|~class_Groups_Ocomm__monoid__mult(X1395))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__image__1])])])])])). 4.05/4.30 fof(c_0_6897, plain, ![X14287, X14288, X14289, X14290, X14291, X14292]:(~class_Groups_Ocomm__monoid__add(X14292)|(~c_Fun_Oinj__on(X14291,X14290,X14289,X14288)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14291,X14292),hAPP(c_Fun_Ocomp(X14290,X14292,X14291,X14287),X14289)),X14288)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14290,X14292),X14287),hAPP(c_Set_Oimage(X14291,X14290,X14289),X14288)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__reindex])])])). 4.05/4.30 cnf(c_0_6898, 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_5132])). 4.05/4.30 cnf(c_0_6899, 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|X3=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X1)!=X4), inference(split_conjunct,[status(thm)],[c_0_5194])). 4.05/4.30 fof(c_0_6900, plain, ![X4046, X4047, X4048, X4049]:(~hBOOL(hAPP(hAPP(c_member(X4049),X4048),X4047))|hAPP(hAPP(c_Set_Oinsert(X4049),X4048),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4049,tc_HOL_Obool)),X4047),X4046))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4049,tc_HOL_Obool)),X4047),hAPP(hAPP(c_Set_Oinsert(X4049),X4048),X4046))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__insert__right__if1])])])). 4.05/4.30 fof(c_0_6901, plain, ![X6533, X6534, X6535, X6536]:(~class_Groups_Oordered__ab__group__add__abs(X6536)|hAPP(c_Groups_Oabs__class_Oabs(X6536),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6535,X6536),hAPP(hAPP(c_COMBB(X6536,X6536,X6535),c_Groups_Oabs__class_Oabs(X6536)),X6534)),X6533))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X6535,X6536),hAPP(hAPP(c_COMBB(X6536,X6536,X6535),c_Groups_Oabs__class_Oabs(X6536)),X6534)),X6533)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__setsum__abs])])])). 4.05/4.30 cnf(c_0_6902, 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_5217])). 4.05/4.30 cnf(c_0_6903, plain, (hAPP(hAPP(c_Set_Oinsert(X1),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_Set_Oinsert(X1),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_5218]), ['final']). 4.05/4.30 cnf(c_0_6904, 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_5219]), ['final']). 4.05/4.30 cnf(c_0_6905, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X4),X7)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X2),X6),X8)|hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),esk286_8(X4,X6,X7,X8,X5,X1,X3,X2))!=hAPP(X6,esk286_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_5193])). 4.05/4.30 cnf(c_0_6906, 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)),X5),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X5),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_5220])). 4.05/4.30 cnf(c_0_6907, 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_5221])). 4.05/4.30 cnf(c_0_6908, plain, (X1=c_List_Olist_ONil(X2)|c_List_Obutlast(X2,X1)=c_List_OtakeWhile(X2,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2),c_fNot),hAPP(hAPP(c_COMBC(X2,X2,tc_HOL_Obool),c_fequal),c_List_Olast(X2,X1))),X1)|~hBOOL(hAPP(c_List_Odistinct(X2),X1))), inference(split_conjunct,[status(thm)],[c_0_5222])). 4.05/4.30 fof(c_0_6909, plain, ![X2466, X2467, X2468, X2469, X2470]:(~c_Finite__Set_Ofolding__one__idem(X2470,X2469,X2468)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2470),X2467))|(c_Orderings_Obot__class_Obot(tc_fun(X2470,tc_HOL_Obool))=X2467|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2470),X2466))|(c_Orderings_Obot__class_Obot(tc_fun(X2470,tc_HOL_Obool))=X2466|hAPP(hAPP(X2469,hAPP(X2468,X2467)),hAPP(X2468,X2466))=hAPP(X2468,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2470,tc_HOL_Obool)),X2467),X2466))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one__idem_Ounion__idem])])])). 4.05/4.30 fof(c_0_6910, plain, ![X12276, X12277, X12278, X12279, X12280]:(~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),X12280),X12279)),X12278)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X12280),X12277)),X12276)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12278))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12278),X12280))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X12276),X12280))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12279),X12277)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_unique__quotient__lemma])])])). 4.05/4.30 fof(c_0_6911, plain, ![X13695, X13696, X13697, X13698, X13699]:(~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),X13699),X13698)),X13697)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13699),X13696)),X13695)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13695),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13699),X13695))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13699),X13697))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13696),X13698)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_unique__quotient__lemma__neg])])])). 4.05/4.30 fof(c_0_6912, plain, ![X9368, X9369, X9370, X9371]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk287_4(X9368,X9369,X9370,X9371)),X9371))|hAPP(hAPP(c_List_Otake(X9370),X9371),X9369)=hAPP(hAPP(c_List_Otake(X9370),X9371),X9368)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9371),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9370)),X9368)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9371),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9370)),X9369))))&(hAPP(hAPP(c_List_Onth(X9370),X9369),esk287_4(X9368,X9369,X9370,X9371))!=hAPP(hAPP(c_List_Onth(X9370),X9368),esk287_4(X9368,X9369,X9370,X9371))|hAPP(hAPP(c_List_Otake(X9370),X9371),X9369)=hAPP(hAPP(c_List_Otake(X9370),X9371),X9368)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9371),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9370)),X9368)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X9371),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9370)),X9369))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__take__lemma])])])])). 4.05/4.30 cnf(c_0_6913, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X4,X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X2,X3)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X3))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5223])). 4.05/4.30 fof(c_0_6914, plain, ![X13534, X13535, X13536, X13537, X13538, X13539]:(~c_Fun_Oinj__on(X13539,X13538,X13537,X13536)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13538,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13539,X13538,X13537),X13536)),X13535))|(~c_Fun_Oinj__on(X13538,X13539,X13534,X13535)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13539,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13538,X13539,X13534),X13535)),X13536))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13539),X13536))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13538),X13535))|hAPP(c_Finite__Set_Ocard(X13539),X13536)=hAPP(c_Finite__Set_Ocard(X13538),X13535))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__bij__eq])])])). 4.05/4.30 fof(c_0_6915, plain, ![X5581, X5582, X5583, X5584]:(~class_Divides_Osemiring__div(X5584)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5584),X5583),X5581)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5584),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5584),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5584),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X5584),X5583),X5582)),X5582)),c_Divides_Odiv__class_Omod(X5584,X5583,X5582))),X5581)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mod__equality])])])). 4.05/4.30 fof(c_0_6916, plain, ![X10638, X10639, X10640, X10641]:(~class_Divides_Osemiring__div(X10641)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10641),X10639),X10638)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10641),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10641),X10640),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10641),X10639),X10640))),c_Divides_Odiv__class_Omod(X10641,X10639,X10640))),X10638)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mod__equality2])])])). 4.05/4.30 fof(c_0_6917, plain, ![X6783, X6784, X6785]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6785),X6784))|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(X6785),X6783)),hAPP(c_Finite__Set_Ocard(X6785),X6784))),hAPP(c_Finite__Set_Ocard(X6785),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6785,tc_HOL_Obool)),X6783),X6784))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__card__le__card__Diff])])). 4.05/4.30 cnf(c_0_6918, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5224, c_0_4475])). 4.05/4.30 cnf(c_0_6919, 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_5225, c_0_4519]), c_0_4519])). 4.05/4.30 cnf(c_0_6920, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)=hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))), inference(rw,[status(thm)],[c_0_5226, c_0_4519]), ['final']). 4.05/4.30 fof(c_0_6921, plain, ![X5036, X5037, X5038]:(~class_Orderings_Olinorder(X5038)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5038),X5037))|(X5036=c_Orderings_Obot__class_Obot(tc_fun(X5038,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5038,tc_HOL_Obool)),X5036),X5037))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X5038),c_Big__Operators_Olattice_OInf__fin(X5038,c_Orderings_Oord__class_Omin(X5038),X5036)),c_Big__Operators_Olattice_OInf__fin(X5038,c_Orderings_Oord__class_Omin(X5038),X5037))=c_Big__Operators_Olattice_OInf__fin(X5038,c_Orderings_Oord__class_Omin(X5038),X5037))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Osubset__idem])])])). 4.05/4.30 fof(c_0_6922, plain, ![X6190, X6191, X6192]:(~class_Orderings_Olinorder(X6192)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6192),X6191))|(X6190=c_Orderings_Obot__class_Obot(tc_fun(X6192,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6192,tc_HOL_Obool)),X6190),X6191))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X6192),c_Big__Operators_Olattice_OSup__fin(X6192,c_Orderings_Oord__class_Omax(X6192),X6190)),c_Big__Operators_Olattice_OSup__fin(X6192,c_Orderings_Oord__class_Omax(X6192),X6191))=c_Big__Operators_Olattice_OSup__fin(X6192,c_Orderings_Oord__class_Omax(X6192),X6191))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Osubset__idem])])])). 4.05/4.30 fof(c_0_6923, plain, ![X14977, X14978, X14979, X14980, X14981, X14982]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X14982,X14981),tc_HOL_Obool)),X14980),hAPP(hAPP(c_Product__Type_OSigma(X14982,X14981),X14979),hAPP(c_COMBK(tc_fun(X14981,tc_HOL_Obool),X14982),X14978))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14981,tc_HOL_Obool)),hAPP(c_Relation_OImage(X14982,X14981,X14980),X14977)),X14978))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__subset])])). 4.05/4.30 cnf(c_0_6924, 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|c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,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))|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_5227])). 4.05/4.30 fof(c_0_6925, plain, ![X3513, X3514, X3515, X3516]:(~hBOOL(hAPP(hAPP(c_member(X3516),X3515),c_Wellfounded_Oacc(X3516,X3514)))|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3516)),X3513),c_Wellfounded_Oacc(tc_List_Olist(X3516),c_List_Olistrel1(X3516,X3514))))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3516)),hAPP(hAPP(c_List_Olist_OCons(X3516),X3515),X3513)),c_Wellfounded_Oacc(tc_List_Olist(X3516),c_List_Olistrel1(X3516,X3514)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Cons__acc__listrel1I])])])). 4.05/4.30 fof(c_0_6926, plain, ![X6899, X6900, X6901]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6901),X6900))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6901),X6899))|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6901,tc_HOL_Obool)),X6900),X6899)!=c_Orderings_Obot__class_Obot(tc_fun(X6901,tc_HOL_Obool))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X6901),X6900)),hAPP(c_Finite__Set_Ocard(X6901),X6899))=hAPP(c_Finite__Set_Ocard(X6901),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6901,tc_HOL_Obool)),X6900),X6899))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Un__disjoint])])). 4.05/4.30 cnf(c_0_6927, plain, (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),X2)),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_5162])). 4.05/4.30 fof(c_0_6928, plain, ![X15969, X15970, X15971, X15972]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15972),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15971)),X15970)))|hAPP(hAPP(c_List_Onth(X15971),X15969),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15972),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15971)),X15970)))=hAPP(hAPP(c_List_Onth(X15971),hAPP(hAPP(c_List_Oappend(X15971),X15970),X15969)),X15972))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15972),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15971)),X15970)))|hAPP(hAPP(c_List_Onth(X15971),hAPP(hAPP(c_List_Oappend(X15971),X15970),X15969)),X15972)=hAPP(hAPP(c_List_Onth(X15971),X15970),X15972))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__append])])])). 4.05/4.30 cnf(c_0_6929, 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_5228])). 4.05/4.30 cnf(c_0_6930, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk474_5(X1,X2,X3,X4,X5)))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X1),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X2),X4)|~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_5229])). 4.05/4.30 cnf(c_0_6931, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk139_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)|X3!=X4|~class_Groups_Ocomm__monoid__mult(X5)|~class_Groups_Ocomm__monoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_5230])). 4.05/4.30 fof(c_0_6932, plain, ![X5978, X5979, X5980]:(~class_Groups_Ocomm__monoid__mult(X5980)|~class_Groups_Ocomm__monoid__add(X5980)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5980),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5980,tc_Int_Oint),X5979),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X5978))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X5980),X5979),X5978)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I2_J])])). 4.05/4.30 fof(c_0_6933, plain, ![X974, X975, X976, X977, X978, X979]:(~class_Divides_Oring__div(X979)|(c_Divides_Odiv__class_Omod(X979,X976,X977)!=c_Divides_Odiv__class_Omod(X979,X978,X977)|(c_Divides_Odiv__class_Omod(X979,X975,X977)!=c_Divides_Odiv__class_Omod(X979,X974,X977)|c_Divides_Odiv__class_Omod(X979,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X979),X978),X975),X977)=c_Divides_Odiv__class_Omod(X979,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X979),X976),X974),X977)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__diff__cong])])])). 4.05/4.30 fof(c_0_6934, plain, ![X1800, X1801, X1802, X1803]:(~class_Orderings_Olinorder(X1803)|(~c_List_Olinorder__class_Osorted(X1803,hAPP(c_List_Orev(X1803),X1802))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1801),X1800))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1800),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1803)),X1802)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1803),hAPP(hAPP(c_List_Onth(X1803),X1802),X1800)),hAPP(hAPP(c_List_Onth(X1803),X1802),X1801))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__rev__nth__mono])])])). 4.05/4.30 fof(c_0_6935, plain, ![X16027, X16028, X16029]:(~class_Groups_Ocomm__monoid__mult(X16029)|~class_Groups_Ocomm__monoid__add(X16029)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X16029),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X16029,tc_Int_Oint),X16028),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X16027))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X16029),X16028),X16027)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__nat__int__sum__prod_I1_J])])])). 4.05/4.30 fof(c_0_6936, plain, ![X16945, X16946, X16947, X16948, X16949, X16950, X16951, X16952]:(~c_Finite__Set_Ofolding__image__simple__idem(X16952,X16951,X16950,X16949,X16948,X16947)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16951),X16946))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16951),X16945))|hAPP(hAPP(X16950,hAPP(X16947,X16946)),hAPP(X16947,X16945))=hAPP(X16947,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16951,tc_HOL_Obool)),X16946),X16945))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple__idem_Ounion__idem])])])). 4.05/4.30 fof(c_0_6937, plain, ![X14006, X14007, X14008, X14009, X14010, X14011]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X14011,X14010),tc_HOL_Obool)),X14009),X14008))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14011,tc_HOL_Obool)),X14007),X14006))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14010,tc_HOL_Obool)),hAPP(c_Relation_OImage(X14011,X14010,X14009),X14007)),hAPP(c_Relation_OImage(X14011,X14010,X14008),X14006))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__mono])])). 4.05/4.30 fof(c_0_6938, plain, ![X10729, X10730, X10731, X10732]:(~class_Groups_Ocomm__monoid__add(X10732)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10732),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10732,tc_Nat_Onat),X10731),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X10730,X10729))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10732),X10731),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X10730),hAPP(c_Nat_OSuc,X10729)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__shift__bounds__cl__Suc__ivl])])])). 4.05/4.30 fof(c_0_6939, plain, ![X14818, X14819, X14820, X14821, X14822, X14823]:(~class_Divides_Osemiring__div(X14823)|(c_Divides_Odiv__class_Omod(X14823,X14820,X14821)!=c_Divides_Odiv__class_Omod(X14823,X14822,X14821)|(c_Divides_Odiv__class_Omod(X14823,X14818,X14821)!=c_Divides_Odiv__class_Omod(X14823,X14819,X14821)|c_Divides_Odiv__class_Omod(X14823,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14823),X14822),X14819),X14821)=c_Divides_Odiv__class_Omod(X14823,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14823),X14820),X14818),X14821)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__mult__cong])])])). 4.05/4.30 fof(c_0_6940, plain, ![X3537, X3538, X3539, X3540]:(~class_Fields_Olinordered__field(X3540)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3540),X3539),X3538))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3540),c_Groups_Ozero__class_Ozero(X3540)),X3537))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3540),c_Groups_Ozero__class_Ozero(X3540)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3540),X3538),X3539)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3540),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3540),X3537),X3538)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3540),X3537),X3539))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__strict__left__mono])])])). 4.05/4.30 fof(c_0_6941, plain, ![X4080, X4081, X4082, X4083]:(~class_Fields_Olinordered__field(X4083)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4083),X4082),X4081))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4083),c_Groups_Ozero__class_Ozero(X4083)),X4080))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4083),c_Groups_Ozero__class_Ozero(X4083)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4083),X4081),X4082)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4083),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4083),X4080),X4081)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4083),X4080),X4082))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__left__mono])])])). 4.05/4.30 fof(c_0_6942, plain, ![X5932, X5933, X5934, X5935]:(~class_Fields_Olinordered__field(X5935)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5935),X5934),X5933))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5935),X5932),c_Groups_Ozero__class_Ozero(X5935)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5935),c_Groups_Ozero__class_Ozero(X5935)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5935),X5934),X5933)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5935),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5935),X5932),X5934)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5935),X5932),X5933))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__strict__left__mono__neg])])])). 4.05/4.30 cnf(c_0_6943, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk73_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk71_2(X1,X2)),X2))))|~hBOOL(hAPP(X1,esk70_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5097])). 4.05/4.30 fof(c_0_6944, plain, ![X1197, X1198, X1199, X1200]:(~c_Equiv__Relations_Oequiv(X1200,X1199,X1198)|(~hBOOL(hAPP(hAPP(c_member(X1200),X1197),X1199))|hBOOL(hAPP(hAPP(c_member(X1200),X1197),hAPP(c_Relation_OImage(X1200,X1200,X1198),hAPP(hAPP(c_Set_Oinsert(X1200),X1197),c_Orderings_Obot__class_Obot(tc_fun(X1200,tc_HOL_Obool)))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equiv__class__self])])])). 4.05/4.30 fof(c_0_6945, plain, ![X2519, X2520, X2521, X2522, X2523, X2524]:(~class_Divides_Osemiring__div(X2524)|(c_Divides_Odiv__class_Omod(X2524,X2523,X2522)!=c_Divides_Odiv__class_Omod(X2524,X2521,X2522)|(c_Divides_Odiv__class_Omod(X2524,X2519,X2522)!=c_Divides_Odiv__class_Omod(X2524,X2520,X2522)|c_Divides_Odiv__class_Omod(X2524,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2524),X2521),X2519),X2522)=c_Divides_Odiv__class_Omod(X2524,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2524),X2523),X2520),X2522)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__add__cong])])])). 4.05/4.30 fof(c_0_6946, plain, ![X15717, X15718, X15719, X15720]:(~hBOOL(hAPP(hAPP(c_member(X15720),X15719),hAPP(c_List_Oset(X15720),X15718)))|(hBOOL(hAPP(X15717,X15719))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15720)),hAPP(c_List_Ofilter(X15720,X15717),X15718))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15720)),X15718))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_length__filter__less])])])). 4.05/4.30 fof(c_0_6947, plain, ![X9172, X9173, X9174, X9175, X9176]:(~hBOOL(hAPP(hAPP(c_member(X9176),X9175),X9174))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9173,tc_HOL_Obool)),hAPP(X9172,X9175)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9176,tc_fun(X9173,tc_HOL_Obool)),X9174),X9172))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9176,tc_fun(X9173,tc_HOL_Obool)),X9174),X9172)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__absorb])])). 4.05/4.30 fof(c_0_6948, plain, ![X5892, X5893, X5894, X5895, X5896]:(~hBOOL(hAPP(hAPP(c_member(X5896),X5895),X5894))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5896,tc_fun(X5893,tc_HOL_Obool)),X5894),X5892)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5893,tc_HOL_Obool)),hAPP(X5892,X5895)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5896,tc_fun(X5893,tc_HOL_Obool)),X5894),X5892))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__absorb])])). 4.05/4.30 fof(c_0_6949, plain, ![X10519, X10520, X10521, X10522, X10523, X10524]:(~c_Finite__Set_Ofolding(X10524,X10523,X10522,X10521)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10524),X10520))|hAPP(c_Fun_Ocomp(X10523,X10523,X10523,hAPP(X10521,X10520)),hAPP(X10522,X10519))=hAPP(c_Fun_Ocomp(X10523,X10523,X10523,hAPP(X10522,X10519)),hAPP(X10521,X10520)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H])])). 4.05/4.30 fof(c_0_6950, plain, ![X15248, X15249, X15250, X15251, X15253]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15249,tc_HOL_Obool)),hAPP(c_Set_Oimage(X15251,X15249,esk459_4(X15248,X15249,X15250,X15251)),X15250)),X15248))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X15251),X15250)),hAPP(c_Finite__Set_Ocard(X15249),X15248)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15249),X15248))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15251),X15250)))&(c_Fun_Oinj__on(X15251,X15249,esk459_4(X15248,X15249,X15250,X15251),X15250)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X15251),X15250)),hAPP(c_Finite__Set_Ocard(X15249),X15248)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15249),X15248))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15251),X15250))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15249,tc_HOL_Obool)),hAPP(c_Set_Oimage(X15251,X15249,X15253),X15250)),X15248))|~c_Fun_Oinj__on(X15251,X15249,X15253,X15250)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X15251),X15250)),hAPP(c_Finite__Set_Ocard(X15249),X15248)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15249),X15248))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15251),X15250)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__iff__card__le])])])])])])). 4.05/4.30 cnf(c_0_6951, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk199_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_5231])). 4.05/4.30 cnf(c_0_6952, 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_5232, c_0_4519]), c_0_4519])). 4.05/4.30 cnf(c_0_6953, plain, (hAPP(c_Product__Type_Oapsnd(X3,X6,X2,X5),X4)=hAPP(c_Product__Type_Oapsnd(X3,X6,X2,X1),X4)|hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4))!=hAPP(X5,hAPP(c_Product__Type_Osnd(X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5233])). 4.05/4.30 cnf(c_0_6954, 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_5234])). 4.05/4.30 cnf(c_0_6955, 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_5235])). 4.05/4.30 cnf(c_0_6956, 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_5074])). 4.05/4.30 cnf(c_0_6957, 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_5207])). 4.05/4.30 fof(c_0_6958, plain, ![X7212, X7213, X7214, X7215, X7216]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7216),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7215)),X7214)))|hAPP(hAPP(c_List_Oappend(X7215),hAPP(hAPP(c_List_Olist__update(X7215,X7214),X7216),X7212)),X7213)=hAPP(hAPP(c_List_Olist__update(X7215,hAPP(hAPP(c_List_Oappend(X7215),X7214),X7213)),X7216),X7212)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__append1])])). 4.05/4.30 fof(c_0_6959, plain, ![X16634, X16635, X16636, X16638]:((hBOOL(hAPP(X16635,esk496_3(X16634,X16635,X16636)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16634))|(~hBOOL(hAPP(X16635,X16638))|hBOOL(hAPP(X16635,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X16638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16634),X16636))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16636)))&(~hBOOL(hAPP(X16635,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk496_3(X16634,X16635,X16636)),X16636)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16634))|(~hBOOL(hAPP(X16635,X16638))|hBOOL(hAPP(X16635,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X16638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X16634),X16636))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16636)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_decr__mult__lemma])])])])])])). 4.05/4.30 fof(c_0_6960, plain, ![X1124, X1125, X1126, X1127]:((hBOOL(hAPP(hAPP(c_member(X1127),esk28_4(X1124,X1125,X1126,X1127)),hAPP(c_List_Oset(X1127),X1126)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X1127,X1125,X1126)),c_List_Olist_Olist__size(X1127,X1124,X1126))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1125,esk28_4(X1124,X1125,X1126,X1127))),hAPP(X1124,esk28_4(X1124,X1125,X1126,X1127))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X1127,X1125,X1126)),c_List_Olist_Olist__size(X1127,X1124,X1126))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__size__pointwise])])])])])). 4.05/4.30 cnf(c_0_6961, 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_5236])). 4.05/4.30 cnf(c_0_6962, 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_5237]), ['final']). 4.05/4.30 cnf(c_0_6963, 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_5238]), ['final']). 4.05/4.30 cnf(c_0_6964, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk117_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_5239])). 4.05/4.30 fof(c_0_6965, plain, ![X6449, X6450, X6451, X6452]:(~class_Fields_Ofield(X6452)|(c_Groups_Ozero__class_Ozero(X6452)=X6451|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6450),X6449))|hAPP(hAPP(c_Power_Opower__class_Opower(X6452),X6451),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6449),X6450))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6452),hAPP(hAPP(c_Power_Opower__class_Opower(X6452),X6451),X6449)),hAPP(hAPP(c_Power_Opower__class_Opower(X6452),X6451),X6450))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__diff])])])). 4.05/4.30 cnf(c_0_6966, 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),esk473_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_5240])). 4.05/4.30 fof(c_0_6967, plain, ![X16856, X16857, X16858]:(~class_Groups_Oordered__ab__group__add__abs(X16858)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16858),hAPP(c_Groups_Oabs__class_Oabs(X16858),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16858),hAPP(c_Groups_Oabs__class_Oabs(X16858),X16857)),hAPP(c_Groups_Oabs__class_Oabs(X16858),X16856)))),hAPP(c_Groups_Oabs__class_Oabs(X16858),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16858),X16857),X16856))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__triangle__ineq3])])])). 4.05/4.30 cnf(c_0_6968, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk116_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_5241])). 4.05/4.30 cnf(c_0_6969, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk248_3(X1,X2,X3)),esk247_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_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_5212])). 4.05/4.30 cnf(c_0_6970, 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__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(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))|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_5227])). 4.05/4.30 cnf(c_0_6971, 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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[c_0_5242, c_0_4475])). 4.05/4.30 cnf(c_0_6972, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5243, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6973, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5244, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_6974, plain, ![X10272, X10273, X10274, X10275]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10274),X10275),X10272))|~hBOOL(hAPP(hAPP(c_member(X10274),X10275),X10273))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10274),hAPP(c_Finite__Set_Ofold1(X10274,c_Orderings_Oord__class_Omin(X10274)),X10273)),X10272))|c_Orderings_Obot__class_Obot(tc_fun(X10274,tc_HOL_Obool))=X10273|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10274),X10273))|~class_Orderings_Olinorder(X10274))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10274),esk312_3(X10272,X10273,X10274)),X10272))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10274),hAPP(c_Finite__Set_Ofold1(X10274,c_Orderings_Oord__class_Omin(X10274)),X10273)),X10272))|c_Orderings_Obot__class_Obot(tc_fun(X10274,tc_HOL_Obool))=X10273|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10274),X10273))|~class_Orderings_Olinorder(X10274))&(hBOOL(hAPP(hAPP(c_member(X10274),esk312_3(X10272,X10273,X10274)),X10273))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10274),hAPP(c_Finite__Set_Ofold1(X10274,c_Orderings_Oord__class_Omin(X10274)),X10273)),X10272))|c_Orderings_Obot__class_Obot(tc_fun(X10274,tc_HOL_Obool))=X10273|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10274),X10273))|~class_Orderings_Olinorder(X10274)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__strict__below__iff])])])])])])). 4.05/4.30 fof(c_0_6975, plain, ![X14560, X14561, X14562, X14564]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14562),esk443_3(X14560,X14561,X14562)),X14560))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14562),hAPP(c_Finite__Set_Ofold1(X14562,c_Orderings_Oord__class_Omin(X14562)),X14561)),X14560))|c_Orderings_Obot__class_Obot(tc_fun(X14562,tc_HOL_Obool))=X14561|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14562),X14561))|~class_Orderings_Olinorder(X14562))&(hBOOL(hAPP(hAPP(c_member(X14562),esk443_3(X14560,X14561,X14562)),X14561))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14562),hAPP(c_Finite__Set_Ofold1(X14562,c_Orderings_Oord__class_Omin(X14562)),X14561)),X14560))|c_Orderings_Obot__class_Obot(tc_fun(X14562,tc_HOL_Obool))=X14561|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14562),X14561))|~class_Orderings_Olinorder(X14562)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14562),X14564),X14560))|~hBOOL(hAPP(hAPP(c_member(X14562),X14564),X14561))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14562),hAPP(c_Finite__Set_Ofold1(X14562,c_Orderings_Oord__class_Omin(X14562)),X14561)),X14560))|c_Orderings_Obot__class_Obot(tc_fun(X14562,tc_HOL_Obool))=X14561|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14562),X14561))|~class_Orderings_Olinorder(X14562))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__below__iff])])])])])])). 4.05/4.30 cnf(c_0_6976, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk453_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|X4=X2|X2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5245])). 4.05/4.30 cnf(c_0_6977, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5246, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_6978, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))|~class_Int_Onumber__ring(X1)|~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5247, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.30 fof(c_0_6979, plain, ![X1250, X1251, X1252, X1253, X1254]:(~c_Finite__Set_Ofolding__one__idem(X1254,X1253,X1252)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1254),X1251))|(X1250=c_Orderings_Obot__class_Obot(tc_fun(X1254,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1254,tc_HOL_Obool)),X1250),X1251))|hAPP(X1252,X1251)=hAPP(hAPP(X1253,hAPP(X1252,X1250)),hAPP(X1252,X1251)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one__idem_Osubset__idem])])])). 4.05/4.30 cnf(c_0_6980, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),esk318_2(X2,X1))),hAPP(c_List_Oset(X1),esk319_2(X2,X1)))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(X1),esk317_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_5059])). 4.05/4.30 cnf(c_0_6981, 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_5248])). 4.05/4.30 cnf(c_0_6982, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|X3=hAPP(c_Set_Oimage(tc_prod(X1,X4),X4,c_Product__Type_Osnd(X1,X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_5249])). 4.05/4.30 cnf(c_0_6983, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk68_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|X4=X2|X2!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5250])). 4.05/4.30 fof(c_0_6984, plain, ![X12226, X12227, X12228, X12229]:(~class_Fields_Olinordered__field__inverse__zero(X12229)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12229),X12228),X12227))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12229),X12226),c_Groups_Ozero__class_Ozero(X12229)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12229),c_Groups_Ozero__class_Ozero(X12229)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12229),X12228),X12227)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12229),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12229),X12226),X12228)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12229),X12226),X12227))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__left__mono__neg])])])). 4.05/4.30 fof(c_0_6985, plain, ![X16205, X16206, X16207, X16208, X16209, X16210, X16211, X16212]:(~c_Finite__Set_Ofolding__image__simple(X16212,X16211,X16210,X16209,X16208,X16207)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16211),X16206))|(hBOOL(hAPP(hAPP(c_member(X16211),X16205),X16206))|hAPP(hAPP(X16210,hAPP(X16208,X16205)),hAPP(X16207,X16206))=hAPP(X16207,hAPP(hAPP(c_Set_Oinsert(X16211),X16205),X16206))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert])])])). 4.05/4.30 cnf(c_0_6986, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|X3=hAPP(c_Set_Oimage(tc_prod(X4,X2),X4,c_Product__Type_Ofst(X4,X2)),hAPP(hAPP(c_Product__Type_OSigma(X4,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X4),X1)))), inference(split_conjunct,[status(thm)],[c_0_5251])). 4.05/4.30 cnf(c_0_6987, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X3,tc_HOL_Obool)),X2))=hAPP(c_Finite__Set_Ocard(X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X3,tc_HOL_Obool),X2))|esk106_3(X1,X2,X3)!=esk105_3(X1,X2,X3)|hAPP(c_Finite__Set_Ocard(X3),esk104_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_5062])). 4.05/4.30 fof(c_0_6988, plain, ![X8349, X8350, X8351]:(~class_Rings_Olinordered__semidom(X8351)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8351),c_Groups_Ozero__class_Ozero(X8351)),X8350))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8351),X8350),c_Groups_Oone__class_Oone(X8351)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8351),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8351),X8350),hAPP(hAPP(c_Power_Opower__class_Opower(X8351),X8350),X8349))),hAPP(hAPP(c_Power_Opower__class_Opower(X8351),X8350),X8349)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__Suc__less])])])). 4.05/4.30 cnf(c_0_6989, 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_5252])). 4.05/4.30 cnf(c_0_6990, 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_5115])). 4.05/4.30 cnf(c_0_6991, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X5))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5253])). 4.05/4.30 cnf(c_0_6992, 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_5254]), ['final']). 4.05/4.30 cnf(c_0_6993, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|X3=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4),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))|~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), inference(split_conjunct,[status(thm)],[c_0_5194])). 4.05/4.30 fof(c_0_6994, plain, ![X15673, X15674]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15674),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15674),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15674),c_Groups_Oone__class_Oone(X15674)),X15673)),X15673)),c_Groups_Ozero__class_Ozero(X15674)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15674),X15673),c_Groups_Ozero__class_Ozero(X15674)))|~hBOOL(hAPP(hAPP(c_member(X15674),X15673),c_Int_Oring__1__class_OInts(X15674)))|~class_Rings_Olinordered__idom(X15674))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15674),X15673),c_Groups_Ozero__class_Ozero(X15674)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15674),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15674),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15674),c_Groups_Oone__class_Oone(X15674)),X15673)),X15673)),c_Groups_Ozero__class_Ozero(X15674)))|~hBOOL(hAPP(hAPP(c_member(X15674),X15673),c_Int_Oring__1__class_OInts(X15674)))|~class_Rings_Olinordered__idom(X15674))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__odd__less__0])])])])). 4.05/4.30 fof(c_0_6995, plain, ![X13507, X13508]:((~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)),X13508)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X13507)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X13508),X13507)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X13508),X13507))|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)),X13508)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X13507))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I4_J])])). 4.05/4.30 cnf(c_0_6996, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Set_Oimage(tc_prod(X1,X3),X1,c_Product__Type_Ofst(X1,X3)),hAPP(c_List_Oset(tc_prod(X1,X3)),X4))))|c_Option_Ooption_ONone(X3)=hAPP(hAPP(c_Map_Omap__of(X1,X3),X4),X2)), inference(split_conjunct,[status(thm)],[c_0_5255])). 4.05/4.30 cnf(c_0_6997, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5253])). 4.05/4.30 cnf(c_0_6998, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5256])). 4.05/4.30 cnf(c_0_6999, 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_5257])). 4.05/4.30 cnf(c_0_7000, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk212_4(X3,X1,X2,X4)),X4)),X3))|c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=X4|X4!=hAPP(c_Set_Oimage(X1,X2,X5),X3)), inference(split_conjunct,[status(thm)],[c_0_5258])). 4.05/4.30 fof(c_0_7001, plain, ![X1459, X1460, X1461, X1462, X1463]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X1461,X1463)),hAPP(hAPP(c_Product__Type_OPair(X1461,X1463),X1459),X1462)),X1460))|hBOOL(hAPP(hAPP(c_member(X1463),X1462),hAPP(c_Relation_OImage(X1461,X1463,X1460),hAPP(hAPP(c_Set_Oinsert(X1461),X1459),c_Orderings_Obot__class_Obot(tc_fun(X1461,tc_HOL_Obool)))))))&(~hBOOL(hAPP(hAPP(c_member(X1463),X1462),hAPP(c_Relation_OImage(X1461,X1463,X1460),hAPP(hAPP(c_Set_Oinsert(X1461),X1459),c_Orderings_Obot__class_Obot(tc_fun(X1461,tc_HOL_Obool))))))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1461,X1463)),hAPP(hAPP(c_Product__Type_OPair(X1461,X1463),X1459),X1462)),X1460)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__singleton__iff])])). 4.05/4.30 fof(c_0_7002, plain, ![X1839, X1840, X1841, X1842, X1843, X1844, X1845, X1846, X1847, X1848, X1849]:((~hBOOL(hAPP(hAPP(c_member(X1843),X1842),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1841,tc_fun(X1843,tc_HOL_Obool)),X1840),X1839)))|(~hBOOL(hAPP(hAPP(c_member(X1841),X1844),X1840))|hBOOL(hAPP(hAPP(c_member(X1843),X1842),hAPP(X1839,X1844)))))&((hBOOL(hAPP(hAPP(c_member(X1847),esk65_5(X1845,X1846,X1847,X1848,X1849)),X1846))|hBOOL(hAPP(hAPP(c_member(X1849),X1848),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1847,tc_fun(X1849,tc_HOL_Obool)),X1846),X1845))))&(~hBOOL(hAPP(hAPP(c_member(X1849),X1848),hAPP(X1845,esk65_5(X1845,X1846,X1847,X1848,X1849))))|hBOOL(hAPP(hAPP(c_member(X1849),X1848),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1847,tc_fun(X1849,tc_HOL_Obool)),X1846),X1845)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__iff])])])])])])). 4.05/4.30 fof(c_0_7003, plain, ![X10842, X10843, X10844, X10845, X10846]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X10846,X10845)),hAPP(hAPP(c_Product__Type_OPair(X10846,X10845),X10843),X10842)),hAPP(c_List_Oset(tc_prod(X10846,X10845)),X10844)))|hAPP(hAPP(c_Map_Omap__of(X10846,X10845),X10844),X10843)=hAPP(c_Option_Ooption_OSome(X10845),X10842)|~hBOOL(hAPP(c_List_Odistinct(X10846),hAPP(hAPP(c_List_Omap(tc_prod(X10846,X10845),X10846),c_Product__Type_Ofst(X10846,X10845)),X10844))))&(hAPP(hAPP(c_Map_Omap__of(X10846,X10845),X10844),X10843)!=hAPP(c_Option_Ooption_OSome(X10845),X10842)|hBOOL(hAPP(hAPP(c_member(tc_prod(X10846,X10845)),hAPP(hAPP(c_Product__Type_OPair(X10846,X10845),X10843),X10842)),hAPP(c_List_Oset(tc_prod(X10846,X10845)),X10844)))|~hBOOL(hAPP(c_List_Odistinct(X10846),hAPP(hAPP(c_List_Omap(tc_prod(X10846,X10845),X10846),c_Product__Type_Ofst(X10846,X10845)),X10844))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__eq__Some__iff])])])])). 4.05/4.30 fof(c_0_7004, plain, ![X9376, X9377, X9378, X9379, X9380]:(~class_Groups_Ocomm__monoid__mult(X9380)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9379),X9378))|(hBOOL(hAPP(hAPP(c_member(X9379),X9377),X9378))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9380),hAPP(X9376,X9377)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9379,X9380),X9376),X9378))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9379,X9380),X9376),hAPP(hAPP(c_Set_Oinsert(X9379),X9377),X9378))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__insert])])])). 4.05/4.30 fof(c_0_7005, plain, ![X795, X796, X797, X798]:(~class_Int_Onumber__ring(X798)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X798),hAPP(c_Int_Onumber__class_Onumber__of(X798),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X797),X796))),X795)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X798),hAPP(c_Int_Onumber__class_Onumber__of(X798),X797)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X798),hAPP(c_Int_Onumber__class_Onumber__of(X798),X796)),X795))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__left])])). 4.05/4.30 fof(c_0_7006, plain, ![X7449, X7450, X7451]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7451),X7450))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7449))|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),X7449)),X7451)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7449)),X7450))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult__zless__mono2__lemma])])])). 4.05/4.30 fof(c_0_7007, plain, ![X1795, X1796, X1797, X1798]:((hBOOL(hAPP(hAPP(c_member(X1798),esk62_4(X1795,X1796,X1797,X1798)),X1797))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1796),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1798,tc_fun(X1796,tc_HOL_Obool)),X1797),X1795)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1798),X1797)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1796),hAPP(X1795,esk62_4(X1795,X1796,X1797,X1798))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1796),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1798,tc_fun(X1796,tc_HOL_Obool)),X1797),X1795)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1798),X1797)))), 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])])])])])). 4.05/4.30 fof(c_0_7008, plain, ![X1203, X1204, X1205, X1206, X1208]:(((hBOOL(hAPP(hAPP(c_member(X1206),esk33_4(X1203,X1204,X1205,X1206)),X1205))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1204),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1206,tc_fun(X1204,tc_HOL_Obool)),X1205),X1203)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1206),X1205)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1204),hAPP(X1203,esk33_4(X1203,X1204,X1205,X1206))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1204),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1206,tc_fun(X1204,tc_HOL_Obool)),X1205),X1203)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1206),X1205))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1204),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1206,tc_fun(X1204,tc_HOL_Obool)),X1205),X1203)))|(~hBOOL(hAPP(hAPP(c_member(X1206),X1208),X1205))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1204),hAPP(X1203,X1208))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1206),X1205)))), 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__UN])])])])])])). 4.05/4.30 fof(c_0_7009, plain, ![X382, X383, X384, X385]:((hBOOL(hAPP(hAPP(c_member(X385),esk2_4(X382,X383,X384,X385)),X384))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X385,X383)),hAPP(hAPP(c_Product__Type_OSigma(X385,X383),X384),X382)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X385),X384)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X383),hAPP(X382,esk2_4(X382,X383,X384,X385))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X385,X383)),hAPP(hAPP(c_Product__Type_OSigma(X385,X383),X384),X382)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X385),X384)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__SigmaI])])])])])). 4.05/4.30 fof(c_0_7010, plain, ![X12851, X12852, X12853, X12854, X12855]:((~hBOOL(hAPP(hAPP(c_member(X12855),X12854),hAPP(c_List_Oset(X12855),X12853)))|hAPP(hAPP(c_Map_Omap__of(X12855,X12852),hAPP(hAPP(c_List_Ozip(X12855,X12852),X12853),hAPP(hAPP(c_List_Omap(X12855,X12852),X12851),X12853))),X12854)=hAPP(c_Option_Ooption_OSome(X12852),hAPP(X12851,X12854)))&(hBOOL(hAPP(hAPP(c_member(X12855),X12854),hAPP(c_List_Oset(X12855),X12853)))|hAPP(hAPP(c_Map_Omap__of(X12855,X12852),hAPP(hAPP(c_List_Ozip(X12855,X12852),X12853),hAPP(hAPP(c_List_Omap(X12855,X12852),X12851),X12853))),X12854)=c_Option_Ooption_ONone(X12852))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__zip__map])])])). 4.05/4.30 fof(c_0_7011, plain, ![X9640, X9641]:((~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),X9641)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X9640)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X9641),X9640))|~c_Nat__Transfer_Onat__set(X9640)|~c_Nat__Transfer_Onat__set(X9641))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X9641),X9640))|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),X9641)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X9640)))|~c_Nat__Transfer_Onat__set(X9640)|~c_Nat__Transfer_Onat__set(X9641))), 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])])])])). 4.05/4.30 fof(c_0_7012, plain, ![X16095, X16096, X16098, X16099, X16100, X16101]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X16096,X16096)),hAPP(hAPP(c_Product__Type_OPair(X16096,X16096),hAPP(esk480_2(X16095,X16096),hAPP(c_Nat_OSuc,X16098))),hAPP(esk480_2(X16095,X16096),X16098))),X16095))|c_Wellfounded_Owf(X16096,X16095))&(~c_Wellfounded_Owf(X16100,X16099)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16100,X16100)),hAPP(hAPP(c_Product__Type_OPair(X16100,X16100),hAPP(X16101,hAPP(c_Nat_OSuc,esk481_3(X16099,X16100,X16101)))),hAPP(X16101,esk481_3(X16099,X16100,X16101)))),X16099)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__iff__no__infinite__down__chain])])])])])). 4.05/4.30 fof(c_0_7013, plain, ![X1006, X1007, X1008, X1009]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1009,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1009,tc_HOL_Obool)),X1008),hAPP(hAPP(c_Set_Oinsert(X1009),X1007),c_Orderings_Obot__class_Obot(tc_fun(X1009,tc_HOL_Obool))))),X1006))|(~hBOOL(hAPP(hAPP(c_member(X1009),X1007),X1008))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1009,tc_HOL_Obool)),X1008),hAPP(hAPP(c_Set_Oinsert(X1009),X1007),X1006))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__single__insert])])])). 4.05/4.30 cnf(c_0_7014, 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_5259])). 4.05/4.30 cnf(c_0_7015, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),X4)=hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(X1)),X4)),c_Orderings_Otop__class_Otop(X1)),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5260])). 4.05/4.30 fof(c_0_7016, plain, ![X7322, X7323, X7324, X7325, X7326]:(~class_Groups_Ocomm__monoid__add(X7326)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7325),X7324))|(hBOOL(hAPP(hAPP(c_member(X7325),X7323),X7324))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7325,X7326),X7322),hAPP(hAPP(c_Set_Oinsert(X7325),X7323),X7324))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7326),hAPP(X7322,X7323)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7325,X7326),X7322),X7324))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__insert])])])). 4.05/4.30 cnf(c_0_7017, 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_5261])). 4.05/4.30 cnf(c_0_7018, 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_5262]), ['final']). 4.05/4.30 fof(c_0_7019, plain, ![X4095, X4096]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4096))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4095))|hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4096),X4095)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4096,X4095))=c_Divides_OposDivAlg(X4096,X4095))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg__div__mod])])). 4.05/4.30 fof(c_0_7020, plain, ![X11392, X11393]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11393),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)),X11392))|c_Divides_OnegDivAlg(X11393,X11392)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11393),X11392)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11393,X11392)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_negDivAlg__div__mod])])])). 4.05/4.30 cnf(c_0_7021, 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_5263])). 4.05/4.30 cnf(c_0_7022, plain, (c_Wellfounded_Omeasure(X1)=hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than)), inference(split_conjunct,[status(thm)],[c_0_5264])). 4.05/4.30 fof(c_0_7023, plain, ![X15363, X15364, X15365]:(~class_Lattices_Olattice(X15365)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15365),X15364))|(c_Orderings_Obot__class_Obot(tc_fun(X15365,tc_HOL_Obool))=X15364|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15365),X15363))|(c_Orderings_Obot__class_Obot(tc_fun(X15365,tc_HOL_Obool))=X15363|c_Big__Operators_Olattice__class_OInf__fin(X15365,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15365,tc_HOL_Obool)),X15364),X15363))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15365),c_Big__Operators_Olattice__class_OInf__fin(X15365,X15364)),c_Big__Operators_Olattice__class_OInf__fin(X15365,X15363))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Ounion__idem])])])). 4.05/4.30 fof(c_0_7024, plain, ![X4623, X4624, X4625, X4626, X4627, X4628]:(((hBOOL(hAPP(hAPP(c_member(X4628),X4626),X4624))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4628,X4627)),hAPP(hAPP(c_Product__Type_OPair(X4628,X4627),X4626),X4625)),hAPP(hAPP(c_Product__Type_OSigma(X4628,X4627),X4624),X4623))))&(hBOOL(hAPP(hAPP(c_member(X4627),X4625),hAPP(X4623,X4626)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4628,X4627)),hAPP(hAPP(c_Product__Type_OPair(X4628,X4627),X4626),X4625)),hAPP(hAPP(c_Product__Type_OSigma(X4628,X4627),X4624),X4623)))))&(~hBOOL(hAPP(hAPP(c_member(X4628),X4626),X4624))|~hBOOL(hAPP(hAPP(c_member(X4627),X4625),hAPP(X4623,X4626)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4628,X4627)),hAPP(hAPP(c_Product__Type_OPair(X4628,X4627),X4626),X4625)),hAPP(hAPP(c_Product__Type_OSigma(X4628,X4627),X4624),X4623))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__Sigma__iff])])])). 4.05/4.30 cnf(c_0_7025, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk180_3(X2,X3,X1))),esk181_3(X2,X3,X1))=X3|hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5265])). 4.05/4.30 fof(c_0_7026, plain, ![X14012, X14013, X14014]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X14014,tc_HOL_Obool)),esk429_3(X14012,X14013,X14014)),X14013))|(X14013=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X14014,tc_HOL_Obool),tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14014,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X14014,tc_HOL_Obool),X14013)),X14012))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14014,tc_HOL_Obool)),esk429_3(X14012,X14013,X14014)),X14012))|(X14013=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X14014,tc_HOL_Obool),tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14014,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X14014,tc_HOL_Obool),X14013)),X14012))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inter__subset])])])])])). 4.05/4.30 cnf(c_0_7027, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3))),c_Groups_Ozero__class_Ozero(X2)))|X1!=c_Groups_Ozero__class_Ozero(X2)|c_Groups_Ozero__class_Ozero(X2)!=X3|~class_Rings_Olinordered__ring__strict(X2)), inference(split_conjunct,[status(thm)],[c_0_5266])). 4.05/4.30 fof(c_0_7028, plain, ![X13303, X13304, X13305]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13305),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13304)),X13303)))|hAPP(hAPP(c_List_Onth(X13304),X13303),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13304)),X13303)),hAPP(c_Nat_OSuc,X13305)))=hAPP(hAPP(c_List_Onth(X13304),hAPP(c_List_Orev(X13304),X13303)),X13305)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rev__nth])])])). 4.05/4.30 fof(c_0_7029, plain, ![X6053, X6054, X6055, X6056, X6057]:(~class_Fields_Ofield__inverse__zero(X6057)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6057),X6056),X6054)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6057),X6055),X6053))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6057),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6057),X6056),X6055)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6057),X6054),X6053))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_times__divide__times__eq])])])). 4.05/4.30 fof(c_0_7030, plain, ![X14260, X14261]:(~class_Orderings_Oorder(X14261)|hAPP(hAPP(c_Set_Oinsert(X14261),X14260),c_Orderings_Obot__class_Obot(tc_fun(X14261,tc_HOL_Obool)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14261,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X14261),X14260),c_Orderings_Obot__class_Obot(tc_fun(X14261,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X14261),X14260))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_single__Diff__lessThan])])])). 4.05/4.30 fof(c_0_7031, plain, ![X10697, X10698, X10699, X10700, X10701, X10702, X10703]:((hAPP(hAPP(X10701,X10699),esk325_7(X10697,X10698,X10699,X10700,X10701,X10702,X10703))=X10697|hBOOL(hAPP(hAPP(c_member(X10703),X10699),X10698))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10703,X10702,X10701,X10700,hAPP(hAPP(c_Set_Oinsert(X10703),X10699),X10698)),X10697))|~c_Finite__Set_Ofun__left__comm(X10703,X10702,X10701))&(hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10703,X10702,X10701,X10700,X10698),esk325_7(X10697,X10698,X10699,X10700,X10701,X10702,X10703)))|hBOOL(hAPP(hAPP(c_member(X10703),X10699),X10698))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10703,X10702,X10701,X10700,hAPP(hAPP(c_Set_Oinsert(X10703),X10699),X10698)),X10697))|~c_Finite__Set_Ofun__left__comm(X10703,X10702,X10701))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE])])])])])). 4.05/4.30 cnf(c_0_7032, 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,esk245_8(X2,X1,X3,X4,X5,X6,X7,X8))!=hAPP(X2,hAPP(X5,esk245_8(X2,X1,X3,X4,X5,X6,X7,X8)))|hAPP(c_Set_Oimage(X7,X6,X5),X4)!=X3|~c_Fun_Oinj__on(X7,X6,X5,X4)|~class_Groups_Ocomm__monoid__add(X8)), inference(split_conjunct,[status(thm)],[c_0_5191])). 4.05/4.30 cnf(c_0_7033, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),X2))|~class_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))), inference(rw,[status(thm)],[c_0_5267, c_0_4475])). 4.05/4.30 cnf(c_0_7034, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),X2))|~class_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))), inference(rw,[status(thm)],[c_0_5268, c_0_4475])). 4.05/4.30 cnf(c_0_7035, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))|~class_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))), inference(rw,[status(thm)],[c_0_5269, c_0_4475])). 4.05/4.30 fof(c_0_7036, plain, ![X15310, X15311, X15312, X15313, X15314, X15315, X15316, X15317]:(~c_List_Olist__all2(X15317,X15316,X15315,X15314,X15313)|(~hBOOL(hAPP(hAPP(X15315,X15312),X15311))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15310),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15316)),X15313)))|c_List_Olist__all2(X15317,X15316,X15315,hAPP(hAPP(c_List_Olist__update(X15317,X15314),X15310),X15312),hAPP(hAPP(c_List_Olist__update(X15316,X15313),X15310),X15311))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2__update__cong2])])])). 4.05/4.30 fof(c_0_7037, plain, ![X5442, X5443, X5444, X5445, X5446, X5447, X5448, X5449]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5449),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5448)),X5447)))|(~c_List_Olist__all2(X5448,X5446,X5445,X5447,X5444)|(~hBOOL(hAPP(hAPP(X5445,X5443),X5442))|c_List_Olist__all2(X5448,X5446,X5445,hAPP(hAPP(c_List_Olist__update(X5448,X5447),X5449),X5443),hAPP(hAPP(c_List_Olist__update(X5446,X5444),X5449),X5442))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__update__cong])])). 4.05/4.30 cnf(c_0_7038, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),c_List_OtakeWhile(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5))|c_List_OdropWhile(X2,X3,X1)!=hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_5169])). 4.05/4.30 fof(c_0_7039, plain, ![X4697, X4698, X4699, X4700]:(~class_Orderings_Olinorder(X4700)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4700),X4699),X4698))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4700),X4698),X4697))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4700,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4700,X4699),X4698)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4700,X4698),X4697))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4700,X4699),X4697)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I17_J])])])). 4.05/4.30 cnf(c_0_7040, 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_5207])). 4.05/4.30 cnf(c_0_7041, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))|~class_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))), inference(rw,[status(thm)],[c_0_5270, c_0_4475])). 4.05/4.30 fof(c_0_7042, plain, ![X2321, X2322]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2322))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2321),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2322),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2321))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2322),X2321))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__pos__neg])])])). 4.05/4.30 fof(c_0_7043, plain, ![X13060, X13061, X13062]:(~class_Orderings_Olinorder(X13062)|(hAPP(X13061,hAPP(hAPP(c_Orderings_Oord__class_Omax(X13062),esk398_3(X13060,X13061,X13062)),esk399_3(X13060,X13061,X13062)))!=hAPP(hAPP(c_Orderings_Oord__class_Omax(X13062),hAPP(X13061,esk398_3(X13060,X13061,X13062))),hAPP(X13061,esk399_3(X13060,X13061,X13062)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13062),X13060))|(c_Orderings_Obot__class_Obot(tc_fun(X13062,tc_HOL_Obool))=X13060|c_Big__Operators_Olinorder__class_OMax(X13062,hAPP(c_Set_Oimage(X13062,X13062,X13061),X13060))=hAPP(X13061,c_Big__Operators_Olinorder__class_OMax(X13062,X13060)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Ohom__commute])])])])). 4.05/4.30 fof(c_0_7044, plain, ![X15376, X15377, X15378]:(~class_Lattices_Olattice(X15378)|(hAPP(X15377,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15378),esk464_3(X15376,X15377,X15378)),esk465_3(X15376,X15377,X15378)))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15378),hAPP(X15377,esk464_3(X15376,X15377,X15378))),hAPP(X15377,esk465_3(X15376,X15377,X15378)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15378),X15376))|(c_Orderings_Obot__class_Obot(tc_fun(X15378,tc_HOL_Obool))=X15376|c_Big__Operators_Olattice__class_OInf__fin(X15378,hAPP(c_Set_Oimage(X15378,X15378,X15377),X15376))=hAPP(X15377,c_Big__Operators_Olattice__class_OInf__fin(X15378,X15376)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ohom__commute])])])). 4.05/4.30 fof(c_0_7045, plain, ![X4569, X4570, X4571]:(~class_Orderings_Olinorder(X4571)|(hAPP(hAPP(c_Orderings_Oord__class_Omin(X4571),hAPP(X4570,esk141_3(X4569,X4570,X4571))),hAPP(X4570,esk142_3(X4569,X4570,X4571)))!=hAPP(X4570,hAPP(hAPP(c_Orderings_Oord__class_Omin(X4571),esk141_3(X4569,X4570,X4571)),esk142_3(X4569,X4570,X4571)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4571),X4569))|(c_Orderings_Obot__class_Obot(tc_fun(X4571,tc_HOL_Obool))=X4569|hAPP(X4570,c_Big__Operators_Olinorder__class_OMin(X4571,X4569))=c_Big__Operators_Olinorder__class_OMin(X4571,hAPP(c_Set_Oimage(X4571,X4571,X4570),X4569)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Ohom__commute])])])])). 4.05/4.30 fof(c_0_7046, plain, ![X6820, X6821, X6822, X6823, X6824, X6825]:(X6824=X6825|hAPP(hAPP(c_List_Olist__update(X6823,hAPP(hAPP(c_List_Olist__update(X6823,X6822),X6825),X6821)),X6824),X6820)=hAPP(hAPP(c_List_Olist__update(X6823,hAPP(hAPP(c_List_Olist__update(X6823,X6822),X6824),X6820)),X6825),X6821)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__update__swap])])])). 4.05/4.30 cnf(c_0_7047, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X1),X7),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X8),X5)|~class_Groups_Ocomm__monoid__mult(X1)|~c_Fun_Oinj__on(X2,X3,X4,X5)|X6!=hAPP(c_Set_Oimage(X2,X3,X4),X5)|hAPP(c_Fun_Ocomp(X3,X1,X2,X7),X4)!=X8), inference(split_conjunct,[status(thm)],[c_0_5271])). 4.05/4.30 fof(c_0_7048, plain, ![X10184, X10185]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10185),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10184),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X10185),X10184)=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),X10185),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X10184)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__neg__neg])])])). 4.05/4.30 fof(c_0_7049, plain, ![X4833, X4834, X4835, X4836]:(~class_Fields_Ofield(X4836)|(c_Groups_Ozero__class_Ozero(X4836)=X4835|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4836),X4834),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4836),X4833),X4835))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4836),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4836),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4836),X4835),X4834)),X4833)),X4835))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff])])). 4.05/4.30 fof(c_0_7050, plain, ![X2884, X2885, X2886, X2887]:(~class_Fields_Ofield(X2887)|(X2886=c_Groups_Ozero__class_Ozero(X2887)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2887),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2887),X2886),X2885)),X2884)),X2886)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2887),X2885),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2887),X2884),X2886)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__eq__iff])])). 4.05/4.30 fof(c_0_7051, plain, ![X7709, X7710, X7711, X7712]:(~class_Fields_Ofield(X7712)|(c_Groups_Ozero__class_Ozero(X7712)=X7711|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7712),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7712),X7710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7712),X7711),X7709))),X7711)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7712),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7712),X7710),X7711)),X7709))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__diff__eq__iff])])])). 4.05/4.30 fof(c_0_7052, plain, ![X7900, X7901, X7902]:(~class_Lattices_Olattice(X7902)|(hAPP(X7901,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7902),esk252_3(X7900,X7901,X7902)),esk253_3(X7900,X7901,X7902)))!=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7902),hAPP(X7901,esk252_3(X7900,X7901,X7902))),hAPP(X7901,esk253_3(X7900,X7901,X7902)))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7902),X7900))|(X7900=c_Orderings_Obot__class_Obot(tc_fun(X7902,tc_HOL_Obool))|hAPP(X7901,c_Big__Operators_Olattice__class_OSup__fin(X7902,X7900))=c_Big__Operators_Olattice__class_OSup__fin(X7902,hAPP(c_Set_Oimage(X7902,X7902,X7901),X7900)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Ohom__commute])])])])). 4.05/4.30 fof(c_0_7053, plain, ![X6282, X6283, X6284, X6285]:(~class_Fields_Ofield(X6285)|(c_Groups_Ozero__class_Ozero(X6285)=X6284|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6285),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6285),X6283),X6284)),X6282)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6285),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6285),X6283),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6285),X6284),X6282))),X6284))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__add__eq__iff])])])). 4.05/4.30 fof(c_0_7054, plain, ![X6730, X6731, X6732]:(~class_Lattices_Olattice(X6732)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6732),X6731))|(X6731=c_Orderings_Obot__class_Obot(tc_fun(X6732,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6732),X6730))|(c_Orderings_Obot__class_Obot(tc_fun(X6732,tc_HOL_Obool))=X6730|c_Big__Operators_Olattice__class_OSup__fin(X6732,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6732,tc_HOL_Obool)),X6731),X6730))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6732),c_Big__Operators_Olattice__class_OSup__fin(X6732,X6731)),c_Big__Operators_Olattice__class_OSup__fin(X6732,X6730))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Ounion__idem])])])). 4.05/4.30 fof(c_0_7055, plain, ![X13201, X13202, X13203, X13204]:(~class_Fields_Ofield__inverse__zero(X13204)|(X13203=c_Groups_Ozero__class_Ozero(X13204)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13204),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13204),X13202),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13204),X13201),X13203))),X13203)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13204),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13204),X13202),X13203)),X13201))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__frac__num])])])). 4.05/4.30 fof(c_0_7056, plain, ![X331, X332, X333, X334]:(~class_Divides_Osemiring__div(X334)|(c_Groups_Ozero__class_Ozero(X334)=X333|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X334),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X334),X332),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X334),X331),X333))),X333)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X334),X331),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X334),X332),X333)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__self1])])])). 4.05/4.30 fof(c_0_7057, plain, ![X13554, X13555, X13556, X13557]:(~class_Fields_Ofield__inverse__zero(X13557)|(X13556=c_Groups_Ozero__class_Ozero(X13557)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13557),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13557),X13554),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13557),X13555),X13556))),X13556)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13557),X13555),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13557),X13554),X13556)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__num__frac])])). 4.05/4.30 fof(c_0_7058, plain, ![X5574, X5575, X5576, X5577]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5577),X5576))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5575,tc_HOL_Obool)),hAPP(c_List_Oset(X5575),hAPP(hAPP(c_List_Odrop(X5575),X5576),X5574))),hAPP(c_List_Oset(X5575),hAPP(hAPP(c_List_Odrop(X5575),X5577),X5574))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__drop__subset__set__drop])])])). 4.05/4.30 fof(c_0_7059, plain, ![X11899, X11900, X11901, X11902]:(~class_Divides_Osemiring__div(X11902)|(X11901=c_Groups_Ozero__class_Ozero(X11902)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11902),X11899),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11902),X11900),X11901))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11902),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11902),X11900),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11902),X11901),X11899))),X11901))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__self2])])])). 4.05/4.30 cnf(c_0_7060, 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_5272])). 4.05/4.30 cnf(c_0_7061, 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_5273]), ['final']). 4.05/4.30 fof(c_0_7062, plain, ![X1701, X1702, X1703, X1704, X1705]:(~class_Orderings_Olinorder(X1705)|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1705,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1705),X1704),X1702)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1705),X1703),X1701))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1705,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1705,X1704),X1703)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1705,X1702),X1701))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastLessThan])])). 4.05/4.30 fof(c_0_7063, plain, ![X12888, X12889, X12890]:(~class_Orderings_Olinorder(X12890)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12890),X12889))|(X12889=c_Orderings_Obot__class_Obot(tc_fun(X12890,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12890),X12888))|(c_Orderings_Obot__class_Obot(tc_fun(X12890,tc_HOL_Obool))=X12888|hAPP(hAPP(c_Orderings_Oord__class_Omin(X12890),c_Big__Operators_Olinorder__class_OMin(X12890,X12889)),c_Big__Operators_Olinorder__class_OMin(X12890,X12888))=c_Big__Operators_Olinorder__class_OMin(X12890,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12890,tc_HOL_Obool)),X12889),X12888))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min__Un])])])). 4.05/4.30 fof(c_0_7064, plain, ![X17697, X17698, X17699, X17700]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17700),X17699))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17698,tc_HOL_Obool)),hAPP(c_List_Oset(X17698),hAPP(hAPP(c_List_Otake(X17698),X17700),X17697))),hAPP(c_List_Oset(X17698),hAPP(hAPP(c_List_Otake(X17698),X17699),X17697))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__take__subset__set__take])])). 4.05/4.30 fof(c_0_7065, plain, ![X11598, X11599, X11600, X11601, X11602, X11603]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11602),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11601,X11602),X11600),X11599)),X11598))|(~hBOOL(hAPP(hAPP(c_member(X11601),X11603),X11600))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11602),hAPP(X11599,X11603)),X11598)))|~class_Complete__Lattice_Ocomplete__lattice(X11602))&((hBOOL(hAPP(hAPP(c_member(X11601),esk358_5(X11598,X11599,X11600,X11601,X11602)),X11600))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11602),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11601,X11602),X11600),X11599)),X11598))|~class_Complete__Lattice_Ocomplete__lattice(X11602))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11602),hAPP(X11599,esk358_5(X11598,X11599,X11600,X11601,X11602))),X11598))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11602),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11601,X11602),X11600),X11599)),X11598))|~class_Complete__Lattice_Ocomplete__lattice(X11602)))), 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])])])])])). 4.05/4.30 fof(c_0_7066, plain, ![X17431, X17432, X17433, X17434, X17435, X17436]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17435),X17434),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17433,X17435),X17432),X17431)))|(~hBOOL(hAPP(hAPP(c_member(X17433),X17436),X17432))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17435),X17434),hAPP(X17431,X17436))))|~class_Complete__Lattice_Ocomplete__lattice(X17435))&((hBOOL(hAPP(hAPP(c_member(X17433),esk522_5(X17431,X17432,X17433,X17434,X17435)),X17432))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17435),X17434),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17433,X17435),X17432),X17431)))|~class_Complete__Lattice_Ocomplete__lattice(X17435))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17435),X17434),hAPP(X17431,esk522_5(X17431,X17432,X17433,X17434,X17435))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17435),X17434),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17433,X17435),X17432),X17431)))|~class_Complete__Lattice_Ocomplete__lattice(X17435)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__INF__iff])])])])])])). 4.05/4.30 fof(c_0_7067, plain, ![X12219, X12220, X12221, X12222]:((hBOOL(hAPP(hAPP(c_member(X12221),esk378_4(X12219,X12220,X12221,X12222)),X12220))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12222),c_Groups_Ozero__class_Ozero(X12222)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12221,X12222),X12219),X12220)))|~class_Rings_Olinordered__semidom(X12222))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12222),c_Groups_Ozero__class_Ozero(X12222)),hAPP(X12219,esk378_4(X12219,X12220,X12221,X12222))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12222),c_Groups_Ozero__class_Ozero(X12222)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X12221,X12222),X12219),X12220)))|~class_Rings_Olinordered__semidom(X12222))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__pos])])])])])). 4.05/4.30 fof(c_0_7068, plain, ![X813, X814, X815, X817, X818, X819, X820]:(((hBOOL(hAPP(hAPP(c_member(X815),esk16_3(X813,X814,X815)),X814))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X815,X815),tc_HOL_Obool)),X813),hAPP(hAPP(c_Product__Type_OSigma(X815,X815),X814),hAPP(c_COMBK(tc_fun(X815,tc_HOL_Obool),X815),X814))))|c_Relation_Orefl__on(X815,X814,X813))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X815,X815)),hAPP(hAPP(c_Product__Type_OPair(X815,X815),esk16_3(X813,X814,X815)),esk16_3(X813,X814,X815))),X813))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X815,X815),tc_HOL_Obool)),X813),hAPP(hAPP(c_Product__Type_OSigma(X815,X815),X814),hAPP(c_COMBK(tc_fun(X815,tc_HOL_Obool),X815),X814))))|c_Relation_Orefl__on(X815,X814,X813)))&((~hBOOL(hAPP(hAPP(c_member(X819),X820),X818))|hBOOL(hAPP(hAPP(c_member(tc_prod(X819,X819)),hAPP(hAPP(c_Product__Type_OPair(X819,X819),X820),X820)),X817))|~c_Relation_Orefl__on(X819,X818,X817))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X819,X819),tc_HOL_Obool)),X817),hAPP(hAPP(c_Product__Type_OSigma(X819,X819),X818),hAPP(c_COMBK(tc_fun(X819,tc_HOL_Obool),X819),X818))))|~c_Relation_Orefl__on(X819,X818,X817)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__def])])])])])])). 4.05/4.30 fof(c_0_7069, plain, ![X8425, X8426, X8427, X8428]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8428),X8427))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X8428,X8428),tc_HOL_Obool)),X8426),hAPP(hAPP(c_Product__Type_OSigma(X8428,X8428),X8427),hAPP(c_COMBK(tc_fun(X8428,tc_HOL_Obool),X8428),X8427))))|(~hBOOL(hAPP(hAPP(c_member(tc_fun(X8428,tc_HOL_Obool)),X8425),hAPP(hAPP(c_Equiv__Relations_Oquotient(X8428),X8427),X8426)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X8428),X8425))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__equiv__class])])])). 4.05/4.30 fof(c_0_7070, plain, ![X15483, X15484, X15485]:(~c_Equiv__Relations_Oequiv(X15485,X15484,X15483)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15485,X15485),tc_HOL_Obool)),X15483),hAPP(hAPP(c_Product__Type_OSigma(X15485,X15485),X15484),hAPP(c_COMBK(tc_fun(X15485,tc_HOL_Obool),X15485),X15484))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equiv__type])])])). 4.05/4.30 fof(c_0_7071, plain, ![X11261, X11262, X11263]:(~class_Orderings_Olinorder(X11263)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11263),X11262))|(X11262=c_Orderings_Obot__class_Obot(tc_fun(X11263,tc_HOL_Obool))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11263),X11261))|(X11261=c_Orderings_Obot__class_Obot(tc_fun(X11263,tc_HOL_Obool))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X11263),c_Big__Operators_Olinorder__class_OMax(X11263,X11262)),c_Big__Operators_Olinorder__class_OMax(X11263,X11261))=c_Big__Operators_Olinorder__class_OMax(X11263,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11263,tc_HOL_Obool)),X11262),X11261))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max__Un])])])). 4.05/4.30 fof(c_0_7072, plain, ![X8401, X8402, X8403, X8404]:((hBOOL(hAPP(hAPP(c_member(X8403),esk269_4(X8401,X8402,X8403,X8404)),X8402))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8404),c_Groups_Ozero__class_Ozero(X8404)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8403,X8404),X8401),X8402)))|~class_Rings_Olinordered__semidom(X8404))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8404),c_Groups_Ozero__class_Ozero(X8404)),hAPP(X8401,esk269_4(X8401,X8402,X8403,X8404))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8404),c_Groups_Ozero__class_Ozero(X8404)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8403,X8404),X8401),X8402)))|~class_Rings_Olinordered__semidom(X8404))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__nonneg])])])])])). 4.05/4.30 fof(c_0_7073, plain, ![X15488, X15489, X15490, X15491]:(~class_Int_Onumber__ring(X15491)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15491),hAPP(c_Int_Onumber__class_Onumber__of(X15491),X15490)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15491),hAPP(c_Int_Onumber__class_Onumber__of(X15491),X15489)),X15488))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15491),hAPP(c_Int_Onumber__class_Onumber__of(X15491),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15490),X15489))),X15488)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__number__of__diff1])])])). 4.05/4.30 fof(c_0_7074, plain, ![X9613, X9614, X9615, X9616]:(~class_Int_Onumber__ring(X9616)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9616),hAPP(c_Int_Onumber__class_Onumber__of(X9616),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9615),X9614))),X9613)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9616),hAPP(c_Int_Onumber__class_Onumber__of(X9616),X9615)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9616),hAPP(c_Int_Onumber__class_Onumber__of(X9616),X9614)),X9613))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__number__of__left])])])). 4.05/4.30 fof(c_0_7075, plain, ![X3532, X3533]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3533))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3532),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),X3533),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3532))))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X3533,X3532))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__pos__neg])])])). 4.05/4.30 fof(c_0_7076, plain, ![X9065, X9066, X9067, X9068]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X9068,X9068)),X9067),c_Transitive__Closure_Ortrancl(X9068,X9065)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9068,X9068)),X9067),c_Transitive__Closure_Ortrancl(X9068,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X9068,X9068),tc_HOL_Obool)),X9066),X9065)))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9068,X9068)),X9067),c_Transitive__Closure_Ortrancl(X9068,X9066)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X9068,X9068)),X9067),c_Transitive__Closure_Ortrancl(X9068,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X9068,X9068),tc_HOL_Obool)),X9066),X9065)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rtrancl__UnI])])])). 4.05/4.30 fof(c_0_7077, plain, ![X6058, X6059]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6059),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6058),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X6059,X6058)=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),X6059),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6058)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__neg])])). 4.05/4.30 fof(c_0_7078, plain, ![X12996, X12997, X12998]:(~class_Fields_Olinordered__field(X12998)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12998),X12997),X12996))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12998),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12998),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12998),X12997),X12996)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12998),c_Groups_Oone__class_Oone(X12998)),c_Groups_Oone__class_Oone(X12998)))),X12996)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gt__half__sum])])). 4.05/4.30 fof(c_0_7079, plain, ![X10269, X10270, X10271]:(~class_Fields_Olinordered__field(X10271)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10271),X10270),X10269))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10271),X10270),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10271),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10271),X10270),X10269)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10271),c_Groups_Oone__class_Oone(X10271)),c_Groups_Oone__class_Oone(X10271))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__half__sum])])])). 4.05/4.30 cnf(c_0_7080, 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),esk349_2(X1,X2)),hAPP(X2,esk349_2(X1,X2))))), inference(split_conjunct,[status(thm)],[c_0_5274])). 4.05/4.30 cnf(c_0_7081, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk24_4(X2,X3,X1,X4)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|hAPP(X2,X4)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5275])). 4.05/4.30 fof(c_0_7082, plain, ![X15495, X15496, X15497, X15498, X15499]:(~c_Fun_Oinj__on(X15499,X15498,X15497,X15496)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15498,tc_HOL_Obool)),hAPP(c_Set_Oimage(X15499,X15498,X15497),X15496)),X15495))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15498),X15495))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X15499),X15496)),hAPP(c_Finite__Set_Ocard(X15498),X15495)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__inj__on__le])])])). 4.05/4.30 fof(c_0_7083, plain, ![X3379, X3380, X3381]:(~class_Rings_Oring__1(X3381)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3381),hAPP(hAPP(c_Power_Opower__class_Opower(X3381),hAPP(c_Groups_Ouminus__class_Ouminus(X3381),c_Groups_Oone__class_Oone(X3381))),X3379)),hAPP(hAPP(c_Power_Opower__class_Opower(X3381),X3380),X3379))=hAPP(hAPP(c_Power_Opower__class_Opower(X3381),hAPP(c_Groups_Ouminus__class_Ouminus(X3381),X3380)),X3379)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus])])). 4.05/4.30 cnf(c_0_7084, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk454_4(X1,X2,X3,X4)),esk453_4(X1,X2,X3,X4))=X4|X4=X2|X2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5245])). 4.05/4.30 fof(c_0_7085, plain, ![X5012, X5013, X5014, X5015, X5016, X5017, X5018]:(hBOOL(hAPP(hAPP(c_member(X5018),X5017),X5016))|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5018,X5015,X5014,X5013,X5016),X5012))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5018,X5015,X5014,X5013,hAPP(hAPP(c_Set_Oinsert(X5018),X5017),X5016)),hAPP(hAPP(X5014,X5017),X5012))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__graph_OinsertI])])])). 4.05/4.30 cnf(c_0_7086, 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(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)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[c_0_5276, c_0_4422])). 4.05/4.30 fof(c_0_7087, plain, ![X1192, X1193, X1194, X1195, X1196]:(~class_Rings_Osemiring__0(X1196)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1194,X1196),hAPP(hAPP(c_COMBB(X1196,X1196,X1194),hAPP(c_Groups_Otimes__class_Otimes(X1196),X1195)),X1193)),X1192)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1196),X1195),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1194,X1196),X1193),X1192))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__right__distrib])])])). 4.05/4.30 fof(c_0_7088, plain, ![X10651, X10652, X10653, X10654, X10655]:(~c_Finite__Set_Ofun__left__comm__idem(X10655,X10654,X10653)|hAPP(c_List_Ofoldl(X10654,X10655,hAPP(c_COMBC(X10655,X10654,X10654),X10653),X10652),X10651)=hAPP(hAPP(c_Finite__Set_Ofold(X10655,X10654,X10653),X10652),hAPP(c_List_Oset(X10655),X10651))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__set])])). 4.05/4.30 fof(c_0_7089, plain, ![X13875, X13876, X13877, X13878, X13879]:(hAPP(X13879,X13878)!=c_Option_Ooption_ONone(X13877)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13876,tc_HOL_Obool)),c_Map_Odom(X13876,X13877,X13879)),hAPP(hAPP(c_Set_Oinsert(X13876),X13878),X13875))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13876,tc_HOL_Obool)),c_Map_Odom(X13876,X13877,X13879)),X13875)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_dom__minus])])])). 4.05/4.30 cnf(c_0_7090, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk69_4(X2,X3,X4,X1)),esk68_4(X2,X3,X4,X1))|X1=X3|X3!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X4)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))), inference(split_conjunct,[status(thm)],[c_0_5250])). 4.05/4.30 fof(c_0_7091, plain, ![X1187, X1188, X1189, X1190, X1191]:((hAPP(hAPP(c_Map_Omap__of(X1191,X1189),hAPP(hAPP(c_List_Ozip(X1191,X1189),X1190),X1188)),X1187)!=c_Option_Ooption_ONone(X1189)|~hBOOL(hAPP(hAPP(c_member(X1191),X1187),hAPP(c_List_Oset(X1191),X1190)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1189)),X1188)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1191)),X1190))&(hBOOL(hAPP(hAPP(c_member(X1191),X1187),hAPP(c_List_Oset(X1191),X1190)))|hAPP(hAPP(c_Map_Omap__of(X1191,X1189),hAPP(hAPP(c_List_Ozip(X1191,X1189),X1190),X1188)),X1187)=c_Option_Ooption_ONone(X1189)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1189)),X1188)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1191)),X1190))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__zip__is__None])])])])). 4.05/4.30 fof(c_0_7092, plain, ![X2352, X2353, X2354, X2355, X2356]:(~c_Finite__Set_Ofolding__one(X2356,X2355,X2354)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2356),X2353))|(hBOOL(hAPP(hAPP(c_member(X2356),X2352),X2353))|hAPP(hAPP(c_Finite__Set_Ofold(X2356,X2356,X2355),X2352),X2353)=hAPP(X2354,hAPP(hAPP(c_Set_Oinsert(X2356),X2352),X2353))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Oeq__fold_H])])])). 4.05/4.30 fof(c_0_7093, plain, ![X7021, X7022, X7023, X7024, X7025, X7026, X7027]:(((X7022=X7024|hAPP(X7025,X7022)!=hAPP(c_Option_Ooption_OSome(X7026),X7021)|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7027,tc_Option_Ooption(X7026)),X7025),X7024),hAPP(c_Option_Ooption_OSome(X7026),X7023)),X7022)=hAPP(c_Option_Ooption_OSome(X7026),X7021))&(X7024!=X7022|X7021!=X7023|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7027,tc_Option_Ooption(X7026)),X7025),X7024),hAPP(c_Option_Ooption_OSome(X7026),X7023)),X7022)=hAPP(c_Option_Ooption_OSome(X7026),X7021)))&(((X7024=X7022|X7022!=X7024|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7027,tc_Option_Ooption(X7026)),X7025),X7024),hAPP(c_Option_Ooption_OSome(X7026),X7023)),X7022)!=hAPP(c_Option_Ooption_OSome(X7026),X7021))&(X7021=X7023|X7022!=X7024|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7027,tc_Option_Ooption(X7026)),X7025),X7024),hAPP(c_Option_Ooption_OSome(X7026),X7023)),X7022)!=hAPP(c_Option_Ooption_OSome(X7026),X7021)))&((X7024=X7022|hAPP(X7025,X7022)=hAPP(c_Option_Ooption_OSome(X7026),X7021)|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7027,tc_Option_Ooption(X7026)),X7025),X7024),hAPP(c_Option_Ooption_OSome(X7026),X7023)),X7022)!=hAPP(c_Option_Ooption_OSome(X7026),X7021))&(X7021=X7023|hAPP(X7025,X7022)=hAPP(c_Option_Ooption_OSome(X7026),X7021)|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7027,tc_Option_Ooption(X7026)),X7025),X7024),hAPP(c_Option_Ooption_OSome(X7026),X7023)),X7022)!=hAPP(c_Option_Ooption_OSome(X7026),X7021))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__upd__Some__unfold])])])). 4.05/4.30 cnf(c_0_7094, 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_5277])). 4.05/4.30 fof(c_0_7095, plain, ![X10251, X10252, X10253]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10253,X10253),tc_HOL_Obool)),X10252),X10251))|(~c_Relation_Orefl__on(X10253,c_Orderings_Otop__class_Otop(tc_fun(X10253,tc_HOL_Obool)),X10251)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X10253),tc_List_Olist(X10253)),tc_HOL_Obool)),c_List_Olistrel1(X10253,X10252)),c_List_Olistrel(X10253,X10251))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__subset__listrel])])). 4.05/4.30 fof(c_0_7096, plain, ![X7258, X7259, X7260]:(~hBOOL(hAPP(c_List_Odistinct(X7260),X7259))|hAPP(c_List_Oset(X7260),c_List_Oremove1(X7260,X7258,X7259))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7260,tc_HOL_Obool)),hAPP(c_List_Oset(X7260),X7259)),hAPP(hAPP(c_Set_Oinsert(X7260),X7258),c_Orderings_Obot__class_Obot(tc_fun(X7260,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__remove1__eq])])])). 4.05/4.30 fof(c_0_7097, plain, ![X6768, X6769, X6770, X6771]:(~class_Rings_Olinordered__semidom(X6771)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6771),X6770),X6769))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6771),c_Groups_Ozero__class_Ozero(X6771)),X6770))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6768))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6771),hAPP(hAPP(c_Power_Opower__class_Opower(X6771),X6770),X6768)),hAPP(hAPP(c_Power_Opower__class_Opower(X6771),X6769),X6768))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__strict__mono])])])). 4.05/4.30 fof(c_0_7098, plain, ![X801, X802, X803, X804]:(~class_Rings_Olinordered__semidom(X804)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X803),X802))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X804),c_Groups_Ozero__class_Ozero(X804)),X801))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X804),X801),c_Groups_Oone__class_Oone(X804)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X804),hAPP(hAPP(c_Power_Opower__class_Opower(X804),X801),X802)),hAPP(hAPP(c_Power_Opower__class_Opower(X804),X801),X803))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__strict__decreasing])])])). 4.05/4.30 fof(c_0_7099, plain, ![X10332, X10333, X10334, X10335]:(~class_Rings_Olinordered__semidom(X10335)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10334),X10333))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10335),c_Groups_Ozero__class_Ozero(X10335)),X10332))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10335),X10332),c_Groups_Oone__class_Oone(X10335)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10335),hAPP(hAPP(c_Power_Opower__class_Opower(X10335),X10332),X10333)),hAPP(hAPP(c_Power_Opower__class_Opower(X10335),X10332),X10334))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__decreasing])])). 4.05/4.30 fof(c_0_7100, plain, ![X1518, X1519, X1520, X1521, X1522]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1522,tc_HOL_Obool)),hAPP(c_List_Oset(X1522),X1521)),X1520))|(~hBOOL(hAPP(hAPP(c_member(X1522),X1519),X1520))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1522,tc_HOL_Obool)),hAPP(c_List_Oset(X1522),hAPP(hAPP(c_List_Olist__update(X1522,X1521),X1518),X1519))),X1520)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__update__subsetI])])])). 4.05/4.30 fof(c_0_7101, plain, ![X8581, X8582, X8583, X8584, X8585, X8586]:(~c_Map_Omap__le(X8586,X8585,X8584,X8583)|c_Map_Omap__le(X8586,X8585,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X8586,tc_Option_Ooption(X8585)),X8584),X8582),X8581),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X8586,tc_Option_Ooption(X8585)),X8583),X8582),X8581))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__le__upd])])])). 4.05/4.30 fof(c_0_7102, plain, ![X12381, X12382, X12383]:(~c_Relation_Orefl__on(X12383,X12382,X12381)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X12383,X12383),tc_HOL_Obool)),X12381),hAPP(hAPP(c_Relation_Orel__comp(X12383,X12383,X12383),hAPP(c_Relation_Oconverse(X12383,X12383),X12381)),X12381)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__comp__subset])])). 4.05/4.30 fof(c_0_7103, plain, ![X11080, X11081, X11082, X11083]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X11082,tc_HOL_Obool)),esk337_4(X11080,X11081,X11082,X11083)),X11083))|c_Fun_Oinj__on(X11082,X11081,X11080,c_Complete__Lattice_OInf__class_OInf(tc_fun(X11082,tc_HOL_Obool),X11083))|X11083=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X11082,tc_HOL_Obool),tc_HOL_Obool)))&(~c_Fun_Oinj__on(X11082,X11081,X11080,esk337_4(X11080,X11081,X11082,X11083))|c_Fun_Oinj__on(X11082,X11081,X11080,c_Complete__Lattice_OInf__class_OInf(tc_fun(X11082,tc_HOL_Obool),X11083))|X11083=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X11082,tc_HOL_Obool),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])])])])])). 4.05/4.30 fof(c_0_7104, plain, ![X17072, X17073, X17074, X17075, X17076]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X17076,X17075)),hAPP(hAPP(c_Product__Type_OPair(X17076,X17075),X17074),X17073)),X17072))|hBOOL(hAPP(hAPP(c_member(tc_prod(X17075,X17076)),hAPP(hAPP(c_Product__Type_OPair(X17075,X17076),X17073),X17074)),hAPP(c_Relation_Oconverse(X17076,X17075),X17072)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_converseI])])])). 4.05/4.30 fof(c_0_7105, plain, ![X3359, X3360, X3361, X3362, X3363]:(hAPP(c_Option_Ooption_OSome(X3362),X3359)!=hAPP(hAPP(c_Map_Omap__of(X3363,X3362),X3361),X3360)|hBOOL(hAPP(hAPP(c_member(tc_prod(X3363,X3362)),hAPP(hAPP(c_Product__Type_OPair(X3363,X3362),X3360),X3359)),hAPP(c_List_Oset(tc_prod(X3363,X3362)),X3361)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__of__is__SomeD])])). 4.05/4.30 fof(c_0_7106, plain, ![X5410, X5411, X5412, X5413]:((~c_List_Olinorder__class_Osorted(X5411,X5410)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5412),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5411)),X5410)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5413),X5412))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5411),hAPP(hAPP(c_List_Onth(X5411),X5410),X5413)),hAPP(hAPP(c_List_Onth(X5411),X5410),X5412)))))|~class_Orderings_Olinorder(X5411))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk169_2(X5410,X5411)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5411)),X5410)))|c_List_Olinorder__class_Osorted(X5411,X5410)|~class_Orderings_Olinorder(X5411))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk170_2(X5410,X5411)),esk169_2(X5410,X5411)))|c_List_Olinorder__class_Osorted(X5411,X5410)|~class_Orderings_Olinorder(X5411))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5411),hAPP(hAPP(c_List_Onth(X5411),X5410),esk170_2(X5410,X5411))),hAPP(hAPP(c_List_Onth(X5411),X5410),esk169_2(X5410,X5411))))|c_List_Olinorder__class_Osorted(X5411,X5410)|~class_Orderings_Olinorder(X5411))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__equals__nth__mono])])])])])])). 4.05/4.30 fof(c_0_7107, plain, ![X7180, X7181, X7182, X7184, X7185, X7186, X7187, X7189]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk222_3(X7180,X7181,X7182)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7182)),X7181)))|(~hBOOL(hAPP(hAPP(c_member(X7182),X7184),hAPP(c_List_Oset(X7182),X7181)))|hBOOL(hAPP(X7180,X7184))))&(~hBOOL(hAPP(X7180,hAPP(hAPP(c_List_Onth(X7182),X7181),esk222_3(X7180,X7181,X7182))))|(~hBOOL(hAPP(hAPP(c_member(X7182),X7184),hAPP(c_List_Oset(X7182),X7181)))|hBOOL(hAPP(X7180,X7184)))))&((hBOOL(hAPP(hAPP(c_member(X7187),esk223_3(X7185,X7186,X7187)),hAPP(c_List_Oset(X7187),X7186)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7189),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7187)),X7186)))|hBOOL(hAPP(X7185,hAPP(hAPP(c_List_Onth(X7187),X7186),X7189)))))&(~hBOOL(hAPP(X7185,esk223_3(X7185,X7186,X7187)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7189),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7187)),X7186)))|hBOOL(hAPP(X7185,hAPP(hAPP(c_List_Onth(X7187),X7186),X7189))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_all__set__conv__all__nth])])])])])])])). 4.05/4.30 fof(c_0_7108, plain, ![X2825, X2826, X2827]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2827),c_Groups_Ozero__class_Ozero(X2827)),X2826))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2827),c_Groups_Ozero__class_Ozero(X2827)),X2825))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2827),hAPP(c_Groups_Oabs__class_Oabs(X2827),X2826)),hAPP(c_Groups_Oabs__class_Oabs(X2827),X2825))=hAPP(c_Groups_Oabs__class_Oabs(X2827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2827),X2826),X2825))|~class_Rings_Oordered__ring__abs(X2827))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2827),X2826),c_Groups_Ozero__class_Ozero(X2827)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2827),c_Groups_Ozero__class_Ozero(X2827)),X2825))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2827),hAPP(c_Groups_Oabs__class_Oabs(X2827),X2826)),hAPP(c_Groups_Oabs__class_Oabs(X2827),X2825))=hAPP(c_Groups_Oabs__class_Oabs(X2827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2827),X2826),X2825))|~class_Rings_Oordered__ring__abs(X2827)))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2827),c_Groups_Ozero__class_Ozero(X2827)),X2826))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2827),X2825),c_Groups_Ozero__class_Ozero(X2827)))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2827),hAPP(c_Groups_Oabs__class_Oabs(X2827),X2826)),hAPP(c_Groups_Oabs__class_Oabs(X2827),X2825))=hAPP(c_Groups_Oabs__class_Oabs(X2827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2827),X2826),X2825))|~class_Rings_Oordered__ring__abs(X2827))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2827),X2826),c_Groups_Ozero__class_Ozero(X2827)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2827),X2825),c_Groups_Ozero__class_Ozero(X2827)))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2827),hAPP(c_Groups_Oabs__class_Oabs(X2827),X2826)),hAPP(c_Groups_Oabs__class_Oabs(X2827),X2825))=hAPP(c_Groups_Oabs__class_Oabs(X2827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2827),X2826),X2825))|~class_Rings_Oordered__ring__abs(X2827)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__eq__mult])])])])). 4.05/4.30 cnf(c_0_7109, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,X1,esk228_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)),esk227_2(X2,X1))))=X2|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5278])). 4.05/4.30 cnf(c_0_7110, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_5279])). 4.05/4.30 cnf(c_0_7111, 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))|X2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(X5,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_5093])). 4.05/4.30 cnf(c_0_7112, 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_4647])). 4.05/4.30 cnf(c_0_7113, 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_5280]), ['final']). 4.05/4.30 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)))|X2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X4))|~hBOOL(hAPP(X5,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_5093])). 4.05/4.30 fof(c_0_7115, plain, ![X4850, X4851, X4852, X4853, X4854, X4855, X4856]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X4852,X4852)),X4851),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4852,X4852),tc_HOL_Obool),X4853),X4850)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4852,X4852)),X4851),c_Transitive__Closure_Ortrancl(X4852,X4850))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4856,X4856)),X4855),c_Transitive__Closure_Ortrancl(X4856,X4854)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4856,X4856)),X4855),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4856,X4856),tc_HOL_Obool),esk149_3(X4854,X4855,X4856)),X4854))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__power])])])])])). 4.05/4.30 fof(c_0_7116, plain, ![X13824, X13825, X13826]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13826),X13825))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13826,tc_HOL_Obool)),X13825),X13824))|hAPP(c_Finite__Set_Ocard(X13826),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13826,tc_HOL_Obool)),X13824),X13825))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X13826),X13824)),hAPP(c_Finite__Set_Ocard(X13826),X13825)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff__subset])])). 4.05/4.30 fof(c_0_7117, plain, ![X10669, X10670]:(~class_Orderings_Olinorder(X10670)|c_List_Olinorder__class_Osort__key(X10670,X10670,c_COMBI(X10670),X10669)=hAPP(c_List_Ofoldl(tc_List_Olist(X10670),X10670,hAPP(c_COMBC(X10670,tc_List_Olist(X10670),tc_List_Olist(X10670)),c_List_Olinorder__class_Oinsort__key(X10670,X10670,c_COMBI(X10670))),c_List_Olist_ONil(X10670)),X10669)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sort__foldl__insort])])])). 4.05/4.30 cnf(c_0_7118, plain, (X1=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),X1),esk180_3(X1,X2,X3))),esk181_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_5265])). 4.05/4.30 fof(c_0_7119, plain, ![X1912, X1913, X1914]:(hBOOL(hAPP(hAPP(c_member(X1914),X1913),X1912))|X1912=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1914,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1914),X1913),X1912)),hAPP(hAPP(c_Set_Oinsert(X1914),X1913),c_Orderings_Obot__class_Obot(tc_fun(X1914,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Diff__insert__absorb])])])). 4.05/4.30 fof(c_0_7120, plain, ![X3740, X3741, X3742, X3743]:(~class_Lattices_Osemilattice__sup(X3743)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3743),X3742))|hAPP(hAPP(c_Finite__Set_Ofold(X3743,X3743,c_Lattices_Osemilattice__sup__class_Osup(X3743)),X3741),hAPP(hAPP(c_Set_Oinsert(X3743),X3740),X3742))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3743),X3740),hAPP(hAPP(c_Finite__Set_Ofold(X3743,X3743,c_Lattices_Osemilattice__sup__class_Osup(X3743)),X3741),X3742)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__sup__insert])])])). 4.05/4.30 fof(c_0_7121, plain, ![X13068, X13069, X13070, X13071]:(~class_Orderings_Olinorder(X13071)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13071),X13070))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X13071),X13068),hAPP(hAPP(c_Finite__Set_Ofold(X13071,X13071,c_Orderings_Oord__class_Omin(X13071)),X13069),X13070))=hAPP(hAPP(c_Finite__Set_Ofold(X13071,X13071,c_Orderings_Oord__class_Omin(X13071)),X13069),hAPP(hAPP(c_Set_Oinsert(X13071),X13068),X13070)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ofold__inf__insert])])])). 4.05/4.30 fof(c_0_7122, plain, ![X8869, X8870, X8871, X8872]:(~class_Fields_Ofield(X8872)|(c_Groups_Ozero__class_Ozero(X8872)=X8871|hAPP(hAPP(c_Power_Opower__class_Opower(X8872),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8872),X8870),X8871)),X8869)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8872),hAPP(hAPP(c_Power_Opower__class_Opower(X8872),X8870),X8869)),hAPP(hAPP(c_Power_Opower__class_Opower(X8872),X8871),X8869)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonzero__power__divide])])])). 4.05/4.30 fof(c_0_7123, plain, ![X14338, X14339, X14340, X14341]:(~class_Orderings_Olinorder(X14341)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14341),X14340))|(~hBOOL(hAPP(hAPP(c_member(X14341),X14339),X14340))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14341),hAPP(hAPP(c_Finite__Set_Ofold(X14341,X14341,c_Orderings_Oord__class_Omin(X14341)),X14338),X14340)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X14341),X14339),X14338)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ofold__inf__le__inf])])])). 4.05/4.30 fof(c_0_7124, plain, ![X14565, X14566, X14567, X14568]:(~class_Lattices_Osemilattice__inf(X14568)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14568),X14567))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14568),X14565),hAPP(hAPP(c_Finite__Set_Ofold(X14568,X14568,c_Lattices_Osemilattice__inf__class_Oinf(X14568)),X14566),X14567))=hAPP(hAPP(c_Finite__Set_Ofold(X14568,X14568,c_Lattices_Osemilattice__inf__class_Oinf(X14568)),X14566),hAPP(hAPP(c_Set_Oinsert(X14568),X14565),X14567)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__inf__insert])])])). 4.05/4.30 fof(c_0_7125, plain, ![X809, X810, X811, X812]:(~class_Orderings_Olinorder(X812)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X812),X811))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X812),X809),hAPP(hAPP(c_Finite__Set_Ofold(X812,X812,c_Orderings_Oord__class_Omax(X812)),X810),X811))=hAPP(hAPP(c_Finite__Set_Ofold(X812,X812,c_Orderings_Oord__class_Omax(X812)),X810),hAPP(hAPP(c_Set_Oinsert(X812),X809),X811)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__insert])])). 4.05/4.30 fof(c_0_7126, plain, ![X2545, X2546, X2547, X2548]:((X2547=hAPP(c_Relation_OImage(X2548,X2548,X2545),hAPP(hAPP(c_Set_Oinsert(X2548),esk89_4(X2545,X2546,X2547,X2548)),c_Orderings_Obot__class_Obot(tc_fun(X2548,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2548,tc_HOL_Obool)),X2547),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2548),X2546),X2545))))&(hBOOL(hAPP(hAPP(c_member(X2548),esk89_4(X2545,X2546,X2547,X2548)),X2546))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2548,tc_HOL_Obool)),X2547),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2548),X2546),X2545))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_quotientE])])])])])). 4.05/4.30 cnf(c_0_7127, 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_5281])). 4.05/4.30 fof(c_0_7128, plain, ![X15286, X15287, X15288, X15289]:(~class_Lattices_Osemilattice__inf(X15289)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15289),X15288))|(~hBOOL(hAPP(hAPP(c_member(X15289),X15287),X15288))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15289),hAPP(hAPP(c_Finite__Set_Ofold(X15289,X15289,c_Lattices_Osemilattice__inf__class_Oinf(X15289)),X15286),X15288)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15289),X15287),X15286)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__inf__le__inf])])])). 4.05/4.30 fof(c_0_7129, plain, ![X9168, X9169, X9170, X9171]:(~class_Orderings_Olinorder(X9171)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9171),X9170))|(~hBOOL(hAPP(hAPP(c_member(X9171),X9169),X9170))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9171),hAPP(hAPP(c_Orderings_Oord__class_Omax(X9171),X9169),X9168)),hAPP(hAPP(c_Finite__Set_Ofold(X9171,X9171,c_Orderings_Oord__class_Omax(X9171)),X9168),X9170)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__le__fold__sup])])])). 4.05/4.30 fof(c_0_7130, plain, ![X3989, X3990, X3991, X3992]:(~class_Lattices_Osemilattice__sup(X3992)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3992),X3991))|(~hBOOL(hAPP(hAPP(c_member(X3992),X3990),X3991))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3992),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3992),X3990),X3989)),hAPP(hAPP(c_Finite__Set_Ofold(X3992,X3992,c_Lattices_Osemilattice__sup__class_Osup(X3992)),X3989),X3991)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__le__fold__sup])])])). 4.05/4.30 fof(c_0_7131, plain, ![X13047, X13048, X13049, X13050]:((((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),c_Groups_Ozero__class_Ozero(X13050)),X13048))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),c_Groups_Ozero__class_Ozero(X13050)),X13048))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13050),X13049),X13048)),X13047))|~class_Fields_Olinordered__field__inverse__zero(X13050))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),X13048),c_Groups_Ozero__class_Ozero(X13050)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),X13048),c_Groups_Ozero__class_Ozero(X13050)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),c_Groups_Ozero__class_Ozero(X13050)),X13048))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13050),X13049),X13048)),X13047))|~class_Fields_Olinordered__field__inverse__zero(X13050))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13050),X13047),X13048)),X13049))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),X13048),c_Groups_Ozero__class_Ozero(X13050)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),c_Groups_Ozero__class_Ozero(X13050)),X13048))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13050),X13049),X13048)),X13047))|~class_Fields_Olinordered__field__inverse__zero(X13050)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),X13048),c_Groups_Ozero__class_Ozero(X13050)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),c_Groups_Ozero__class_Ozero(X13050)),X13047))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),c_Groups_Ozero__class_Ozero(X13050)),X13048))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13050),X13049),X13048)),X13047))|~class_Fields_Olinordered__field__inverse__zero(X13050))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13050),X13047),X13048)),X13049))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),c_Groups_Ozero__class_Ozero(X13050)),X13047))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),c_Groups_Ozero__class_Ozero(X13050)),X13048))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13050),X13049),X13048)),X13047))|~class_Fields_Olinordered__field__inverse__zero(X13050)))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),c_Groups_Ozero__class_Ozero(X13050)),X13048))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),X13049),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13050),X13047),X13048)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13050),X13049),X13048)),X13047))|~class_Fields_Olinordered__field__inverse__zero(X13050))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),X13048),c_Groups_Ozero__class_Ozero(X13050)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),X13048),c_Groups_Ozero__class_Ozero(X13050)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),X13049),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13050),X13047),X13048)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13050),X13049),X13048)),X13047))|~class_Fields_Olinordered__field__inverse__zero(X13050))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13050),X13047),X13048)),X13049))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),X13048),c_Groups_Ozero__class_Ozero(X13050)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),X13049),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13050),X13047),X13048)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13050),X13049),X13048)),X13047))|~class_Fields_Olinordered__field__inverse__zero(X13050)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),X13048),c_Groups_Ozero__class_Ozero(X13050)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),c_Groups_Ozero__class_Ozero(X13050)),X13047))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),X13049),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13050),X13047),X13048)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13050),X13049),X13048)),X13047))|~class_Fields_Olinordered__field__inverse__zero(X13050))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13050),X13047),X13048)),X13049))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),c_Groups_Ozero__class_Ozero(X13050)),X13047))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),X13049),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13050),X13047),X13048)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13050),X13049),X13048)),X13047))|~class_Fields_Olinordered__field__inverse__zero(X13050))))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),c_Groups_Ozero__class_Ozero(X13050)),X13048))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),X13049),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13050),X13047),X13048)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13050),X13049),X13048)),X13047))|~class_Fields_Olinordered__field__inverse__zero(X13050))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),X13048),c_Groups_Ozero__class_Ozero(X13050)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),c_Groups_Ozero__class_Ozero(X13050)),X13047))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),c_Groups_Ozero__class_Ozero(X13050)),X13048))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13050),X13049),X13048)),X13047))|~class_Fields_Olinordered__field__inverse__zero(X13050))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),X13048),c_Groups_Ozero__class_Ozero(X13050)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13050),X13047),X13048)),X13049))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),c_Groups_Ozero__class_Ozero(X13050)),X13048))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13050),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13050),X13049),X13048)),X13047))|~class_Fields_Olinordered__field__inverse__zero(X13050))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__less__eq])])])])). 4.05/4.30 fof(c_0_7132, plain, ![X13989, X13990, X13991, X13992, X13993]:(~c_Fun_Oinj__on(X13993,X13992,X13991,X13990)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13993,tc_HOL_Obool)),X13989),X13990))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13992,tc_HOL_Obool)),hAPP(c_Set_Oimage(X13993,X13992,X13991),X13989)),hAPP(c_Set_Oimage(X13993,X13992,X13991),X13990))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__strict__subset])])])). 4.05/4.30 fof(c_0_7133, plain, ![X14751, X14752, X14753, X14754]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),c_Groups_Ozero__class_Ozero(X14754)),X14752))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),c_Groups_Ozero__class_Ozero(X14754)),X14752))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14754),X14753),X14752)),X14751))|~class_Fields_Olinordered__field__inverse__zero(X14754))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),X14753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14754),X14751),X14752)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),c_Groups_Ozero__class_Ozero(X14754)),X14752))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14754),X14753),X14752)),X14751))|~class_Fields_Olinordered__field__inverse__zero(X14754)))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),c_Groups_Ozero__class_Ozero(X14754)),X14752))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),X14752),c_Groups_Ozero__class_Ozero(X14754)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),X14752),c_Groups_Ozero__class_Ozero(X14754))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14754),X14753),X14752)),X14751))|~class_Fields_Olinordered__field__inverse__zero(X14754))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),X14753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14754),X14751),X14752)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),X14752),c_Groups_Ozero__class_Ozero(X14754)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),X14752),c_Groups_Ozero__class_Ozero(X14754))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14754),X14753),X14752)),X14751))|~class_Fields_Olinordered__field__inverse__zero(X14754)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),c_Groups_Ozero__class_Ozero(X14754)),X14752))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),c_Groups_Ozero__class_Ozero(X14754)),X14751))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),X14752),c_Groups_Ozero__class_Ozero(X14754))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14754),X14753),X14752)),X14751))|~class_Fields_Olinordered__field__inverse__zero(X14754))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),X14753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14754),X14751),X14752)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),c_Groups_Ozero__class_Ozero(X14754)),X14751))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),X14752),c_Groups_Ozero__class_Ozero(X14754))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14754),X14753),X14752)),X14751))|~class_Fields_Olinordered__field__inverse__zero(X14754))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),c_Groups_Ozero__class_Ozero(X14754)),X14752))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),X14752),c_Groups_Ozero__class_Ozero(X14754)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14754),X14751),X14752)),X14753)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14754),X14753),X14752)),X14751))|~class_Fields_Olinordered__field__inverse__zero(X14754))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),X14753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14754),X14751),X14752)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),X14752),c_Groups_Ozero__class_Ozero(X14754)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14754),X14751),X14752)),X14753)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14754),X14753),X14752)),X14751))|~class_Fields_Olinordered__field__inverse__zero(X14754)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),c_Groups_Ozero__class_Ozero(X14754)),X14752))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),c_Groups_Ozero__class_Ozero(X14754)),X14751))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14754),X14751),X14752)),X14753)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14754),X14753),X14752)),X14751))|~class_Fields_Olinordered__field__inverse__zero(X14754))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),X14753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14754),X14751),X14752)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),c_Groups_Ozero__class_Ozero(X14754)),X14751))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14754),X14751),X14752)),X14753)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14754),X14753),X14752)),X14751))|~class_Fields_Olinordered__field__inverse__zero(X14754))))))&(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),X14752),c_Groups_Ozero__class_Ozero(X14754)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14754),X14751),X14752)),X14753))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),c_Groups_Ozero__class_Ozero(X14754)),X14752))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14754),X14753),X14752)),X14751))|~class_Fields_Olinordered__field__inverse__zero(X14754))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),X14752),c_Groups_Ozero__class_Ozero(X14754)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),c_Groups_Ozero__class_Ozero(X14754)),X14751))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),c_Groups_Ozero__class_Ozero(X14754)),X14752))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14754),X14753),X14752)),X14751))|~class_Fields_Olinordered__field__inverse__zero(X14754)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14754),c_Groups_Ozero__class_Ozero(X14754)),X14752))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),X14753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14754),X14751),X14752)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14754),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14754),X14753),X14752)),X14751))|~class_Fields_Olinordered__field__inverse__zero(X14754)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__le__eq])])])])). 4.05/4.30 fof(c_0_7134, plain, ![X3095, X3096, X3097, X3098]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),c_Groups_Ozero__class_Ozero(X3098)),X3095))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),c_Groups_Ozero__class_Ozero(X3098)),X3095))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3098),X3096),X3095)))|~class_Fields_Olinordered__field__inverse__zero(X3098))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3098),X3097),X3095)),X3096))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),c_Groups_Ozero__class_Ozero(X3098)),X3095))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3098),X3096),X3095)))|~class_Fields_Olinordered__field__inverse__zero(X3098)))&((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),c_Groups_Ozero__class_Ozero(X3098)),X3095))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3095),c_Groups_Ozero__class_Ozero(X3098)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3095),c_Groups_Ozero__class_Ozero(X3098))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3098),X3096),X3095)))|~class_Fields_Olinordered__field__inverse__zero(X3098))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3098),X3097),X3095)),X3096))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3095),c_Groups_Ozero__class_Ozero(X3098)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3095),c_Groups_Ozero__class_Ozero(X3098))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3098),X3096),X3095)))|~class_Fields_Olinordered__field__inverse__zero(X3098)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),c_Groups_Ozero__class_Ozero(X3098)),X3095))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),c_Groups_Ozero__class_Ozero(X3098)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3095),c_Groups_Ozero__class_Ozero(X3098))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3098),X3096),X3095)))|~class_Fields_Olinordered__field__inverse__zero(X3098))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3098),X3097),X3095)),X3096))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),c_Groups_Ozero__class_Ozero(X3098)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3095),c_Groups_Ozero__class_Ozero(X3098))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3098),X3096),X3095)))|~class_Fields_Olinordered__field__inverse__zero(X3098))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),c_Groups_Ozero__class_Ozero(X3098)),X3095))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3095),c_Groups_Ozero__class_Ozero(X3098)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3098),X3097),X3095))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3098),X3096),X3095)))|~class_Fields_Olinordered__field__inverse__zero(X3098))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3098),X3097),X3095)),X3096))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3095),c_Groups_Ozero__class_Ozero(X3098)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3098),X3097),X3095))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3098),X3096),X3095)))|~class_Fields_Olinordered__field__inverse__zero(X3098)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),c_Groups_Ozero__class_Ozero(X3098)),X3095))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),c_Groups_Ozero__class_Ozero(X3098)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3098),X3097),X3095))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3098),X3096),X3095)))|~class_Fields_Olinordered__field__inverse__zero(X3098))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3098),X3097),X3095)),X3096))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),c_Groups_Ozero__class_Ozero(X3098)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3098),X3097),X3095))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3098),X3096),X3095)))|~class_Fields_Olinordered__field__inverse__zero(X3098))))))&(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3095),c_Groups_Ozero__class_Ozero(X3098)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3098),X3097),X3095)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),c_Groups_Ozero__class_Ozero(X3098)),X3095))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3098),X3096),X3095)))|~class_Fields_Olinordered__field__inverse__zero(X3098))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3095),c_Groups_Ozero__class_Ozero(X3098)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),c_Groups_Ozero__class_Ozero(X3098)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),c_Groups_Ozero__class_Ozero(X3098)),X3095))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3098),X3096),X3095)))|~class_Fields_Olinordered__field__inverse__zero(X3098)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),c_Groups_Ozero__class_Ozero(X3098)),X3095))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3098),X3097),X3095)),X3096))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3098),X3097),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3098),X3096),X3095)))|~class_Fields_Olinordered__field__inverse__zero(X3098)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__divide__eq])])])])). 4.05/4.30 fof(c_0_7135, plain, ![X375, X376, X377, X378]:((((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),c_Groups_Ozero__class_Ozero(X378)),X375))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),c_Groups_Ozero__class_Ozero(X378)),X375))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X378),X376),X375)))|~class_Fields_Olinordered__field__inverse__zero(X378))&(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),X375),c_Groups_Ozero__class_Ozero(X378)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),X375),c_Groups_Ozero__class_Ozero(X378)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),c_Groups_Ozero__class_Ozero(X378)),X375))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X378),X376),X375)))|~class_Fields_Olinordered__field__inverse__zero(X378))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),c_Groups_Ozero__class_Ozero(X378)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),X375),c_Groups_Ozero__class_Ozero(X378)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),c_Groups_Ozero__class_Ozero(X378)),X375))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X378),X376),X375)))|~class_Fields_Olinordered__field__inverse__zero(X378)))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),X375),c_Groups_Ozero__class_Ozero(X378)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X378),X377),X375)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),c_Groups_Ozero__class_Ozero(X378)),X375))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X378),X376),X375)))|~class_Fields_Olinordered__field__inverse__zero(X378))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),c_Groups_Ozero__class_Ozero(X378)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X378),X377),X375)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),c_Groups_Ozero__class_Ozero(X378)),X375))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X378),X376),X375)))|~class_Fields_Olinordered__field__inverse__zero(X378)))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),c_Groups_Ozero__class_Ozero(X378)),X375))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X378),X377),X375)),X376))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X378),X376),X375)))|~class_Fields_Olinordered__field__inverse__zero(X378))&(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),X375),c_Groups_Ozero__class_Ozero(X378)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),X375),c_Groups_Ozero__class_Ozero(X378)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X378),X377),X375)),X376))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X378),X376),X375)))|~class_Fields_Olinordered__field__inverse__zero(X378))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),c_Groups_Ozero__class_Ozero(X378)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),X375),c_Groups_Ozero__class_Ozero(X378)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X378),X377),X375)),X376))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X378),X376),X375)))|~class_Fields_Olinordered__field__inverse__zero(X378)))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),X375),c_Groups_Ozero__class_Ozero(X378)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X378),X377),X375)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X378),X377),X375)),X376))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X378),X376),X375)))|~class_Fields_Olinordered__field__inverse__zero(X378))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),c_Groups_Ozero__class_Ozero(X378)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X378),X377),X375)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X378),X377),X375)),X376))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X378),X376),X375)))|~class_Fields_Olinordered__field__inverse__zero(X378))))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),c_Groups_Ozero__class_Ozero(X378)),X375))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X378),X377),X375)),X376))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X378),X376),X375)))|~class_Fields_Olinordered__field__inverse__zero(X378))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),X375),c_Groups_Ozero__class_Ozero(X378)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X378),X377),X375)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),c_Groups_Ozero__class_Ozero(X378)),X375))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X378),X376),X375)))|~class_Fields_Olinordered__field__inverse__zero(X378))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),X375),c_Groups_Ozero__class_Ozero(X378)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),c_Groups_Ozero__class_Ozero(X378)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X378),c_Groups_Ozero__class_Ozero(X378)),X375))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X378),X377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X378),X376),X375)))|~class_Fields_Olinordered__field__inverse__zero(X378))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__divide__eq])])])])). 4.05/4.30 cnf(c_0_7136, 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_5162])). 4.05/4.30 fof(c_0_7137, plain, ![X11353, X11354, X11355]:(~class_Groups_Oordered__ab__group__add__abs(X11355)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11355),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X11355),hAPP(c_Groups_Oabs__class_Oabs(X11355),X11354)),hAPP(c_Groups_Oabs__class_Oabs(X11355),X11353))),hAPP(c_Groups_Oabs__class_Oabs(X11355),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X11355),X11354),X11353))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2])])). 4.05/4.30 fof(c_0_7138, plain, ![X4025, X4026, X4027]:(~class_Groups_Oordered__ab__group__add__abs(X4027)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4027),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4027),hAPP(c_Groups_Oabs__class_Oabs(X4027),X4026)),hAPP(c_Groups_Oabs__class_Oabs(X4027),X4025))),hAPP(c_Groups_Oabs__class_Oabs(X4027),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4027),X4025),X4026))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym])])). 4.05/4.30 fof(c_0_7139, plain, ![X2969, X2970, X2971]:(~class_Groups_Oordered__ab__group__add__abs(X2971)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2971),hAPP(c_Groups_Oabs__class_Oabs(X2971),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2971),X2970),X2969))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2971),hAPP(c_Groups_Oabs__class_Oabs(X2971),X2970)),hAPP(c_Groups_Oabs__class_Oabs(X2971),X2969))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__triangle__ineq4])])])). 4.05/4.30 fof(c_0_7140, plain, ![X8541, X8542, X8543, X8544, X8545, X8547, X8548, X8549, X8550, X8551, X8552]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X8543,X8545)),hAPP(hAPP(c_Product__Type_OPair(X8543,X8545),esk273_5(X8541,X8542,X8543,X8544,X8545)),X8544)),X8542))|~hBOOL(hAPP(hAPP(c_member(X8545),X8544),hAPP(c_Relation_OImage(X8543,X8545,X8542),X8541))))&(hBOOL(hAPP(hAPP(c_member(X8543),esk273_5(X8541,X8542,X8543,X8544,X8545)),X8541))|~hBOOL(hAPP(hAPP(c_member(X8545),X8544),hAPP(c_Relation_OImage(X8543,X8545,X8542),X8541)))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X8549,X8551)),hAPP(hAPP(c_Product__Type_OPair(X8549,X8551),X8552),X8550)),X8548))|~hBOOL(hAPP(hAPP(c_member(X8549),X8552),X8547))|hBOOL(hAPP(hAPP(c_member(X8551),X8550),hAPP(c_Relation_OImage(X8549,X8551,X8548),X8547))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__iff])])])])])])). 4.05/4.30 fof(c_0_7141, plain, ![X5710, X5711, X5712]:(~class_Groups_Oordered__ab__group__add__abs(X5712)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5712),hAPP(c_Groups_Oabs__class_Oabs(X5712),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5712),X5711),X5710))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5712),hAPP(c_Groups_Oabs__class_Oabs(X5712),X5711)),hAPP(c_Groups_Oabs__class_Oabs(X5712),X5710))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__triangle__ineq])])])). 4.05/4.30 fof(c_0_7142, plain, ![X16173, X16174, X16175, X16176, X16177]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X16177,X16176)),hAPP(X16177,X16175)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X16174,X16174)),hAPP(hAPP(c_Product__Type_OPair(X16174,X16174),X16176),X16175)),c_Wellfounded_Omlex__prod(X16174,X16177,X16173)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mlex__less])])])). 4.05/4.30 cnf(c_0_7143, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5282, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_7144, plain, ![X7381, X7382, X7383, X7384, X7385]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X7383,X7385)),hAPP(hAPP(c_Product__Type_OPair(X7383,X7385),esk233_5(X7381,X7382,X7383,X7384,X7385)),X7384)),X7382))|~hBOOL(hAPP(hAPP(c_member(X7385),X7384),hAPP(c_Relation_OImage(X7383,X7385,X7382),X7381))))&(hBOOL(hAPP(hAPP(c_member(X7383),esk233_5(X7381,X7382,X7383,X7384,X7385)),X7381))|~hBOOL(hAPP(hAPP(c_member(X7385),X7384),hAPP(c_Relation_OImage(X7383,X7385,X7382),X7381))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ImageE])])])])])). 4.05/4.30 fof(c_0_7145, plain, ![X6749, X6750, X6751, X6752, X6753, X6754, X6755]:(~hBOOL(hAPP(hAPP(c_member(X6755),X6754),X6753))|(~c_Nitpick_Ofold__graph_H(X6755,X6752,X6751,X6750,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6755,tc_HOL_Obool)),X6753),hAPP(hAPP(c_Set_Oinsert(X6755),X6754),c_Orderings_Obot__class_Obot(tc_fun(X6755,tc_HOL_Obool)))),X6749)|c_Nitpick_Ofold__graph_H(X6755,X6752,X6751,X6750,X6753,hAPP(hAPP(X6751,X6754),X6749)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold__graph_H_Ointros_I2_J])])])). 4.05/4.30 fof(c_0_7146, plain, ![X1991, X1992, X1993, X1994, X1995, X1996]:(~c_Finite__Set_Ofolding(X1996,X1995,X1994,X1993)|hAPP(c_Fun_Ocomp(X1995,X1995,X1995,hAPP(X1994,X1991)),hAPP(X1994,X1992))=hAPP(c_Fun_Ocomp(X1995,X1995,X1995,hAPP(X1994,X1992)),hAPP(X1994,X1991))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Ocommute__comp])])])). 4.05/4.30 cnf(c_0_7147, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5283, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_7148, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5284, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_7149, plain, ![X2403, X2404, X2405, X2406, X2407]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk86_5(X2403,X2404,X2405,X2406,X2407)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2407)),X2406)))|c_List_Olist__all2(X2407,X2405,X2403,X2406,X2404)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2407)),X2406)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2405)),X2404))&(~hBOOL(hAPP(hAPP(X2403,hAPP(hAPP(c_List_Onth(X2407),X2406),esk86_5(X2403,X2404,X2405,X2406,X2407))),hAPP(hAPP(c_List_Onth(X2405),X2404),esk86_5(X2403,X2404,X2405,X2406,X2407))))|c_List_Olist__all2(X2407,X2405,X2403,X2406,X2404)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2407)),X2406)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2405)),X2404))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2__all__nthI])])])])])). 4.05/4.30 fof(c_0_7150, plain, ![X14536, X14537, X14538, X14539, X14540, X14541, X14542, X14543, X14544, X14545, X14546]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14541),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14540)),X14537)))|hBOOL(hAPP(hAPP(X14538,hAPP(hAPP(c_List_Onth(X14540),X14537),X14541)),hAPP(hAPP(c_List_Onth(X14539),X14536),X14541)))|~c_List_Olist__all2(X14540,X14539,X14538,X14537,X14536))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14540)),X14537)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14539)),X14536)|~c_List_Olist__all2(X14540,X14539,X14538,X14537,X14536)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk442_5(X14542,X14543,X14544,X14545,X14546)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14546)),X14543)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14546)),X14543)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14545)),X14542)|c_List_Olist__all2(X14546,X14545,X14544,X14543,X14542))&(~hBOOL(hAPP(hAPP(X14544,hAPP(hAPP(c_List_Onth(X14546),X14543),esk442_5(X14542,X14543,X14544,X14545,X14546))),hAPP(hAPP(c_List_Onth(X14545),X14542),esk442_5(X14542,X14543,X14544,X14545,X14546))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14546)),X14543)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14545)),X14542)|c_List_Olist__all2(X14546,X14545,X14544,X14543,X14542)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__conv__all__nth])])])])])])). 4.05/4.30 cnf(c_0_7151, 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_5285, c_0_4519]), c_0_4519])). 4.05/4.30 fof(c_0_7152, plain, ![X13299, X13300, X13301, X13302]:((~hBOOL(hAPP(hAPP(c_member(X13302),X13301),X13300))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13302,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X13302),X13301),X13299)),X13300)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13302,tc_HOL_Obool)),X13299),X13300))&(hBOOL(hAPP(hAPP(c_member(X13302),X13301),X13300))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13302,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X13302),X13301),X13299)),X13300)=hAPP(hAPP(c_Set_Oinsert(X13302),X13301),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13302,tc_HOL_Obool)),X13299),X13300)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__Diff__if])])])). 4.05/4.30 cnf(c_0_7153, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5286, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_7154, plain, ![X717, X718, X719]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X719),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X718)),X717)))|hAPP(hAPP(c_List_Olist_OCons(X718),hAPP(hAPP(c_List_Onth(X718),X717),X719)),hAPP(hAPP(c_List_Odrop(X718),hAPP(c_Nat_OSuc,X719)),X717))=hAPP(hAPP(c_List_Odrop(X718),X719),X717)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__drop_H])])])). 4.05/4.30 fof(c_0_7155, plain, ![X9934, X9935, X9936, X9937, X9938, X9939]:(~c_Fun_Oinj__on(X9939,X9938,X9937,X9936)|(~hBOOL(hAPP(hAPP(c_member(X9938),X9935),hAPP(c_Set_Oimage(X9939,X9938,X9937),X9936)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9939,tc_HOL_Obool)),X9936),X9934))|hBOOL(hAPP(hAPP(c_member(X9939),hAPP(c_Fun_Othe__inv__into(X9939,X9938,X9936,X9937),X9935)),X9934))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_the__inv__into__into])])])). 4.05/4.30 fof(c_0_7156, plain, ![X12105, X12106, X12107]:(~c_Wellfounded_Owf(X12107,X12106)|(~c_Wellfounded_Owf(X12107,X12105)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X12107,X12107),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X12107,X12107,X12107),X12106),X12105)),X12106))|c_Wellfounded_Owf(X12107,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X12107,X12107),tc_HOL_Obool)),X12106),X12105))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__union__compatible])])])). 4.05/4.30 cnf(c_0_7157, 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),c_Transitive__Closure_Ortrancl(X1,X4)),X4)))), inference(rw,[status(thm)],[c_0_5287, c_0_5018])). 4.05/4.30 fof(c_0_7158, plain, ![X12666, X12667, X12668, X12669]:(~c_Fun_Oinj__on(X12669,X12668,X12667,c_Orderings_Otop__class_Otop(tc_fun(X12669,tc_HOL_Obool)))|c_Fun_Oinj__on(X12669,tc_fun(X12666,X12668),hAPP(hAPP(c_COMBB(X12668,tc_fun(X12666,X12668),X12669),c_COMBK(X12668,X12666)),X12667),c_Orderings_Otop__class_Otop(tc_fun(X12669,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__fun])])). 4.05/4.30 cnf(c_0_7159, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),esk173_3(X3,X2,X1))),esk174_3(X3,X2,X1))=X2|hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5288])). 4.05/4.30 fof(c_0_7160, plain, ![X7617, X7618, X7619, X7620, X7621, X7622, X7623, X7624, X7625, X7626, X7627, X7628, X7629, X7630, X7631]:((~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7623,tc_fun(X7622,tc_fun(X7621,tc_HOL_Obool))),X7620),X7619),X7618),X7617))|(~hBOOL(hAPP(hAPP(c_member(X7623),X7624),X7620))|hBOOL(hAPP(hAPP(hAPP(X7619,X7624),X7618),X7617))))&((hBOOL(hAPP(hAPP(c_member(X7631),esk243_7(X7625,X7626,X7627,X7628,X7629,X7630,X7631)),X7628))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7631,tc_fun(X7630,tc_fun(X7629,tc_HOL_Obool))),X7628),X7627),X7626),X7625)))&(~hBOOL(hAPP(hAPP(hAPP(X7627,esk243_7(X7625,X7626,X7627,X7628,X7629,X7630,X7631)),X7626),X7625))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7631,tc_fun(X7630,tc_fun(X7629,tc_HOL_Obool))),X7628),X7627),X7626),X7625))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF2__iff])])])])])])). 4.05/4.30 cnf(c_0_7161, plain, (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(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),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),X4)),X2)!=X3), inference(split_conjunct,[status(thm)],[c_0_5227])). 4.05/4.30 fof(c_0_7162, plain, ![X14206, X14207, X14208, X14209, X14210, X14211]:(hBOOL(hAPP(hAPP(c_member(X14211),X14210),hAPP(c_List_Oset(X14211),X14209)))|hAPP(hAPP(c_List_Omap(X14211,X14208),X14207),X14209)=hAPP(hAPP(c_List_Omap(X14211,X14208),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X14211,X14208),X14207),X14210),X14206)),X14209)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__fun__upd])])])). 4.05/4.30 fof(c_0_7163, plain, ![X14003, X14004, X14005]:(~class_Groups_Oab__semigroup__mult(X14005)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14005),X14004))|(hBOOL(hAPP(hAPP(c_member(X14005),X14003),X14004))|hAPP(hAPP(c_Finite__Set_Ofold(X14005,X14005,c_Groups_Otimes__class_Otimes(X14005)),X14003),X14004)=hAPP(c_Finite__Set_Ofold1(X14005,c_Groups_Otimes__class_Otimes(X14005)),hAPP(hAPP(c_Set_Oinsert(X14005),X14003),X14004))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__eq__fold])])])). 4.05/4.30 fof(c_0_7164, plain, ![X4824, X4825, X4826, X4827]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4827)),X4826)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4825)),X4824)|hAPP(c_List_Orev(tc_prod(X4827,X4825)),hAPP(hAPP(c_List_Ozip(X4827,X4825),X4826),X4824))=hAPP(hAPP(c_List_Ozip(X4827,X4825),hAPP(c_List_Orev(X4827),X4826)),hAPP(c_List_Orev(X4825),X4824))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zip__rev])])])). 4.05/4.30 cnf(c_0_7165, 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_5289])). 4.05/4.30 fof(c_0_7166, plain, ![X17063, X17064, X17065, X17066]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X17066|c_List_Olist_ONil(X17065)=hAPP(hAPP(c_List_Otake(X17065),X17066),hAPP(hAPP(c_List_Olist_OCons(X17065),X17064),X17063)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X17066|hAPP(hAPP(c_List_Olist_OCons(X17065),X17064),hAPP(hAPP(c_List_Otake(X17065),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17066),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X17063))=hAPP(hAPP(c_List_Otake(X17065),X17066),hAPP(hAPP(c_List_Olist_OCons(X17065),X17064),X17063)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_take__Cons_H])])])). 4.05/4.30 fof(c_0_7167, plain, ![X16597, X16598, X16599, X16600, X16601, X16602]:(~hBOOL(hAPP(hAPP(c_member(X16602),X16601),X16600))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X16602,X16599)),hAPP(hAPP(c_Product__Type_OPair(X16602,X16599),X16601),X16598)),X16597))|hBOOL(hAPP(hAPP(c_member(X16599),X16598),hAPP(c_Relation_OImage(X16602,X16599,X16597),X16600))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__ImageI])])). 4.05/4.30 cnf(c_0_7168, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),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)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_5290])). 4.05/4.30 fof(c_0_7169, plain, ![X12372, X12373, X12374, X12375]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12375,tc_HOL_Obool)),X12374),X12373))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12375,tc_HOL_Obool)),X12373),X12372))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12375,tc_HOL_Obool)),X12373),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12375,tc_HOL_Obool)),X12372),X12374))=X12374)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__diff])])). 4.05/4.30 cnf(c_0_7170, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),X1))), inference(rw,[status(thm)],[c_0_5291, c_0_4475])). 4.05/4.30 cnf(c_0_7171, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),X1))), inference(rw,[status(thm)],[c_0_5292, c_0_4475])). 4.05/4.30 cnf(c_0_7172, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))), inference(rw,[status(thm)],[c_0_5293, c_0_4475])). 4.05/4.30 cnf(c_0_7173, plain, (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),X1),esk173_3(X1,X2,X3))),esk174_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_5288])). 4.05/4.30 fof(c_0_7174, plain, ![X10865, X10866, X10867, X10868, X10869]:(~c_Finite__Set_Ofun__left__comm(X10869,X10868,X10867)|hAPP(c_Fun_Ocomp(X10868,X10868,X10868,hAPP(X10867,X10866)),hAPP(X10867,X10865))=hAPP(c_Fun_Ocomp(X10868,X10868,X10868,hAPP(X10867,X10865)),hAPP(X10867,X10866))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__comp__comm])])). 4.05/4.30 fof(c_0_7175, plain, ![X4242, X4243, X4244, X4245, X4246]:(~c_Relation_Orefl__on(X4246,X4245,X4244)|(~c_Relation_Orefl__on(X4246,X4243,X4242)|c_Relation_Orefl__on(X4246,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4246,tc_HOL_Obool)),X4245),X4243),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4246,X4246),tc_HOL_Obool)),X4244),X4242)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__on__Int])])])). 4.05/4.30 fof(c_0_7176, plain, ![X5026, X5027, X5028, X5029, X5030]:(~c_Relation_Orefl__on(X5030,X5029,X5028)|(~c_Relation_Orefl__on(X5030,X5027,X5026)|c_Relation_Orefl__on(X5030,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5030,tc_HOL_Obool)),X5029),X5027),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5030,X5030),tc_HOL_Obool)),X5028),X5026)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__on__Un])])])). 4.05/4.30 cnf(c_0_7177, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))), inference(rw,[status(thm)],[c_0_5294, c_0_4475])). 4.05/4.30 fof(c_0_7178, plain, ![X14268, X14269, X14270, X14271]:((hBOOL(hAPP(hAPP(c_member(X14271),X14270),X14269))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14271,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X14271),X14270),X14268)),X14269)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14271,tc_HOL_Obool)),X14268),X14269))&(~hBOOL(hAPP(hAPP(c_member(X14271),X14270),X14269))|hAPP(hAPP(c_Set_Oinsert(X14271),X14270),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14271,tc_HOL_Obool)),X14268),X14269))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14271,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X14271),X14270),X14268)),X14269))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__insert__left])])])). 4.05/4.30 fof(c_0_7179, plain, ![X4581, X4582, X4583, X4584]:(~class_Enum_Oenum(X4584)|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4583)),X4582)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4584)),c_Enum_Oenum__class_Oenum(X4584))|hAPP(hAPP(c_Map_Omap__of(X4584,X4583),hAPP(hAPP(c_List_Ozip(X4584,X4583),c_Enum_Oenum__class_Oenum(X4584)),X4582)),X4581)=hAPP(c_Option_Ooption_OSome(X4583),esk143_4(X4581,X4582,X4583,X4584)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__zip__enum__is__Some])])])])). 4.05/4.30 fof(c_0_7180, plain, ![X6588, X6589, X6590, X6591, X6592]:((hBOOL(hAPP(hAPP(c_member(X6592),esk200_5(X6588,X6589,X6590,X6591,X6592)),X6589))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6592,X6591)),X6590),hAPP(hAPP(c_Product__Type_OSigma(X6592,X6591),X6589),X6588))))&((hBOOL(hAPP(hAPP(c_member(X6591),esk201_5(X6588,X6589,X6590,X6591,X6592)),hAPP(X6588,esk200_5(X6588,X6589,X6590,X6591,X6592))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6592,X6591)),X6590),hAPP(hAPP(c_Product__Type_OSigma(X6592,X6591),X6589),X6588))))&(hAPP(hAPP(c_Product__Type_OPair(X6592,X6591),esk200_5(X6588,X6589,X6590,X6591,X6592)),esk201_5(X6588,X6589,X6590,X6591,X6592))=X6590|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6592,X6591)),X6590),hAPP(hAPP(c_Product__Type_OSigma(X6592,X6591),X6589),X6588)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SigmaE])])])])])). 4.05/4.30 fof(c_0_7181, plain, ![X2144, X2145, X2146, X2150, X2151, X2152, X2153, X2154, X2155]:(((hBOOL(hAPP(hAPP(c_member(tc_prod(X2146,X2145)),hAPP(hAPP(c_Product__Type_OPair(X2146,X2145),esk78_3(X2144,X2145,X2146)),esk79_3(X2144,X2145,X2146))),X2144))|c_Relation_Osingle__valued(X2146,X2145,X2144))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X2146,X2145)),hAPP(hAPP(c_Product__Type_OPair(X2146,X2145),esk78_3(X2144,X2145,X2146)),esk80_3(X2144,X2145,X2146))),X2144))|c_Relation_Osingle__valued(X2146,X2145,X2144))&(esk79_3(X2144,X2145,X2146)!=esk80_3(X2144,X2145,X2146)|c_Relation_Osingle__valued(X2146,X2145,X2144))))&(~c_Relation_Osingle__valued(X2152,X2151,X2150)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X2152,X2151)),hAPP(hAPP(c_Product__Type_OPair(X2152,X2151),X2153),X2154)),X2150))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X2152,X2151)),hAPP(hAPP(c_Product__Type_OPair(X2152,X2151),X2153),X2155)),X2150))|X2154=X2155)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_single__valued__def])])])])])])])). 4.05/4.30 fof(c_0_7182, plain, ![X7843, X7844, X7845, X7846]:(~class_Orderings_Olinorder(X7846)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7846),X7845),X7844))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7846),X7844),X7843))|c_SetInterval_Oord__class_OgreaterThanLessThan(X7846,X7845,X7843)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7846,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7846,X7845,X7844)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X7846,X7844),X7843))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I15_J])])])). 4.05/4.30 fof(c_0_7183, plain, ![X10186, X10187, X10188, X10189]:(~class_Orderings_Olinorder(X10189)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10189),X10188),X10187))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10189),X10187),X10186))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10189,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10189,X10188),X10187)),c_SetInterval_Oord__class_OatLeastAtMost(X10189,X10187,X10186))=c_SetInterval_Oord__class_OatLeastAtMost(X10189,X10188,X10186)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I21_J])])])). 4.05/4.30 fof(c_0_7184, plain, ![X5145, X5146, X5147, X5148, X5149, X5150, X5151]:(~c_Finite__Set_Ofolding__idem(X5151,X5150,X5149,X5148)|hAPP(c_Fun_Ocomp(X5150,X5150,X5147,hAPP(X5149,X5146)),hAPP(c_Fun_Ocomp(X5150,X5150,X5147,hAPP(X5149,X5146)),X5145))=hAPP(c_Fun_Ocomp(X5150,X5150,X5147,hAPP(X5149,X5146)),X5145)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__left__comp])])). 4.05/4.30 fof(c_0_7185, plain, ![X14143, X14144, X14145]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14145),hAPP(c_Int_Onumber__class_Onumber__of(X14145),X14144)),hAPP(c_Int_Onumber__class_Onumber__of(X14145),X14143)))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X14145),hAPP(c_Int_Onumber__class_Onumber__of(X14145),X14144)),hAPP(c_Int_Onumber__class_Onumber__of(X14145),X14143))=hAPP(c_Int_Onumber__class_Onumber__of(X14145),X14143)|(~class_Orderings_Oord(X14145)|~class_Int_Onumber(X14145)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14145),hAPP(c_Int_Onumber__class_Onumber__of(X14145),X14144)),hAPP(c_Int_Onumber__class_Onumber__of(X14145),X14143)))|hAPP(c_Int_Onumber__class_Onumber__of(X14145),X14144)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X14145),hAPP(c_Int_Onumber__class_Onumber__of(X14145),X14144)),hAPP(c_Int_Onumber__class_Onumber__of(X14145),X14143))|(~class_Orderings_Oord(X14145)|~class_Int_Onumber(X14145)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__number__of])])])])). 4.05/4.30 cnf(c_0_7186, plain, (hBOOL(hAPP(X5,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),X2)!=X4|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X5,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1)))), inference(split_conjunct,[status(thm)],[c_0_5096])). 4.05/4.30 cnf(c_0_7187, plain, (hBOOL(hAPP(X5,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),X2)!=X4|~hBOOL(hAPP(X5,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1)))), inference(split_conjunct,[status(thm)],[c_0_5096])). 4.05/4.30 fof(c_0_7188, plain, ![X13618, X13619, X13620]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13620),hAPP(c_Int_Onumber__class_Onumber__of(X13620),X13619)),hAPP(c_Int_Onumber__class_Onumber__of(X13620),X13618)))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X13620),hAPP(c_Int_Onumber__class_Onumber__of(X13620),X13619)),hAPP(c_Int_Onumber__class_Onumber__of(X13620),X13618))=hAPP(c_Int_Onumber__class_Onumber__of(X13620),X13619)|(~class_Orderings_Oord(X13620)|~class_Int_Onumber(X13620)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13620),hAPP(c_Int_Onumber__class_Onumber__of(X13620),X13619)),hAPP(c_Int_Onumber__class_Onumber__of(X13620),X13618)))|hAPP(c_Int_Onumber__class_Onumber__of(X13620),X13618)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X13620),hAPP(c_Int_Onumber__class_Onumber__of(X13620),X13619)),hAPP(c_Int_Onumber__class_Onumber__of(X13620),X13618))|(~class_Orderings_Oord(X13620)|~class_Int_Onumber(X13620)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_max__number__of])])])])). 4.05/4.30 fof(c_0_7189, plain, ![X12285, X12286, X12287]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12287))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12286))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12286),X12285))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12287),X12285)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12287),X12286)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono2])])])). 4.05/4.30 fof(c_0_7190, plain, ![X7198, X7199, X7200, X7201, X7202]:((hBOOL(hAPP(hAPP(c_member(X7201),esk224_5(X7198,X7199,X7200,X7201,X7202)),hAPP(c_List_Oset(X7201),X7200)))|hAPP(hAPP(c_List_Olist_OCons(X7201),X7198),X7200)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7201,X7202,X7199),X7198),X7200)|~class_Orderings_Olinorder(X7202))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7202),hAPP(X7199,X7198)),hAPP(X7199,esk224_5(X7198,X7199,X7200,X7201,X7202))))|hAPP(hAPP(c_List_Olist_OCons(X7201),X7198),X7200)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X7201,X7202,X7199),X7198),X7200)|~class_Orderings_Olinorder(X7202))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__is__Cons])])])])])). 4.05/4.30 fof(c_0_7191, plain, ![X868, X869, X872, X874, X875, X876, X877, X879]:(((hBOOL(hAPP(hAPP(c_member(X869),esk18_2(X868,X869)),esk17_2(X868,X869)))|c_Wellfounded_Owf(X869,X868))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X869,X869)),hAPP(hAPP(c_Product__Type_OPair(X869,X869),esk19_3(X868,X869,X872)),X872)),X868))|~hBOOL(hAPP(hAPP(c_member(X869),X872),esk17_2(X868,X869)))|c_Wellfounded_Owf(X869,X868))&(hBOOL(hAPP(hAPP(c_member(X869),esk19_3(X868,X869,X872)),esk17_2(X868,X869)))|~hBOOL(hAPP(hAPP(c_member(X869),X872),esk17_2(X868,X869)))|c_Wellfounded_Owf(X869,X868))))&((~hBOOL(hAPP(hAPP(c_member(tc_prod(X875,X875)),hAPP(hAPP(c_Product__Type_OPair(X875,X875),X879),esk20_3(X874,X875,X876))),X874))|~hBOOL(hAPP(hAPP(c_member(X875),X879),X876))|~hBOOL(hAPP(hAPP(c_member(X875),X877),X876))|~c_Wellfounded_Owf(X875,X874))&(hBOOL(hAPP(hAPP(c_member(X875),esk20_3(X874,X875,X876)),X876))|~hBOOL(hAPP(hAPP(c_member(X875),X877),X876))|~c_Wellfounded_Owf(X875,X874)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__eq__minimal])])])])])])])). 4.05/4.30 fof(c_0_7192, plain, ![X4948, X4949, X4950, X4951]:(~class_Rings_Osemiring__1(X4951)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4951),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4951),hAPP(c_Finite__Set_Ocard(X4950),X4948))),X4949)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4950,X4951),hAPP(c_COMBK(X4951,X4950),X4949)),X4948)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__constant])])). 4.05/4.30 fof(c_0_7193, plain, ![X14065, X14066, X14067]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14067),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)),X14066))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14066),X14065))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14067),X14066)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14067),X14065)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono2__neg])])])). 4.05/4.30 fof(c_0_7194, plain, ![X13530, X13531, X13532, X13533]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13533),X13532))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13531),X13530))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X13533,X13531)),hAPP(hAPP(c_Product__Type_OSigma(X13533,X13531),X13532),hAPP(c_COMBK(tc_fun(X13531,tc_HOL_Obool),X13533),X13530)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__cartesian__product])])])). 4.05/4.30 fof(c_0_7195, plain, ![X1958, X1959, X1960, X1961, X1962, X1963, X1964, X1965]:(~hBOOL(hAPP(hAPP(c_member(X1965),X1964),X1963))|(~hBOOL(hAPP(hAPP(hAPP(X1962,X1964),X1961),X1960))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1965,tc_fun(X1959,tc_fun(X1958,tc_HOL_Obool))),X1963),X1962),X1961),X1960)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUP2__I])])])). 4.05/4.30 fof(c_0_7196, plain, ![X7654, X7655, X7656, X7657, X7658, X7659]:(~c_Finite__Set_Ofolding__idem(X7659,X7658,X7657,X7656)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7659),X7655))|hAPP(X7656,hAPP(hAPP(c_Set_Oinsert(X7659),X7654),X7655))=hAPP(c_Fun_Ocomp(X7658,X7658,X7658,hAPP(X7656,X7655)),hAPP(X7657,X7654)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__idem_Oinsert__idem])])])). 4.05/4.30 fof(c_0_7197, plain, ![X8394, X8395, X8396, X8398, X8399]:((((hBOOL(hAPP(hAPP(c_member(X8396),esk267_3(X8394,X8395,X8396)),X8395))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8396,tc_Nat_Onat),X8394),X8395)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8396),X8395)))&(~hBOOL(hAPP(hAPP(c_member(X8396),X8398),X8395))|(X8398=esk267_3(X8394,X8395,X8396)|hAPP(X8394,X8398)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8396,tc_Nat_Onat),X8394),X8395)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8396),X8395))))&(c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(X8394,esk267_3(X8394,X8395,X8396))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8396,tc_Nat_Onat),X8394),X8395)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8396),X8395))))&((hBOOL(hAPP(hAPP(c_member(X8396),esk268_4(X8394,X8395,X8396,X8399)),X8395))|~hBOOL(hAPP(hAPP(c_member(X8396),X8399),X8395))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X8394,X8399)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8396,tc_Nat_Onat),X8394),X8395)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8396),X8395)))&((esk268_4(X8394,X8395,X8396,X8399)!=X8399|~hBOOL(hAPP(hAPP(c_member(X8396),X8399),X8395))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X8394,X8399)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8396,tc_Nat_Onat),X8394),X8395)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8396),X8395)))&(hAPP(X8394,esk268_4(X8394,X8395,X8396,X8399))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X8396),X8399),X8395))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X8394,X8399)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8396,tc_Nat_Onat),X8394),X8395)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8396),X8395)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__eq__1__iff])])])])])])). 4.05/4.30 fof(c_0_7198, plain, ![X2726, X2727, X2728]:(~class_Divides_Osemiring__div(X2728)|(c_Groups_Ozero__class_Ozero(X2728)=X2727|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2728),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2728),X2726),X2727)),c_Groups_Oone__class_Oone(X2728))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2728),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2728),X2727),X2726)),X2727))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__add__self1])])])). 4.05/4.30 cnf(c_0_7199, 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_5084])). 4.05/4.30 fof(c_0_7200, plain, ![X14362, X14363, X14364, X14365]:((hBOOL(hAPP(hAPP(c_member(X14364),esk439_4(X14362,X14363,X14364,X14365)),hAPP(c_List_Oset(X14364),X14363)))|hBOOL(hAPP(X14362,hAPP(hAPP(c_List_Onth(X14364),X14363),X14365)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14365),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14364)),X14363))))&(~hBOOL(hAPP(X14362,esk439_4(X14362,X14363,X14364,X14365)))|hBOOL(hAPP(X14362,hAPP(hAPP(c_List_Onth(X14364),X14363),X14365)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14365),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14364)),X14363))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__ball__nth])])])])])). 4.05/4.30 cnf(c_0_7201, 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_5295])). 4.05/4.30 fof(c_0_7202, plain, ![X5968, X5969, X5970]:(~class_Int_Onumber__ring(X5970)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5970),hAPP(c_Int_Onumber__class_Onumber__of(X5970),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5969))),X5968)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5970),hAPP(c_Groups_Ouminus__class_Ouminus(X5970),hAPP(c_Int_Onumber__class_Onumber__of(X5970),X5969))),X5968)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__number__of__mult])])). 4.05/4.30 cnf(c_0_7203, 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_5296])). 4.05/4.30 fof(c_0_7204, plain, ![X467, X468, X469, X470, X471]:((hBOOL(hAPP(hAPP(c_member(X470),esk7_5(X467,X468,X469,X470,X471)),X469))|(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X470,X471),X468),X469)!=c_Groups_Ozero__class_Ozero(X471)|(~hBOOL(hAPP(hAPP(c_member(X470),X467),X469))|c_Groups_Ozero__class_Ozero(X471)=hAPP(X468,X467)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X470),X469))|~class_Groups_Oordered__ab__group__add(X471))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X471),c_Groups_Ozero__class_Ozero(X471)),hAPP(X468,esk7_5(X467,X468,X469,X470,X471))))|(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X470,X471),X468),X469)!=c_Groups_Ozero__class_Ozero(X471)|(~hBOOL(hAPP(hAPP(c_member(X470),X467),X469))|c_Groups_Ozero__class_Ozero(X471)=hAPP(X468,X467)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X470),X469))|~class_Groups_Oordered__ab__group__add(X471))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__nonneg__0])])])])])). 4.05/4.30 fof(c_0_7205, plain, ![X7907, X7908, X7909, X7910, X7911]:(c_Option_Ooption_ONone(X7909)!=hAPP(X7911,X7910)|hAPP(hAPP(c_Set_Oinsert(X7909),X7907),c_Map_Oran(X7908,X7909,X7911))=c_Map_Oran(X7908,X7909,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7908,tc_Option_Ooption(X7909)),X7911),X7910),hAPP(c_Option_Ooption_OSome(X7909),X7907)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ran__map__upd])])])). 4.05/4.30 fof(c_0_7206, plain, ![X12391, X12392, X12393]:(~class_Divides_Osemiring__div(X12393)|(X12392=c_Groups_Ozero__class_Ozero(X12393)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12393),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X12393),X12391),X12392)),c_Groups_Oone__class_Oone(X12393))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X12393),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12393),X12391),X12392)),X12392))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__add__self2])])])). 4.05/4.30 fof(c_0_7207, plain, ![X9963, X9964, X9965, X9966, X9967, X9969]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9967),hAPP(X9964,esk306_5(X9963,X9964,X9965,X9966,X9967))),X9963))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9967),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9966,X9967),X9965),X9964)),X9963))|(~class_Complete__Lattice_Ocomplete__lattice(X9967)|~class_Orderings_Olinorder(X9967)))&(hBOOL(hAPP(hAPP(c_member(X9966),esk306_5(X9963,X9964,X9965,X9966,X9967)),X9965))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9967),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9966,X9967),X9965),X9964)),X9963))|(~class_Complete__Lattice_Ocomplete__lattice(X9967)|~class_Orderings_Olinorder(X9967))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9967),hAPP(X9964,X9969)),X9963))|~hBOOL(hAPP(hAPP(c_member(X9966),X9969),X9965))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9967),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9966,X9967),X9965),X9964)),X9963))|(~class_Complete__Lattice_Ocomplete__lattice(X9967)|~class_Orderings_Olinorder(X9967)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF__less__iff])])])])])])). 4.05/4.30 fof(c_0_7208, plain, ![X3949, X3950, X3951, X3952, X3953, X3955]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3953),X3952),hAPP(X3949,esk122_5(X3949,X3950,X3951,X3952,X3953))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3953),X3952),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3951,X3953),X3950),X3949)))|(~class_Orderings_Olinorder(X3953)|~class_Complete__Lattice_Ocomplete__lattice(X3953)))&(hBOOL(hAPP(hAPP(c_member(X3951),esk122_5(X3949,X3950,X3951,X3952,X3953)),X3950))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3953),X3952),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3951,X3953),X3950),X3949)))|(~class_Orderings_Olinorder(X3953)|~class_Complete__Lattice_Ocomplete__lattice(X3953))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3953),X3952),hAPP(X3949,X3955)))|~hBOOL(hAPP(hAPP(c_member(X3951),X3955),X3950))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3953),X3952),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3951,X3953),X3950),X3949)))|(~class_Orderings_Olinorder(X3953)|~class_Complete__Lattice_Ocomplete__lattice(X3953)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SUP__iff])])])])])). 4.05/4.30 fof(c_0_7209, plain, ![X10594, X10595, X10596]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10596,tc_HOL_Obool)),X10595),X10594))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10596,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10596,tc_HOL_Obool)),X10594)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10596,tc_HOL_Obool)),X10595)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Compl__anti__mono])])])). 4.05/4.30 cnf(c_0_7210, plain, (c_Map_Omap__comp(X1,X5,X8,X7,X3,X4)=hAPP(c_Option_Ooption_OSome(X5),X6)|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(X3,X4)|hAPP(c_Option_Ooption_OSome(X5),X6)!=hAPP(X7,X2)), inference(split_conjunct,[status(thm)],[c_0_5297])). 4.05/4.30 cnf(c_0_7211, plain, (c_Map_Omap__comp(X1,X2,X3,X4,X5,X6)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X2),X1,c_Option_Ooption_ONone(X2),X4),hAPP(X5,X6))), inference(split_conjunct,[status(thm)],[c_0_5298])). 4.05/4.30 fof(c_0_7212, plain, ![X15705, X15706, X15707, X15708, X15709, X15710, X15711, X15712, X15713, X15714, X15715]:((hAPP(hAPP(c_List_Omap(X15709,X15708),X15707),X15706)!=hAPP(hAPP(c_List_Omap(X15709,X15708),X15705),X15706)|(~hBOOL(hAPP(hAPP(c_member(X15709),X15710),hAPP(c_List_Oset(X15709),X15706)))|hAPP(X15705,X15710)=hAPP(X15707,X15710)))&((hBOOL(hAPP(hAPP(c_member(X15715),esk472_5(X15711,X15712,X15713,X15714,X15715)),hAPP(c_List_Oset(X15715),X15712)))|hAPP(hAPP(c_List_Omap(X15715,X15714),X15713),X15712)=hAPP(hAPP(c_List_Omap(X15715,X15714),X15711),X15712))&(hAPP(X15711,esk472_5(X15711,X15712,X15713,X15714,X15715))!=hAPP(X15713,esk472_5(X15711,X15712,X15713,X15714,X15715))|hAPP(hAPP(c_List_Omap(X15715,X15714),X15713),X15712)=hAPP(hAPP(c_List_Omap(X15715,X15714),X15711),X15712)))), 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_map__eq__conv])])])])])])])). 4.05/4.30 cnf(c_0_7213, plain, (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_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__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_5299])). 4.05/4.30 fof(c_0_7214, plain, ![X3886, X3887, X3888]:(~class_Rings_Olinordered__semidom(X3888)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3888),c_Groups_Oone__class_Oone(X3888)),X3887))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3888),hAPP(hAPP(c_Power_Opower__class_Opower(X3888),X3887),X3886)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3888),X3887),hAPP(hAPP(c_Power_Opower__class_Opower(X3888),X3887),X3886)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__less__power__Suc])])])). 4.05/4.30 cnf(c_0_7215, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))), inference(split_conjunct,[status(thm)],[c_0_5300])). 4.05/4.30 fof(c_0_7216, plain, ![X3915, X3916, X3917, X3918]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3918,tc_HOL_Obool)),X3917),X3916))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3918,tc_HOL_Obool)),X3915),X3916))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3918,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3918,tc_HOL_Obool)),X3917),X3915)),X3916)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Un__least])])])). 4.05/4.30 fof(c_0_7217, plain, ![X10581, X10582, X10583, X10584]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10584,tc_HOL_Obool)),X10583),X10582))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10584,tc_HOL_Obool)),X10583),X10581))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10584,tc_HOL_Obool)),X10583),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10584,tc_HOL_Obool)),X10582),X10581))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__greatest])])])). 4.05/4.30 fof(c_0_7218, plain, ![X2695, X2696, X2697, X2698]:((~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(X2697,tc_Nat_Onat),X2695),X2696)))|(~hBOOL(hAPP(hAPP(c_member(X2697),X2698),X2696))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X2695,X2698))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2697),X2696)))&((hBOOL(hAPP(hAPP(c_member(X2697),esk93_3(X2695,X2696,X2697)),X2696))|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(X2697,tc_Nat_Onat),X2695),X2696)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2697),X2696)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X2695,esk93_3(X2695,X2696,X2697))))|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(X2697,tc_Nat_Onat),X2695),X2696)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2697),X2696))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__pos__nat__iff])])])])])])). 4.05/4.30 fof(c_0_7219, plain, ![X10165, X10166, X10167]:(~class_Rings_Ocomm__semiring__1(X10167)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10167),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10167),X10166),c_Groups_Oone__class_Oone(X10167))),X10165)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10167),X10166),X10165)),X10165)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])])). 4.05/4.30 fof(c_0_7220, plain, ![X889, X890, X891, X892]:((~c_Enum_Oall__n__lists(X891,X890,X889)|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X891)),X892),hAPP(c_List_Oset(tc_List_Olist(X891)),c_Enum_On__lists(X891,X889,c_Enum_Oenum__class_Oenum(X891)))))|hBOOL(hAPP(X890,X892)))|~class_Enum_Oenum(X891))&((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X891)),esk21_3(X889,X890,X891)),hAPP(c_List_Oset(tc_List_Olist(X891)),c_Enum_On__lists(X891,X889,c_Enum_Oenum__class_Oenum(X891)))))|c_Enum_Oall__n__lists(X891,X890,X889)|~class_Enum_Oenum(X891))&(~hBOOL(hAPP(X890,esk21_3(X889,X890,X891)))|c_Enum_Oall__n__lists(X891,X890,X889)|~class_Enum_Oenum(X891)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_all__n__lists__def])])])])])])). 4.05/4.30 fof(c_0_7221, plain, ![X1320, X1321, X1322, X1323, X1324]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X1324,X1323)),hAPP(hAPP(c_Product__Type_OPair(X1324,X1323),X1322),X1321)),hAPP(c_List_Oset(tc_prod(X1324,X1323)),X1320)))|hAPP(c_Option_Ooption_OSome(X1323),esk35_5(X1320,X1321,X1322,X1323,X1324))=hAPP(hAPP(c_Map_Omap__of(X1324,X1323),X1320),X1322)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_weak__map__of__SomeI])])])). 4.05/4.30 fof(c_0_7222, plain, ![X15066, X15067, X15068, X15069, X15070, X15071, X15072, X15073, X15074, X15075, X15076]:((~hBOOL(hAPP(hAPP(c_member(X15068),X15071),X15067))|~hBOOL(hAPP(hAPP(c_member(X15070),X15069),hAPP(X15066,X15071)))|hBOOL(hAPP(hAPP(c_member(X15070),X15069),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15068,tc_fun(X15070,tc_HOL_Obool)),X15067),X15066))))&((hBOOL(hAPP(hAPP(c_member(X15074),esk452_5(X15072,X15073,X15074,X15075,X15076)),X15073))|~hBOOL(hAPP(hAPP(c_member(X15076),X15075),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15074,tc_fun(X15076,tc_HOL_Obool)),X15073),X15072))))&(hBOOL(hAPP(hAPP(c_member(X15076),X15075),hAPP(X15072,esk452_5(X15072,X15073,X15074,X15075,X15076))))|~hBOOL(hAPP(hAPP(c_member(X15076),X15075),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X15074,tc_fun(X15076,tc_HOL_Obool)),X15073),X15072)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__iff])])])])])])). 4.05/4.30 fof(c_0_7223, plain, ![X17534, X17535, X17536, X17537]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17537),X17536)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17535)),X17534)))|hAPP(hAPP(c_List_Onth(X17535),hAPP(hAPP(c_List_Odrop(X17535),X17537),X17534)),X17536)=hAPP(hAPP(c_List_Onth(X17535),X17534),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17537),X17536))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__drop])])])). 4.05/4.30 fof(c_0_7224, plain, ![X11753, X11754, X11755, X11756]:(~hBOOL(hAPP(hAPP(c_member(X11756),X11755),hAPP(c_Relation_ORange(X11754,X11756),X11753)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X11754,X11756)),hAPP(hAPP(c_Product__Type_OPair(X11754,X11756),esk365_4(X11753,X11754,X11755,X11756)),X11755)),X11753))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_RangeE])])])])). 4.05/4.30 fof(c_0_7225, plain, ![X8412, X8413, X8414, X8415, X8416, X8417, X8418, X8419, X8420]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X8413,X8415)),hAPP(hAPP(c_Product__Type_OPair(X8413,X8415),X8416),X8414)),X8412))|hBOOL(hAPP(hAPP(c_member(X8415),X8414),hAPP(c_Relation_ORange(X8413,X8415),X8412))))&(~hBOOL(hAPP(hAPP(c_member(X8420),X8419),hAPP(c_Relation_ORange(X8418,X8420),X8417)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X8418,X8420)),hAPP(hAPP(c_Product__Type_OPair(X8418,X8420),esk270_4(X8417,X8418,X8419,X8420)),X8419)),X8417)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Range__iff])])])])])). 4.05/4.30 fof(c_0_7226, plain, ![X17671, X17672, X17673, X17674]:(~hBOOL(hAPP(hAPP(c_member(X17674),X17673),hAPP(c_Relation_ODomain(X17674,X17672),X17671)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X17674,X17672)),hAPP(hAPP(c_Product__Type_OPair(X17674,X17672),X17673),esk527_4(X17671,X17672,X17673,X17674))),X17671))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_DomainE])])])])). 4.05/4.30 fof(c_0_7227, plain, ![X8873, X8874, X8875, X8876, X8878, X8879, X8880, X8881, X8882]:((~hBOOL(hAPP(hAPP(c_member(X8876),X8875),hAPP(c_Relation_ODomain(X8876,X8874),X8873)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X8876,X8874)),hAPP(hAPP(c_Product__Type_OPair(X8876,X8874),X8875),esk281_4(X8873,X8874,X8875,X8876))),X8873)))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X8881,X8879)),hAPP(hAPP(c_Product__Type_OPair(X8881,X8879),X8880),X8882)),X8878))|hBOOL(hAPP(hAPP(c_member(X8881),X8880),hAPP(c_Relation_ODomain(X8881,X8879),X8878))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__iff])])])])])). 4.05/4.30 fof(c_0_7228, plain, ![X3157, X3158, X3159, X3160]:((hBOOL(hAPP(hAPP(c_member(X3160),esk108_4(X3157,X3158,X3159,X3160)),hAPP(c_List_Oset(X3160),X3159)))|c_List_OtakeWhile(X3160,X3158,hAPP(hAPP(c_List_Oappend(X3160),X3159),X3157))=hAPP(hAPP(c_List_Oappend(X3160),X3159),c_List_OtakeWhile(X3160,X3158,X3157)))&(~hBOOL(hAPP(X3158,esk108_4(X3157,X3158,X3159,X3160)))|c_List_OtakeWhile(X3160,X3158,hAPP(hAPP(c_List_Oappend(X3160),X3159),X3157))=hAPP(hAPP(c_List_Oappend(X3160),X3159),c_List_OtakeWhile(X3160,X3158,X3157)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__append2])])])])). 4.05/4.30 fof(c_0_7229, plain, ![X11026, X11027, X11028, X11029]:((~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X11029)),X11028),c_List_Olists(X11029,X11026)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X11029)),X11027),c_List_Olists(X11029,X11026)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X11029)),hAPP(hAPP(c_List_Oappend(X11029),X11028),X11027)),c_List_Olists(X11029,X11026))))&((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X11029)),X11028),c_List_Olists(X11029,X11026)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X11029)),hAPP(hAPP(c_List_Oappend(X11029),X11028),X11027)),c_List_Olists(X11029,X11026))))&(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X11029)),X11027),c_List_Olists(X11029,X11026)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X11029)),hAPP(hAPP(c_List_Oappend(X11029),X11028),X11027)),c_List_Olists(X11029,X11026)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__lists__conv])])])). 4.05/4.30 fof(c_0_7230, plain, ![X8512, X8513, X8514]:(~class_Groups_Oab__semigroup__mult(X8514)|(c_Orderings_Obot__class_Obot(tc_fun(X8514,tc_HOL_Obool))=X8513|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8514),X8513))|(hBOOL(hAPP(hAPP(c_member(X8514),X8512),X8513))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8514),X8512),hAPP(c_Finite__Set_Ofold1(X8514,c_Groups_Otimes__class_Otimes(X8514)),X8513))=hAPP(c_Finite__Set_Ofold1(X8514,c_Groups_Otimes__class_Otimes(X8514)),hAPP(hAPP(c_Set_Oinsert(X8514),X8512),X8513)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__insert])])])). 4.05/4.30 cnf(c_0_7231, 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_5301])). 4.05/4.30 fof(c_0_7232, plain, ![X15219, X15220, X15221, X15222, X15223, X15224, X15225]:((~hBOOL(hAPP(hAPP(c_member(X15221),X15220),c_Wellfounded_Oacc(X15221,X15219)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X15221,X15221)),hAPP(hAPP(c_Product__Type_OPair(X15221,X15221),X15222),X15220)),X15219))|hBOOL(hAPP(hAPP(c_member(X15221),X15222),c_Wellfounded_Oacc(X15221,X15219)))))&((hBOOL(hAPP(hAPP(c_member(tc_prod(X15225,X15225)),hAPP(hAPP(c_Product__Type_OPair(X15225,X15225),esk458_3(X15223,X15224,X15225)),X15224)),X15223))|hBOOL(hAPP(hAPP(c_member(X15225),X15224),c_Wellfounded_Oacc(X15225,X15223))))&(~hBOOL(hAPP(hAPP(c_member(X15225),esk458_3(X15223,X15224,X15225)),c_Wellfounded_Oacc(X15225,X15223)))|hBOOL(hAPP(hAPP(c_member(X15225),X15224),c_Wellfounded_Oacc(X15225,X15223)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc_Osimps])])])])])])). 4.05/4.30 fof(c_0_7233, plain, ![X11129, X11130, X11131, X11132]:(~class_Rings_Odivision__ring(X11132)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X11132),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11132),X11131),X11129)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11132),X11130),X11129))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11132),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X11132),X11131),X11130)),X11129)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__distrib])])). 4.05/4.30 fof(c_0_7234, plain, ![X12153, X12154, X12155, X12156]:(~class_Lattices_Odistrib__lattice(X12156)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12156),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X12156),X12155),X12153)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X12156),X12154),X12153))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X12156),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12156),X12155),X12154)),X12153)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__inf__distrib2])])])). 4.05/4.30 fof(c_0_7235, plain, ![X14919, X14920, X14921, X14922]:(~class_Lattices_Odistrib__lattice(X14922)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X14922),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14922),X14921),X14919)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14922),X14920),X14919))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14922),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X14922),X14921),X14920)),X14919)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib2])])). 4.05/4.30 fof(c_0_7236, plain, ![X9878, X9879, X9880, X9881]:(~class_Rings_Odivision__ring(X9881)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9881),X9880),X9879)),X9878)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9881),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9881),X9880),X9878)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9881),X9879),X9878))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__distrib])])). 4.05/4.30 fof(c_0_7237, plain, ![X11693, X11694, X11695]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X11695,X11695)),hAPP(hAPP(c_Product__Type_OPair(X11695,X11695),esk360_3(X11693,X11694,X11695)),X11694)),X11693))|hBOOL(hAPP(hAPP(c_member(X11695),X11694),c_Wellfounded_Oacc(X11695,X11693))))&(~hBOOL(hAPP(hAPP(c_member(X11695),esk360_3(X11693,X11694,X11695)),c_Wellfounded_Oacc(X11695,X11693)))|hBOOL(hAPP(hAPP(c_member(X11695),X11694),c_Wellfounded_Oacc(X11695,X11693))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__acc__down])])])])])). 4.05/4.30 fof(c_0_7238, plain, ![X1430, X1431, X1432, X1433]:(~class_Orderings_Olinorder(X1433)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1433),X1432),X1431))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1433),X1431),X1430))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1433,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1433,X1432,X1431)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1433,X1431,X1430))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1433,X1432),X1430)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I18_J])])])). 4.05/4.30 fof(c_0_7239, plain, ![X13702, X13703, X13704, X13705]:(~class_Orderings_Olinorder(X13705)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13705),X13704),X13703))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13705,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13705,X13704),X13702)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13705,X13704),X13703))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13705,X13703),X13702))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__diff])])])). 4.05/4.30 fof(c_0_7240, plain, ![X4194, X4195, X4196, X4197, X4198]:((hAPP(hAPP(c_Set_Oinsert(X4198),esk130_5(X4194,X4195,X4196,X4197,X4198)),esk131_5(X4194,X4195,X4196,X4197,X4198))=hAPP(hAPP(c_Set_Oinsert(X4198),X4196),X4195)|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4198,X4197,hAPP(hAPP(c_Set_Oinsert(X4198),X4196),X4195)),X4194)))&((hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4198,X4198,X4197,esk130_5(X4194,X4195,X4196,X4197,X4198),esk131_5(X4194,X4195,X4196,X4197,X4198)),X4194))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4198,X4197,hAPP(hAPP(c_Set_Oinsert(X4198),X4196),X4195)),X4194)))&(~hBOOL(hAPP(hAPP(c_member(X4198),esk130_5(X4194,X4195,X4196,X4197,X4198)),esk131_5(X4194,X4195,X4196,X4197,X4198)))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4198,X4197,hAPP(hAPP(c_Set_Oinsert(X4198),X4196),X4195)),X4194))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__fold1SetE])])])])])). 4.05/4.30 fof(c_0_7241, plain, ![X9882, X9883, X9884]:((hBOOL(hAPP(hAPP(c_member(tc_prod(X9884,X9884)),hAPP(hAPP(c_Product__Type_OPair(X9884,X9884),esk300_3(X9882,X9883,X9884)),X9883)),X9882))|hBOOL(hAPP(hAPP(c_member(X9884),X9883),c_Wellfounded_Oacc(X9884,X9882))))&(~hBOOL(hAPP(hAPP(c_member(X9884),esk300_3(X9882,X9883,X9884)),c_Wellfounded_Oacc(X9884,X9882)))|hBOOL(hAPP(hAPP(c_member(X9884),X9883),c_Wellfounded_Oacc(X9884,X9882))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc_OaccI])])])])). 4.05/4.30 cnf(c_0_7242, plain, (hAPP(c_List_Oset(X3),X4)=c_Map_Odom(X3,X1,hAPP(c_Map_Omap__of(X3,X1),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)|~hBOOL(hAPP(c_List_Odistinct(X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5302])). 4.05/4.30 cnf(c_0_7243, plain, (c_Map_Odom(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3))=hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))), inference(rw,[status(thm)],[c_0_5303, c_0_5304]), ['final']). 4.05/4.30 fof(c_0_7244, plain, ![X4127, X4128, X4129, X4130]:(~class_Rings_Ocomm__semiring(X4130)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4130),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4130),X4129),X4128)),X4127)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4130),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4130),X4129),X4127)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4130),X4128),X4127))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__class_Odistrib])])])). 4.05/4.30 fof(c_0_7245, plain, ![X10355, X10356, X10357, X10358]:(~class_Rings_Ocomm__semiring__1(X10358)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10358),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10358),X10357),X10356)),X10355)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10358),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10358),X10357),X10355)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10358),X10356),X10355))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])])). 4.05/4.30 fof(c_0_7246, plain, ![X4445, X4446, X4447, X4448]:(~class_Groups_Oordered__ab__semigroup__add__imp__le(X4448)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4448),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4448),X4447),X4446)),X4445)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X4448),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4448),X4447),X4445)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4448),X4446),X4445))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__add__distrib__left])])). 4.05/4.30 fof(c_0_7247, plain, ![X573, X574, X575, X576, X577, X578, X579]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X579)),X578)),X577))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X577),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X576)),X575)))|c_Map_Omap__upds(X579,X576,X574,X578,hAPP(hAPP(c_List_Olist__update(X576,X575),X577),X573))=c_Map_Omap__upds(X579,X576,X574,X578,X575))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__upds__list__update2__drop])])])). 4.05/4.30 cnf(c_0_7248, 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_5305])). 4.05/4.30 fof(c_0_7249, plain, ![X5180, X5181, X5182, X5183, X5184]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5184,tc_HOL_Obool)),X5183),X5182))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5181,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5184,X5181,X5180),X5183)),hAPP(c_Set_Oimage(X5184,X5181,X5180),X5182)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])])). 4.05/4.30 fof(c_0_7250, plain, ![X7576, X7577, X7578, X7579]:(~class_Groups_Oordered__ab__semigroup__add__imp__le(X7579)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7579),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7579),X7578),X7577)),X7576)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X7579),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7579),X7578),X7576)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7579),X7577),X7576))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__add__distrib__left])])). 4.05/4.30 fof(c_0_7251, plain, ![X9945, X9946, X9947, X9948]:(~class_Lattices_Odistrib__lattice(X9948)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9948),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9948),X9947),X9946)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9948),X9947),X9945))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9948),X9947),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9948),X9946),X9945))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib1])])). 4.05/4.30 fof(c_0_7252, plain, ![X12057, X12058, X12059, X12060]:(~class_Lattices_Odistrib__lattice(X12060)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12060),X12059),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X12060),X12058),X12057))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X12060),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12060),X12059),X12058)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12060),X12059),X12057))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib1])])). 4.05/4.30 fof(c_0_7253, plain, ![X13359, X13360, X13361, X13362]:(~class_Rings_Ocomm__semiring__1(X13362)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13362),X13361),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13362),X13360),X13359))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13362),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13362),X13361),X13360)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13362),X13361),X13359))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])])). 4.05/4.30 fof(c_0_7254, plain, ![X14858, X14859, X14860, X14861]:(~hBOOL(hAPP(hAPP(c_member(X14861),X14860),c_Wellfounded_Oacc(X14861,X14859)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X14861,X14861)),hAPP(hAPP(c_Product__Type_OPair(X14861,X14861),X14858),X14860)),c_Transitive__Closure_Ortrancl(X14861,X14859)))|hBOOL(hAPP(hAPP(c_member(X14861),X14858),c_Wellfounded_Oacc(X14861,X14859))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acc__downwards])])])). 4.05/4.30 fof(c_0_7255, plain, ![X2180, X2181, X2182]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2182,tc_HOL_Obool),tc_HOL_Obool)),X2181),X2180))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2182,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2182,tc_HOL_Obool),X2181)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2182,tc_HOL_Obool),X2180)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__mono])])). 4.05/4.30 fof(c_0_7256, plain, ![X8916, X8917, X8918]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X8918,tc_HOL_Obool),tc_HOL_Obool)),X8917),X8916))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8918,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X8918,tc_HOL_Obool),X8916)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X8918,tc_HOL_Obool),X8917)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inter__anti__mono])])])). 4.05/4.30 cnf(c_0_7257, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3))|~class_Groups_Ocomm__monoid__add(X1)|c_Groups_Ozero__class_Ozero(X1)!=hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5306])). 4.05/4.30 fof(c_0_7258, plain, ![X9647, X9648, X9649, X9650]:(~class_Groups_Omonoid__mult(X9650)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9650),hAPP(hAPP(c_Power_Opower__class_Opower(X9650),X9649),X9648)),hAPP(hAPP(c_Power_Opower__class_Opower(X9650),X9649),X9647))=hAPP(hAPP(c_Power_Opower__class_Opower(X9650),X9649),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9648),X9647))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])])). 4.05/4.30 cnf(c_0_7259, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OPls))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5307, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.30 cnf(c_0_7260, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5308, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.30 cnf(c_0_7261, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5309, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.30 cnf(c_0_7262, 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_5310])). 4.05/4.30 cnf(c_0_7263, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5311, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.30 cnf(c_0_7264, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5312, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.30 cnf(c_0_7265, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5313, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.30 cnf(c_0_7266, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5314, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.30 fof(c_0_7267, plain, ![X11414, X11415, X11416, X11417]:(~class_Rings_Oring__1(X11417)|~class_Groups_Ocomm__monoid__mult(X11417)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X11416,X11417),hAPP(hAPP(c_COMBB(tc_Int_Oint,X11417,X11416),c_Int_Oring__1__class_Oof__int(X11417)),X11415)),X11414)=hAPP(c_Int_Oring__1__class_Oof__int(X11417),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X11416,tc_Int_Oint),X11415),X11414))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__setprod])])). 4.05/4.30 fof(c_0_7268, plain, ![X10060, X10061, X10062, X10063]:(~class_Rings_Osemiring__1(X10063)|~class_Groups_Ocomm__monoid__mult(X10063)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10062,X10063),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10063,X10062),c_Nat_Osemiring__1__class_Oof__nat(X10063)),X10061)),X10060)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10063),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10062,tc_Nat_Onat),X10061),X10060))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__setprod])])). 4.05/4.30 fof(c_0_7269, plain, ![X5139, X5140, X5141]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5141),X5140))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5141,X5141),tc_HOL_Obool)),X5139),hAPP(hAPP(c_Product__Type_OSigma(X5141,X5141),X5140),hAPP(c_COMBK(tc_fun(X5141,tc_HOL_Obool),X5141),X5140))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5141,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5141),X5140),X5139))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__quotient])])])). 4.05/4.30 cnf(c_0_7270, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5315, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.30 cnf(c_0_7271, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5316, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.30 cnf(c_0_7272, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5317, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.30 cnf(c_0_7273, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5318, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.30 fof(c_0_7274, plain, ![X4061, X4062, X4063, X4064, X4065]:((((c_List_Olinorder__class_Osorted(X4063,X4062)|~c_List_Olinorder__class_Osorted(X4063,hAPP(hAPP(c_List_Oappend(X4063),X4062),X4061))|~class_Orderings_Olinorder(X4063))&(c_List_Olinorder__class_Osorted(X4063,X4061)|~c_List_Olinorder__class_Osorted(X4063,hAPP(hAPP(c_List_Oappend(X4063),X4062),X4061))|~class_Orderings_Olinorder(X4063)))&(~hBOOL(hAPP(hAPP(c_member(X4063),X4064),hAPP(c_List_Oset(X4063),X4062)))|(~hBOOL(hAPP(hAPP(c_member(X4063),X4065),hAPP(c_List_Oset(X4063),X4061)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4063),X4064),X4065)))|~c_List_Olinorder__class_Osorted(X4063,hAPP(hAPP(c_List_Oappend(X4063),X4062),X4061))|~class_Orderings_Olinorder(X4063)))&((hBOOL(hAPP(hAPP(c_member(X4063),esk126_3(X4061,X4062,X4063)),hAPP(c_List_Oset(X4063),X4062)))|(~c_List_Olinorder__class_Osorted(X4063,X4062)|~c_List_Olinorder__class_Osorted(X4063,X4061))|c_List_Olinorder__class_Osorted(X4063,hAPP(hAPP(c_List_Oappend(X4063),X4062),X4061))|~class_Orderings_Olinorder(X4063))&((hBOOL(hAPP(hAPP(c_member(X4063),esk127_3(X4061,X4062,X4063)),hAPP(c_List_Oset(X4063),X4061)))|(~c_List_Olinorder__class_Osorted(X4063,X4062)|~c_List_Olinorder__class_Osorted(X4063,X4061))|c_List_Olinorder__class_Osorted(X4063,hAPP(hAPP(c_List_Oappend(X4063),X4062),X4061))|~class_Orderings_Olinorder(X4063))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4063),esk126_3(X4061,X4062,X4063)),esk127_3(X4061,X4062,X4063)))|(~c_List_Olinorder__class_Osorted(X4063,X4062)|~c_List_Olinorder__class_Osorted(X4063,X4061))|c_List_Olinorder__class_Osorted(X4063,hAPP(hAPP(c_List_Oappend(X4063),X4062),X4061))|~class_Orderings_Olinorder(X4063))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__append])])])])])])). 4.05/4.30 fof(c_0_7275, plain, ![X9092, X9093, X9094, X9095, X9096]:(~class_Orderings_Olinorder(X9096)|c_SetInterval_Oord__class_OatLeastAtMost(X9096,hAPP(hAPP(c_Orderings_Oord__class_Omax(X9096),X9095),X9093),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9096),X9094),X9092))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9096,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X9096,X9095,X9094)),c_SetInterval_Oord__class_OatLeastAtMost(X9096,X9093,X9092))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__atLeastAtMost])])])). 4.05/4.30 fof(c_0_7276, plain, ![X9840, X9841, X9842, X9843, X9844]:(~class_Orderings_Olinorder(X9844)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9844,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X9844,X9843,X9842)),c_SetInterval_Oord__class_OgreaterThanAtMost(X9844,X9841,X9840))=c_SetInterval_Oord__class_OgreaterThanAtMost(X9844,hAPP(hAPP(c_Orderings_Oord__class_Omax(X9844),X9843),X9841),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9844),X9842),X9840))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__greaterThanAtMost])])])). 4.05/4.30 fof(c_0_7277, plain, ![X5093, X5094, X5095, X5096, X5097]:(~class_Orderings_Olinorder(X5097)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5097,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5097,X5096,X5095)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5097,X5094,X5093))=c_SetInterval_Oord__class_OgreaterThanLessThan(X5097,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5097),X5096),X5094),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5097),X5095),X5093))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greaterThanLessThan])])). 4.05/4.30 fof(c_0_7278, plain, ![X1758, X1759, X1760, X1761, X1762]:(~c_Finite__Set_Ofolding__one(X1762,X1761,X1760)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1762),X1759))|(hBOOL(hAPP(hAPP(c_member(X1762),X1758),X1759))|(c_Orderings_Obot__class_Obot(tc_fun(X1762,tc_HOL_Obool))=X1759|hAPP(hAPP(X1761,X1758),hAPP(X1760,X1759))=hAPP(X1760,hAPP(hAPP(c_Set_Oinsert(X1762),X1758),X1759)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Oinsert])])])). 4.05/4.30 cnf(c_0_7279, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk248_3(X1,X2,X3)),X1))|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),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_5212])). 4.05/4.30 cnf(c_0_7280, 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_5319])). 4.05/4.30 fof(c_0_7281, plain, ![X7703, X7704, X7705]:(~class_Groups_Oordered__ab__group__add__abs(X7705)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7705),hAPP(c_Groups_Oabs__class_Oabs(X7705),X7704)),hAPP(c_Groups_Oabs__class_Oabs(X7705),X7703))=hAPP(c_Groups_Oabs__class_Oabs(X7705),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7705),hAPP(c_Groups_Oabs__class_Oabs(X7705),X7704)),hAPP(c_Groups_Oabs__class_Oabs(X7705),X7703)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__add__abs])])])). 4.05/4.30 fof(c_0_7282, plain, ![X15724, X15725]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X15724),X15725))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X15725),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))|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(X15725,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X15724),X15725)))=c_Random_Olog(X15725,X15724))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X15724),X15725))|c_Random_Olog(X15725,X15724)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X15725),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))|c_Random_Olog(X15725,X15724)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_log_Osimps])])])). 4.05/4.30 fof(c_0_7283, plain, ![X11605, X11606]:(~class_Groups_Oordered__ab__group__add__abs(X11606)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11606),hAPP(c_Groups_Oabs__class_Oabs(X11606),hAPP(c_List_Omonoid__add__class_Olistsum(X11606),X11605))),hAPP(c_List_Omonoid__add__class_Olistsum(X11606),hAPP(hAPP(c_List_Omap(X11606,X11606),c_Groups_Oabs__class_Oabs(X11606)),X11605))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__abs])])])). 4.05/4.30 fof(c_0_7284, plain, ![X1925, X1926, X1927]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1927),X1926))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1926),X1925)),X1927)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1926),X1927)),X1925)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__add__assoc2])])])). 4.05/4.30 fof(c_0_7285, plain, ![X6023, X6024, X6025, X6026, X6027, X6028, X6029, X6030]:(~c_Finite__Set_Ofolding__image__simple__idem(X6030,X6029,X6028,X6027,X6026,X6025)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6029),X6024))|hAPP(X6025,hAPP(hAPP(c_Set_Oinsert(X6029),X6023),X6024))=hAPP(hAPP(X6028,hAPP(X6026,X6023)),hAPP(X6025,X6024)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem])])])). 4.05/4.30 fof(c_0_7286, plain, ![X12657, X12658]:(~class_Lattices_Oab__semigroup__idem__mult(X12658)|(X12657=c_List_Olist_ONil(X12658)|hAPP(c_List_Ofoldl(X12658,X12658,c_Groups_Otimes__class_Otimes(X12658),hAPP(c_List_Ohd(X12658),X12657)),hAPP(c_List_Otl(X12658),X12657))=hAPP(c_Finite__Set_Ofold1(X12658,c_Groups_Otimes__class_Otimes(X12658)),hAPP(c_List_Oset(X12658),X12657)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__set])])])). 4.05/4.30 cnf(c_0_7287, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))!=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))|~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),c_Transitive__Closure_Ortrancl(X1,X2)),X2)))), inference(rw,[status(thm)],[c_0_5320, c_0_5018])). 4.05/4.30 fof(c_0_7288, plain, ![X15155, X15156, X15157, X15158]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15158,tc_HOL_Obool)),X15157),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15158,tc_HOL_Obool)),X15156),X15155)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15158,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15158,tc_HOL_Obool)),X15157),X15156)),X15155)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15158,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X15158,tc_HOL_Obool)),X15157),X15156)),X15155))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15158,tc_HOL_Obool)),X15157),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15158,tc_HOL_Obool)),X15156),X15155))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__subset__conv])])). 4.05/4.30 fof(c_0_7289, plain, ![X8553, X8554, X8555, X8556]:(~class_Rings_Osemiring__1(X8556)|hAPP(c_List_Omonoid__add__class_Olistsum(X8556),hAPP(hAPP(c_List_Omap(X8555,X8556),hAPP(c_COMBK(X8556,X8555),X8554)),X8553))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8556),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8556),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8555)),X8553))),X8554)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__triv])])). 4.05/4.30 cnf(c_0_7290, 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_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,hAPP(c_Nat_OSuc,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(split_conjunct,[status(thm)],[c_0_5321])). 4.05/4.30 fof(c_0_7291, plain, ![X12088, X12089]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12089))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12088),X12089))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X12088),X12089)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12088),X12089)),X12089)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__geq])])])). 4.05/4.30 fof(c_0_7292, plain, ![X11006, X11007, X11008, X11009]:(~class_Groups_Oordered__ab__group__add__abs(X11009)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11009),c_Groups_Ozero__class_Ozero(X11009)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11008,X11009),hAPP(hAPP(c_COMBB(X11009,X11009,X11008),c_Groups_Oabs__class_Oabs(X11009)),X11007)),X11006)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__abs__ge__zero])])). 4.05/4.30 cnf(c_0_7293, plain, (hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)=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))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5322])). 4.05/4.30 fof(c_0_7294, plain, ![X4889, X4890]:((((c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X4890|c_Divides_Odivmod__int(X4890,X4889)=hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4890),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4889)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4889))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4890)))&(X4890!=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(X4890,X4889)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4889))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4890))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4889))|c_Divides_Odivmod__int(X4890,X4889)=c_Divides_OposDivAlg(X4890,X4889)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4890))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4889))|c_Divides_Odivmod__int(X4890,X4889)=hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4890),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4889)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4890)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4889))|c_Divides_Odivmod__int(X4890,X4889)=c_Divides_OnegDivAlg(X4890,X4889)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4890))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__def])])])])). 4.05/4.30 fof(c_0_7295, plain, ![X10151, X10152]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X10152),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X10151),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10151),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X10152)))))|X10152=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X10151),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10151),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X10152)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__card__intvl__is__intvl])])). 4.05/4.30 cnf(c_0_7296, 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_5323])). 4.05/4.30 fof(c_0_7297, plain, ![X14767, X14768, X14769, X14770, X14771, X14772]:(~c_Finite__Set_Ofolding__idem(X14772,X14771,X14770,X14769)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14772),X14768))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14772,tc_HOL_Obool)),X14767),X14768))|hAPP(c_Fun_Ocomp(X14771,X14771,X14771,hAPP(X14769,X14768)),hAPP(X14769,X14767))=hAPP(X14769,X14768)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__idem_Osubset__comp__idem])])])). 4.05/4.30 fof(c_0_7298, plain, ![X14256, X14257, X14258, X14259]:(~class_Rings_Osemiring__1(X14259)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X14259),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14258,tc_Nat_Onat),X14257),X14256))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14258,X14259),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X14259,X14258),c_Nat_Osemiring__1__class_Oof__nat(X14259)),X14257)),X14256)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__setsum])])). 4.05/4.30 fof(c_0_7299, plain, ![X2431, X2432, X2433]:(~class_Rings_Ocomm__semiring__1(X2433)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2433),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2433),X2431),c_Groups_Oone__class_Oone(X2433))),X2432)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2433),X2432),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2433),X2431),X2432))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])])). 4.05/4.30 cnf(c_0_7300, 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_5324])). 4.05/4.30 fof(c_0_7301, plain, ![X6605, X6606, X6607, X6608, X6609]:(~class_Complete__Lattice_Ocomplete__lattice(X6609)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6608,tc_HOL_Obool)),X6607),X6606))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6609),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6608,X6609),X6606),X6605)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6608,X6609),X6607),X6605))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__subset])])). 4.05/4.30 fof(c_0_7302, plain, ![X1231, X1232, X1233, X1234, X1235]:(~class_Complete__Lattice_Ocomplete__lattice(X1235)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1234,tc_HOL_Obool)),X1233),X1232))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1235),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1234,X1235),X1233),X1231)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1234,X1235),X1232),X1231))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUP__subset])])])). 4.05/4.30 fof(c_0_7303, plain, ![X3814, X3815, X3816]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3816,X3816),tc_HOL_Obool)),X3815),X3814))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X3816),tc_List_Olist(X3816)),tc_HOL_Obool)),c_List_Olistrel1(X3816,X3815)),c_List_Olistrel1(X3816,X3814)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel1__mono])])])). 4.05/4.30 fof(c_0_7304, plain, ![X17441, X17442, X17443]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X17443,X17443),tc_HOL_Obool)),X17442),X17441))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X17443),tc_List_Olist(X17443)),tc_HOL_Obool)),c_List_Olistrel(X17443,X17442)),c_List_Olistrel(X17443,X17441)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__mono])])). 4.05/4.30 cnf(c_0_7305, 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_5325])). 4.05/4.30 fof(c_0_7306, plain, ![X9817, X9818, X9819, X9820]:(~class_Fields_Olinordered__field(X9820)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9820),X9819),X9818))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9820),c_Groups_Ozero__class_Ozero(X9820)),X9817))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9820),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9820),X9819),X9817)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9820),X9818),X9817)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__strict__right__mono])])])). 4.05/4.30 fof(c_0_7307, plain, ![X11328, X11329, X11330, X11331]:(~class_Rings_Olinordered__semiring__strict(X11331)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11331),X11330),X11329))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11331),c_Groups_Ozero__class_Ozero(X11331)),X11328))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11331),X11330),X11328)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11331),X11329),X11328)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__right__mono])])])). 4.05/4.30 fof(c_0_7308, plain, ![X6601, X6602, X6603, X6604]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),c_Groups_Ozero__class_Ozero(X6604)),X6602))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),X6602),c_Groups_Ozero__class_Ozero(X6604)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6604),X6603),X6602)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6604),X6601),X6602)))|~class_Rings_Olinordered__ring__strict(X6604))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),X6603),X6601))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),X6602),c_Groups_Ozero__class_Ozero(X6604)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6604),X6603),X6602)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6604),X6601),X6602)))|~class_Rings_Olinordered__ring__strict(X6604)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),c_Groups_Ozero__class_Ozero(X6604)),X6602))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),X6601),X6603))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6604),X6603),X6602)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6604),X6601),X6602)))|~class_Rings_Olinordered__ring__strict(X6604))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),X6603),X6601))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),X6601),X6603))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6604),X6603),X6602)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6604),X6601),X6602)))|~class_Rings_Olinordered__ring__strict(X6604))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),X6602),c_Groups_Ozero__class_Ozero(X6604)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),X6601),X6603))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6604),X6603),X6602)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6604),X6601),X6602)))|~class_Rings_Olinordered__ring__strict(X6604))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),c_Groups_Ozero__class_Ozero(X6604)),X6602))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),X6603),X6601))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6604),X6603),X6602)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6604),X6601),X6602)))|~class_Rings_Olinordered__ring__strict(X6604)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__cancel__right__disj])])])])). 4.05/4.30 fof(c_0_7309, plain, ![X15917, X15918, X15919, X15920, X15921, X15922]:(~c_Fun_Oinj__on(X15922,X15921,X15920,X15919)|(hBOOL(hAPP(hAPP(c_member(X15921),X15918),hAPP(c_Set_Oimage(X15922,X15921,X15920),X15919)))|c_Fun_Oinj__on(X15922,X15921,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X15922,X15921),X15920),X15917),X15918),X15919))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__fun__updI])])])). 4.05/4.30 fof(c_0_7310, plain, ![X10019, X10020]:((X10019=c_List_Olist_ONil(tc_List_Olist(X10020))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10020)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X10020)),X10019),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10020))),c_List_Otranspose(X10020,X10019))|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10020),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X10020))),X10019))))&(c_List_Olist_ONil(tc_List_Olist(X10020))!=X10019|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10020))),c_List_Otranspose(X10020,X10019))|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10020),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X10020))),X10019))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_length__transpose__sorted])])])])). 4.05/4.30 fof(c_0_7311, plain, ![X15927, X15928, X15929, X15930]:(~class_Orderings_Olinorder(X15930)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15930),X15929),X15928))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15930),X15928),X15927))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15930,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X15930,X15929,X15928)),c_SetInterval_Oord__class_OgreaterThanAtMost(X15930,X15928,X15927))=c_SetInterval_Oord__class_OgreaterThanAtMost(X15930,X15929,X15927)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I20_J])])])). 4.05/4.30 fof(c_0_7312, plain, ![X11809, X11810, X11811, X11812]:(~class_Orderings_Olinorder(X11812)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11812),X11811),X11810))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11812),X11810),X11809))|c_SetInterval_Oord__class_OgreaterThanAtMost(X11812,X11811,X11809)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11812,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X11812,X11811,X11810)),c_SetInterval_Oord__class_OatLeastAtMost(X11812,X11810,X11809))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I19_J])])])). 4.05/4.30 fof(c_0_7313, plain, ![X10743, X10744, X10745, X10746]:(~class_Rings_Olinordered__comm__semiring__strict(X10746)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10746),X10745),X10744))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10746),c_Groups_Ozero__class_Ozero(X10746)),X10743))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10746),X10743),X10745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10746),X10743),X10744)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__mult__strict__left__mono])])])). 4.05/4.30 fof(c_0_7314, plain, ![X6581, X6582, X6583, X6584]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6584),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6584),X6583),X6582)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6584),X6583),X6581)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6584),X6582),X6581))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6584),c_Groups_Ozero__class_Ozero(X6584)),X6583))|~class_Rings_Olinordered__ring__strict(X6584))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6584),X6582),X6581))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6584),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6584),X6583),X6582)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6584),X6583),X6581)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6584),c_Groups_Ozero__class_Ozero(X6584)),X6583))|~class_Rings_Olinordered__ring__strict(X6584))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__cancel__left__pos])])])])). 4.05/4.30 fof(c_0_7315, plain, ![X13653, X13654, X13655, X13656]:(~class_Rings_Olinordered__semiring__strict(X13656)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13656),X13655),X13654))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13656),c_Groups_Ozero__class_Ozero(X13656)),X13653))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13656),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13656),X13653),X13655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13656),X13653),X13654)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__left__mono])])])). 4.05/4.30 fof(c_0_7316, plain, ![X6171, X6172, X6173, X6174]:(~class_Rings_Oordered__semiring(X6174)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6174),X6173),X6172))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6174),c_Groups_Ozero__class_Ozero(X6174)),X6171))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6174),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6174),X6173),X6171)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6174),X6172),X6171)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right__mono])])])). 4.05/4.30 fof(c_0_7317, plain, ![X8263, X8264, X8265, X8266]:(~class_Orderings_Olinorder(X8266)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8266),X8265),X8264))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8266),X8264),X8263))|c_SetInterval_Oord__class_OgreaterThanLessThan(X8266,X8265,X8263)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8266,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X8266,X8265,X8264)),c_SetInterval_Oord__class_OgreaterThanLessThan(X8266,X8264,X8263))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I16_J])])])). 4.05/4.30 fof(c_0_7318, plain, ![X14656, X14657, X14658, X14659]:(~class_Orderings_Olinorder(X14659)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14659),X14658),X14657))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14659),X14657),X14656))|c_SetInterval_Oord__class_OatLeastAtMost(X14659,X14658,X14656)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14659,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X14659,X14658,X14657)),c_SetInterval_Oord__class_OgreaterThanAtMost(X14659,X14657,X14656))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I22_J])])])). 4.05/4.30 fof(c_0_7319, plain, ![X17594, X17595, X17596]:(~class_Orderings_Olinorder(X17596)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17596),X17595))|(c_Orderings_Obot__class_Obot(tc_fun(X17596,tc_HOL_Obool))=X17595|c_Big__Operators_Olattice_OInf__fin(X17596,c_Orderings_Oord__class_Omin(X17596),hAPP(hAPP(c_Set_Oinsert(X17596),X17594),X17595))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X17596),X17594),c_Big__Operators_Olattice_OInf__fin(X17596,c_Orderings_Oord__class_Omin(X17596),X17595))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oinsert__idem])])])). 4.05/4.30 fof(c_0_7320, plain, ![X3099, X3100, X3101]:(~class_Orderings_Olinorder(X3101)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X3101),X3100))|(c_Orderings_Obot__class_Obot(tc_fun(X3101,tc_HOL_Obool))=X3100|c_Big__Operators_Olattice_OSup__fin(X3101,c_Orderings_Oord__class_Omax(X3101),hAPP(hAPP(c_Set_Oinsert(X3101),X3099),X3100))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X3101),X3099),c_Big__Operators_Olattice_OSup__fin(X3101,c_Orderings_Oord__class_Omax(X3101),X3100))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oinsert__idem])])])). 4.05/4.30 fof(c_0_7321, plain, ![X16393, X16394]:(~hBOOL(hAPP(c_List_Odistinct(X16394),X16393))|hBOOL(hAPP(c_List_Odistinct(tc_fun(X16394,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X16394),tc_fun(X16394,tc_HOL_Obool)),c_List_Oset(X16394)),c_Enum_Osublists(X16394,X16393))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__set__sublists])])). 4.05/4.30 fof(c_0_7322, plain, ![X3891, X3892, X3893, X3894]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3894),X3893),X3892)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3894),X3893),X3891)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3894),X3892),X3891))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3894),c_Groups_Ozero__class_Ozero(X3894)),X3893))|~class_Rings_Olinordered__ring__strict(X3894))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3894),X3892),X3891))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3894),X3893),X3892)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3894),X3893),X3891)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3894),c_Groups_Ozero__class_Ozero(X3894)),X3893))|~class_Rings_Olinordered__ring__strict(X3894))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__cancel__left__pos])])])])). 4.05/4.30 fof(c_0_7323, plain, ![X6317, X6318, X6319, X6320]:(~class_Rings_Oordered__comm__semiring(X6320)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6320),X6319),X6318))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6320),c_Groups_Ozero__class_Ozero(X6320)),X6317))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6320),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6320),X6317),X6319)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6320),X6317),X6318)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__mult__left__mono])])])). 4.05/4.30 fof(c_0_7324, plain, ![X1932, X1933, X1934, X1935]:(~class_Rings_Oordered__semiring(X1935)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1935),X1934),X1933))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1935),c_Groups_Ozero__class_Ozero(X1935)),X1932))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1935),X1932),X1934)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1935),X1932),X1933)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left__mono])])])). 4.05/4.30 fof(c_0_7325, plain, ![X3642, X3643, X3644, X3645]:(~class_Fields_Olinordered__field(X3645)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3645),X3644),X3643))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3645),X3642),c_Groups_Ozero__class_Ozero(X3645)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3645),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3645),X3643),X3642)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3645),X3644),X3642)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__strict__right__mono__neg])])])). 4.05/4.30 cnf(c_0_7326, plain, (hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oconcat(X2,X1)))|esk318_2(X1,X2)!=esk319_2(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(X2),esk317_2(X1,X2)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1))), inference(split_conjunct,[status(thm)],[c_0_5059])). 4.05/4.30 fof(c_0_7327, plain, ![X321, X322]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X322),X321))|hAPP(c_Finite__Set_Ocard(X322),X321)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X322,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X322),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X321)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card_Oeq__fold__g])])])). 4.05/4.30 fof(c_0_7328, plain, ![X11309, X11310, X11311, X11312]:(~class_Divides_Osemiring__div(X11312)|(c_Groups_Ozero__class_Ozero(X11312)=X11311|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11312),X11310),X11311)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11312),X11309),X11311))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X11312),X11310),X11309))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__mult2])])])). 4.05/4.30 fof(c_0_7329, plain, ![X15108, X15109, X15110, X15111]:(~class_Rings_Oring__1(X15111)|hAPP(c_Int_Oring__1__class_Oof__int(X15111),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15110,tc_Int_Oint),X15109),X15108))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X15110,X15111),hAPP(hAPP(c_COMBB(tc_Int_Oint,X15111,X15110),c_Int_Oring__1__class_Oof__int(X15111)),X15109)),X15108)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__setsum])])). 4.05/4.30 fof(c_0_7330, plain, ![X14663, X14664, X14665, X14666, X14667]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14667)),X14666)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14665)),X14664)|(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14667)),X14663)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14665)),X14664)|(~hBOOL(hAPP(c_List_Odistinct(X14665),X14664))|(hAPP(c_Map_Omap__of(X14665,X14667),hAPP(hAPP(c_List_Ozip(X14665,X14667),X14664),X14666))!=hAPP(c_Map_Omap__of(X14665,X14667),hAPP(hAPP(c_List_Ozip(X14665,X14667),X14664),X14663))|X14663=X14666)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__of__zip__inject])])])). 4.05/4.30 fof(c_0_7331, plain, ![X1981, X1982, X1983, X1984, X1985, X1986, X1987, X1988]:(~c_Finite__Set_Ofolding__image(X1988,X1987,X1986,X1985,X1984)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1987),X1983))|(~c_Fun_Oinj__on(X1987,X1987,X1982,X1983)|hAPP(hAPP(X1984,hAPP(c_Fun_Ocomp(X1987,X1988,X1987,X1981),X1982)),X1983)=hAPP(hAPP(X1984,X1981),hAPP(c_Set_Oimage(X1987,X1987,X1982),X1983))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image_Oreindex])])])). 4.05/4.30 cnf(c_0_7332, 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,esk199_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_5231])). 4.05/4.30 fof(c_0_7333, plain, ![X8309, X8310, X8311, X8312]:(~class_Rings_Olinordered__ring__strict(X8312)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8312),X8311),X8310))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8312),X8309),c_Groups_Ozero__class_Ozero(X8312)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8312),X8309),X8310)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8312),X8309),X8311)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__strict__left__mono__neg])])])). 4.05/4.30 fof(c_0_7334, plain, ![X7244, X7245, X7246, X7247]:(~class_Rings_Oordered__ring(X7247)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7247),X7246),X7245))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7247),X7244),c_Groups_Ozero__class_Ozero(X7247)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7247),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7247),X7245),X7244)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7247),X7246),X7244)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right__mono__neg])])])). 4.05/4.30 fof(c_0_7335, plain, ![X7507, X7508, X7509, X7510]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7510),X7507),X7508))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7510),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7510),X7509),X7508)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7510),X7509),X7507)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7510),X7509),c_Groups_Ozero__class_Ozero(X7510)))|~class_Rings_Olinordered__ring__strict(X7510))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7510),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7510),X7509),X7508)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7510),X7509),X7507)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7510),X7507),X7508))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7510),X7509),c_Groups_Ozero__class_Ozero(X7510)))|~class_Rings_Olinordered__ring__strict(X7510))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg])])])). 4.05/4.30 fof(c_0_7336, plain, ![X9810, X9811, X9812, X9813]:(~class_Rings_Oordered__ring(X9813)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9813),X9812),X9811))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9813),X9810),c_Groups_Ozero__class_Ozero(X9813)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9813),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9813),X9810),X9811)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9813),X9810),X9812)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])])). 4.05/4.30 fof(c_0_7337, plain, ![X7147, X7148, X7149, X7150, X7151, X7152]:(~c_Finite__Set_Ofun__left__comm(X7152,X7151,X7150)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7152),X7149))|hAPP(hAPP(X7150,X7148),hAPP(hAPP(c_Finite__Set_Ofold(X7152,X7151,X7150),X7147),X7149))=hAPP(hAPP(c_Finite__Set_Ofold(X7152,X7151,X7150),hAPP(hAPP(X7150,X7148),X7147)),X7149))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__fun__comm])])])). 4.05/4.30 fof(c_0_7338, plain, ![X16302, X16303, X16304, X16305]:((~hBOOL(hAPP(X16303,X16305))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X16304)),X16305),hAPP(c_List_Oset(tc_List_Olist(X16304)),c_Enum_On__lists(X16304,X16302,c_Enum_Oenum__class_Oenum(X16304)))))|c_Enum_Oex__n__lists(X16304,X16303,X16302)|~class_Enum_Oenum(X16304))&((hBOOL(hAPP(X16303,esk487_3(X16302,X16303,X16304)))|~c_Enum_Oex__n__lists(X16304,X16303,X16302)|~class_Enum_Oenum(X16304))&(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X16304)),esk487_3(X16302,X16303,X16304)),hAPP(c_List_Oset(tc_List_Olist(X16304)),c_Enum_On__lists(X16304,X16302,c_Enum_Oenum__class_Oenum(X16304)))))|~c_Enum_Oex__n__lists(X16304,X16303,X16302)|~class_Enum_Oenum(X16304)))), 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__n__lists__def])])])])])])). 4.05/4.30 fof(c_0_7339, plain, ![X10642, X10643, X10644, X10645]:(~class_Fields_Ofield__inverse__zero(X10645)|(c_Groups_Ozero__class_Ozero(X10645)=X10644|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10645),X10643),X10642)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10645),X10644),X10643)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10645),X10644),X10642)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__divide__mult__cancel__left])])])). 4.05/4.30 fof(c_0_7340, plain, ![X16063, X16064, X16065, X16066]:(~class_Orderings_Olinorder(X16066)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X16066),hAPP(hAPP(c_Orderings_Oord__class_Omax(X16066),X16065),X16063)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X16066),X16064),X16063))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X16066),hAPP(hAPP(c_Orderings_Oord__class_Omin(X16066),X16065),X16064)),X16063)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__inf__distrib2])])])). 4.05/4.30 fof(c_0_7341, plain, ![X8009, X8010, X8011, X8012]:(~class_Orderings_Olinorder(X8012)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X8012),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8012),X8011),X8009)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X8012),X8010),X8009))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X8012),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8012),X8011),X8010)),X8009)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib2])])). 4.05/4.30 fof(c_0_7342, plain, ![X10427, X10428]:(~class_Orderings_Olinorder(X10428)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10428),X10427))|(X10427=c_Orderings_Obot__class_Obot(tc_fun(X10428,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10428),c_Big__Operators_Olattice_OInf__fin(X10428,c_Orderings_Oord__class_Omin(X10428),X10427)),c_Big__Operators_Olattice_OSup__fin(X10428,c_Orderings_Oord__class_Omax(X10428),X10427)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__le__Sup])])])). 4.05/4.30 fof(c_0_7343, plain, ![X14000, X14001, X14002]:(~class_Orderings_Olinorder(X14002)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14002),X14001))|(c_Orderings_Obot__class_Obot(tc_fun(X14002,tc_HOL_Obool))=X14000|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14002,tc_HOL_Obool)),X14000),X14001))|c_Big__Operators_Olinorder__class_OMax(X14002,X14001)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X14002),c_Big__Operators_Olinorder__class_OMax(X14002,X14000)),c_Big__Operators_Olinorder__class_OMax(X14002,X14001)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Osubset__idem])])])). 4.05/4.30 fof(c_0_7344, plain, ![X6530, X6531, X6532]:(~class_Lattices_Olattice(X6532)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6532),X6531))|(X6530=c_Orderings_Obot__class_Obot(tc_fun(X6532,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6532,tc_HOL_Obool)),X6530),X6531))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6532),c_Big__Operators_Olattice__class_OInf__fin(X6532,X6530)),c_Big__Operators_Olattice__class_OInf__fin(X6532,X6531))=c_Big__Operators_Olattice__class_OInf__fin(X6532,X6531))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Osubset__idem])])])). 4.05/4.30 fof(c_0_7345, plain, ![X15701, X15702, X15703]:(~class_Orderings_Olinorder(X15703)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15703),X15702))|(X15701=c_Orderings_Obot__class_Obot(tc_fun(X15703,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15703,tc_HOL_Obool)),X15701),X15702))|c_Big__Operators_Olinorder__class_OMin(X15703,X15702)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X15703),c_Big__Operators_Olinorder__class_OMin(X15703,X15701)),c_Big__Operators_Olinorder__class_OMin(X15703,X15702)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Osubset__idem])])])). 4.05/4.30 fof(c_0_7346, plain, ![X16011, X16012, X16013, X16014]:(~class_Fields_Ofield__inverse__zero(X16014)|(c_Groups_Ozero__class_Ozero(X16014)=X16013|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16014),X16012),X16011)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16014),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16014),X16012),X16013)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16014),X16011),X16013)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__divide__mult__cancel__right])])])). 4.05/4.30 fof(c_0_7347, plain, ![X2787, X2788, X2789, X2790]:(~class_Groups_Oordered__ab__group__add(X2790)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X2790),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2790),X2789),X2787)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2790),X2788),X2787))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2790),hAPP(hAPP(c_Orderings_Oord__class_Omax(X2790),X2789),X2788)),X2787)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_max__diff__distrib__left])])])). 4.05/4.30 fof(c_0_7348, plain, ![X7775, X7776, X7777, X7778]:(~class_Fields_Ofield__inverse__zero(X7778)|hAPP(hAPP(c_Power_Opower__class_Opower(X7778),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7778),X7777),X7776)),X7775)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7778),hAPP(hAPP(c_Power_Opower__class_Opower(X7778),X7777),X7775)),hAPP(hAPP(c_Power_Opower__class_Opower(X7778),X7776),X7775))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__divide])])])). 4.05/4.30 fof(c_0_7349, plain, ![X6978, X6979, X6980, X6981]:(~class_Groups_Ocomm__monoid__mult(X6981)|hAPP(hAPP(c_Power_Opower__class_Opower(X6981),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6981),X6980),X6979)),X6978)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6981),hAPP(hAPP(c_Power_Opower__class_Opower(X6981),X6980),X6978)),hAPP(hAPP(c_Power_Opower__class_Opower(X6981),X6979),X6978))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult__distrib])])). 4.05/4.30 fof(c_0_7350, plain, ![X1607, X1608, X1609, X1610]:(~class_Rings_Ocomm__semiring__1(X1610)|hAPP(hAPP(c_Power_Opower__class_Opower(X1610),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1610),X1609),X1608)),X1607)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1610),hAPP(hAPP(c_Power_Opower__class_Opower(X1610),X1609),X1607)),hAPP(hAPP(c_Power_Opower__class_Opower(X1610),X1608),X1607))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])])])). 4.05/4.30 fof(c_0_7351, plain, ![X4191, X4192, X4193]:(~class_Lattices_Olattice(X4193)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4193),X4192))|(X4191=c_Orderings_Obot__class_Obot(tc_fun(X4193,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4193,tc_HOL_Obool)),X4191),X4192))|c_Big__Operators_Olattice__class_OSup__fin(X4193,X4192)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X4193),c_Big__Operators_Olattice__class_OSup__fin(X4193,X4191)),c_Big__Operators_Olattice__class_OSup__fin(X4193,X4192)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Osubset__idem])])])). 4.05/4.30 fof(c_0_7352, plain, ![X15080, X15081, X15082, X15083]:(~class_Divides_Osemiring__div(X15083)|(X15082=c_Groups_Ozero__class_Ozero(X15083)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15083),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15083),X15082),X15081)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15083),X15082),X15080))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X15083),X15081),X15080))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__mult1])])])). 4.05/4.30 fof(c_0_7353, plain, ![X15085, X15086, X15087, X15088]:(~class_Groups_Oordered__ab__group__add(X15088)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15088),hAPP(hAPP(c_Orderings_Oord__class_Omin(X15088),X15087),X15086)),X15085)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X15088),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15088),X15087),X15085)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15088),X15086),X15085))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__diff__distrib__left])])). 4.05/4.30 fof(c_0_7354, plain, ![X2796, X2797, X2798, X2799]:(~class_Orderings_Olinorder(X2799)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X2799),X2798),hAPP(hAPP(c_Orderings_Oord__class_Omax(X2799),X2797),X2796))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X2799),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2799),X2798),X2797)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2799),X2798),X2796))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__sup__distrib1])])])). 4.05/4.30 fof(c_0_7355, plain, ![X12173, X12174, X12175, X12176]:(~class_Orderings_Olinorder(X12176)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X12176),X12175),hAPP(hAPP(c_Orderings_Oord__class_Omin(X12176),X12174),X12173))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X12176),hAPP(hAPP(c_Orderings_Oord__class_Omax(X12176),X12175),X12174)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X12176),X12175),X12173))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__inf__distrib1])])])). 4.05/4.30 fof(c_0_7356, plain, ![X15259, X15260, X15261, X15262]:(~class_Rings_Ocomm__semiring__1(X15262)|hAPP(hAPP(c_Power_Opower__class_Opower(X15262),X15261),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15260),X15259))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15262),hAPP(hAPP(c_Power_Opower__class_Opower(X15262),X15261),X15260)),hAPP(hAPP(c_Power_Opower__class_Opower(X15262),X15261),X15259))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])])). 4.05/4.30 fof(c_0_7357, plain, ![X990, X991, X992, X993]:(~hBOOL(hAPP(hAPP(c_member(X993),X992),c_Wellfounded_Oacc(X993,X991)))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X993,X993)),hAPP(hAPP(c_Product__Type_OPair(X993,X993),X990),X992)),X991))|hBOOL(hAPP(hAPP(c_member(X993),X990),c_Wellfounded_Oacc(X993,X991))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downward])])). 4.05/4.30 fof(c_0_7358, plain, ![X13843, X13844, X13845, X13846]:(~class_Groups_Oab__group__add(X13846)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13845,X13846),hAPP(hAPP(c_COMBB(X13846,X13846,X13845),c_Groups_Ouminus__class_Ouminus(X13846)),X13844)),X13843)=hAPP(c_Groups_Ouminus__class_Ouminus(X13846),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X13845,X13846),X13844),X13843))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__negf])])])). 4.05/4.30 cnf(c_0_7359, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(X1),X2))=hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5326])). 4.05/4.30 cnf(c_0_7360, 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_5263])). 4.05/4.30 cnf(c_0_7361, 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_5327])). 4.05/4.30 cnf(c_0_7362, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5328, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_7363, plain, ![X7107, X7108, X7109, X7110]:((~hBOOL(hAPP(hAPP(c_member(tc_prod(X7110,X7110)),hAPP(hAPP(c_Product__Type_OPair(X7110,X7110),X7109),X7107)),c_Transitive__Closure_Ortrancl(X7110,X7108)))|X7107=X7109|hBOOL(hAPP(hAPP(c_member(X7110),X7109),hAPP(c_Relation_ODomain(X7110,X7110),X7108))))&(X7107!=X7109|hBOOL(hAPP(hAPP(c_member(tc_prod(X7110,X7110)),hAPP(hAPP(c_Product__Type_OPair(X7110,X7110),X7109),X7107)),c_Transitive__Closure_Ortrancl(X7110,X7108)))|hBOOL(hAPP(hAPP(c_member(X7110),X7109),hAPP(c_Relation_ODomain(X7110,X7110),X7108))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Not__Domain__rtrancl])])])])). 4.05/4.30 fof(c_0_7364, plain, ![X11975, X11976, X11977, X11980, X11981, X11982, X11983, X11984]:(((hAPP(hAPP(c_List_Oappend(X11977),esk369_3(X11975,X11976,X11977)),hAPP(hAPP(c_List_Olist_OCons(X11977),X11976),esk370_3(X11975,X11976,X11977)))=X11975|~hBOOL(hAPP(hAPP(c_member(X11977),X11976),hAPP(c_List_Oset(X11977),X11975))))&(~hBOOL(hAPP(hAPP(c_member(X11977),X11976),hAPP(c_List_Oset(X11977),esk370_3(X11975,X11976,X11977))))|~hBOOL(hAPP(hAPP(c_member(X11977),X11976),hAPP(c_List_Oset(X11977),X11975)))))&(hAPP(hAPP(c_List_Oappend(X11982),X11983),hAPP(hAPP(c_List_Olist_OCons(X11982),X11981),X11984))!=X11980|hBOOL(hAPP(hAPP(c_member(X11982),X11981),hAPP(c_List_Oset(X11982),X11984)))|hBOOL(hAPP(hAPP(c_member(X11982),X11981),hAPP(c_List_Oset(X11982),X11980))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__set__conv__decomp__last])])])])])])])). 4.05/4.30 fof(c_0_7365, plain, ![X12490, X12491, X12492, X12493, X12494, X12495, X12496, X12497]:((X12490!=hAPP(hAPP(c_List_Oappend(X12492),X12493),hAPP(hAPP(c_List_Olist_OCons(X12492),X12491),X12494))|hBOOL(hAPP(hAPP(c_member(X12492),X12491),hAPP(c_List_Oset(X12492),X12493)))|hBOOL(hAPP(hAPP(c_member(X12492),X12491),hAPP(c_List_Oset(X12492),X12490))))&((X12495=hAPP(hAPP(c_List_Oappend(X12497),esk382_3(X12495,X12496,X12497)),hAPP(hAPP(c_List_Olist_OCons(X12497),X12496),esk383_3(X12495,X12496,X12497)))|~hBOOL(hAPP(hAPP(c_member(X12497),X12496),hAPP(c_List_Oset(X12497),X12495))))&(~hBOOL(hAPP(hAPP(c_member(X12497),X12496),hAPP(c_List_Oset(X12497),esk382_3(X12495,X12496,X12497))))|~hBOOL(hAPP(hAPP(c_member(X12497),X12496),hAPP(c_List_Oset(X12497),X12495)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__set__conv__decomp__first])])])])])])])). 4.05/4.30 fof(c_0_7366, plain, ![X16281, X16282, X16283]:(~class_Lattices_Oab__semigroup__idem__mult(X16283)|(c_Orderings_Obot__class_Obot(tc_fun(X16283,tc_HOL_Obool))=X16282|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16283),X16282))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16283),X16281),hAPP(c_Finite__Set_Ofold1(X16283,c_Groups_Otimes__class_Otimes(X16283)),X16282))=hAPP(c_Finite__Set_Ofold1(X16283,c_Groups_Otimes__class_Otimes(X16283)),hAPP(hAPP(c_Set_Oinsert(X16283),X16281),X16282))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__insert__idem])])])). 4.05/4.30 cnf(c_0_7367, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X1))), inference(rw,[status(thm)],[c_0_5329, c_0_4434])). 4.05/4.30 fof(c_0_7368, plain, ![X7801, X7802, X7803]:(~class_Rings_Olinordered__ring(X7803)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7803),c_Groups_Ozero__class_Ozero(X7803)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7803),X7802),X7802)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7803),X7801),X7801))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero])])). 4.05/4.30 fof(c_0_7369, plain, ![X9981, X9982, X9983, X9984]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X9984,X9983),tc_HOL_Obool)),X9982),X9981))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9984,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X9984,X9983),X9982)),hAPP(c_Relation_ODomain(X9984,X9983),X9981)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Domain__mono])])])). 4.05/4.30 cnf(c_0_7370, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Product__Type_Ofst(tc_Nat_Onat,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),X2)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2))!=X3), inference(split_conjunct,[status(thm)],[c_0_5084])). 4.05/4.30 cnf(c_0_7371, 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)), inference(split_conjunct,[status(thm)],[c_0_5330]), ['final']). 4.05/4.30 cnf(c_0_7372, 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_5331]), ['final']). 4.05/4.30 cnf(c_0_7373, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk37_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_5332])). 4.05/4.30 fof(c_0_7374, plain, ![X15639, X15640, X15641]:(~class_Orderings_Olinorder(X15641)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15641),X15640),X15639))|hAPP(c_SetInterval_Oord__class_OatLeast(X15641),X15640)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15641,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X15641,X15640),X15639)),hAPP(c_SetInterval_Oord__class_OatLeast(X15641),X15639)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I14_J])])). 4.05/4.30 fof(c_0_7375, plain, ![X4547, X4548, X4549]:(~class_Orderings_Olinorder(X4549)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4549),X4548),X4547))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4549,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X4549),X4548)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X4549,X4548),X4547))=hAPP(c_SetInterval_Oord__class_OlessThan(X4549),X4547))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I8_J])])). 4.05/4.30 fof(c_0_7376, plain, ![X11540, X11541, X11542]:(X11542=c_List_Olist_ONil(X11541)|hAPP(hAPP(c_List_Olist_OCons(X11541),hAPP(c_List_Ohd(X11541),X11542)),hAPP(hAPP(c_List_Otake(X11541),X11540),hAPP(c_List_Otl(X11541),X11542)))=hAPP(hAPP(c_List_Otake(X11541),hAPP(c_Nat_OSuc,X11540)),X11542)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_take__Suc])])])). 4.05/4.30 cnf(c_0_7377, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))=X2|~class_Fields_Ofield(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5333, c_0_4475])). 4.05/4.30 fof(c_0_7378, plain, ![X6430, X6431, X6432]:(~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),X6432),X6431)),X6430)),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)),X6430))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6432))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6431),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_q__neg__lemma])])])). 4.05/4.30 fof(c_0_7379, plain, ![X16051, X16052, X16053, X16054, X16055, X16056, X16057, X16058, X16059, X16060, X16061]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16053,tc_HOL_Obool)),X16056),X16051))|X16054!=hAPP(c_Set_Oimage(X16053,X16055,X16052),X16056)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16055,tc_HOL_Obool)),X16054),hAPP(c_Set_Oimage(X16053,X16055,X16052),X16051))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16059,tc_HOL_Obool)),esk479_5(X16057,X16058,X16059,X16060,X16061)),X16057))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16061,tc_HOL_Obool)),X16060),hAPP(c_Set_Oimage(X16059,X16061,X16058),X16057))))&(X16060=hAPP(c_Set_Oimage(X16059,X16061,X16058),esk479_5(X16057,X16058,X16059,X16060,X16061))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16061,tc_HOL_Obool)),X16060),hAPP(c_Set_Oimage(X16059,X16061,X16058),X16057)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__image__iff])])])])])])). 4.05/4.30 fof(c_0_7380, plain, ![X10906, X10907, X10908, X10909, X10910, X10911, X10912, X10913]:(~c_Finite__Set_Ofolding__image__simple__idem(X10913,X10912,X10911,X10910,X10909,X10908)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10912),X10907))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10912,tc_HOL_Obool)),X10906),X10907))|hAPP(X10908,X10907)=hAPP(hAPP(X10911,hAPP(X10908,X10906)),hAPP(X10908,X10907))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem])])])). 4.05/4.30 fof(c_0_7381, plain, ![X7424, X7425, X7426, X7427]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X7427|hAPP(hAPP(c_List_Onth(X7426),hAPP(hAPP(c_List_Olist_OCons(X7426),X7425),X7424)),X7427)=X7425)&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X7427|hAPP(hAPP(c_List_Onth(X7426),X7424),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7427),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_List_Onth(X7426),hAPP(hAPP(c_List_Olist_OCons(X7426),X7425),X7424)),X7427))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__Cons_H])])])). 4.05/4.30 cnf(c_0_7382, 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_5334])). 4.05/4.30 cnf(c_0_7383, 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_5335])). 4.05/4.30 fof(c_0_7384, plain, ![X12977, X12978, X12979, X12980]:(~class_Rings_Ocomm__semiring__1(X12980)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12980),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12980),X12979),X12977)),X12978)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12980),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12980),X12979),X12978)),X12977)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])])])). 4.05/4.30 fof(c_0_7385, plain, ![X16776, X16777, X16778, X16779]:(~class_Rings_Ocomm__semiring__1(X16779)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16779),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16779),X16778),X16777)),X16776)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16779),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16779),X16778),X16776)),X16777)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])])])). 4.05/4.30 fof(c_0_7386, plain, ![X11340, X11341, X11342, X11344, X11345, X11346, X11347, X11348]:((((hBOOL(hAPP(hAPP(c_member(X11342),esk346_3(X11340,X11341,X11342)),hAPP(c_List_Oset(X11342),X11340)))|~c_List_Olist__ex1(X11342,X11341,X11340))&(~hBOOL(hAPP(X11341,X11344))|~hBOOL(hAPP(hAPP(c_member(X11342),X11344),hAPP(c_List_Oset(X11342),X11340)))|X11344=esk346_3(X11340,X11341,X11342)|~c_List_Olist__ex1(X11342,X11341,X11340)))&(hBOOL(hAPP(X11341,esk346_3(X11340,X11341,X11342)))|~c_List_Olist__ex1(X11342,X11341,X11340)))&(((hBOOL(hAPP(X11346,esk347_4(X11345,X11346,X11347,X11348)))|~hBOOL(hAPP(hAPP(c_member(X11347),X11348),hAPP(c_List_Oset(X11347),X11345)))|~hBOOL(hAPP(X11346,X11348))|c_List_Olist__ex1(X11347,X11346,X11345))&(hBOOL(hAPP(hAPP(c_member(X11347),esk347_4(X11345,X11346,X11347,X11348)),hAPP(c_List_Oset(X11347),X11345)))|~hBOOL(hAPP(hAPP(c_member(X11347),X11348),hAPP(c_List_Oset(X11347),X11345)))|~hBOOL(hAPP(X11346,X11348))|c_List_Olist__ex1(X11347,X11346,X11345)))&(esk347_4(X11345,X11346,X11347,X11348)!=X11348|~hBOOL(hAPP(hAPP(c_member(X11347),X11348),hAPP(c_List_Oset(X11347),X11345)))|~hBOOL(hAPP(X11346,X11348))|c_List_Olist__ex1(X11347,X11346,X11345)))), 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__ex1__iff])])])])])])])). 4.05/4.30 fof(c_0_7387, plain, ![X11584, X11585, X11586, X11587]:(~class_Groups_Ocomm__monoid__add(X11587)|(~hBOOL(hAPP(c_List_Odistinct(X11586),X11585))|hAPP(c_List_Omonoid__add__class_Olistsum(X11587),hAPP(hAPP(c_List_Omap(X11586,X11587),X11584),X11585))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X11586,X11587),X11584),hAPP(c_List_Oset(X11586),X11585)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__distinct__conv__setsum__set])])])). 4.05/4.30 fof(c_0_7388, plain, ![X11935, X11936, X11937]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11937),X11936))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X11936)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11937),X11935))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11936),X11937))),X11935)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2])])). 4.05/4.30 fof(c_0_7389, plain, ![X17049, X17050, X17051]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17051),X17050))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17049),X17051)),hAPP(c_Nat_OSuc,X17050))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17049),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17050),X17051)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__Suc__diff__eq1])])])). 4.05/4.30 fof(c_0_7390, plain, ![X13106, X13107, X13108]:(~class_Rings_Olinordered__idom(X13108)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13108),c_Groups_Ozero__class_Ozero(X13108)),X13107))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13108),c_Groups_Ozero__class_Ozero(X13108)),X13106))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13108),X13106),c_Groups_Oone__class_Oone(X13108)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13108),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13108),X13107),X13106)),X13107)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right__le__one__le])])])). 4.05/4.30 fof(c_0_7391, plain, ![X5204, X5205, X5206]:(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5204,X5205)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5206,X5205)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5204),X5206))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5204),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5205),esk159_3(X5204,X5205,X5206)))=X5206)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__mod__eq__lemma])])])])). 4.05/4.30 fof(c_0_7392, plain, ![X8661, X8662, X8663]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X8663),esk277_3(X8661,X8662,X8663)))|hBOOL(hAPP(X8661,c_Orderings_Obot__class_Obot(tc_fun(X8663,tc_HOL_Obool))))|~hBOOL(hAPP(X8661,X8662))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8663),X8662)))&((hBOOL(hAPP(hAPP(c_member(X8663),esk276_3(X8661,X8662,X8663)),esk277_3(X8661,X8662,X8663)))|hBOOL(hAPP(X8661,c_Orderings_Obot__class_Obot(tc_fun(X8663,tc_HOL_Obool))))|~hBOOL(hAPP(X8661,X8662))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8663),X8662)))&((hBOOL(hAPP(X8661,esk277_3(X8661,X8662,X8663)))|hBOOL(hAPP(X8661,c_Orderings_Obot__class_Obot(tc_fun(X8663,tc_HOL_Obool))))|~hBOOL(hAPP(X8661,X8662))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8663),X8662)))&(~hBOOL(hAPP(X8661,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8663,tc_HOL_Obool)),esk277_3(X8661,X8662,X8663)),hAPP(hAPP(c_Set_Oinsert(X8663),esk276_3(X8661,X8662,X8663)),c_Orderings_Obot__class_Obot(tc_fun(X8663,tc_HOL_Obool))))))|hBOOL(hAPP(X8661,c_Orderings_Obot__class_Obot(tc_fun(X8663,tc_HOL_Obool))))|~hBOOL(hAPP(X8661,X8662))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8663),X8662)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__empty__induct])])])])])). 4.05/4.30 fof(c_0_7393, plain, ![X14212, X14213, X14214]:(~class_Rings_Olinordered__idom(X14214)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14214),c_Groups_Ozero__class_Ozero(X14214)),X14213))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14214),c_Groups_Ozero__class_Ozero(X14214)),X14212))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14214),X14212),c_Groups_Oone__class_Oone(X14214)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14214),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14214),X14212),X14213)),X14213)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left__le__one__le])])])). 4.05/4.30 cnf(c_0_7394, 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_5336])). 4.05/4.30 fof(c_0_7395, plain, ![X3145, X3146, X3147]:((hBOOL(hAPP(hAPP(c_member(X3147),esk107_3(X3145,X3146,X3147)),X3145))|c_Relation_Orefl__on(X3147,X3145,X3146)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3147,X3147),tc_HOL_Obool)),X3146),hAPP(hAPP(c_Product__Type_OSigma(X3147,X3147),X3145),hAPP(c_COMBK(tc_fun(X3147,tc_HOL_Obool),X3147),X3145)))))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X3147,X3147)),hAPP(hAPP(c_Product__Type_OPair(X3147,X3147),esk107_3(X3145,X3146,X3147)),esk107_3(X3145,X3146,X3147))),X3146))|c_Relation_Orefl__on(X3147,X3145,X3146)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3147,X3147),tc_HOL_Obool)),X3146),hAPP(hAPP(c_Product__Type_OSigma(X3147,X3147),X3145),hAPP(c_COMBK(tc_fun(X3147,tc_HOL_Obool),X3147),X3145)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onI])])])])). 4.05/4.30 fof(c_0_7396, plain, ![X11514, X11515, X11516, X11517, X11519, X11520, X11521, X11522, X11523]:(((hBOOL(hAPP(hAPP(c_member(X11517),esk356_4(X11514,X11515,X11516,X11517)),hAPP(c_List_Oset(X11517),c_List_Oreplicate(X11517,X11516,X11515))))|(hBOOL(hAPP(X11514,X11515))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X11516))&(~hBOOL(hAPP(X11514,esk356_4(X11514,X11515,X11516,X11517)))|(hBOOL(hAPP(X11514,X11515))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X11516)))&((~hBOOL(hAPP(X11519,X11520))|(~hBOOL(hAPP(hAPP(c_member(X11522),X11523),hAPP(c_List_Oset(X11522),c_List_Oreplicate(X11522,X11521,X11520))))|hBOOL(hAPP(X11519,X11523))))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X11521|(~hBOOL(hAPP(hAPP(c_member(X11522),X11523),hAPP(c_List_Oset(X11522),c_List_Oreplicate(X11522,X11521,X11520))))|hBOOL(hAPP(X11519,X11523)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ball__set__replicate])])])])])])). 4.05/4.30 fof(c_0_7397, plain, ![X15896, X15897, X15898, X15899, X15900]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X15900)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15900),X15899),X15898))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15900),X15897),X15896))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15900),X15899),X15897)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15900),X15898),X15896)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__mono])])])). 4.05/4.30 fof(c_0_7398, plain, ![X9783, X9784, X9785, X9786, X9787]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X9787)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9787),X9786),X9785))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9787),X9784),X9783))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9787),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9787),X9786),X9784)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9787),X9785),X9783)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__less__mono])])])). 4.05/4.30 fof(c_0_7399, plain, ![X14836, X14837, X14838, X14839, X14840]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X14840)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14840),X14839),X14838))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14840),X14837),X14836))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14840),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14840),X14839),X14837)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14840),X14838),X14836)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__less__le__mono])])])). 4.05/4.30 cnf(c_0_7400, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X3)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3))), inference(rw,[status(thm)],[c_0_5337, c_0_5018])). 4.05/4.30 fof(c_0_7401, plain, ![X4168, X4169, X4170, X4171]:(~class_Fields_Olinordered__field(X4171)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4170,X4171),hAPP(hAPP(c_COMBB(X4171,X4171,X4170),c_Groups_Oabs__class_Oabs(X4171)),X4169)),X4168)=hAPP(c_Groups_Oabs__class_Oabs(X4171),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4170,X4171),X4169),X4168))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__setprod])])])). 4.05/4.30 fof(c_0_7402, plain, ![X8769, X8770, X8771, X8772, X8773]:(~class_Lattices_Osemilattice__inf(X8773)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8773),X8772),X8771))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8773),X8770),X8769))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8773),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8773),X8772),X8770)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8773),X8771),X8769)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__mono])])])). 4.05/4.30 fof(c_0_7403, plain, ![X9642, X9643, X9644, X9645, X9646]:(~class_Lattices_Osemilattice__sup(X9646)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9646),X9645),X9644))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9646),X9643),X9642))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9646),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9646),X9645),X9643)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9646),X9644),X9642)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__mono])])])). 4.05/4.30 fof(c_0_7404, plain, ![X8677, X8678, X8679, X8680, X8681]:(~class_Groups_Oordered__ab__semigroup__add(X8681)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8681),X8680),X8679))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8681),X8678),X8677))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8681),X8680),X8678)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8681),X8679),X8677)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__mono])])])). 4.05/4.30 fof(c_0_7405, plain, ![X9288, X9289, X9290, X9291]:(~class_Rings_Olinordered__semidom(X9291)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9291),X9290),X9289))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9291),c_Groups_Ozero__class_Ozero(X9291)),X9290))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9291),hAPP(hAPP(c_Power_Opower__class_Opower(X9291),X9290),X9288)),hAPP(hAPP(c_Power_Opower__class_Opower(X9291),X9289),X9288)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__mono])])])). 4.05/4.30 cnf(c_0_7406, plain, (hAPP(X1,X2)=hAPP(c_Option_Ooption_OSome(X3),esk208_6(X2,X1,X4,X5,X6,X3))|hAPP(X1,X2)=c_Option_Ooption_ONone(X3)|c_Option_Ooption_ONone(X6)!=c_Map_Omap__comp(X3,X6,X5,X4,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5338])). 4.05/4.30 cnf(c_0_7407, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk23_3(X1,X2,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),X2),hAPP(hAPP(c_Relation_Orel__comp(X3,X3,X3),c_Transitive__Closure_Ortrancl(X3,X1)),X1)))), inference(rw,[status(thm)],[c_0_5339, c_0_5018])). 4.05/4.30 fof(c_0_7408, plain, ![X8993, X8994, X8995, X8996]:(~class_Fields_Olinordered__field__inverse__zero(X8996)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8996),X8995),X8994))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8996),c_Groups_Ozero__class_Ozero(X8996)),X8993))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8996),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8996),X8995),X8993)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8996),X8994),X8993)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__right__mono])])])). 4.05/4.30 fof(c_0_7409, plain, ![X13523, X13524, X13525, X13526]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13526),hAPP(hAPP(c_Power_Opower__class_Opower(X13526),X13525),X13524)),hAPP(hAPP(c_Power_Opower__class_Opower(X13526),X13525),X13523)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13524),X13523))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13526),c_Groups_Oone__class_Oone(X13526)),X13525))|~class_Rings_Olinordered__semidom(X13526))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13524),X13523))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13526),hAPP(hAPP(c_Power_Opower__class_Opower(X13526),X13525),X13524)),hAPP(hAPP(c_Power_Opower__class_Opower(X13526),X13525),X13523)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13526),c_Groups_Oone__class_Oone(X13526)),X13525))|~class_Rings_Olinordered__semidom(X13526))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__strict__increasing__iff])])])])). 4.05/4.30 fof(c_0_7410, plain, ![X11718, X11719, X11720, X11721]:(~class_Rings_Olinordered__semidom(X11721)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11720),X11719))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11721),c_Groups_Oone__class_Oone(X11721)),X11718))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11721),hAPP(hAPP(c_Power_Opower__class_Opower(X11721),X11718),X11720)),hAPP(hAPP(c_Power_Opower__class_Opower(X11721),X11718),X11719)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__increasing])])])). 4.05/4.30 fof(c_0_7411, plain, ![X6353, X6354, X6355, X6356]:(hBOOL(hAPP(hAPP(c_member(X6356),X6355),X6354))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6356,tc_HOL_Obool)),X6354),hAPP(hAPP(c_Set_Oinsert(X6356),X6355),X6353))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6356,tc_HOL_Obool)),X6354),X6353)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__insert__right__if0])])])). 4.05/4.30 fof(c_0_7412, plain, ![X7607, X7608]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7608),X7607))|c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X7607,X7608))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7608),X7607))|c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X7607,X7608)=hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X7607),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X7607),c_Groups_Oone__class_Oone(tc_Int_Oint)),X7608)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_simp__from__to])])])). 4.05/4.30 cnf(c_0_7413, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk454_4(X1,X2,X3,X4)),X1))|X4=X2|X2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5245])). 4.05/4.30 fof(c_0_7414, plain, ![X14569, X14570, X14571, X14572]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14570),X14569))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14572),hAPP(hAPP(c_Power_Opower__class_Opower(X14572),X14571),X14570)),hAPP(hAPP(c_Power_Opower__class_Opower(X14572),X14571),X14569)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14572),c_Groups_Oone__class_Oone(X14572)),X14571))|~class_Rings_Olinordered__semidom(X14572))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14572),hAPP(hAPP(c_Power_Opower__class_Opower(X14572),X14571),X14570)),hAPP(hAPP(c_Power_Opower__class_Opower(X14572),X14571),X14569)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14570),X14569))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14572),c_Groups_Oone__class_Oone(X14572)),X14571))|~class_Rings_Olinordered__semidom(X14572))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__increasing__iff])])])])). 4.05/4.30 fof(c_0_7415, plain, ![X14607, X14608, X14609, X14610]:(~class_Fields_Olinordered__field__inverse__zero(X14610)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14610),X14609),X14608))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14610),X14607),c_Groups_Ozero__class_Ozero(X14610)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14610),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14610),X14608),X14607)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14610),X14609),X14607)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__right__mono__neg])])])). 4.05/4.30 fof(c_0_7416, plain, ![X5494, X5495]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5495),X5494))|c_Lazy__Sequence_Oempty(tc_Int_Oint)=c_Lazy__Sequence_Osmall__lazy_H(X5495,X5494))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5495),X5494))|c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X5494),c_Lazy__Sequence_Osmall__lazy_H(X5495,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5494),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Lazy__Sequence_Osmall__lazy_H(X5495,X5494))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_small__lazy_H_Osimps])])])). 4.05/4.30 fof(c_0_7417, plain, ![X4726, X4727, X4728, X4729]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X4729),esk145_4(X4726,X4727,X4728,X4729)))|hBOOL(hAPP(X4726,X4728))|~hBOOL(hAPP(X4726,c_Orderings_Obot__class_Obot(tc_fun(X4729,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4729,tc_HOL_Obool)),X4728),X4727))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4729),X4728)))&((hBOOL(hAPP(hAPP(c_member(X4729),esk144_4(X4726,X4727,X4728,X4729)),X4727))|hBOOL(hAPP(X4726,X4728))|~hBOOL(hAPP(X4726,c_Orderings_Obot__class_Obot(tc_fun(X4729,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4729,tc_HOL_Obool)),X4728),X4727))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4729),X4728)))&((~hBOOL(hAPP(hAPP(c_member(X4729),esk144_4(X4726,X4727,X4728,X4729)),esk145_4(X4726,X4727,X4728,X4729)))|hBOOL(hAPP(X4726,X4728))|~hBOOL(hAPP(X4726,c_Orderings_Obot__class_Obot(tc_fun(X4729,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4729,tc_HOL_Obool)),X4728),X4727))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4729),X4728)))&((hBOOL(hAPP(X4726,esk145_4(X4726,X4727,X4728,X4729)))|hBOOL(hAPP(X4726,X4728))|~hBOOL(hAPP(X4726,c_Orderings_Obot__class_Obot(tc_fun(X4729,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4729,tc_HOL_Obool)),X4728),X4727))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4729),X4728)))&(~hBOOL(hAPP(X4726,hAPP(hAPP(c_Set_Oinsert(X4729),esk144_4(X4726,X4727,X4728,X4729)),esk145_4(X4726,X4727,X4728,X4729))))|hBOOL(hAPP(X4726,X4728))|~hBOOL(hAPP(X4726,c_Orderings_Obot__class_Obot(tc_fun(X4729,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4729,tc_HOL_Obool)),X4728),X4727))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4729),X4728))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__subset__induct])])])])])). 4.05/4.30 fof(c_0_7418, plain, ![X5761, X5762]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X5762|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X5761,X5762),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X5761),X5762)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X5761,X5762))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div__mod])])). 4.05/4.30 cnf(c_0_7419, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk69_4(X1,X2,X3,X4)),X1))|X4=X2|X2!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_5250])). 4.05/4.30 fof(c_0_7420, plain, ![X7177, X7178, X7179]:((((c_Orderings_Obot__class_Obot(tc_fun(X7179,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7179,tc_HOL_Obool)),hAPP(c_List_Oset(X7179),X7178)),hAPP(c_List_Oset(X7179),X7177))|~hBOOL(hAPP(c_List_Odistinct(X7179),hAPP(hAPP(c_List_Oappend(X7179),X7178),X7177))))&(hBOOL(hAPP(c_List_Odistinct(X7179),X7177))|~hBOOL(hAPP(c_List_Odistinct(X7179),hAPP(hAPP(c_List_Oappend(X7179),X7178),X7177)))))&(hBOOL(hAPP(c_List_Odistinct(X7179),X7178))|~hBOOL(hAPP(c_List_Odistinct(X7179),hAPP(hAPP(c_List_Oappend(X7179),X7178),X7177)))))&(c_Orderings_Obot__class_Obot(tc_fun(X7179,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7179,tc_HOL_Obool)),hAPP(c_List_Oset(X7179),X7178)),hAPP(c_List_Oset(X7179),X7177))|~hBOOL(hAPP(c_List_Odistinct(X7179),X7177))|~hBOOL(hAPP(c_List_Odistinct(X7179),X7178))|hBOOL(hAPP(c_List_Odistinct(X7179),hAPP(hAPP(c_List_Oappend(X7179),X7178),X7177))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__append])])])). 4.05/4.30 fof(c_0_7421, plain, ![X7030, X7031, X7032]:(~class_Rings_Oring__1(X7032)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7031),X7030))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7032),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7032),X7030)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7032),X7031))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X7032),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7030),X7031)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__diff])])])). 4.05/4.30 fof(c_0_7422, plain, ![X4364, X4365, X4366, X4367]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk135_4(X4364,X4365,X4366,X4367)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4367)),X4366)))|(~hBOOL(hAPP(hAPP(c_member(X4367),X4364),hAPP(c_List_Oset(X4367),X4366)))|hBOOL(hAPP(X4365,X4364))))&(~hBOOL(hAPP(X4365,hAPP(hAPP(c_List_Onth(X4367),X4366),esk135_4(X4364,X4365,X4366,X4367))))|(~hBOOL(hAPP(hAPP(c_member(X4367),X4364),hAPP(c_List_Oset(X4367),X4366)))|hBOOL(hAPP(X4365,X4364))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_all__nth__imp__all__set])])])])). 4.05/4.30 fof(c_0_7423, plain, ![X11847, X11848, X11849]:(X11849=c_List_Olist_ONil(X11848)|hBOOL(hAPP(hAPP(c_member(X11848),hAPP(c_Product__Type_Ofst(X11848,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X11848,X11849),X11847))),hAPP(c_List_Oset(X11848),X11849)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_select])])])). 4.05/4.30 fof(c_0_7424, plain, ![X10565, X10566, X10567]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10567))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10567),X10566)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10567),X10565))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X10566),X10565)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1])])). 4.05/4.30 fof(c_0_7425, plain, ![X8976, X8977, X8978, X8979, X8980, X8981]:(~c_List_Olist__all2(X8981,X8980,X8979,X8978,X8977)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8976),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8980)),X8977)))|hBOOL(hAPP(hAPP(X8979,hAPP(hAPP(c_List_Onth(X8981),X8978),X8976)),hAPP(hAPP(c_List_Onth(X8980),X8977),X8976))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__nthD2])])). 4.05/4.30 cnf(c_0_7426, 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_5340, c_0_5341]), c_0_5341])). 4.05/4.30 fof(c_0_7427, plain, ![X6829, X6830, X6831, X6832]:(~class_Groups_Osemigroup__add(X6832)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6832),X6831),hAPP(c_List_Ofoldl(X6832,X6832,c_Groups_Oplus__class_Oplus(X6832),X6830),X6829))=hAPP(c_List_Ofoldl(X6832,X6832,c_Groups_Oplus__class_Oplus(X6832),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6832),X6831),X6830)),X6829)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_foldl__assoc])])])). 4.05/4.30 fof(c_0_7428, plain, ![X8279, X8280, X8281, X8282, X8283, X8284]:(~c_Finite__Set_Ofolding__idem(X8284,X8283,X8282,X8281)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8284),X8280))|(~hBOOL(hAPP(hAPP(c_member(X8284),X8279),X8280))|hAPP(c_Fun_Ocomp(X8283,X8283,X8283,hAPP(X8281,X8280)),hAPP(X8282,X8279))=hAPP(X8281,X8280)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oin__comp__idem])])). 4.05/4.30 fof(c_0_7429, plain, ![X1763, X1764, X1765, X1766, X1768, X1769, X1770, X1771, X1772]:(((hBOOL(hAPP(X1763,esk59_4(X1763,X1764,X1765,X1766)))|(~hBOOL(hAPP(X1763,X1764))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1765))&(hBOOL(hAPP(hAPP(c_member(X1766),esk59_4(X1763,X1764,X1765,X1766)),hAPP(c_List_Oset(X1766),c_List_Oreplicate(X1766,X1765,X1764))))|(~hBOOL(hAPP(X1763,X1764))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1765)))&((hBOOL(hAPP(X1768,X1769))|(~hBOOL(hAPP(X1768,X1772))|~hBOOL(hAPP(hAPP(c_member(X1771),X1772),hAPP(c_List_Oset(X1771),c_List_Oreplicate(X1771,X1770,X1769))))))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1770|(~hBOOL(hAPP(X1768,X1772))|~hBOOL(hAPP(hAPP(c_member(X1771),X1772),hAPP(c_List_Oset(X1771),c_List_Oreplicate(X1771,X1770,X1769)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Bex__set__replicate])])])])])])). 4.05/4.30 cnf(c_0_7430, plain, (hBOOL(hAPP(X1,esk73_2(X1,X2)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk71_2(X1,X2)),X2))))|~hBOOL(hAPP(X1,esk70_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5097])). 4.05/4.30 fof(c_0_7431, plain, ![X6292, X6293]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X6293|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6292),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6293),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X6292))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6293),X6292))&(X6293!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6293),X6292)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__if])])). 4.05/4.30 fof(c_0_7432, plain, ![X15788, X15789, X15790, X15791]:((X15791!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Odrop(X15790),X15791),hAPP(hAPP(c_List_Olist_OCons(X15790),X15789),X15788))=hAPP(hAPP(c_List_Olist_OCons(X15790),X15789),X15788))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X15791|hAPP(hAPP(c_List_Odrop(X15790),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15791),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X15788)=hAPP(hAPP(c_List_Odrop(X15790),X15791),hAPP(hAPP(c_List_Olist_OCons(X15790),X15789),X15788)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_drop__Cons_H])])])). 4.05/4.30 fof(c_0_7433, plain, ![X8213, X8214, X8215, X8216]:(((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8216)),X8214),c_List_Olists(X8216,X8213)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8216)),hAPP(hAPP(c_List_Olist_OCons(X8216),X8215),X8214)),c_List_Olists(X8216,X8213))))&(hBOOL(hAPP(hAPP(c_member(X8216),X8215),X8213))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8216)),hAPP(hAPP(c_List_Olist_OCons(X8216),X8215),X8214)),c_List_Olists(X8216,X8213)))))&(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8216)),X8214),c_List_Olists(X8216,X8213)))|~hBOOL(hAPP(hAPP(c_member(X8216),X8215),X8213))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8216)),hAPP(hAPP(c_List_Olist_OCons(X8216),X8215),X8214)),c_List_Olists(X8216,X8213))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lists__iff])])])). 4.05/4.30 fof(c_0_7434, plain, ![X16677, X16678, X16679]:(~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),X16679),X16678)),X16677)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16677),X16679))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16679))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16678))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_q__pos__lemma])])])). 4.05/4.30 fof(c_0_7435, plain, ![X14262, X14263]:(c_List_Olist_ONil(X14262)=X14263|hAPP(hAPP(c_List_Oappend(X14262),hAPP(c_List_Otl(X14262),X14263)),hAPP(hAPP(c_List_Olist_OCons(X14262),hAPP(c_List_Ohd(X14262),X14263)),c_List_Olist_ONil(X14262)))=hAPP(c_List_Orotate1(X14262),X14263)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rotate1__hd__tl])])])). 4.05/4.30 cnf(c_0_7436, 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_5342])). 4.05/4.30 fof(c_0_7437, plain, ![X11199, X11200, X11201, X11202, X11203]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11203),X11201),X11199))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11203),X11202),X11201))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11203,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X11203,X11202,X11201)),c_SetInterval_Oord__class_OatLeastAtMost(X11203,X11200,X11199)))|~class_Orderings_Oorder(X11203))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11203),X11200),X11202))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11203),X11202),X11201))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11203,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X11203,X11202,X11201)),c_SetInterval_Oord__class_OatLeastAtMost(X11203,X11200,X11199)))|~class_Orderings_Oorder(X11203)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11203),X11202),X11201))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11203,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X11203,X11202,X11201)),c_SetInterval_Oord__class_OatLeastAtMost(X11203,X11200,X11199)))|~class_Orderings_Oorder(X11203))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11203),X11201),X11199))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11203),X11200),X11202))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11203,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X11203,X11202,X11201)),c_SetInterval_Oord__class_OatLeastAtMost(X11203,X11200,X11199)))|~class_Orderings_Oorder(X11203)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastatMost__subset__iff])])])])). 4.05/4.30 fof(c_0_7438, plain, ![X13306, X13307, X13308]:(~class_Orderings_Olinorder(X13308)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13308,tc_HOL_Obool)),X13307),X13306))|(c_Orderings_Obot__class_Obot(tc_fun(X13308,tc_HOL_Obool))=X13307|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13308),X13306))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13308),c_Big__Operators_Olinorder__class_OMax(X13308,X13307)),c_Big__Operators_Olinorder__class_OMax(X13308,X13306))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max__mono])])])). 4.05/4.30 fof(c_0_7439, plain, ![X7821, X7822, X7823]:(~class_Orderings_Olinorder(X7823)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7823,tc_HOL_Obool)),X7822),X7821))|(c_Orderings_Obot__class_Obot(tc_fun(X7823,tc_HOL_Obool))=X7822|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7823),X7821))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7823),c_Big__Operators_Olinorder__class_OMin(X7823,X7821)),c_Big__Operators_Olinorder__class_OMin(X7823,X7822))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__antimono])])). 4.05/4.30 fof(c_0_7440, plain, ![X16728, X16729]:(~class_Groups_Ocomm__monoid__add(X16729)|hAPP(c_List_Omonoid__add__class_Olistsum(X16729),X16728)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X16729),hAPP(c_List_Onth(X16729),X16728)),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(X16729)),X16728)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__setsum__nth])])). 4.05/4.30 fof(c_0_7441, plain, ![X14991, X14992, X14993, X14994]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),X14991),X14992))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),c_Groups_Ozero__class_Ozero(X14994)),X14993))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14994),X14993),X14992)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14994),X14993),X14991)))|~class_Rings_Olinordered__ring__strict(X14994))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),X14993),c_Groups_Ozero__class_Ozero(X14994)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),c_Groups_Ozero__class_Ozero(X14994)),X14993))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14994),X14993),X14992)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14994),X14993),X14991)))|~class_Rings_Olinordered__ring__strict(X14994)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),X14991),X14992))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),X14992),X14991))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14994),X14993),X14992)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14994),X14993),X14991)))|~class_Rings_Olinordered__ring__strict(X14994))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),X14993),c_Groups_Ozero__class_Ozero(X14994)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),X14992),X14991))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14994),X14993),X14992)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14994),X14993),X14991)))|~class_Rings_Olinordered__ring__strict(X14994))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),c_Groups_Ozero__class_Ozero(X14994)),X14993))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),X14992),X14991))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14994),X14993),X14992)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14994),X14993),X14991)))|~class_Rings_Olinordered__ring__strict(X14994))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),X14991),X14992))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),X14993),c_Groups_Ozero__class_Ozero(X14994)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14994),X14993),X14992)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14994),X14993),X14991)))|~class_Rings_Olinordered__ring__strict(X14994)))), 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])])])])). 4.05/4.30 cnf(c_0_7442, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5343, c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_7443, plain, ![X15003, X15004, X15005, X15006, X15007]:(((X15005!=X15003|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15007),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15007),X15006),X15003)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15007),X15004),X15005))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15007),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15007),X15006),X15005)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15007),X15004),X15003))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X15007))&(X15006!=X15004|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15007),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15007),X15006),X15003)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15007),X15004),X15005))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15007),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15007),X15006),X15005)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15007),X15004),X15003))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X15007)))&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15007),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15007),X15006),X15003)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15007),X15004),X15005))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15007),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15007),X15006),X15005)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15007),X15004),X15003))|(X15005=X15003|X15006=X15004)|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X15007))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])])). 4.05/4.30 cnf(c_0_7444, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5344, c_0_4475]), c_0_4475])). 4.05/4.30 cnf(c_0_7445, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5345, c_0_4475]), c_0_4475])). 4.05/4.30 fof(c_0_7446, plain, ![X15452, X15453, X15454, X15455]:(~c_Relation_Orefl__on(X15455,X15454,X15453)|(~hBOOL(hAPP(hAPP(c_member(X15455),X15452),X15454))|hBOOL(hAPP(hAPP(c_member(tc_prod(X15455,X15455)),hAPP(hAPP(c_Product__Type_OPair(X15455,X15455),X15452),X15452)),X15453)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__onD])])])). 4.05/4.30 fof(c_0_7447, plain, ![X16314, X16315, X16316, X16317, X16318, X16319]:(~class_Complete__Lattice_Ocomplete__lattice(X16319)|hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16318,tc_fun(X16317,X16319)),X16316),X16315),X16314)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X16318,X16319),X16316),hAPP(hAPP(c_COMBC(X16318,X16317,X16319),X16315),X16314))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INFI__apply])])])). 4.05/4.30 fof(c_0_7448, plain, ![X1099, X1100, X1101, X1102, X1103, X1104]:(~class_Complete__Lattice_Ocomplete__lattice(X1104)|hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1103,tc_fun(X1102,X1104)),X1101),X1100),X1099)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1103,X1104),X1101),hAPP(hAPP(c_COMBC(X1103,X1102,X1104),X1100),X1099))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__apply])])). 4.05/4.30 cnf(c_0_7449, 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_5346])). 4.05/4.30 fof(c_0_7450, plain, ![X14314, X14315, X14317, X14318, X14319, X14321]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk436_2(X14314,X14315)),X14315))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X14317),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14315)))|hBOOL(hAPP(X14314,X14317))))&(~hBOOL(hAPP(X14314,esk436_2(X14314,X14315)))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X14317),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14315)))|hBOOL(hAPP(X14314,X14317)))))&((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk437_2(X14318,X14319)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14319)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14321),X14319))|hBOOL(hAPP(X14318,X14321))))&(~hBOOL(hAPP(X14318,esk437_2(X14318,X14319)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14321),X14319))|hBOOL(hAPP(X14318,X14321)))))), 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])])])])])])])). 4.05/4.30 fof(c_0_7451, plain, ![X3591, X3592]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3592))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3592),X3591))|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3591),X3592)),X3592))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3591),X3592))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__div__geq])])])). 4.05/4.30 fof(c_0_7452, plain, ![X12135, X12136, X12137, X12138, X12139]:(~hBOOL(hAPP(hAPP(c_member(X12139),X12138),X12137))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12136,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12139,tc_fun(X12136,tc_HOL_Obool)),X12137),X12135)),hAPP(X12135,X12138)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__lower])])])). 4.05/4.30 fof(c_0_7453, plain, ![X12603, X12604, X12605, X12606, X12607]:(~hBOOL(hAPP(hAPP(c_member(X12607),X12606),X12605))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12604,tc_HOL_Obool)),hAPP(X12603,X12606)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12607,tc_fun(X12604,tc_HOL_Obool)),X12605),X12603)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__upper])])). 4.05/4.30 fof(c_0_7454, plain, ![X5641, X5642, X5643, X5644, X5645]:((~c_Relation_Oirrefl(X5642,X5641)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5642,X5642)),hAPP(hAPP(c_Product__Type_OPair(X5642,X5642),X5643),X5643)),X5641)))&(hBOOL(hAPP(hAPP(c_member(tc_prod(X5645,X5645)),hAPP(hAPP(c_Product__Type_OPair(X5645,X5645),esk177_2(X5644,X5645)),esk177_2(X5644,X5645))),X5644))|c_Relation_Oirrefl(X5645,X5644))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_irrefl__def])])])])])])). 4.05/4.30 fof(c_0_7455, plain, ![X398, X399, X400, X401, X402, X404, X405, X406, X407, X408, X409]:((((hAPP(hAPP(c_List_Olist_OCons(X402),X401),X400)=X398|X400=hAPP(hAPP(c_List_Oappend(X402),esk3_5(X398,X399,X400,X401,X402)),X398)|hAPP(hAPP(c_List_Olist_OCons(X402),X401),X400)!=hAPP(hAPP(c_List_Oappend(X402),X399),X398))&(X399=c_List_Olist_ONil(X402)|X400=hAPP(hAPP(c_List_Oappend(X402),esk3_5(X398,X399,X400,X401,X402)),X398)|hAPP(hAPP(c_List_Olist_OCons(X402),X401),X400)!=hAPP(hAPP(c_List_Oappend(X402),X399),X398)))&((hAPP(hAPP(c_List_Olist_OCons(X402),X401),X400)=X398|X399=hAPP(hAPP(c_List_Olist_OCons(X402),X401),esk3_5(X398,X399,X400,X401,X402))|hAPP(hAPP(c_List_Olist_OCons(X402),X401),X400)!=hAPP(hAPP(c_List_Oappend(X402),X399),X398))&(X399=c_List_Olist_ONil(X402)|X399=hAPP(hAPP(c_List_Olist_OCons(X402),X401),esk3_5(X398,X399,X400,X401,X402))|hAPP(hAPP(c_List_Olist_OCons(X402),X401),X400)!=hAPP(hAPP(c_List_Oappend(X402),X399),X398))))&((X406!=hAPP(hAPP(c_List_Oappend(X408),X409),X404)|X405!=hAPP(hAPP(c_List_Olist_OCons(X408),X407),X409)|hAPP(hAPP(c_List_Olist_OCons(X408),X407),X406)=hAPP(hAPP(c_List_Oappend(X408),X405),X404))&(hAPP(hAPP(c_List_Olist_OCons(X408),X407),X406)!=X404|X405!=c_List_Olist_ONil(X408)|hAPP(hAPP(c_List_Olist_OCons(X408),X407),X406)=hAPP(hAPP(c_List_Oappend(X408),X405),X404)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__eq__append__conv])])])])])])). 4.05/4.30 fof(c_0_7456, plain, ![X13788, X13789, X13790, X13791, X13792, X13793, X13794, X13795, X13796, X13797, X13798]:(((X13790!=hAPP(hAPP(c_List_Olist_OCons(X13792),X13789),X13788)|X13791!=c_List_Olist_ONil(X13792)|hAPP(hAPP(c_List_Oappend(X13792),X13791),X13790)=hAPP(hAPP(c_List_Olist_OCons(X13792),X13789),X13788))&(hAPP(hAPP(c_List_Oappend(X13792),X13793),X13790)!=X13788|hAPP(hAPP(c_List_Olist_OCons(X13792),X13789),X13793)!=X13791|hAPP(hAPP(c_List_Oappend(X13792),X13791),X13790)=hAPP(hAPP(c_List_Olist_OCons(X13792),X13789),X13788)))&(((hAPP(hAPP(c_List_Oappend(X13798),esk428_5(X13794,X13795,X13796,X13797,X13798)),X13796)=X13794|X13796=hAPP(hAPP(c_List_Olist_OCons(X13798),X13795),X13794)|hAPP(hAPP(c_List_Oappend(X13798),X13797),X13796)!=hAPP(hAPP(c_List_Olist_OCons(X13798),X13795),X13794))&(hAPP(hAPP(c_List_Olist_OCons(X13798),X13795),esk428_5(X13794,X13795,X13796,X13797,X13798))=X13797|X13796=hAPP(hAPP(c_List_Olist_OCons(X13798),X13795),X13794)|hAPP(hAPP(c_List_Oappend(X13798),X13797),X13796)!=hAPP(hAPP(c_List_Olist_OCons(X13798),X13795),X13794)))&((hAPP(hAPP(c_List_Oappend(X13798),esk428_5(X13794,X13795,X13796,X13797,X13798)),X13796)=X13794|X13797=c_List_Olist_ONil(X13798)|hAPP(hAPP(c_List_Oappend(X13798),X13797),X13796)!=hAPP(hAPP(c_List_Olist_OCons(X13798),X13795),X13794))&(hAPP(hAPP(c_List_Olist_OCons(X13798),X13795),esk428_5(X13794,X13795,X13796,X13797,X13798))=X13797|X13797=c_List_Olist_ONil(X13798)|hAPP(hAPP(c_List_Oappend(X13798),X13797),X13796)!=hAPP(hAPP(c_List_Olist_OCons(X13798),X13795),X13794))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__Cons__conv])])])])])])). 4.05/4.30 fof(c_0_7457, plain, ![X12966, X12967, X12968, X12969]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12969,tc_HOL_Obool)),X12968),X12967))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12969,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X12969),X12966),X12968)),hAPP(hAPP(c_Set_Oinsert(X12969),X12966),X12967)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])])). 4.05/4.30 fof(c_0_7458, plain, ![X12288, X12289, X12290, X12291, X12292]:(~class_Orderings_Olinorder(X12292)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12292),X12291),X12290))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12292),X12289),X12288))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12292),hAPP(hAPP(c_Orderings_Oord__class_Omin(X12292),X12291),X12289)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X12292),X12290),X12288)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__mono])])])). 4.05/4.30 fof(c_0_7459, plain, ![X9534, X9535, X9536, X9537, X9538]:(~class_Orderings_Olinorder(X9538)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9538),X9537),X9536))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9538),X9535),X9534))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9538),hAPP(hAPP(c_Orderings_Oord__class_Omax(X9538),X9537),X9535)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X9538),X9536),X9534)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__mono])])])). 4.05/4.30 fof(c_0_7460, plain, ![X8255, X8256, X8258, X8259, X8260, X8262]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk260_2(X8255,X8256)),X8256))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X8258),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X8256)))|hBOOL(hAPP(X8255,X8258))))&(~hBOOL(hAPP(X8255,esk260_2(X8255,X8256)))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X8258),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X8256)))|hBOOL(hAPP(X8255,X8258)))))&((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk261_2(X8259,X8260)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X8260)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8262),X8260))|hBOOL(hAPP(X8259,X8262))))&(~hBOOL(hAPP(X8259,esk261_2(X8259,X8260)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8262),X8260))|hBOOL(hAPP(X8259,X8262)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_all__nat__less])])])])])])])). 4.05/4.30 fof(c_0_7461, plain, ![X11679, X11680]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X11680,tc_HOL_Obool)),esk359_2(X11679,X11680)),X11679))|hBOOL(hAPP(c_Finite__Set_Ofinite(X11680),c_Complete__Lattice_OSup__class_OSup(tc_fun(X11680,tc_HOL_Obool),X11679)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X11680,tc_HOL_Obool)),X11679)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11680),esk359_2(X11679,X11680)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X11680),c_Complete__Lattice_OSup__class_OSup(tc_fun(X11680,tc_HOL_Obool),X11679)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X11680,tc_HOL_Obool)),X11679)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Union])])])])])). 4.05/4.30 fof(c_0_7462, plain, ![X10001, X10002, X10003]:(~class_Rings_Olinordered__semidom(X10003)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10003),c_Groups_Oone__class_Oone(X10003)),X10002))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10003),c_Groups_Oone__class_Oone(X10003)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10003),X10002),hAPP(hAPP(c_Power_Opower__class_Opower(X10003),X10002),X10001)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__gt1__lemma])])])). 4.05/4.30 fof(c_0_7463, plain, ![X9892, X9893, X9894]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9894))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9894),X9892))!=X9894|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9893))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9892),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_self__quotient__aux2])])])). 4.05/4.30 fof(c_0_7464, plain, ![X6700, X6701, X6702, X6703]:(~c_Wellfounded_Owf(X6703,X6702)|(~c_Fun_Oinj__on(X6703,X6701,X6700,c_Orderings_Otop__class_Otop(tc_fun(X6703,tc_HOL_Obool)))|c_Wellfounded_Owf(X6701,hAPP(c_Set_Oimage(tc_prod(X6703,X6703),tc_prod(X6701,X6701),c_Product__Type_Omap__pair(X6703,X6701,X6703,X6701,X6700,X6700)),X6702)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__map__pair__image])])])). 4.05/4.30 cnf(c_0_7465, 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_5347])). 4.05/4.30 fof(c_0_7466, plain, ![X13567, X13568, X13569, X13570, X13571]:(~c_Finite__Set_Ofun__left__comm(X13571,X13570,X13569)|hAPP(hAPP(c_Finite__Set_Ofold(X13571,X13570,X13569),X13568),hAPP(c_List_Oset(X13571),X13567))=hAPP(c_List_Ofoldl(X13570,X13571,hAPP(c_COMBC(X13571,X13570,X13570),X13569),X13568),c_List_Oremdups(X13571,X13567))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__set__remdups])])])). 4.05/4.30 fof(c_0_7467, plain, ![X3519, X3520, X3521, X3522]:(~hBOOL(hAPP(hAPP(c_member(X3522),X3521),X3520))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3522,tc_HOL_Obool)),X3519),X3520)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3522,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X3522),X3521),X3519)),X3520)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__Diff1])])])). 4.05/4.30 cnf(c_0_7468, plain, (hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X1,X3)),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_5348])). 4.05/4.30 fof(c_0_7469, plain, ![X7399, X7400, X7401]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7401,tc_HOL_Obool)),X7400),hAPP(hAPP(c_Set_Oinsert(X7401),X7399),c_Orderings_Obot__class_Obot(tc_fun(X7401,tc_HOL_Obool)))))|(X7400=c_Orderings_Obot__class_Obot(tc_fun(X7401,tc_HOL_Obool))|hAPP(hAPP(c_Set_Oinsert(X7401),X7399),c_Orderings_Obot__class_Obot(tc_fun(X7401,tc_HOL_Obool)))=X7400)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__singletonD])])])). 4.05/4.30 fof(c_0_7470, plain, ![X13680, X13681, X13682, X13683]:(~class_Divides_Oring__div(X13683)|c_Divides_Odiv__class_Omod(X13683,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13683),X13682),X13681),X13680)=c_Divides_Odiv__class_Omod(X13683,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13683),c_Divides_Odiv__class_Omod(X13683,X13682,X13680)),c_Divides_Odiv__class_Omod(X13683,X13681,X13680)),X13680)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__diff__eq])])])). 4.05/4.30 fof(c_0_7471, plain, ![X629, X630]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X630)),X629))|(hBOOL(hAPP(X629,c_Option_Ooption_ONone(X630)))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X630),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X630),tc_HOL_Obool,X630),X629),c_Option_Ooption_OSome(X630)))))|~class_Enum_Oenum(X630))&((~hBOOL(hAPP(X629,c_Option_Ooption_ONone(X630)))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X630)),X629))|~class_Enum_Oenum(X630))&(~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X630),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X630),tc_HOL_Obool,X630),X629),c_Option_Ooption_OSome(X630))))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X630)),X629))|~class_Enum_Oenum(X630)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__ex__option__def])])])). 4.05/4.30 cnf(c_0_7472, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|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_5265])). 4.05/4.30 fof(c_0_7473, plain, ![X557, X558, X559, X560, X561]:(~hBOOL(hAPP(hAPP(c_member(X561),X560),hAPP(c_List_Oset(X561),X559)))|(hBOOL(hAPP(X558,X560))|c_List_OtakeWhile(X561,X558,X559)=c_List_OtakeWhile(X561,X558,hAPP(hAPP(c_List_Oappend(X561),X559),X557)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile__append1])])])). 4.05/4.30 fof(c_0_7474, plain, ![X11868, X11869, X11870, X11871]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X11871),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11871,tc_HOL_Obool)),X11870),hAPP(hAPP(c_Set_Oinsert(X11871),X11869),X11868))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X11871),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11871,tc_HOL_Obool)),X11870),X11868))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11871),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11871,tc_HOL_Obool)),X11870),X11868)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X11871),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11871,tc_HOL_Obool)),X11870),hAPP(hAPP(c_Set_Oinsert(X11871),X11869),X11868)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff__insert])])). 4.05/4.30 fof(c_0_7475, plain, ![X9279, X9280, X9281, X9282]:((~hBOOL(hAPP(hAPP(c_member(X9282),X9281),hAPP(c_List_Oset(X9282),c_List_Obutlast(X9282,X9279))))|hBOOL(hAPP(hAPP(c_member(X9282),X9281),hAPP(c_List_Oset(X9282),c_List_Obutlast(X9282,hAPP(hAPP(c_List_Oappend(X9282),X9280),X9279))))))&(~hBOOL(hAPP(hAPP(c_member(X9282),X9281),hAPP(c_List_Oset(X9282),c_List_Obutlast(X9282,X9280))))|hBOOL(hAPP(hAPP(c_member(X9282),X9281),hAPP(c_List_Oset(X9282),c_List_Obutlast(X9282,hAPP(hAPP(c_List_Oappend(X9282),X9280),X9279))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__set__butlast__appendI])])])])). 4.05/4.30 cnf(c_0_7476, 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_5349])). 4.05/4.30 fof(c_0_7477, plain, ![X12722, X12723, X12724, X12725, X12726]:(~c_Fun_Oinj__on(X12726,X12725,X12724,c_Orderings_Otop__class_Otop(tc_fun(X12726,tc_HOL_Obool)))|(~c_Fun_Oinj__on(X12723,X12726,X12722,c_Orderings_Otop__class_Otop(tc_fun(X12723,tc_HOL_Obool)))|c_Fun_Oinj__on(X12723,X12725,hAPP(c_Fun_Ocomp(X12726,X12725,X12723,X12724),X12722),c_Orderings_Otop__class_Otop(tc_fun(X12723,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__comp])])])). 4.05/4.30 cnf(c_0_7478, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_5290])). 4.05/4.30 cnf(c_0_7479, 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_5350])). 4.05/4.30 cnf(c_0_7480, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))), inference(split_conjunct,[status(thm)],[c_0_5351])). 4.05/4.30 cnf(c_0_7481, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X2),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X1),X4)|hAPP(X1,esk474_5(X2,X1,X3,X4,X5))!=hAPP(X2,esk474_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_5229])). 4.05/4.30 cnf(c_0_7482, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X1),X4)|hAPP(X1,esk139_5(X2,X1,X3,X4,X5))!=hAPP(X2,esk139_5(X2,X1,X3,X4,X5))|~c_Nat__Transfer_Onat__set(X3)|X3!=X4|~class_Groups_Ocomm__monoid__mult(X5)|~class_Groups_Ocomm__monoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_5230])). 4.05/4.30 fof(c_0_7483, plain, ![X10878, X10879]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10879),hAPP(c_Int_Onumber__class_Onumber__of(X10879),X10878)),c_Groups_Ozero__class_Ozero(X10879)))|hAPP(c_Groups_Oabs__class_Oabs(X10879),hAPP(c_Int_Onumber__class_Onumber__of(X10879),X10878))=hAPP(c_Groups_Ouminus__class_Ouminus(X10879),hAPP(c_Int_Onumber__class_Onumber__of(X10879),X10878))|(~class_Rings_Olinordered__idom(X10879)|~class_Int_Onumber__ring(X10879)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10879),hAPP(c_Int_Onumber__class_Onumber__of(X10879),X10878)),c_Groups_Ozero__class_Ozero(X10879)))|hAPP(c_Groups_Oabs__class_Oabs(X10879),hAPP(c_Int_Onumber__class_Onumber__of(X10879),X10878))=hAPP(c_Int_Onumber__class_Onumber__of(X10879),X10878)|(~class_Rings_Olinordered__idom(X10879)|~class_Int_Onumber__ring(X10879)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__number__of])])])])). 4.05/4.30 fof(c_0_7484, plain, ![X3876, X3877, X3878]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3878,tc_HOL_Obool)),X3877),X3876))|hBOOL(hAPP(hAPP(c_member(X3878),esk120_3(X3876,X3877,X3878)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3878,tc_HOL_Obool)),X3876),X3877)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__ex__mem])])])). 4.05/4.30 fof(c_0_7485, plain, ![X11841, X11842, X11843]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11843,tc_HOL_Obool)),X11842),X11841))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X11843,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X11843),X11842)),hAPP(c_Set_OPow(X11843),X11841)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pow__mono])])). 4.05/4.30 fof(c_0_7486, plain, ![X5070, X5071, X5072, X5073]:(~class_Rings_Olinordered__semidom(X5073)|(hAPP(hAPP(c_Power_Opower__class_Opower(X5073),X5070),X5071)!=hAPP(hAPP(c_Power_Opower__class_Opower(X5073),X5072),X5071)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5073),c_Groups_Ozero__class_Ozero(X5073)),X5072))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5073),c_Groups_Ozero__class_Ozero(X5073)),X5070))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5071))|X5072=X5070))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__eq__imp__eq__base])])])). 4.05/4.30 cnf(c_0_7487, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk87_2(X2,X1)),esk87_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_5352])). 4.05/4.30 cnf(c_0_7488, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Relation_OId__on(X3,X4)))|X1!=X2|~hBOOL(hAPP(hAPP(c_member(X3),X1),X4))), inference(split_conjunct,[status(thm)],[c_0_5353])). 4.05/4.30 fof(c_0_7489, plain, ![X7459, X7460, X7461]:(~class_Rings_Olinordered__semidom(X7461)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7461),c_Groups_Ozero__class_Ozero(X7461)),X7460))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7461),X7460),c_Groups_Oone__class_Oone(X7461)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7461),hAPP(hAPP(c_Power_Opower__class_Opower(X7461),X7460),hAPP(c_Nat_OSuc,X7459))),c_Groups_Oone__class_Oone(X7461)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__Suc__less__one])])])). 4.05/4.30 fof(c_0_7490, plain, ![X2769, X2770, X2771, X2772, X2773]:(~hBOOL(hAPP(hAPP(c_member(X2773),X2772),hAPP(c_List_Oset(X2773),X2771)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2770),hAPP(X2769,X2772)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2770),c_List_Olist_Olist__size(X2773,X2769,X2771))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__size__estimation])])])). 4.05/4.30 fof(c_0_7491, plain, ![X14309, X14310, X14311, X14312, X14313]:(~hBOOL(hAPP(hAPP(c_member(X14313),X14312),hAPP(c_List_Oset(X14313),X14311)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14310),hAPP(X14309,X14312)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14310),c_List_Olist_Olist__size(X14313,X14309,X14311))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__size__estimation_H])])). 4.05/4.30 fof(c_0_7492, plain, ![X2336, X2337, X2338]:(~class_Fields_Ofield__inverse__zero(X2338)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2338),c_Groups_Oone__class_Oone(X2338)),hAPP(hAPP(c_Power_Opower__class_Opower(X2338),X2337),X2336))=hAPP(hAPP(c_Power_Opower__class_Opower(X2338),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2338),c_Groups_Oone__class_Oone(X2338)),X2337)),X2336)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__over])])). 4.05/4.30 fof(c_0_7493, plain, ![X17281, X17282, X17283]:(~class_Complete__Lattice_Ocomplete__lattice(X17283)|c_Complete__Lattice_OSup__class_OSup(X17283,hAPP(hAPP(c_Set_Oinsert(X17283),X17282),hAPP(hAPP(c_Set_Oinsert(X17283),X17281),c_Orderings_Obot__class_Obot(tc_fun(X17283,tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17283),X17282),X17281)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__binary])])])). 4.05/4.30 fof(c_0_7494, plain, ![X15950, X15951, X15952, X15953, X15954]:(~c_Finite__Set_Ofolding__one__idem(X15954,X15953,X15952)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15954),X15951))|(c_Orderings_Obot__class_Obot(tc_fun(X15954,tc_HOL_Obool))=X15951|hAPP(X15952,hAPP(hAPP(c_Set_Oinsert(X15954),X15950),X15951))=hAPP(hAPP(X15953,X15950),hAPP(X15952,X15951))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one__idem_Oinsert__idem])])])). 4.05/4.30 cnf(c_0_7495, plain, (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),X2)|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_5325])). 4.05/4.30 fof(c_0_7496, plain, ![X13800, X13801, X13802, X13803, X13804]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13801),hAPP(X13800,X13804)))|~hBOOL(hAPP(hAPP(c_member(X13803),X13804),X13802))|hBOOL(hAPP(c_Finite__Set_Ofinite(X13801),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13803,tc_fun(X13801,tc_HOL_Obool)),X13802),X13800)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__INT])])])])). 4.05/4.30 fof(c_0_7497, plain, ![X12567, X12568, X12569]:(~class_Complete__Lattice_Ocomplete__lattice(X12569)|c_Complete__Lattice_OInf__class_OInf(X12569,hAPP(hAPP(c_Set_Oinsert(X12569),X12568),hAPP(hAPP(c_Set_Oinsert(X12569),X12567),c_Orderings_Obot__class_Obot(tc_fun(X12569,tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12569),X12568),X12567)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__binary])])). 4.05/4.30 fof(c_0_7498, plain, ![X5849, X5850, X5851, X5852, X5853, X5854]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5854,X5853)),hAPP(hAPP(c_Product__Type_OPair(X5854,X5853),X5852),X5851)),hAPP(c_List_Oset(tc_prod(X5854,X5853)),hAPP(hAPP(c_List_Ozip(X5854,X5853),X5850),X5849))))|hBOOL(hAPP(hAPP(c_member(X5854),X5852),hAPP(c_List_Oset(X5854),X5850)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__zip__leftD])])). 4.05/4.30 fof(c_0_7499, plain, ![X5118, X5119, X5120, X5121, X5122, X5123]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5123,X5122)),hAPP(hAPP(c_Product__Type_OPair(X5123,X5122),X5121),X5120)),hAPP(c_List_Oset(tc_prod(X5123,X5122)),hAPP(hAPP(c_List_Ozip(X5123,X5122),X5119),X5118))))|hBOOL(hAPP(hAPP(c_member(X5122),X5120),hAPP(c_List_Oset(X5122),X5118)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__zip__rightD])])])). 4.05/4.30 fof(c_0_7500, plain, ![X13912, X13913, X13914]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X13914,X13914),tc_HOL_Obool)),X13913),c_Transitive__Closure_Ortrancl(X13914,X13912)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X13914,X13914),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X13914,X13913)),c_Transitive__Closure_Ortrancl(X13914,X13912)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__subset__rtrancl])])])). 4.05/4.30 fof(c_0_7501, plain, ![X17002, X17003, X17004, X17005]:((hBOOL(hAPP(hAPP(c_member(X17005),X17004),hAPP(c_List_Oset(X17005),X17003)))|hAPP(hAPP(c_List_Oappend(X17005),X17003),c_List_Oremove1(X17005,X17004,X17002))=c_List_Oremove1(X17005,X17004,hAPP(hAPP(c_List_Oappend(X17005),X17003),X17002)))&(~hBOOL(hAPP(hAPP(c_member(X17005),X17004),hAPP(c_List_Oset(X17005),X17003)))|c_List_Oremove1(X17005,X17004,hAPP(hAPP(c_List_Oappend(X17005),X17003),X17002))=hAPP(hAPP(c_List_Oappend(X17005),c_List_Oremove1(X17005,X17004,X17003)),X17002))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remove1__append])])])). 4.05/4.30 fof(c_0_7502, plain, ![X14371, X14372, X14373, X14374, X14375]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14375),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14374)),X14373)))|hAPP(hAPP(c_List_Onth(X14372),hAPP(hAPP(c_List_Omap(X14374,X14372),X14371),X14373)),X14375)=hAPP(X14371,hAPP(hAPP(c_List_Onth(X14374),X14373),X14375))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__map])])])). 4.05/4.30 fof(c_0_7503, plain, ![X11204, X11205, X11206]:((hBOOL(hAPP(hAPP(c_member(X11206),esk339_3(X11204,X11205,X11206)),X11205))|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(X11206,tc_Nat_Onat),X11204),X11205)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11206),X11205)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X11204,esk339_3(X11204,X11205,X11206))))|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(X11206,tc_Nat_Onat),X11204),X11205)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X11206),X11205)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__pos__nat])])])])])). 4.05/4.30 cnf(c_0_7504, 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_5354])). 4.05/4.30 fof(c_0_7505, plain, ![X1402, X1403, X1404]:((hBOOL(hAPP(hAPP(c_member(X1404),esk41_3(X1402,X1403,X1404)),hAPP(c_List_Oset(X1404),X1403)))|(~c_List_Olinorder__class_Osorted(X1404,X1403)|c_List_Olinorder__class_Osorted(X1404,hAPP(hAPP(c_List_Olist_OCons(X1404),X1402),X1403)))|~class_Orderings_Olinorder(X1404))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1404),X1402),esk41_3(X1402,X1403,X1404)))|(~c_List_Olinorder__class_Osorted(X1404,X1403)|c_List_Olinorder__class_Osorted(X1404,hAPP(hAPP(c_List_Olist_OCons(X1404),X1402),X1403)))|~class_Orderings_Olinorder(X1404))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted_OCons])])])])])). 4.05/4.30 fof(c_0_7506, plain, ![X15544, X15545, X15546, X15547]:(((~hBOOL(hAPP(hAPP(c_member(X15546),X15547),hAPP(c_List_Oset(X15546),X15544)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15546),X15545),X15547))|~c_List_Olinorder__class_Osorted(X15546,hAPP(hAPP(c_List_Olist_OCons(X15546),X15545),X15544))|~class_Orderings_Olinorder(X15546))&(c_List_Olinorder__class_Osorted(X15546,X15544)|~c_List_Olinorder__class_Osorted(X15546,hAPP(hAPP(c_List_Olist_OCons(X15546),X15545),X15544))|~class_Orderings_Olinorder(X15546)))&((hBOOL(hAPP(hAPP(c_member(X15546),esk468_3(X15544,X15545,X15546)),hAPP(c_List_Oset(X15546),X15544)))|~c_List_Olinorder__class_Osorted(X15546,X15544)|c_List_Olinorder__class_Osorted(X15546,hAPP(hAPP(c_List_Olist_OCons(X15546),X15545),X15544))|~class_Orderings_Olinorder(X15546))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15546),X15545),esk468_3(X15544,X15545,X15546)))|~c_List_Olinorder__class_Osorted(X15546,X15544)|c_List_Olinorder__class_Osorted(X15546,hAPP(hAPP(c_List_Olist_OCons(X15546),X15545),X15544))|~class_Orderings_Olinorder(X15546)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__Cons])])])])])])). 4.05/4.30 fof(c_0_7507, plain, ![X15265, X15266, X15267, X15269]:(((hBOOL(hAPP(hAPP(c_member(X15267),esk460_3(X15265,X15266,X15267)),hAPP(c_List_Oset(X15267),X15265)))|~c_List_Olinorder__class_Osorted(X15267,X15265)|c_List_Olinorder__class_Osorted(X15267,hAPP(hAPP(c_List_Olist_OCons(X15267),X15266),X15265))|~class_Orderings_Olinorder(X15267))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15267),X15266),esk460_3(X15265,X15266,X15267)))|~c_List_Olinorder__class_Osorted(X15267,X15265)|c_List_Olinorder__class_Osorted(X15267,hAPP(hAPP(c_List_Olist_OCons(X15267),X15266),X15265))|~class_Orderings_Olinorder(X15267)))&((~hBOOL(hAPP(hAPP(c_member(X15267),X15269),hAPP(c_List_Oset(X15267),X15265)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15267),X15266),X15269))|~c_List_Olinorder__class_Osorted(X15267,hAPP(hAPP(c_List_Olist_OCons(X15267),X15266),X15265))|~class_Orderings_Olinorder(X15267))&(c_List_Olinorder__class_Osorted(X15267,X15265)|~c_List_Olinorder__class_Osorted(X15267,hAPP(hAPP(c_List_Olist_OCons(X15267),X15266),X15265))|~class_Orderings_Olinorder(X15267)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted_Oequations_I2_J])])])])])])). 4.05/4.30 fof(c_0_7508, plain, ![X6415, X6416]:(~class_Orderings_Oorder(X6416)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6416,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X6416),X6415)),hAPP(c_SetInterval_Oord__class_OatLeast(X6416),X6415))=hAPP(hAPP(c_Set_Oinsert(X6416),X6415),c_Orderings_Obot__class_Obot(tc_fun(X6416,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__Int__atLeast])])). 4.05/4.30 cnf(c_0_7509, plain, (X4=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)))|hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=hAPP(c_List_Orev(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_5355])). 4.05/4.30 cnf(c_0_7510, 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_5356]), ['final']). 4.05/4.30 fof(c_0_7511, plain, ![X15254, X15255, X15256, X15257, X15258]:(((~hBOOL(hAPP(hAPP(c_member(X15257),X15255),hAPP(c_List_Oset(X15257),X15254)))|~hBOOL(hAPP(c_List_Odistinct(X15257),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X15257,X15258,X15256),X15255),X15254)))|~class_Orderings_Olinorder(X15258))&(hBOOL(hAPP(c_List_Odistinct(X15257),X15254))|~hBOOL(hAPP(c_List_Odistinct(X15257),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X15257,X15258,X15256),X15255),X15254)))|~class_Orderings_Olinorder(X15258)))&(hBOOL(hAPP(hAPP(c_member(X15257),X15255),hAPP(c_List_Oset(X15257),X15254)))|~hBOOL(hAPP(c_List_Odistinct(X15257),X15254))|hBOOL(hAPP(c_List_Odistinct(X15257),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X15257,X15258,X15256),X15255),X15254)))|~class_Orderings_Olinorder(X15258))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__insort])])])])). 4.05/4.30 fof(c_0_7512, plain, ![X8820, X8821, X8822, X8823]:(~class_Divides_Osemiring__div(X8823)|c_Divides_Odiv__class_Omod(X8823,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8823),c_Divides_Odiv__class_Omod(X8823,X8822,X8820)),c_Divides_Odiv__class_Omod(X8823,X8821,X8820)),X8820)=c_Divides_Odiv__class_Omod(X8823,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8823),X8822),X8821),X8820)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__eq])])). 4.05/4.30 fof(c_0_7513, plain, ![X17158, X17159, X17160, X17161]:(~class_Divides_Osemiring__div(X17161)|c_Divides_Odiv__class_Omod(X17161,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17161),c_Divides_Odiv__class_Omod(X17161,X17160,X17158)),c_Divides_Odiv__class_Omod(X17161,X17159,X17158)),X17158)=c_Divides_Odiv__class_Omod(X17161,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17161),X17160),X17159),X17158)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__eq])])). 4.05/4.30 fof(c_0_7514, plain, ![X8168, X8169, X8170]:(~class_Groups_Oordered__ab__group__add(X8170)|c_SetInterval_Oord__class_OgreaterThanAtMost(X8170,hAPP(c_Groups_Ouminus__class_Ouminus(X8170),X8168),hAPP(c_Groups_Ouminus__class_Ouminus(X8170),X8169))=hAPP(c_Set_Oimage(X8170,X8170,c_Groups_Ouminus__class_Ouminus(X8170)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X8170,X8169),X8168))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastLessThan])])). 4.05/4.30 fof(c_0_7515, plain, ![X11179, X11180, X11181]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11181),X11180))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11179))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11179),X11181)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11179),X11180))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmult__zless__mono2])])])). 4.05/4.30 fof(c_0_7516, plain, ![X4985, X4986, X4987]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4986))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4987),X4985))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4987),X4986)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4985),X4986))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4986))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4987),X4986)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4985),X4986))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4987),X4985))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4987),X4986)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4985),X4986)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])])). 4.05/4.30 fof(c_0_7517, plain, ![X6931, X6932, X6933, X6934]:(((hBOOL(hAPP(c_Finite__Set_Ofinite(X6934),X6933))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(tc_sum(X6934,X6932)),c_Sum__Type_OPlus(X6934,X6932,X6933,X6931)))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X6932),X6931))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(tc_sum(X6934,X6932)),c_Sum__Type_OPlus(X6934,X6932,X6933,X6931))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6934),X6933))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6932),X6931))|hAPP(c_Finite__Set_Ocard(tc_sum(X6934,X6932)),c_Sum__Type_OPlus(X6934,X6932,X6933,X6931))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X6934),X6933)),hAPP(c_Finite__Set_Ocard(X6932),X6931)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__Plus__conv__if])])])])). 4.05/4.30 fof(c_0_7518, plain, ![X4302, X4303, X4304]:(~class_Orderings_Olinorder(X4304)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4304),X4303),X4302))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4304,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4304,X4303,X4302)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X4304),X4302))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X4304),X4303))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I11_J])])])). 4.05/4.30 fof(c_0_7519, plain, ![X2868, X2869, X2870]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2869),X2868))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2870),X2869)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2870),X2868))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2870))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2870),X2869)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2870),X2868)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2869),X2868))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2870))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2870),X2869)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2870),X2868))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])])). 4.05/4.30 fof(c_0_7520, plain, ![X12624, X12625, X12626]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12626),X12625))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12624))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12626),X12624)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X12625),X12624))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono1])])])). 4.05/4.30 fof(c_0_7521, plain, ![X14186, X14187, X14188]:(~class_Orderings_Olinorder(X14188)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14188),X14187),X14186))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14188,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X14188,X14187,X14186)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X14188),X14186))=hAPP(c_SetInterval_Oord__class_OatLeast(X14188),X14187))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I13_J])])])). 4.05/4.30 fof(c_0_7522, plain, ![X4663, X4664, X4665]:(~class_Orderings_Olinorder(X4665)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4665),X4664),X4663))|hAPP(c_SetInterval_Oord__class_OgreaterThan(X4665),X4664)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4665,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X4665,X4664,X4663)),hAPP(c_SetInterval_Oord__class_OatLeast(X4665),X4663)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I12_J])])])). 4.05/4.30 fof(c_0_7523, plain, ![X412, X413, X414, X415]:(~class_Orderings_Olinorder(X415)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X415,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X415,X414,X413)),hAPP(c_SetInterval_Oord__class_OatLeast(X415),X412))=c_SetInterval_Oord__class_OatLeastAtMost(X415,hAPP(hAPP(c_Orderings_Oord__class_Omax(X415),X414),X412),X413)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__atLeastAtMostL2])])])). 4.05/4.30 fof(c_0_7524, plain, ![X9404, X9405, X9406, X9407]:(~class_Orderings_Olinorder(X9407)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9407,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X9407,X9406,X9405)),hAPP(c_SetInterval_Oord__class_OatMost(X9407),X9404))=c_SetInterval_Oord__class_OatLeastAtMost(X9407,X9406,hAPP(hAPP(c_Orderings_Oord__class_Omin(X9407),X9405),X9404))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL1])])). 4.05/4.30 cnf(c_0_7525, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),X2)=X2|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5357, c_0_4475])). 4.05/4.30 cnf(c_0_7526, 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_5358])). 4.05/4.30 fof(c_0_7527, plain, ![X6135, X6136, X6137]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6137))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6137),X6136))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X6135),X6136)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X6135),X6137))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__le__mono2])])])). 4.05/4.30 fof(c_0_7528, plain, ![X2850, X2851, X2852]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2852),X2851))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2850),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),X2851),X2850)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2852),X2850))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__mono1__neg])])])). 4.05/4.30 cnf(c_0_7529, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))=X2|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5359, c_0_4475])). 4.05/4.30 fof(c_0_7530, plain, ![X13730, X13731, X13732]:(~class_Orderings_Olinorder(X13732)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13732),X13731),X13730))|hAPP(c_SetInterval_Oord__class_OlessThan(X13732),X13730)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13732,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X13732),X13731)),c_SetInterval_Oord__class_OgreaterThanLessThan(X13732,X13731,X13730)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I7_J])])])). 4.05/4.30 fof(c_0_7531, plain, ![X14696, X14697, X14698]:(~class_Orderings_Olinorder(X14698)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14698),X14697),X14696))|hAPP(c_SetInterval_Oord__class_OatMost(X14698),X14696)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14698,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X14698),X14697)),c_SetInterval_Oord__class_OatLeastAtMost(X14698,X14697,X14696)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I10_J])])])). 4.05/4.30 fof(c_0_7532, plain, ![X17305, X17306, X17307]:(~class_Orderings_Olinorder(X17307)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17307),X17306),X17305))|hAPP(c_SetInterval_Oord__class_OatMost(X17307),X17305)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17307,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X17307),X17306)),c_SetInterval_Oord__class_OgreaterThanAtMost(X17307,X17306,X17305)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__un_I9_J])])])). 4.05/4.30 cnf(c_0_7533, 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_5360])). 4.05/4.30 fof(c_0_7534, plain, ![X2085, X2086, X2087, X2088, X2089]:(~class_Groups_Ominus(X2089)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2089),hAPP(X2087,X2085)),hAPP(X2086,X2085))=hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2088,X2089)),X2087),X2086),X2085)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__apply])])])). 4.05/4.30 fof(c_0_7535, plain, ![X5103, X5104, X5105, X5106, X5107]:(~class_Lattices_Olattice(X5107)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5107),hAPP(X5105,X5103)),hAPP(X5104,X5103))=hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5106,X5107)),X5105),X5104),X5103)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__apply])])). 4.05/4.30 fof(c_0_7536, plain, ![X1375, X1376, X1377, X1378, X1379]:(~class_Lattices_Olattice(X1379)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1379),hAPP(X1377,X1375)),hAPP(X1376,X1375))=hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1378,X1379)),X1377),X1376),X1375)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__apply])])). 4.05/4.30 fof(c_0_7537, plain, ![X1036, X1037, X1038, X1039]:(~class_Orderings_Olinorder(X1039)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1039,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1039),X1038)),c_SetInterval_Oord__class_OatLeastAtMost(X1039,X1037,X1036))=c_SetInterval_Oord__class_OatLeastAtMost(X1039,X1037,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1039),X1038),X1036))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR1])])). 4.05/4.30 fof(c_0_7538, plain, ![X4231, X4232, X4233, X4234]:(~class_Orderings_Olinorder(X4234)|c_SetInterval_Oord__class_OatLeastAtMost(X4234,hAPP(hAPP(c_Orderings_Oord__class_Omax(X4234),X4233),X4232),X4231)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4234,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X4234),X4233)),c_SetInterval_Oord__class_OatLeastAtMost(X4234,X4232,X4231))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__atLeastAtMostR2])])])). 4.05/4.30 cnf(c_0_7539, plain, (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)))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X1),X2),c_List_Oupto(X3,X4)))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5361])). 4.05/4.30 cnf(c_0_7540, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)=hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5362]), ['final']). 4.05/4.30 fof(c_0_7541, plain, ![X17644, X17645, X17646, X17647]:((hBOOL(hAPP(X17647,X17646))|hAPP(c_List_Ofilter(X17645,X17647),hAPP(hAPP(c_List_Olist_OCons(X17645),X17646),X17644))=hAPP(c_List_Ofilter(X17645,X17647),X17644))&(~hBOOL(hAPP(X17647,X17646))|hAPP(hAPP(c_List_Olist_OCons(X17645),X17646),hAPP(c_List_Ofilter(X17645,X17647),X17644))=hAPP(c_List_Ofilter(X17645,X17647),hAPP(hAPP(c_List_Olist_OCons(X17645),X17646),X17644)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter_Osimps_I2_J])])])). 4.05/4.30 fof(c_0_7542, plain, ![X5592, X5593, X5594]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5594))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X5593),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5594),X5592))!=X5594|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5593),X5594))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X5592))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_self__quotient__aux1])])])). 4.05/4.30 fof(c_0_7543, plain, ![X12482, X12483, X12484, X12485, X12486, X12487, X12488, X12489]:(~c_Finite__Set_Ofolding__image__simple__idem(X12489,X12488,X12487,X12486,X12485,X12484)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12488),X12483))|(~hBOOL(hAPP(hAPP(c_member(X12488),X12482),X12483))|hAPP(X12484,X12483)=hAPP(hAPP(X12487,hAPP(X12485,X12482)),hAPP(X12484,X12483))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image__simple__idem_Oin__idem])])])). 4.05/4.30 cnf(c_0_7544, 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(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)), inference(split_conjunct,[status(thm)],[c_0_5363])). 4.05/4.30 fof(c_0_7545, plain, ![X14153, X14154, X14155]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14153),X14154))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14154),X14153))|hBOOL(hAPP(X14155,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14154),X14153)))))&(~hBOOL(hAPP(X14155,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14154)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14153))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14154),X14153))|hBOOL(hAPP(X14155,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14154),X14153))))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14153),X14154))|~hBOOL(hAPP(X14155,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X14155,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14154),X14153)))))&(~hBOOL(hAPP(X14155,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14154)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14153))))|~hBOOL(hAPP(X14155,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X14155,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14154),X14153)))))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14154),X14153))|hBOOL(hAPP(X14155,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X14155,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14154),X14153)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14153),X14154))|hBOOL(hAPP(X14155,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14154)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14153))))|~hBOOL(hAPP(X14155,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14154),X14153))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiff__int__split])])])])). 4.05/4.30 fof(c_0_7546, plain, ![X6805, X6806]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6806,tc_HOL_Obool)),esk211_2(X6805,X6806)),hAPP(c_Relation_OImage(X6806,X6806,X6805),esk211_2(X6805,X6806))))|c_Wellfounded_Owf(X6806,X6805))&(c_Orderings_Obot__class_Obot(tc_fun(X6806,tc_HOL_Obool))!=esk211_2(X6805,X6806)|c_Wellfounded_Owf(X6806,X6805))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wfI__pf])])])])])). 4.05/4.30 fof(c_0_7547, plain, ![X13051, X13052, X13053, X13054, X13055, X13056, X13057]:((~c_List_Olist__all2(X13054,X13056,hAPP(hAPP(c_COMBB(X13057,tc_fun(X13056,tc_HOL_Obool),X13054),X13055),X13053),X13052,X13051)|c_List_Olist__all2(X13057,X13056,X13055,hAPP(hAPP(c_List_Omap(X13054,X13057),X13053),X13052),X13051))&(~c_List_Olist__all2(X13057,X13056,X13055,hAPP(hAPP(c_List_Omap(X13054,X13057),X13053),X13052),X13051)|c_List_Olist__all2(X13054,X13056,hAPP(hAPP(c_COMBB(X13057,tc_fun(X13056,tc_HOL_Obool),X13054),X13055),X13053),X13052,X13051))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__map1])])). 4.05/4.30 fof(c_0_7548, plain, ![X4041, X4042, X4043, X4044, X4045]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4045,tc_HOL_Obool)),X4042),X4041))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4044,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4045,X4044,X4043),X4042)),hAPP(c_Set_Oimage(X4045,X4044,X4043),X4041)))|~c_Fun_Oinj__on(X4045,X4044,X4043,c_Orderings_Otop__class_Otop(tc_fun(X4045,tc_HOL_Obool))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4044,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4045,X4044,X4043),X4042)),hAPP(c_Set_Oimage(X4045,X4044,X4043),X4041)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4045,tc_HOL_Obool)),X4042),X4041))|~c_Fun_Oinj__on(X4045,X4044,X4043,c_Orderings_Otop__class_Otop(tc_fun(X4045,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__image__subset__iff])])])])). 4.05/4.30 cnf(c_0_7549, 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_5364])). 4.05/4.30 cnf(c_0_7550, 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_5365]), ['final']). 4.05/4.30 fof(c_0_7551, plain, ![X8596]:(~class_Enum_Oenum(X8596)|c_Enum_Oenum__class_Oenum(tc_Option_Ooption(X8596))=hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(X8596)),c_Option_Ooption_ONone(X8596)),hAPP(hAPP(c_List_Omap(X8596,tc_Option_Ooption(X8596)),c_Option_Ooption_OSome(X8596)),c_Enum_Oenum__class_Oenum(X8596)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_enum__option__def])])])). 4.05/4.30 cnf(c_0_7552, 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(X1)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)), inference(split_conjunct,[status(thm)],[c_0_5363])). 4.05/4.30 fof(c_0_7553, plain, ![X16140, X16141, X16142]:((~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,X16142)),X16141)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X16142)),X16140)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16141),X16140)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16141),X16140))|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,X16142)),X16141)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X16142)),X16140))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1])])). 4.05/4.30 fof(c_0_7554, plain, ![X10197, X10198, X10199, X10201, X10202, X10203]:(((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk310_2(X10197,X10198)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10198)))|(~hBOOL(hAPP(X10197,X10199))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10199),X10198))))&(hBOOL(hAPP(X10197,esk310_2(X10197,X10198)))|(~hBOOL(hAPP(X10197,X10199))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10199),X10198)))))&((hBOOL(hAPP(X10201,esk311_2(X10201,X10202)))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X10203),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10202)))|~hBOOL(hAPP(X10201,X10203))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk311_2(X10201,X10202)),X10202))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X10203),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10202)))|~hBOOL(hAPP(X10201,X10203)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__nat__less__eq])])])])])])). 4.05/4.30 fof(c_0_7555, plain, ![X5476, X5477, X5478, X5479]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(X5479,tc_HOL_Obool)),X5478),X5477))|(~hBOOL(hAPP(hAPP(c_member(X5479),X5476),X5478))|hBOOL(hAPP(hAPP(c_member(X5479),X5476),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5479,tc_HOL_Obool),X5477))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnionI])])). 4.05/4.30 fof(c_0_7556, plain, ![X14196, X14197, X14198, X14199]:(~class_Divides_Osemiring__div(X14199)|c_Divides_Odiv__class_Omod(X14199,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14199),X14198),X14197),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14199),X14196),X14197))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14199),c_Divides_Odiv__class_Omod(X14199,X14198,X14196)),X14197)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__mult__mult2])])])). 4.05/4.30 fof(c_0_7557, plain, ![X387, X388, X389, X390]:(~class_Divides_Osemiring__div(X390)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X390),X389),c_Divides_Odiv__class_Omod(X390,X388,X387))=c_Divides_Odiv__class_Omod(X390,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X390),X389),X388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X390),X389),X387))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult1])])). 4.05/4.30 cnf(c_0_7558, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk400_4(X2,X1,X3,X4)),hAPP(c_List_Oset(X1),X3)))|c_List_Olinorder__class_Osorted(X1,X2)|X2!=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5366])). 4.05/4.30 cnf(c_0_7559, 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_5211])). 4.05/4.30 fof(c_0_7560, plain, ![X1732, X1733, X1734, X1736, X1737, X1738]:(((hBOOL(hAPP(X1732,esk56_2(X1732,X1733)))|(~hBOOL(hAPP(X1732,X1734))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1734),X1733))))&(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk56_2(X1732,X1733)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1733)))|(~hBOOL(hAPP(X1732,X1734))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1734),X1733)))))&((hBOOL(hAPP(X1736,esk57_2(X1736,X1737)))|(~hBOOL(hAPP(X1736,X1738))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1738),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1737)))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk57_2(X1736,X1737)),X1737))|(~hBOOL(hAPP(X1736,X1738))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1738),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1737))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__nat__less])])])])])])). 4.05/4.30 cnf(c_0_7561, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[c_0_5367, c_0_4475])). 4.05/4.30 fof(c_0_7562, plain, ![X7520, X7521, X7522]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7522))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X7521),X7520)),X7522)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X7521),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X7520),X7522))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq])])). 4.05/4.30 fof(c_0_7563, plain, ![X10498, X10499, X10500, X10501]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10501),tc_List_Olist(X10501))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10501),tc_List_Olist(X10501)),X10500),X10499)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10501),c_List_Olistrel1(X10501,X10498))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10501)),X10499)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10501)),X10500)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rtrancl__listrel1__eq__len])])])). 4.05/4.30 fof(c_0_7564, plain, ![X6508, X6509]:(X6509=c_List_Olist_ONil(X6508)|c_Random_Oselect__weight(X6508,hAPP(hAPP(c_List_Omap(X6508,tc_prod(tc_Code__Numeral_Ocode__numeral,X6508)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X6508),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X6509))=c_Random_Oselect(X6508,X6509)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_select__weigth__select])])])). 4.05/4.30 fof(c_0_7565, plain, ![X15579, X15580, X15581]:(~class_Fields_Olinordered__field(X15581)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15581),X15580),c_Groups_Ozero__class_Ozero(X15581)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15581),c_Groups_Ozero__class_Ozero(X15581)),X15579))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15581),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15581),X15580),X15579)),c_Groups_Ozero__class_Ozero(X15581)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__neg__pos])])])). 4.05/4.30 fof(c_0_7566, plain, ![X8210, X8211, X8212]:(~class_Fields_Olinordered__field(X8212)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8212),c_Groups_Ozero__class_Ozero(X8212)),X8211))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8212),X8210),c_Groups_Ozero__class_Ozero(X8212)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8212),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8212),X8211),X8210)),c_Groups_Ozero__class_Ozero(X8212)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__pos__neg])])])). 4.05/4.30 fof(c_0_7567, plain, ![X2458, X2459, X2460]:(~class_Rings_Olinordered__semiring__strict(X2460)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2460),c_Groups_Ozero__class_Ozero(X2460)),X2459))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2460),X2458),c_Groups_Ozero__class_Ozero(X2460)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2460),X2459),X2458)),c_Groups_Ozero__class_Ozero(X2460)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__pos__neg])])])). 4.05/4.30 fof(c_0_7568, plain, ![X14810, X14811, X14812, X14813, X14814, X14815, X14816]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14813),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14810)),X14812)))|hAPP(hAPP(c_List_Onth(X14810),X14811),X14813)=hAPP(hAPP(c_List_Onth(X14810),X14812),X14813)|X14811!=X14812)&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14810)),X14812)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14810)),X14811)|X14811!=X14812))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk446_3(X14814,X14815,X14816)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14814)),X14816)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14814)),X14816)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14814)),X14815)|X14815=X14816)&(hAPP(hAPP(c_List_Onth(X14814),X14815),esk446_3(X14814,X14815,X14816))!=hAPP(hAPP(c_List_Onth(X14814),X14816),esk446_3(X14814,X14815,X14816))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14814)),X14816)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14814)),X14815)|X14815=X14816))), 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__nth__eq])])])])])])). 4.05/4.30 fof(c_0_7569, plain, ![X6672, X6673, X6674, X6675]:(~class_Orderings_Olinorder(X6675)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X6675),X6674),hAPP(hAPP(c_Orderings_Oord__class_Omin(X6675),X6673),X6672))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X6675),X6673),hAPP(hAPP(c_Orderings_Oord__class_Omin(X6675),X6674),X6672))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__commute])])). 4.05/4.30 fof(c_0_7570, plain, ![X9871, X9872, X9873]:(~class_Rings_Olinordered__semiring__strict(X9873)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9873),c_Groups_Ozero__class_Ozero(X9873)),X9872))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9873),X9871),c_Groups_Ozero__class_Ozero(X9873)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9873),X9871),X9872)),c_Groups_Ozero__class_Ozero(X9873)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__pos__neg2])])])). 4.05/4.30 fof(c_0_7571, plain, ![X8439, X8440, X8441]:(~class_Fields_Olinordered__field(X8441)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8441),c_Groups_Ozero__class_Ozero(X8441)),X8440))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8441),X8439),c_Groups_Ozero__class_Ozero(X8441)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8441),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8441),X8440),X8439)),c_Groups_Ozero__class_Ozero(X8441)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__nonneg__neg])])])). 4.05/4.30 fof(c_0_7572, plain, ![X17571, X17572, X17573]:(~class_Fields_Olinordered__field(X17573)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17573),X17572),c_Groups_Ozero__class_Ozero(X17573)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17573),c_Groups_Ozero__class_Ozero(X17573)),X17571))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17573),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17573),X17572),X17571)),c_Groups_Ozero__class_Ozero(X17573)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__nonpos__pos])])])). 4.05/4.30 fof(c_0_7573, plain, ![X3441, X3442, X3443]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),c_Groups_Ozero__class_Ozero(X3443)),X3442))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),X3441),c_Groups_Ozero__class_Ozero(X3443)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3443),X3442),X3441)),c_Groups_Ozero__class_Ozero(X3443)))|~class_Rings_Olinordered__ring__strict(X3443))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),X3442),c_Groups_Ozero__class_Ozero(X3443)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),c_Groups_Ozero__class_Ozero(X3443)),X3441))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3443),X3442),X3441)),c_Groups_Ozero__class_Ozero(X3443)))|~class_Rings_Olinordered__ring__strict(X3443)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),X3442),c_Groups_Ozero__class_Ozero(X3443)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),c_Groups_Ozero__class_Ozero(X3443)),X3442))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3443),X3442),X3441)),c_Groups_Ozero__class_Ozero(X3443)))|~class_Rings_Olinordered__ring__strict(X3443))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),c_Groups_Ozero__class_Ozero(X3443)),X3441))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),c_Groups_Ozero__class_Ozero(X3443)),X3442))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3443),X3442),X3441)),c_Groups_Ozero__class_Ozero(X3443)))|~class_Rings_Olinordered__ring__strict(X3443)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),X3442),c_Groups_Ozero__class_Ozero(X3443)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),X3441),c_Groups_Ozero__class_Ozero(X3443)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3443),X3442),X3441)),c_Groups_Ozero__class_Ozero(X3443)))|~class_Rings_Olinordered__ring__strict(X3443))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),c_Groups_Ozero__class_Ozero(X3443)),X3441))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),X3441),c_Groups_Ozero__class_Ozero(X3443)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3443),X3442),X3441)),c_Groups_Ozero__class_Ozero(X3443)))|~class_Rings_Olinordered__ring__strict(X3443))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__0__iff])])])])). 4.05/4.30 fof(c_0_7574, plain, ![X2888, X2889, X2890, X2891, X2892, X2893, X2894, X2895]:(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2895,tc_fun(X2894,tc_fun(X2893,tc_HOL_Obool))),X2892),X2891),X2890),X2889))|(~hBOOL(hAPP(hAPP(c_member(X2895),X2888),X2892))|hBOOL(hAPP(hAPP(hAPP(X2891,X2888),X2890),X2889)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF2__D])])])). 4.05/4.30 fof(c_0_7575, plain, ![X2453, X2454, X2455]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2455),X2453),c_Groups_Ozero__class_Ozero(X2455)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2455),c_Groups_Ozero__class_Ozero(X2455)),X2454))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2455),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2455),X2454),X2453)),c_Groups_Ozero__class_Ozero(X2455)))|~class_Rings_Oordered__cancel__semiring(X2455))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2455),c_Groups_Ozero__class_Ozero(X2455)),X2453))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2455),X2454),c_Groups_Ozero__class_Ozero(X2455)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2455),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2455),X2454),X2453)),c_Groups_Ozero__class_Ozero(X2455)))|~class_Rings_Oordered__cancel__semiring(X2455))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])])). 4.05/4.30 fof(c_0_7576, plain, ![X10948, X10949, X10950]:(~class_Lattices_Olattice(X10950)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10950),X10949))|hAPP(hAPP(c_Finite__Set_Ofold(X10950,X10950,c_Lattices_Osemilattice__inf__class_Oinf(X10950)),X10948),X10949)=c_Big__Operators_Olattice__class_OInf__fin(X10950,hAPP(hAPP(c_Set_Oinsert(X10950),X10948),X10949)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oeq__fold__idem_H])])])). 4.05/4.30 fof(c_0_7577, plain, ![X16938, X16939, X16940]:(~class_Lattices_Olattice(X16940)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16940),X16939))|hAPP(hAPP(c_Finite__Set_Ofold(X16940,X16940,c_Lattices_Osemilattice__sup__class_Osup(X16940)),X16938),X16939)=c_Big__Operators_Olattice__class_OSup__fin(X16940,hAPP(hAPP(c_Set_Oinsert(X16940),X16938),X16939)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oeq__fold__idem_H])])])). 4.05/4.30 fof(c_0_7578, plain, ![X443, X444, X445]:(~class_Complete__Lattice_Ocomplete__lattice(X445)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X445),X444))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X445),X443),c_Complete__Lattice_OInf__class_OInf(X445,X444))=hAPP(hAPP(c_Finite__Set_Ofold(X445,X445,c_Lattices_Osemilattice__inf__class_Oinf(X445)),X443),X444))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__Inf__fold__inf])])])). 4.05/4.30 fof(c_0_7579, plain, ![X13273, X13274, X13275, X13276]:(~class_Lattices_Osemilattice__inf(X13276)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13276),X13275),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13276),X13274),X13273))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13276),X13274),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13276),X13275),X13273))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__commute])])). 4.05/4.30 fof(c_0_7580, plain, ![X12701, X12702, X12703]:(~class_Groups_Oordered__comm__monoid__add(X12703)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12703),X12702),c_Groups_Ozero__class_Ozero(X12703)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12703),X12701),c_Groups_Ozero__class_Ozero(X12703)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12703),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12703),X12702),X12701)),c_Groups_Ozero__class_Ozero(X12703)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__neg__neg])])])). 4.05/4.30 fof(c_0_7581, plain, ![X11630, X11631, X11632]:(~class_Groups_Oordered__comm__monoid__add(X11632)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11632),X11631),c_Groups_Ozero__class_Ozero(X11632)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11632),X11630),c_Groups_Ozero__class_Ozero(X11632)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11632),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11632),X11631),X11630)),c_Groups_Ozero__class_Ozero(X11632)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__nonpos__neg])])])). 4.05/4.30 fof(c_0_7582, plain, ![X10646, X10647, X10648, X10649, X10650]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10650,X10649)),hAPP(hAPP(c_Product__Type_OPair(X10650,X10649),X10648),X10647)),hAPP(c_Relation_Oconverse(X10649,X10650),X10646)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X10649,X10650)),hAPP(hAPP(c_Product__Type_OPair(X10649,X10650),X10647),X10648)),X10646))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_converseD])])])). 4.05/4.30 fof(c_0_7583, plain, ![X17041, X17042, X17043]:(~c_Wellfounded_Owf(X17043,X17042)|(~c_Wellfounded_Owf(X17043,X17041)|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X17043,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X17043,X17043),X17042)),hAPP(c_Relation_ORange(X17043,X17043),X17041))!=c_Orderings_Obot__class_Obot(tc_fun(X17043,tc_HOL_Obool))|c_Wellfounded_Owf(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_wf__Un])])])). 4.05/4.30 fof(c_0_7584, plain, ![X16487, X16488, X16489, X16490]:(~class_Lattices_Olattice(X16490)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16490),X16489),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16490),X16488),X16487))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16490),X16488),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16490),X16489),X16487))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__aci_I3_J])])])). 4.05/4.30 fof(c_0_7585, plain, ![X9009, X9010, X9011]:(~class_Groups_Oordered__comm__monoid__add(X9011)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9011),X9010),c_Groups_Ozero__class_Ozero(X9011)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9011),X9009),c_Groups_Ozero__class_Ozero(X9011)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9011),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9011),X9010),X9009)),c_Groups_Ozero__class_Ozero(X9011)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__neg__nonpos])])])). 4.05/4.30 fof(c_0_7586, plain, ![X4657, X4658, X4659]:(~class_Groups_Oordered__comm__monoid__add(X4659)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4659),X4658),c_Groups_Ozero__class_Ozero(X4659)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4659),X4657),c_Groups_Ozero__class_Ozero(X4659)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4659),X4658),X4657)),c_Groups_Ozero__class_Ozero(X4659)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__nonpos__nonpos])])])). 4.05/4.30 fof(c_0_7587, plain, ![X1499, X1500, X1501]:(~class_Fields_Olinordered__field(X1501)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1501),c_Groups_Ozero__class_Ozero(X1501)),X1500))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1501),c_Groups_Ozero__class_Ozero(X1501)),X1499))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1501),c_Groups_Ozero__class_Ozero(X1501)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1501),X1500),X1499)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__pos__pos])])])). 4.05/4.30 fof(c_0_7588, plain, ![X10549, X10550, X10551]:(~class_Rings_Olinordered__semiring__strict(X10551)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10551),c_Groups_Ozero__class_Ozero(X10551)),X10550))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10551),c_Groups_Ozero__class_Ozero(X10551)),X10549))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10551),c_Groups_Ozero__class_Ozero(X10551)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10551),X10550),X10549)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__pos__pos])])])). 4.05/4.30 fof(c_0_7589, plain, ![X9951, X9952]:(~class_Rings_Ocomm__semiring__1(X9952)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9952),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9952),c_Groups_Oone__class_Oone(X9952)),c_Groups_Oone__class_Oone(X9952))),X9951)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9952),X9951),X9951)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])])). 4.05/4.30 fof(c_0_7590, plain, ![X5306, X5307, X5308, X5309, X5310]:(~c_Finite__Set_Ofolding__one__idem(X5310,X5309,X5308)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5310),X5307))|hAPP(X5308,hAPP(hAPP(c_Set_Oinsert(X5310),X5306),X5307))=hAPP(hAPP(c_Finite__Set_Ofold(X5310,X5310,X5309),X5306),X5307))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oeq__fold__idem_H])])). 4.05/4.30 cnf(c_0_7591, plain, (hAPP(c_Option_Ooption_OSome(X1),esk477_7(X2,X3,X4,X5,X6,X7,X1))=hAPP(X4,X3)|c_Map_Omap__comp(X1,X7,X6,X5,X4,X3)!=hAPP(c_Option_Ooption_OSome(X7),X2)), inference(split_conjunct,[status(thm)],[c_0_5297])). 4.05/4.30 cnf(c_0_7592, plain, (c_List_Olist_ONil(X1)=c_List_OdropWhile(X1,X2,X3)|~hBOOL(hAPP(X2,hAPP(c_List_Ohd(X1),c_List_OdropWhile(X1,X2,X3))))), inference(split_conjunct,[status(thm)],[c_0_5368])). 4.05/4.30 fof(c_0_7593, plain, ![X9309, X9310, X9311, X9312]:(~class_Rings_Ocomm__semiring__1(X9312)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9312),X9311),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9312),X9310),X9309))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9312),X9310),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9312),X9311),X9309))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])])). 4.05/4.30 fof(c_0_7594, plain, ![X13785, X13786, X13787]:(~class_Groups_Oordered__comm__monoid__add(X13787)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13787),c_Groups_Ozero__class_Ozero(X13787)),X13786))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13787),c_Groups_Ozero__class_Ozero(X13787)),X13785))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13787),c_Groups_Ozero__class_Ozero(X13787)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13787),X13786),X13785)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])])). 4.05/4.30 fof(c_0_7595, plain, ![X5229, X5230, X5231]:(~class_Rings_Olinordered__semidom(X5231)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5231),c_Groups_Oone__class_Oone(X5231)),X5230))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5231),c_Groups_Oone__class_Oone(X5231)),X5229))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5231),c_Groups_Oone__class_Oone(X5231)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5231),X5230),X5229)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__1__mult])])])). 4.05/4.30 cnf(c_0_7596, 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_5369])). 4.05/4.30 fof(c_0_7597, plain, ![X4214, X4215, X4216, X4217, X4218]:((~hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4218,X4217,X4216),X4215),X4214))|hBOOL(hAPP(hAPP(c_member(tc_prod(X4218,X4217)),hAPP(hAPP(c_Product__Type_OPair(X4218,X4217),X4215),X4214)),X4216)))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X4218,X4217)),hAPP(hAPP(c_Product__Type_OPair(X4218,X4217),X4215),X4214)),X4216))|hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4218,X4217,X4216),X4215),X4214)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])])). 4.05/4.30 fof(c_0_7598, plain, ![X14353, X14354, X14355, X14356]:(~class_Rings_Olinordered__semidom(X14356)|(hAPP(hAPP(c_Power_Opower__class_Opower(X14356),X14353),hAPP(c_Nat_OSuc,X14354))!=hAPP(hAPP(c_Power_Opower__class_Opower(X14356),X14355),hAPP(c_Nat_OSuc,X14354))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14356),c_Groups_Ozero__class_Ozero(X14356)),X14355))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14356),c_Groups_Ozero__class_Ozero(X14356)),X14353))|X14353=X14355)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__inject__base])])])). 4.05/4.30 cnf(c_0_7599, plain, (X3=hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X2))),X3)|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(rw,[status(thm)],[c_0_5370, c_0_4655])). 4.05/4.30 fof(c_0_7600, plain, ![X9298, X9299, X9300]:(~class_Fields_Olinordered__field(X9300)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9300),c_Groups_Ozero__class_Ozero(X9300)),X9299))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9300),c_Groups_Ozero__class_Ozero(X9300)),X9298))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9300),c_Groups_Ozero__class_Ozero(X9300)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9300),X9299),X9298)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__nonneg__pos])])])). 4.05/4.30 fof(c_0_7601, plain, ![X12621, X12622, X12623]:(~class_Rings_Oordered__cancel__semiring(X12623)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12623),c_Groups_Ozero__class_Ozero(X12623)),X12622))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12623),c_Groups_Ozero__class_Ozero(X12623)),X12621))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12623),c_Groups_Ozero__class_Ozero(X12623)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12623),X12622),X12621)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__nonneg__nonneg])])])). 4.05/4.30 fof(c_0_7602, plain, ![X15339, X15340, X15341]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),X15339),c_Groups_Ozero__class_Ozero(X15341)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),c_Groups_Ozero__class_Ozero(X15341)),X15339))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),c_Groups_Ozero__class_Ozero(X15341)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15341),X15340),X15339)))|~class_Rings_Olinordered__ring__strict(X15341))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),X15340),c_Groups_Ozero__class_Ozero(X15341)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),c_Groups_Ozero__class_Ozero(X15341)),X15339))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),c_Groups_Ozero__class_Ozero(X15341)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15341),X15340),X15339)))|~class_Rings_Olinordered__ring__strict(X15341)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),X15339),c_Groups_Ozero__class_Ozero(X15341)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),c_Groups_Ozero__class_Ozero(X15341)),X15340))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),c_Groups_Ozero__class_Ozero(X15341)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15341),X15340),X15339)))|~class_Rings_Olinordered__ring__strict(X15341))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),X15340),c_Groups_Ozero__class_Ozero(X15341)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),c_Groups_Ozero__class_Ozero(X15341)),X15340))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),c_Groups_Ozero__class_Ozero(X15341)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15341),X15340),X15339)))|~class_Rings_Olinordered__ring__strict(X15341))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),c_Groups_Ozero__class_Ozero(X15341)),X15339))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),c_Groups_Ozero__class_Ozero(X15341)),X15340))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),c_Groups_Ozero__class_Ozero(X15341)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15341),X15340),X15339)))|~class_Rings_Olinordered__ring__strict(X15341))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),X15339),c_Groups_Ozero__class_Ozero(X15341)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),X15340),c_Groups_Ozero__class_Ozero(X15341)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15341),c_Groups_Ozero__class_Ozero(X15341)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15341),X15340),X15339)))|~class_Rings_Olinordered__ring__strict(X15341)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__mult__iff])])])])). 4.05/4.30 fof(c_0_7603, plain, ![X2020, X2021, X2022]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2022),X2021),c_Groups_Ozero__class_Ozero(X2022)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2022),X2020),c_Groups_Ozero__class_Ozero(X2022)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2022),c_Groups_Ozero__class_Ozero(X2022)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2022),X2021),X2020)))|~class_Rings_Oordered__ring(X2022))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2022),c_Groups_Ozero__class_Ozero(X2022)),X2020))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2022),c_Groups_Ozero__class_Ozero(X2022)),X2021))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2022),c_Groups_Ozero__class_Ozero(X2022)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2022),X2021),X2020)))|~class_Rings_Oordered__ring(X2022))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_split__mult__pos__le])])])])). 4.05/4.30 cnf(c_0_7604, plain, (esk25_3(X4,X3,X1)=X2|hAPP(X4,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~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(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5275])). 4.05/4.30 fof(c_0_7605, plain, ![X14383, X14384, X14385, X14386, X14387, X14388, X14389, X14390, X14391, X14392, X14393, X14394, X14395, X14396, X14397]:((~hBOOL(hAPP(hAPP(c_member(X14389),X14390),X14386))|~hBOOL(hAPP(hAPP(hAPP(X14385,X14390),X14384),X14383))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14389,tc_fun(X14388,tc_fun(X14387,tc_HOL_Obool))),X14386),X14385),X14384),X14383)))&((hBOOL(hAPP(hAPP(c_member(X14397),esk440_7(X14391,X14392,X14393,X14394,X14395,X14396,X14397)),X14394))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14397,tc_fun(X14396,tc_fun(X14395,tc_HOL_Obool))),X14394),X14393),X14392),X14391)))&(hBOOL(hAPP(hAPP(hAPP(X14393,esk440_7(X14391,X14392,X14393,X14394,X14395,X14396,X14397)),X14392),X14391))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14397,tc_fun(X14396,tc_fun(X14395,tc_HOL_Obool))),X14394),X14393),X14392),X14391))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP2__iff])])])])])])). 4.05/4.30 fof(c_0_7606, plain, ![X379, X380, X381]:(~class_Divides_Osemiring__div(X381)|X380=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X381),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X381),X380),X379)),X379)),c_Divides_Odiv__class_Omod(X381,X380,X379))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__div__decomp])])])). 4.05/4.30 fof(c_0_7607, plain, ![X14883, X14884, X14885]:(~class_Rings_Olinordered__semidom(X14885)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14885),c_Groups_Oone__class_Oone(X14885)),X14884))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14883))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14885),c_Groups_Oone__class_Oone(X14885)),hAPP(hAPP(c_Power_Opower__class_Opower(X14885),X14884),X14883)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_one__less__power])])])). 4.05/4.30 fof(c_0_7608, plain, ![X3805, X3806, X3807]:(~class_Fields_Olinordered__field(X3807)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3807),X3806),c_Groups_Ozero__class_Ozero(X3807)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3807),X3805),c_Groups_Ozero__class_Ozero(X3807)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3807),c_Groups_Ozero__class_Ozero(X3807)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3807),X3806),X3805)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__neg])])). 4.05/4.30 fof(c_0_7609, plain, ![X11938, X11939, X11940]:(~class_Rings_Olinordered__ring__strict(X11940)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11940),X11939),c_Groups_Ozero__class_Ozero(X11940)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11940),X11938),c_Groups_Ozero__class_Ozero(X11940)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11940),c_Groups_Ozero__class_Ozero(X11940)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11940),X11939),X11938)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__neg__neg])])])). 4.05/4.30 fof(c_0_7610, plain, ![X8019, X8020, X8021]:(~class_Divides_Osemiring__div(X8021)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8021),c_Divides_Odiv__class_Omod(X8021,X8020,X8019)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8021),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X8021),X8020),X8019)),X8019))=X8020), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_semiring__div__class_Omod__div__equality_H])])])). 4.05/4.30 fof(c_0_7611, plain, ![X5395, X5396, X5397]:(~class_Divides_Osemiring__div(X5397)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5397),X5396),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X5397),X5395),X5396))),c_Divides_Odiv__class_Omod(X5397,X5395,X5396))=X5395), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__div__equality2])])])). 4.05/4.30 cnf(c_0_7612, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|c_Groups_Ozero__class_Ozero(X1)!=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)!=X4|~class_Int_Onumber(X1)|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_5371])). 4.05/4.30 fof(c_0_7613, plain, ![X9450, X9451, X9452]:(~class_Fields_Olinordered__field(X9452)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9452),X9451),c_Groups_Ozero__class_Ozero(X9452)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9452),X9450),c_Groups_Ozero__class_Ozero(X9452)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9452),c_Groups_Ozero__class_Ozero(X9452)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9452),X9451),X9450)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__nonpos__neg])])])). 4.05/4.30 cnf(c_0_7614, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk60_2(X1,X2)),hAPP(c_List_Oset(tc_Nat_Onat),X1)))|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)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2), inference(split_conjunct,[status(thm)],[c_0_5372])). 4.05/4.30 fof(c_0_7615, plain, ![X6575, X6576, X6577]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6577,X6577),tc_HOL_Obool)),X6576),X6575))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6577,X6577),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X6577,X6576)),c_Transitive__Closure_Ortrancl(X6577,X6575)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__mono])])). 4.05/4.30 fof(c_0_7616, plain, ![X6259, X6260, X6261, X6262]:(~class_Rings_Olinordered__semidom(X6262)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6262),hAPP(hAPP(c_Power_Opower__class_Opower(X6262),X6261),hAPP(c_Nat_OSuc,X6260))),hAPP(hAPP(c_Power_Opower__class_Opower(X6262),X6259),hAPP(c_Nat_OSuc,X6260))))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6262),c_Groups_Ozero__class_Ozero(X6262)),X6259))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6262),X6261),X6259))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__le__imp__le__base])])])). 4.05/4.30 fof(c_0_7617, plain, ![X8142, X8143, X8144, X8145]:(~class_Orderings_Olinorder(X8145)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X8145),X8143),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8145),X8144),X8142))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X8145),X8144),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8145),X8143),X8142))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__left__commute])])])). 4.05/4.30 cnf(c_0_7618, plain, (hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5373])). 4.05/4.30 fof(c_0_7619, plain, ![X12269, X12270, X12271, X12272]:(~class_Orderings_Oorder(X12272)|c_Orderings_Obot__class_Obot(tc_fun(X12272,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12272,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X12272,X12271),X12270)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X12272,X12270),X12269))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I11_J])])). 4.05/4.30 cnf(c_0_7620, plain, (c_Option_Ooption_ONone(X1)=hAPP(X2,esk208_6(X3,X4,X2,X5,X1,X6))|hAPP(X4,X3)=c_Option_Ooption_ONone(X6)|c_Option_Ooption_ONone(X1)!=c_Map_Omap__comp(X6,X1,X5,X2,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_5338])). 4.05/4.30 fof(c_0_7621, plain, ![X6152, X6153, X6154, X6155]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6155),X6152),X6154)),X6153))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6155),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6155),X6153),X6154)),X6152))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6155),X6154),c_Groups_Ozero__class_Ozero(X6155)))|~class_Fields_Olinordered__field(X6155))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6155),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6155),X6153),X6154)),X6152))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6155),X6152),X6154)),X6153))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6155),X6154),c_Groups_Ozero__class_Ozero(X6155)))|~class_Fields_Olinordered__field(X6155))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__divide__less__eq])])])])). 4.05/4.30 fof(c_0_7622, plain, ![X13475, X13476, X13477, X13478]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13478),X13475),X13477)),X13476))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13478),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13478),X13476),X13477)),X13475))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13478),X13477),c_Groups_Ozero__class_Ozero(X13478)))|~class_Fields_Olinordered__field(X13478))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13478),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13478),X13476),X13477)),X13475))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13478),X13475),X13477)),X13476))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13478),X13477),c_Groups_Ozero__class_Ozero(X13478)))|~class_Fields_Olinordered__field(X13478))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__divide__le__eq])])])])). 4.05/4.30 fof(c_0_7623, plain, ![X12765, X12766, X12767]:(~class_Groups_Omonoid__add(X12767)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12767),X12766),hAPP(c_List_Ofoldl(X12767,X12767,c_Groups_Oplus__class_Oplus(X12767),c_Groups_Ozero__class_Ozero(X12767)),X12765))=hAPP(c_List_Ofoldl(X12767,X12767,c_Groups_Oplus__class_Oplus(X12767),X12766),X12765)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_foldl__absorb0])])])). 4.05/4.30 fof(c_0_7624, plain, ![X2041, X2042, X2043, X2044]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2043,X2044)),X2042),X2041))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2043,X2044)),X2041),X2042))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2043,X2044)),X2042),X2041))|~class_Orderings_Oord(X2044))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2043,X2044)),X2042),X2041))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2043,X2044)),X2042),X2041))|~class_Orderings_Oord(X2044))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2043,X2044)),X2041),X2042))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2043,X2044)),X2042),X2041))|~class_Orderings_Oord(X2044)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__fun__def])])])])). 4.05/4.30 fof(c_0_7625, plain, ![X8982, X8983]:((c_Divides_Odiv__class_Omod(tc_Int_Oint,X8983,X8982)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X8983,X8982)),X8982)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X8983,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X8982)))&(c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X8983,X8982)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X8983,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X8982)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmod__zminus2__eq__if])])])). 4.05/4.30 fof(c_0_7626, plain, ![X13976, X13977, X13978, X13979]:(~class_Lattices_Osemilattice__sup(X13979)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13979),X13977),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13979),X13978),X13976))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13979),X13978),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13979),X13977),X13976))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__left__commute])])])). 4.05/4.30 fof(c_0_7627, plain, ![X10326, X10327, X10328, X10329]:(~class_Fields_Olinordered__field(X10329)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10329),c_Groups_Ozero__class_Ozero(X10329)),X10328))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10329),X10327),X10328)),X10326))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10329),X10327),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10329),X10326),X10328)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__less__div__pos])])). 4.05/4.30 fof(c_0_7628, plain, ![X3557, X3558, X3559, X3560]:(~class_Fields_Olinordered__field(X3560)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3560),c_Groups_Ozero__class_Ozero(X3560)),X3559))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3560),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3560),X3558),X3559)),X3557))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3560),X3558),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3560),X3557),X3559)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__imp__le__div__pos])])])). 4.05/4.30 cnf(c_0_7629, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X5,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X2)!=X4|~hBOOL(hAPP(X5,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4,X1)))), inference(split_conjunct,[status(thm)],[c_0_5288])). 4.05/4.30 fof(c_0_7630, plain, ![X15430, X15431, X15432, X15433]:(~class_Fields_Olinordered__field(X15433)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15433),c_Groups_Ozero__class_Ozero(X15433)),X15432))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15433),X15431),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15433),X15430),X15432)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15433),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15433),X15431),X15432)),X15430))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__imp__div__pos__less])])])). 4.05/4.30 fof(c_0_7631, plain, ![X13376, X13377, X13378, X13379]:(~class_Fields_Olinordered__field(X13379)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13379),c_Groups_Ozero__class_Ozero(X13379)),X13378))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13379),X13377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13379),X13376),X13378)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13379),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13379),X13377),X13378)),X13376))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__imp__div__pos__le])])])). 4.05/4.30 fof(c_0_7632, plain, ![X1213, X1214, X1215, X1216, X1217, X1218, X1219]:(((hBOOL(hAPP(hAPP(X1217,X1216),X1214))|~c_List_Olist__all2(X1219,X1218,X1217,hAPP(hAPP(c_List_Olist_OCons(X1219),X1216),X1215),hAPP(hAPP(c_List_Olist_OCons(X1218),X1214),X1213)))&(c_List_Olist__all2(X1219,X1218,X1217,X1215,X1213)|~c_List_Olist__all2(X1219,X1218,X1217,hAPP(hAPP(c_List_Olist_OCons(X1219),X1216),X1215),hAPP(hAPP(c_List_Olist_OCons(X1218),X1214),X1213))))&(~hBOOL(hAPP(hAPP(X1217,X1216),X1214))|~c_List_Olist__all2(X1219,X1218,X1217,X1215,X1213)|c_List_Olist__all2(X1219,X1218,X1217,hAPP(hAPP(c_List_Olist_OCons(X1219),X1216),X1215),hAPP(hAPP(c_List_Olist_OCons(X1218),X1214),X1213)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Cons])])])). 4.05/4.30 fof(c_0_7633, plain, ![X12062, X12063, X12064, X12065, X12066, X12067, X12068]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X12067),X12063))|hAPP(hAPP(X12064,X12062),X12063)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X12068,X12067,X12066),X12062),X12065),X12063)|~c_Big__Operators_Ocomm__monoid__big(X12068,X12067,X12066,X12065,X12064))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X12067),X12063))|X12065=hAPP(hAPP(X12064,X12062),X12063)|~c_Big__Operators_Ocomm__monoid__big(X12068,X12067,X12066,X12065,X12064))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__monoid__big_OF__eq])])])])). 4.05/4.30 fof(c_0_7634, plain, ![X11732, X11733, X11734, X11735, X11736, X11737, X11738]:(~c_Finite__Set_Ofolding__image(X11738,X11737,X11736,X11735,X11734)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11737),X11733))|hAPP(hAPP(X11734,X11732),X11733)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X11738,X11737,X11736),X11732),X11735),X11733))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__image_Oeq__fold])])])). 4.05/4.30 fof(c_0_7635, plain, ![X8780, X8781, X8782, X8783]:(~class_Lattices_Olattice(X8783)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8783),X8781),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8783),X8782),X8780))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8783),X8782),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8783),X8781),X8780))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I7_J])])). 4.05/4.30 fof(c_0_7636, plain, ![X11269, X11270, X11271, X11272]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11272),X11270),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11272),X11269),X11271)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11272),X11269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11272),X11270),X11271)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11272),X11271),c_Groups_Ozero__class_Ozero(X11272)))|~class_Fields_Olinordered__field(X11272))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11272),X11269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11272),X11270),X11271)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11272),X11270),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X11272),X11269),X11271)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11272),X11271),c_Groups_Ozero__class_Ozero(X11272)))|~class_Fields_Olinordered__field(X11272))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__less__divide__eq])])])])). 4.05/4.30 fof(c_0_7637, plain, ![X8707, X8708, X8709, X8710]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8710),X8707),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8710),X8708),X8709)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8710),X8708),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8710),X8707),X8709)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8710),X8709),c_Groups_Ozero__class_Ozero(X8710)))|~class_Fields_Olinordered__field(X8710))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8710),X8708),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8710),X8707),X8709)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8710),X8707),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8710),X8708),X8709)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8710),X8709),c_Groups_Ozero__class_Ozero(X8710)))|~class_Fields_Olinordered__field(X8710))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__le__divide__eq])])])])). 4.05/4.30 fof(c_0_7638, plain, ![X10558, X10559, X10560, X10561]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X10561),X10560))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10559),X10558))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10561),X10559)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X10560),X10558))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zadd__zless__mono])])])). 4.05/4.30 fof(c_0_7639, plain, ![X6364, X6365, X6366]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6366),X6365))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6364),X6366))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6366),X6364)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6365),X6364))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__less__mono])])])). 4.05/4.30 cnf(c_0_7640, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)|c_Groups_Ozero__class_Ozero(X1)!=X2|c_Groups_Ozero__class_Ozero(X1)!=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Oordered__comm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5374])). 4.05/4.30 fof(c_0_7641, plain, ![X11637, X11638, X11639]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11639),X11638))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11639),X11637))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11637),X11638)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11637),X11639))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__less__mono2])])])). 4.05/4.30 fof(c_0_7642, plain, ![X9396, X9397, X9398, X9399]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9399),X9398))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9397),X9396))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9399),X9397)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9398),X9396))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__less__mono])])])). 4.05/4.30 fof(c_0_7643, plain, ![X15414, X15415, X15416, X15417]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15417),X15416))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15415),X15414))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15417),X15415)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15416),X15414))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__mono])])])). 4.05/4.30 fof(c_0_7644, plain, ![X8601, X8602, X8603, X8604]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8604),X8603))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8602),X8601))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8604),X8602)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8603),X8601))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__mono])])])). 4.05/4.30 fof(c_0_7645, plain, ![X349, X350, X351, X352, X353, X354]:(~c_Relation_Osingle__valued(X354,X353,X352)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X354,X353)),hAPP(hAPP(c_Product__Type_OPair(X354,X353),X351),X350)),X352))|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X354,X353)),hAPP(hAPP(c_Product__Type_OPair(X354,X353),X351),X349)),X352))|X350=X349))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_single__valuedD])])])). 4.05/4.30 cnf(c_0_7646, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4))=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Divides_Osemiring__div(X2)), inference(split_conjunct,[status(thm)],[c_0_5375])). 4.05/4.30 cnf(c_0_7647, plain, (hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(c_Set_OCollect(X3),X1))))|~hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_5376])). 4.05/4.30 fof(c_0_7648, plain, ![X3364, X3365, X3366, X3367, X3368]:(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X3368,X3368,X3367,X3366,X3365),X3364))|(hBOOL(hAPP(hAPP(c_member(X3368),X3366),X3365))|hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3368,X3367,hAPP(hAPP(c_Set_Oinsert(X3368),X3366),X3365)),X3364)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1Set_Ointros])])])). 4.05/4.30 fof(c_0_7649, plain, ![X14714, X14715, X14716, X14717, X14718]:((~c_List_Olinorder__class_Osorted(X14718,hAPP(hAPP(c_List_Omap(X14717,X14718),X14716),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X14717,X14718,X14716),X14715),X14714)))|c_List_Olinorder__class_Osorted(X14718,hAPP(hAPP(c_List_Omap(X14717,X14718),X14716),X14714))|~class_Orderings_Olinorder(X14718))&(~c_List_Olinorder__class_Osorted(X14718,hAPP(hAPP(c_List_Omap(X14717,X14718),X14716),X14714))|c_List_Olinorder__class_Osorted(X14718,hAPP(hAPP(c_List_Omap(X14717,X14718),X14716),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X14717,X14718,X14716),X14715),X14714)))|~class_Orderings_Olinorder(X14718))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__key])])])). 4.05/4.30 fof(c_0_7650, plain, ![X16842, X16843, X16844]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16844,tc_HOL_Obool)),X16843),X16842))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X16844,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X16844,X16843)),c_Predicate_OPowp(X16844,X16842)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Powp__mono])])])). 4.05/4.30 fof(c_0_7651, plain, ![X12408, X12409, X12410, X12411]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12411,tc_HOL_Obool)),X12410),X12409))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12411,tc_HOL_Obool)),X12409),X12408))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X12411,tc_HOL_Obool)),X12410),X12408)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_psubset__trans])])])). 4.05/4.30 fof(c_0_7652, plain, ![X11367, X11368, X11369, X11370]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11370,tc_HOL_Obool)),X11369),X11368))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X11370,tc_HOL_Obool)),X11368),X11367))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X11370,tc_HOL_Obool)),X11369),X11367)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__psubset__trans])])])). 4.05/4.30 fof(c_0_7653, plain, ![X8561, X8562, X8563, X8564]:(~class_Rings_Ocomm__semiring__1(X8564)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8564),X8562),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8564),X8563),X8561))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8564),X8563),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8564),X8562),X8561))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])])])). 4.05/4.30 cnf(c_0_7654, 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_5377])). 4.05/4.30 cnf(c_0_7655, 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_5378, c_0_5379]), ['final']). 4.05/4.30 fof(c_0_7656, plain, ![X7057, X7058]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7058),X7057))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7057),X7058))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7057)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7058))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiff__int])])). 4.05/4.30 cnf(c_0_7657, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_5380])). 4.05/4.30 fof(c_0_7658, plain, ![X16545, X16546, X16547, X16548]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X16548,tc_HOL_Obool)),X16547),X16546))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16548,tc_HOL_Obool)),X16546),X16545))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X16548,tc_HOL_Obool)),X16547),X16545)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_psubset__subset__trans])])])). 4.05/4.30 fof(c_0_7659, plain, ![X3162, X3163, X3164, X3165]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3165,tc_HOL_Obool)),X3164),X3163))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3165,tc_HOL_Obool)),X3163),X3162))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3165,tc_HOL_Obool)),X3164),X3162)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__trans])])])). 4.05/4.30 fof(c_0_7660, plain, ![X859, X860]:((~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),X860),X859)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X860),X859)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X860),X859))|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),X860),X859)),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])])). 4.05/4.30 fof(c_0_7661, plain, ![X4204, X4205, X4206, X4207]:(~hBOOL(hAPP(hAPP(c_member(X4207),X4206),X4205))|(hBOOL(hAPP(hAPP(c_member(X4207),X4206),X4204))|hBOOL(hAPP(hAPP(c_member(X4207),X4206),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4207,tc_HOL_Obool)),X4205),X4204))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_DiffI])])])). 4.05/4.30 cnf(c_0_7662, 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_5381])). 4.05/4.30 fof(c_0_7663, plain, ![X8488, X8489, X8490]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8490),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8489)),X8488)))|c_List_Obutlast(X8489,hAPP(hAPP(c_List_Otake(X8489),X8490),X8488))=hAPP(hAPP(c_List_Otake(X8489),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8490),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X8488)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__take])])). 4.05/4.30 cnf(c_0_7664, plain, (hAPP(c_Option_Ooption_OSome(X1),X2)=hAPP(X3,esk477_7(X2,X4,X5,X3,X6,X1,X7))|c_Map_Omap__comp(X7,X1,X6,X3,X5,X4)!=hAPP(c_Option_Ooption_OSome(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5297])). 4.05/4.30 cnf(c_0_7665, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_5380])). 4.05/4.30 fof(c_0_7666, plain, ![X12027, X12028, X12029, X12030]:(~class_Divides_Oring__div(X12030)|(c_Divides_Odiv__class_Omod(X12030,X12027,X12028)!=c_Divides_Odiv__class_Omod(X12030,X12029,X12028)|c_Divides_Odiv__class_Omod(X12030,hAPP(c_Groups_Ouminus__class_Ouminus(X12030),X12029),X12028)=c_Divides_Odiv__class_Omod(X12030,hAPP(c_Groups_Ouminus__class_Ouminus(X12030),X12027),X12028))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__cong])])). 4.05/4.30 fof(c_0_7667, plain, ![X12647, X12648, X12649, X12650, X12651, X12652, X12653]:(~c_List_Olist__all2(X12653,X12652,X12651,X12650,X12649)|(~c_List_Olist__all2(X12653,X12652,X12651,X12648,X12647)|c_List_Olist__all2(X12653,X12652,X12651,hAPP(hAPP(c_List_Oappend(X12653),X12650),X12648),hAPP(hAPP(c_List_Oappend(X12652),X12649),X12647)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__appendI])])). 4.05/4.30 cnf(c_0_7668, plain, (hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Set_Oimage(X1,X2,X3),X4))=X4|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5382])). 4.05/4.30 fof(c_0_7669, plain, ![X10279, X10280, X10281]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10281),X10280)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10281),X10279)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10281))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10280),X10279))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10281))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10281),X10280)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10281),X10279))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10280),X10279))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10281),X10280)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10281),X10279)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__cancel1])])])])). 4.05/4.30 fof(c_0_7670, plain, ![X1161, X1162, X1163]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1162))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1163),X1162)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1161),X1162))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1163),X1161))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1163),X1162)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1161),X1162)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1163),X1162)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1161),X1162)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1162))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1163),X1161))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2])])])). 4.05/4.30 fof(c_0_7671, plain, ![X12252, X12253]:(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X12253),hAPP(c_List_Oset(tc_Nat_Onat),X12252)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12253),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)),X12252)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_elem__le__sum])])])). 4.05/4.30 fof(c_0_7672, plain, ![X1444, X1445]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1445),X1444))|c_List_Olist_ONil(tc_Int_Oint)=c_List_Oupto(X1445,X1444))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1445),X1444))|c_List_Oupto(X1445,X1444)=hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X1445),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1445),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1444)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_upto_Osimps])])])). 4.05/4.30 fof(c_0_7673, plain, ![X17106, X17107, X17108, X17109, X17110, X17112, X17113, X17114, X17115, X17116, X17117]:(((hBOOL(hAPP(hAPP(c_member(X17110),esk513_5(X17106,X17107,X17108,X17109,X17110)),X17108))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17110,tc_fun(X17109,tc_HOL_Obool)),X17108),X17107),X17106)))&(~hBOOL(hAPP(hAPP(X17107,esk513_5(X17106,X17107,X17108,X17109,X17110)),X17106))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17110,tc_fun(X17109,tc_HOL_Obool)),X17108),X17107),X17106))))&(~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X17116,tc_fun(X17115,tc_HOL_Obool)),X17114),X17113),X17112))|(~hBOOL(hAPP(hAPP(c_member(X17116),X17117),X17114))|hBOOL(hAPP(hAPP(X17113,X17117),X17112))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF1__iff])])])])])])])). 4.05/4.30 fof(c_0_7674, plain, ![X13927, X13928, X13929, X13930, X13931]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13931),X13929),X13927))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13931),X13929),X13930))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13931,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13931,X13930),X13929)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13931,X13928),X13927)))|~class_Orderings_Olinorder(X13931))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13931),X13928),X13930))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13931),X13929),X13930))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13931,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13931,X13930),X13929)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13931,X13928),X13927)))|~class_Orderings_Olinorder(X13931))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff])])])). 4.05/4.30 cnf(c_0_7675, 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_5383])). 4.05/4.30 fof(c_0_7676, plain, ![X7749, X7750, X7751, X7752]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7752,tc_HOL_Obool)),X7750),X7749))|~hBOOL(hAPP(hAPP(c_member(X7752),X7751),X7749))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7752,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7752),X7751),X7750)),X7749)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7752,tc_HOL_Obool)),X7750),X7749))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7752,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7752),X7751),X7750)),X7749)))&(hBOOL(hAPP(hAPP(c_member(X7752),X7751),X7749))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7752,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X7752),X7751),X7750)),X7749))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])])). 4.05/4.30 fof(c_0_7677, plain, ![X4254, X4255, X4256]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4256,X4256),tc_HOL_Obool)),X4255),X4254))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4256,tc_HOL_Obool)),hAPP(c_Relation_OField(X4256),X4255)),hAPP(c_Relation_OField(X4256),X4254)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mono__Field])])])). 4.05/4.30 fof(c_0_7678, plain, ![X13137, X13138, X13139]:(X13139=c_List_Olist_ONil(X13138)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13137),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13138)),X13139)))|hAPP(c_List_Ohd(X13138),hAPP(hAPP(c_List_Odrop(X13138),X13137),X13139))=hAPP(hAPP(c_List_Onth(X13138),X13139),X13137))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__drop__conv__nth])])])). 4.05/4.30 fof(c_0_7679, plain, ![X12802, X12803]:((~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),X12803)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X12802)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X12803),X12802))|~c_Nat__Transfer_Onat__set(X12802)|~c_Nat__Transfer_Onat__set(X12803))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X12803),X12802))|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),X12803)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X12802)))|~c_Nat__Transfer_Onat__set(X12802)|~c_Nat__Transfer_Onat__set(X12803))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transfer__int__nat__set__relations_I5_J])])])])). 4.05/4.30 fof(c_0_7680, plain, ![X10834, X10835, X10836]:(~class_Orderings_Olinorder(X10836)|(hBOOL(hAPP(hAPP(c_member(X10836),X10835),hAPP(c_List_Oset(X10836),X10834)))|c_List_Olinorder__class_Oinsort__insert__key(X10836,X10836,c_COMBI(X10836),X10835,X10834)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10836,X10836,c_COMBI(X10836)),X10835),X10834))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__insert__insort])])])). 4.05/4.30 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_Oinj__on(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5384])). 4.05/4.30 fof(c_0_7682, plain, ![X16008, X16009, X16010]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16010),X16009))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16008),X16010)),X16009)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16008),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16009),X16010))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__right])])). 4.05/4.30 fof(c_0_7683, plain, ![X2443, X2444, X2445]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2445),X2444))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2443),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2444),X2445))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2443),X2444)),X2445)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc])])). 4.05/4.30 cnf(c_0_7684, 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_5385])). 4.05/4.30 cnf(c_0_7685, 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_5386])). 4.05/4.30 fof(c_0_7686, plain, ![X6563, X6564, X6565]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),X6563),c_Groups_Ozero__class_Ozero(X6565)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),c_Groups_Ozero__class_Ozero(X6565)),X6564))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6565),X6564),X6563)),c_Groups_Ozero__class_Ozero(X6565)))|~class_Fields_Olinordered__field__inverse__zero(X6565))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),X6564),c_Groups_Ozero__class_Ozero(X6565)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),c_Groups_Ozero__class_Ozero(X6565)),X6563))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6565),X6564),X6563)),c_Groups_Ozero__class_Ozero(X6565)))|~class_Fields_Olinordered__field__inverse__zero(X6565)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),X6564),c_Groups_Ozero__class_Ozero(X6565)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),X6563),c_Groups_Ozero__class_Ozero(X6565)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6565),X6564),X6563)),c_Groups_Ozero__class_Ozero(X6565)))|~class_Fields_Olinordered__field__inverse__zero(X6565))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),c_Groups_Ozero__class_Ozero(X6565)),X6563))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),X6563),c_Groups_Ozero__class_Ozero(X6565)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6565),X6564),X6563)),c_Groups_Ozero__class_Ozero(X6565)))|~class_Fields_Olinordered__field__inverse__zero(X6565)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),X6564),c_Groups_Ozero__class_Ozero(X6565)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),c_Groups_Ozero__class_Ozero(X6565)),X6564))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6565),X6564),X6563)),c_Groups_Ozero__class_Ozero(X6565)))|~class_Fields_Olinordered__field__inverse__zero(X6565))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),c_Groups_Ozero__class_Ozero(X6565)),X6563))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),c_Groups_Ozero__class_Ozero(X6565)),X6564))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6565),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6565),X6564),X6563)),c_Groups_Ozero__class_Ozero(X6565)))|~class_Fields_Olinordered__field__inverse__zero(X6565))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__less__0__iff])])])])). 4.05/4.30 fof(c_0_7687, plain, ![X2665, X2666, X2667]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),c_Groups_Ozero__class_Ozero(X2667)),X2666))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),c_Groups_Ozero__class_Ozero(X2667)),X2665))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2667),X2666),X2665)),c_Groups_Ozero__class_Ozero(X2667)))|~class_Fields_Olinordered__field__inverse__zero(X2667))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),X2665),c_Groups_Ozero__class_Ozero(X2667)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),c_Groups_Ozero__class_Ozero(X2667)),X2665))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2667),X2666),X2665)),c_Groups_Ozero__class_Ozero(X2667)))|~class_Fields_Olinordered__field__inverse__zero(X2667)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),c_Groups_Ozero__class_Ozero(X2667)),X2666))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),X2666),c_Groups_Ozero__class_Ozero(X2667)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2667),X2666),X2665)),c_Groups_Ozero__class_Ozero(X2667)))|~class_Fields_Olinordered__field__inverse__zero(X2667))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),X2665),c_Groups_Ozero__class_Ozero(X2667)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),X2666),c_Groups_Ozero__class_Ozero(X2667)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2667),X2666),X2665)),c_Groups_Ozero__class_Ozero(X2667)))|~class_Fields_Olinordered__field__inverse__zero(X2667))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),c_Groups_Ozero__class_Ozero(X2667)),X2665))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),X2666),c_Groups_Ozero__class_Ozero(X2667)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2667),X2666),X2665)),c_Groups_Ozero__class_Ozero(X2667)))|~class_Fields_Olinordered__field__inverse__zero(X2667))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),c_Groups_Ozero__class_Ozero(X2667)),X2666))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),X2665),c_Groups_Ozero__class_Ozero(X2667)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2667),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2667),X2666),X2665)),c_Groups_Ozero__class_Ozero(X2667)))|~class_Fields_Olinordered__field__inverse__zero(X2667)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff])])])). 4.05/4.30 cnf(c_0_7688, plain, (hAPP(X6,hAPP(c_Product__Type_Osnd(X3,X1),X5))=hAPP(X4,hAPP(c_Product__Type_Osnd(X3,X1),X5))|hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X4),X5)!=hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X6),X5)), inference(split_conjunct,[status(thm)],[c_0_5233])). 4.05/4.30 cnf(c_0_7689, 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_5234])). 4.05/4.30 fof(c_0_7690, plain, ![X597, X598, X599]:(~class_Rings_Oring__1(X599)|(~hBOOL(hAPP(hAPP(c_member(X599),X598),c_Int_Oring__1__class_OInts(X599)))|(~hBOOL(hAPP(hAPP(c_member(X599),X597),c_Int_Oring__1__class_OInts(X599)))|hBOOL(hAPP(hAPP(c_member(X599),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X599),X598),X597)),c_Int_Oring__1__class_OInts(X599)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__diff])])])). 4.05/4.30 fof(c_0_7691, plain, ![X9503, X9504, X9505]:(~class_Rings_Osemiring__1(X9505)|(~hBOOL(hAPP(hAPP(c_member(X9505),X9504),c_Nat_Osemiring__1__class_ONats(X9505)))|(~hBOOL(hAPP(hAPP(c_member(X9505),X9503),c_Nat_Osemiring__1__class_ONats(X9505)))|hBOOL(hAPP(hAPP(c_member(X9505),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9505),X9504),X9503)),c_Nat_Osemiring__1__class_ONats(X9505)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nats__mult])])])). 4.05/4.30 fof(c_0_7692, plain, ![X3527, X3528, X3529]:(~class_Rings_Oring__1(X3529)|(~hBOOL(hAPP(hAPP(c_member(X3529),X3528),c_Int_Oring__1__class_OInts(X3529)))|(~hBOOL(hAPP(hAPP(c_member(X3529),X3527),c_Int_Oring__1__class_OInts(X3529)))|hBOOL(hAPP(hAPP(c_member(X3529),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3529),X3528),X3527)),c_Int_Oring__1__class_OInts(X3529)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__mult])])])). 4.05/4.30 fof(c_0_7693, plain, ![X6323, X6324, X6325, X6328, X6329, X6330, X6331, X6332]:((((X6324=hAPP(hAPP(c_List_Olist_OCons(X6325),esk188_3(X6323,X6324,X6325)),esk189_3(X6323,X6324,X6325))|c_List_Olist_ONil(X6325)=X6324|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6325)),X6324),c_List_Olists(X6325,X6323))))&(hBOOL(hAPP(hAPP(c_member(X6325),esk188_3(X6323,X6324,X6325)),X6323))|c_List_Olist_ONil(X6325)=X6324|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6325)),X6324),c_List_Olists(X6325,X6323)))))&(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6325)),esk189_3(X6323,X6324,X6325)),c_List_Olists(X6325,X6323)))|c_List_Olist_ONil(X6325)=X6324|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6325)),X6324),c_List_Olists(X6325,X6323)))))&((X6329!=hAPP(hAPP(c_List_Olist_OCons(X6330),X6331),X6332)|~hBOOL(hAPP(hAPP(c_member(X6330),X6331),X6328))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6330)),X6332),c_List_Olists(X6330,X6328)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6330)),X6329),c_List_Olists(X6330,X6328))))&(c_List_Olist_ONil(X6330)!=X6329|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6330)),X6329),c_List_Olists(X6330,X6328)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists_Osimps])])])])])])). 4.05/4.30 fof(c_0_7694, plain, ![X17522, X17523, X17524, X17525]:(~class_Groups_Ocomm__monoid__add(X17525)|(~c_Fun_Oinj__on(X17524,X17525,X17523,X17522)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17525,X17525),c_Fun_Oid(X17525)),hAPP(c_Set_Oimage(X17524,X17525,X17523),X17522))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X17524,X17525),X17523),X17522))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__reindex__id])])])). 4.05/4.30 fof(c_0_7695, plain, ![X1648, X1649, X1650, X1651]:(~class_Groups_Ocomm__monoid__mult(X1651)|(~c_Fun_Oinj__on(X1650,X1651,X1649,X1648)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1650,X1651),X1649),X1648)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1651,X1651),c_Fun_Oid(X1651)),hAPP(c_Set_Oimage(X1650,X1651,X1649),X1648)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__reindex__id])])])). 4.05/4.30 cnf(c_0_7696, plain, (hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_fequal,X3))),X2)=c_List_Oremove1(X1,X3,X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(rw,[status(thm)],[c_0_5387, c_0_4655])). 4.05/4.30 cnf(c_0_7697, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X4,X1,hAPP(c_COMBK(X1,X4),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_5388])). 4.05/4.30 fof(c_0_7698, plain, ![X12794, X12795, X12796]:(~class_Rings_Osemiring__1(X12796)|(~hBOOL(hAPP(hAPP(c_member(X12796),X12795),c_Nat_Osemiring__1__class_ONats(X12796)))|(~hBOOL(hAPP(hAPP(c_member(X12796),X12794),c_Nat_Osemiring__1__class_ONats(X12796)))|hBOOL(hAPP(hAPP(c_member(X12796),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12796),X12795),X12794)),c_Nat_Osemiring__1__class_ONats(X12796)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nats__add])])])). 4.05/4.30 fof(c_0_7699, plain, ![X17098, X17099, X17100]:(~class_Rings_Oring__1(X17100)|(~hBOOL(hAPP(hAPP(c_member(X17100),X17099),c_Int_Oring__1__class_OInts(X17100)))|(~hBOOL(hAPP(hAPP(c_member(X17100),X17098),c_Int_Oring__1__class_OInts(X17100)))|hBOOL(hAPP(hAPP(c_member(X17100),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17100),X17099),X17098)),c_Int_Oring__1__class_OInts(X17100)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__add])])])). 4.05/4.30 cnf(c_0_7700, plain, (hAPP(X4,X2)=X5|~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_5389])). 4.05/4.30 cnf(c_0_7701, 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_5390])). 4.05/4.30 fof(c_0_7702, plain, ![X538, X539, X540, X541, X542, X543]:(hBOOL(hAPP(hAPP(c_member(X543),X542),hAPP(c_List_Oset(X543),X541)))|hAPP(c_Map_Omap__upds(X543,X540,X539,X541,X538),X542)=hAPP(X539,X542)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__upds__apply__nontin])])])). 4.05/4.30 fof(c_0_7703, plain, ![X2808, X2809, X2810]:((c_Orderings_Obot__class_Obot(tc_fun(X2810,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2810,tc_HOL_Obool)),X2809),X2808)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2810,tc_HOL_Obool)),X2809),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2810,tc_HOL_Obool)),X2808))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2810,tc_HOL_Obool)),X2809),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2810,tc_HOL_Obool)),X2808)))|c_Orderings_Obot__class_Obot(tc_fun(X2810,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2810,tc_HOL_Obool)),X2809),X2808))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_disjoint__eq__subset__Compl])])). 4.05/4.30 fof(c_0_7704, plain, ![X4385, X4386, X4387, X4388]:(~class_Orderings_Olinorder(X4388)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4388),X4387),X4386))|(~c_List_Olinorder__class_Osorted(X4388,hAPP(hAPP(c_List_Olist_OCons(X4388),X4386),X4385))|c_List_Olinorder__class_Osorted(X4388,hAPP(hAPP(c_List_Olist_OCons(X4388),X4387),hAPP(hAPP(c_List_Olist_OCons(X4388),X4386),X4385)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__many])])])). 4.05/4.30 cnf(c_0_7705, 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_5388])). 4.05/4.30 cnf(c_0_7706, 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_5391])). 4.05/4.30 fof(c_0_7707, plain, ![X6272, X6273]:((~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)),X6273)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X6272)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X6273),X6272)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X6273),X6272))|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)),X6273)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X6272))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I5_J])])). 4.05/4.30 fof(c_0_7708, plain, ![X9363, X9364, X9365]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),c_Groups_Ozero__class_Ozero(X9365)),X9363))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),X9363),c_Groups_Ozero__class_Ozero(X9365)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),c_Groups_Ozero__class_Ozero(X9365)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9365),X9364),X9363)))|~class_Fields_Olinordered__field__inverse__zero(X9365))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),c_Groups_Ozero__class_Ozero(X9365)),X9364))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),X9363),c_Groups_Ozero__class_Ozero(X9365)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),c_Groups_Ozero__class_Ozero(X9365)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9365),X9364),X9363)))|~class_Fields_Olinordered__field__inverse__zero(X9365)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),c_Groups_Ozero__class_Ozero(X9365)),X9363))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),X9364),c_Groups_Ozero__class_Ozero(X9365)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),c_Groups_Ozero__class_Ozero(X9365)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9365),X9364),X9363)))|~class_Fields_Olinordered__field__inverse__zero(X9365))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),c_Groups_Ozero__class_Ozero(X9365)),X9364))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),X9364),c_Groups_Ozero__class_Ozero(X9365)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),c_Groups_Ozero__class_Ozero(X9365)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9365),X9364),X9363)))|~class_Fields_Olinordered__field__inverse__zero(X9365))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),X9363),c_Groups_Ozero__class_Ozero(X9365)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),X9364),c_Groups_Ozero__class_Ozero(X9365)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),c_Groups_Ozero__class_Ozero(X9365)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9365),X9364),X9363)))|~class_Fields_Olinordered__field__inverse__zero(X9365))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),c_Groups_Ozero__class_Ozero(X9365)),X9363))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),c_Groups_Ozero__class_Ozero(X9365)),X9364))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9365),c_Groups_Ozero__class_Ozero(X9365)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9365),X9364),X9363)))|~class_Fields_Olinordered__field__inverse__zero(X9365)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__divide__iff])])])])). 4.05/4.30 fof(c_0_7709, plain, ![X13739, X13740, X13741]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),c_Groups_Ozero__class_Ozero(X13741)),X13739))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),c_Groups_Ozero__class_Ozero(X13741)),X13740))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),c_Groups_Ozero__class_Ozero(X13741)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13741),X13740),X13739)))|~class_Fields_Olinordered__field__inverse__zero(X13741))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),X13740),c_Groups_Ozero__class_Ozero(X13741)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),X13739),c_Groups_Ozero__class_Ozero(X13741)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),c_Groups_Ozero__class_Ozero(X13741)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13741),X13740),X13739)))|~class_Fields_Olinordered__field__inverse__zero(X13741)))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),X13740),c_Groups_Ozero__class_Ozero(X13741)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),c_Groups_Ozero__class_Ozero(X13741)),X13739))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),c_Groups_Ozero__class_Ozero(X13741)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13741),X13740),X13739)))|~class_Fields_Olinordered__field__inverse__zero(X13741))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),X13739),c_Groups_Ozero__class_Ozero(X13741)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),c_Groups_Ozero__class_Ozero(X13741)),X13739))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),c_Groups_Ozero__class_Ozero(X13741)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13741),X13740),X13739)))|~class_Fields_Olinordered__field__inverse__zero(X13741)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),X13740),c_Groups_Ozero__class_Ozero(X13741)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),c_Groups_Ozero__class_Ozero(X13741)),X13740))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),c_Groups_Ozero__class_Ozero(X13741)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13741),X13740),X13739)))|~class_Fields_Olinordered__field__inverse__zero(X13741))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),X13739),c_Groups_Ozero__class_Ozero(X13741)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),c_Groups_Ozero__class_Ozero(X13741)),X13740))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13741),c_Groups_Ozero__class_Ozero(X13741)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13741),X13740),X13739)))|~class_Fields_Olinordered__field__inverse__zero(X13741))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff])])])). 4.05/4.30 fof(c_0_7710, plain, ![X9876, X9877]:(c_List_Olist_ONil(X9876)=X9877|hAPP(hAPP(c_List_Onth(X9876),X9877),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9876)),X9877)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_List_Olast(X9876,X9877)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__conv__nth])])). 4.05/4.30 fof(c_0_7711, plain, ![X4792, X4793, X4794, X4795]:((c_Orderings_Obot__class_Obot(tc_fun(X4794,tc_HOL_Obool))=X4795|hAPP(hAPP(c_Set_Oinsert(X4793),X4792),c_Orderings_Obot__class_Obot(tc_fun(X4793,tc_HOL_Obool)))=hAPP(c_Set_Oimage(X4794,X4793,hAPP(c_COMBK(X4793,X4794),X4792)),X4795))&(c_Orderings_Obot__class_Obot(tc_fun(X4794,tc_HOL_Obool))!=X4795|hAPP(c_Set_Oimage(X4794,X4793,hAPP(c_COMBK(X4793,X4794),X4792)),X4795)=c_Orderings_Obot__class_Obot(tc_fun(X4793,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__constant__conv])])])). 4.05/4.30 fof(c_0_7712, plain, ![X848, X849, X850, X851]:((c_Orderings_Obot__class_Obot(tc_fun(X850,tc_HOL_Obool))=X851|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X850,tc_fun(X849,tc_HOL_Obool)),X851),hAPP(c_COMBK(tc_fun(X849,tc_HOL_Obool),X850),X848))=X848)&(X851!=c_Orderings_Obot__class_Obot(tc_fun(X850,tc_HOL_Obool))|c_Orderings_Otop__class_Otop(tc_fun(X849,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X850,tc_fun(X849,tc_HOL_Obool)),X851),hAPP(c_COMBK(tc_fun(X849,tc_HOL_Obool),X850),X848)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INT__constant])])])). 4.05/4.30 cnf(c_0_7713, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))), inference(rw,[status(thm)],[c_0_5392, c_0_4475])). 4.05/4.30 cnf(c_0_7714, 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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))), inference(rw,[status(thm)],[c_0_5393, c_0_4475])). 4.05/4.30 cnf(c_0_7715, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_Opred(X2))=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))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5394])). 4.05/4.30 fof(c_0_7716, plain, ![X5791, X5792, X5793, X5794, X5795]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X5795,X5794)),hAPP(hAPP(c_Product__Type_OPair(X5795,X5794),X5793),X5792)),X5791))|hBOOL(hAPP(hAPP(c_member(X5795),X5793),hAPP(c_Relation_ODomain(X5795,X5794),X5791)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_DomainI])])])). 4.05/4.30 cnf(c_0_7717, plain, (c_Option_Ooption_ONone(X5)=c_Map_Omap__comp(X3,X5,X7,X6,X1,X2)|hAPP(X1,X2)!=hAPP(c_Option_Ooption_OSome(X3),X4)|c_Option_Ooption_ONone(X5)!=hAPP(X6,X4)), inference(split_conjunct,[status(thm)],[c_0_5338])). 4.05/4.30 fof(c_0_7718, plain, ![X5466, X5467, X5468, X5469, X5470, X5471, X5472]:(((X5467!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5466),X5469)|hBOOL(hAPP(X5468,X5469))|~hBOOL(hAPP(X5468,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5467),X5466))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5467),X5466))|hBOOL(hAPP(X5468,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X5468,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5467),X5466)))))&(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5471),X5470))|X5471=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5470),esk171_3(X5470,X5471,X5472))|hBOOL(hAPP(X5472,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5471),X5470))))&(~hBOOL(hAPP(X5472,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|X5471=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5470),esk171_3(X5470,X5471,X5472))|hBOOL(hAPP(X5472,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5471),X5470)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5471),X5470))|~hBOOL(hAPP(X5472,esk171_3(X5470,X5471,X5472)))|hBOOL(hAPP(X5472,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5471),X5470))))&(~hBOOL(hAPP(X5472,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X5472,esk171_3(X5470,X5471,X5472)))|hBOOL(hAPP(X5472,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5471),X5470))))))), 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])])])])])])])). 4.05/4.30 fof(c_0_7719, plain, ![X5695, X5696, X5697, X5698]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5698)|hAPP(hAPP(c_List_Odrop(X5697),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5698)),hAPP(hAPP(c_List_Olist_OCons(X5697),X5696),X5695))=hAPP(hAPP(c_List_Odrop(X5697),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5698)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X5695))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5698)|hAPP(hAPP(c_List_Olist_OCons(X5697),X5696),X5695)=hAPP(hAPP(c_List_Odrop(X5697),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5698)),hAPP(hAPP(c_List_Olist_OCons(X5697),X5696),X5695)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_drop__Cons__number__of])])])). 4.05/4.30 fof(c_0_7720, plain, ![X4744, X4745, X4746, X4748, X4749, X4750, X4751]:((((~hBOOL(hAPP(X4746,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|X4745=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4744),esk146_3(X4744,X4745,X4746))|hBOOL(hAPP(X4746,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4745),X4744))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4745),X4744))|X4745=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4744),esk146_3(X4744,X4745,X4746))|hBOOL(hAPP(X4746,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4745),X4744)))))&((~hBOOL(hAPP(X4746,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X4746,esk146_3(X4744,X4745,X4746)))|hBOOL(hAPP(X4746,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4745),X4744))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4745),X4744))|~hBOOL(hAPP(X4746,esk146_3(X4744,X4745,X4746)))|hBOOL(hAPP(X4746,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4745),X4744))))))&((X4749!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4748),X4751)|hBOOL(hAPP(X4750,X4751))|~hBOOL(hAPP(X4750,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4749),X4748))))&(hBOOL(hAPP(X4750,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4749),X4748))|~hBOOL(hAPP(X4750,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4749),X4748)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__diff__split__asm])])])])])])])). 4.05/4.30 cnf(c_0_7721, 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_5395])). 4.05/4.30 fof(c_0_7722, plain, ![X13938, X13939, X13940]:(~class_Fields_Olinordered__field(X13940)|(c_Groups_Ozero__class_Ozero(X13940)=X13939|hAPP(c_Groups_Oabs__class_Oabs(X13940),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13940),X13938),X13939))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13940),hAPP(c_Groups_Oabs__class_Oabs(X13940),X13938)),hAPP(c_Groups_Oabs__class_Oabs(X13940),X13939)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonzero__abs__divide])])])). 4.05/4.30 fof(c_0_7723, plain, ![X17711, X17712, X17713]:((hBOOL(hAPP(hAPP(c_member(tc_fun(X17713,tc_HOL_Obool)),esk530_3(X17711,X17712,X17713)),X17712))|hBOOL(hAPP(hAPP(c_member(X17713),X17711),c_Complete__Lattice_OInf__class_OInf(tc_fun(X17713,tc_HOL_Obool),X17712))))&(~hBOOL(hAPP(hAPP(c_member(X17713),X17711),esk530_3(X17711,X17712,X17713)))|hBOOL(hAPP(hAPP(c_member(X17713),X17711),c_Complete__Lattice_OInf__class_OInf(tc_fun(X17713,tc_HOL_Obool),X17712))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterI])])])])). 4.05/4.30 cnf(c_0_7724, 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_5396])). 4.05/4.30 fof(c_0_7725, plain, ![X8499, X8500]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X8499),c_Orderings_Otop__class_Otop(tc_fun(X8499,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8500),c_Orderings_Otop__class_Otop(tc_fun(X8500,tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X8500,X8499)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X8500,X8499),tc_HOL_Obool)))))&((hBOOL(hAPP(c_Finite__Set_Ofinite(X8499),c_Orderings_Otop__class_Otop(tc_fun(X8499,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X8500,X8499)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X8500,X8499),tc_HOL_Obool)))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X8500),c_Orderings_Otop__class_Otop(tc_fun(X8500,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X8500,X8499)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X8500,X8499),tc_HOL_Obool))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__UNIV__iff])])])). 4.05/4.30 fof(c_0_7726, plain, ![X10277, X10278]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10278),hAPP(c_Nat_OSuc,X10277)))|hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X10277)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X10278,X10277))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X10278,hAPP(c_Nat_OSuc,X10277))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastAtMostSuc__conv])])])). 4.05/4.30 fof(c_0_7727, plain, ![X14966, X14967, X14968, X14969]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14969),X14968))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X14967),hAPP(c_Set_Oimage(X14969,X14967,X14966),X14968))),hAPP(c_Finite__Set_Ocard(X14969),X14968)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image__le])])). 4.05/4.30 cnf(c_0_7728, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5380])). 4.05/4.30 cnf(c_0_7729, 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_5397, c_0_4434])). 4.05/4.30 fof(c_0_7730, plain, ![X14856, X14857]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14857),c_Orderings_Otop__class_Otop(tc_fun(X14857,tc_HOL_Obool))))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14856),c_Orderings_Otop__class_Otop(tc_fun(X14856,tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X14857,X14856)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X14857,X14856),tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Prod__UNIV])])])). 4.05/4.30 fof(c_0_7731, plain, ![X3418, X3419, X3420, X3421]:(~class_Orderings_Oorder(X3421)|c_Orderings_Obot__class_Obot(tc_fun(X3421,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3421,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X3421,X3420,X3419)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3421,X3419),X3418))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I9_J])])])). 4.05/4.30 fof(c_0_7732, plain, ![X10795, X10796, X10797, X10798]:(~class_Orderings_Oorder(X10798)|c_Orderings_Obot__class_Obot(tc_fun(X10798,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10798,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10798,X10797),X10796)),c_SetInterval_Oord__class_OatLeastAtMost(X10798,X10796,X10795))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I15_J])])). 4.05/4.30 fof(c_0_7733, plain, ![X11317, X11318]:(~class_Groups_Olinordered__ab__group__add(X11318)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X11318),X11317))|(c_Orderings_Obot__class_Obot(tc_fun(X11318,tc_HOL_Obool))=X11317|c_Big__Operators_Olinorder__class_OMax(X11318,hAPP(c_Set_Oimage(X11318,X11318,c_Groups_Ouminus__class_Ouminus(X11318)),X11317))=hAPP(c_Groups_Ouminus__class_Ouminus(X11318),c_Big__Operators_Olinorder__class_OMin(X11318,X11317))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__Min__eq__Max])])])). 4.05/4.30 fof(c_0_7734, plain, ![X8294, X8295, X8296, X8297]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8297),X8296),X8294))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8297),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8297),X8296),X8295)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8297),X8294),X8295)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X8297))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8297),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8297),X8296),X8295)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8297),X8294),X8295)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8297),X8296),X8294))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X8297))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])])). 4.05/4.30 cnf(c_0_7735, 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),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5398, c_0_4427]), c_0_4427]), c_0_4505]), c_0_4795])). 4.05/4.30 cnf(c_0_7736, 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),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5399, c_0_4427]), c_0_4427]), c_0_4505]), c_0_4795])). 4.05/4.30 cnf(c_0_7737, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5400, c_0_4427]), c_0_4427]), c_0_4505]), c_0_4795])). 4.05/4.30 fof(c_0_7738, plain, ![X9924, X9925]:(~class_Groups_Olinordered__ab__group__add(X9925)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9925),X9924))|(X9924=c_Orderings_Obot__class_Obot(tc_fun(X9925,tc_HOL_Obool))|hAPP(c_Groups_Ouminus__class_Ouminus(X9925),c_Big__Operators_Olinorder__class_OMax(X9925,X9924))=c_Big__Operators_Olinorder__class_OMin(X9925,hAPP(c_Set_Oimage(X9925,X9925,c_Groups_Ouminus__class_Ouminus(X9925)),X9924))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__Max__eq__Min])])])). 4.05/4.30 fof(c_0_7739, plain, ![X9770, X9771, X9772, X9773, X9774]:(~hBOOL(hAPP(hAPP(c_member(X9774),X9773),X9772))|hAPP(c_Set_Oimage(X9774,X9771,X9770),X9772)=hAPP(hAPP(c_Set_Oinsert(X9771),hAPP(X9770,X9773)),hAPP(c_Set_Oimage(X9774,X9771,X9770),X9772))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__image])])])). 4.05/4.30 fof(c_0_7740, plain, ![X15891, X15892, X15893, X15894, X15895]:(~hBOOL(hAPP(hAPP(c_member(X15895),X15894),X15893))|hAPP(hAPP(c_Set_Oinsert(X15892),X15891),c_Orderings_Obot__class_Obot(tc_fun(X15892,tc_HOL_Obool)))=hAPP(c_Set_Oimage(X15895,X15892,hAPP(c_COMBK(X15892,X15895),X15891)),X15893)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__constant])])). 4.05/4.30 cnf(c_0_7741, 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),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5401, c_0_4427]), c_0_4505]), c_0_4795]), c_0_4427])). 4.05/4.30 cnf(c_0_7742, 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),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5402, c_0_4427]), c_0_4505]), c_0_4795]), c_0_4427])). 4.05/4.30 cnf(c_0_7743, 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),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5403, c_0_4505]), c_0_4795])). 4.05/4.30 cnf(c_0_7744, 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),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5404, c_0_4505]), c_0_4795])). 4.05/4.30 cnf(c_0_7745, 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),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5405, c_0_4505]), c_0_4795])). 4.05/4.30 cnf(c_0_7746, 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),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5406, c_0_4505]), c_0_4795])). 4.05/4.30 fof(c_0_7747, plain, ![X482, X483, X484]:(~class_Lattices_Oab__semigroup__idem__mult(X484)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X484),X483))|hAPP(hAPP(c_Finite__Set_Ofold(X484,X484,c_Groups_Otimes__class_Otimes(X484)),X482),X483)=hAPP(c_Finite__Set_Ofold1(X484,c_Groups_Otimes__class_Otimes(X484)),hAPP(hAPP(c_Set_Oinsert(X484),X482),X483)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold__idem])])). 4.05/4.30 fof(c_0_7748, plain, ![X325, X326, X327, X328, X329, X330]:((X325!=X326|hAPP(hAPP(c_Product__Type_OSigma(X327,X330),X326),hAPP(c_COMBK(tc_fun(X330,tc_HOL_Obool),X327),X328))=hAPP(hAPP(c_Product__Type_OSigma(X327,X330),X325),hAPP(c_COMBK(tc_fun(X330,tc_HOL_Obool),X327),X328))|~hBOOL(hAPP(hAPP(c_member(X330),X329),X328)))&(hAPP(hAPP(c_Product__Type_OSigma(X327,X330),X326),hAPP(c_COMBK(tc_fun(X330,tc_HOL_Obool),X327),X328))!=hAPP(hAPP(c_Product__Type_OSigma(X327,X330),X325),hAPP(c_COMBK(tc_fun(X330,tc_HOL_Obool),X327),X328))|X325=X326|~hBOOL(hAPP(hAPP(c_member(X330),X329),X328)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Times__eq__cancel2])])])])). 4.05/4.30 cnf(c_0_7749, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5407, c_0_4427]), c_0_4505]), c_0_4795]), c_0_4427])). 4.05/4.30 cnf(c_0_7750, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5408, c_0_4427]), c_0_4505]), c_0_4795]), c_0_4427])). 4.05/4.30 cnf(c_0_7751, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5409, c_0_4635]), c_0_4505]), c_0_4795]), c_0_4635])). 4.05/4.30 cnf(c_0_7752, 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_5410])). 4.05/4.30 fof(c_0_7753, plain, ![X14109, X14110, X14111, X14112, X14113]:((hAPP(c_Option_Ooption_OSome(X14113),X14112)=hAPP(X14110,esk430_5(X14109,X14110,X14111,X14112,X14113))|~hBOOL(hAPP(hAPP(c_member(X14113),X14112),c_Map_Oran(X14111,X14113,c_Map_Orestrict__map(X14111,X14113,X14110,X14109)))))&(hBOOL(hAPP(hAPP(c_member(X14111),esk430_5(X14109,X14110,X14111,X14112,X14113)),X14109))|~hBOOL(hAPP(hAPP(c_member(X14113),X14112),c_Map_Oran(X14111,X14113,c_Map_Orestrict__map(X14111,X14113,X14110,X14109)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ran__restrictD])])])])). 4.05/4.30 fof(c_0_7754, plain, ![X10572, X10573, X10574]:(~class_Orderings_Olinorder(X10574)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10574),X10573))|(c_Orderings_Obot__class_Obot(tc_fun(X10574,tc_HOL_Obool))=X10573|hAPP(hAPP(c_Orderings_Oord__class_Omax(X10574),X10572),c_Big__Operators_Olinorder__class_OMax(X10574,X10573))=c_Big__Operators_Olinorder__class_OMax(X10574,hAPP(hAPP(c_Set_Oinsert(X10574),X10572),X10573))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max__insert])])])). 4.05/4.30 fof(c_0_7755, plain, ![X12333, X12334, X12335, X12336]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X12336)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12336),X12335),X12334))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12336),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12336),X12335),X12333)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X12336),X12334),X12333))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__right__mono])])])). 4.05/4.30 fof(c_0_7756, plain, ![X14523, X14524, X14525, X14526]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14526),X14524),X14523))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14526),X14525),X14524)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14526),X14525),X14523)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X14526))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14526),X14525),X14524)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14526),X14525),X14523)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14526),X14524),X14523))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X14526))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])])). 4.05/4.30 fof(c_0_7757, plain, ![X6288, X6289, X6290, X6291]:(~class_Groups_Oordered__cancel__ab__semigroup__add(X6291)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6291),X6290),X6289))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6291),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6291),X6288),X6290)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6291),X6288),X6289))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__left__mono])])])). 4.05/4.30 fof(c_0_7758, plain, ![X11010, X11011, X11012, X11013]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11013),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11013),X11012),X11011)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11013),X11010),X11011)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11013),X11012),X11010))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X11013))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11013),X11012),X11010))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11013),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11013),X11012),X11011)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11013),X11010),X11011)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X11013))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])])). 4.05/4.30 cnf(c_0_7759, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))), inference(rw,[status(thm)],[c_0_5411, c_0_5018])). 4.05/4.30 fof(c_0_7760, plain, ![X15403, X15404, X15405]:(~class_Lattices_Olattice(X15405)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15405),X15404))|(c_Orderings_Obot__class_Obot(tc_fun(X15405,tc_HOL_Obool))=X15404|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15405),X15403),c_Big__Operators_Olattice__class_OSup__fin(X15405,X15404))=c_Big__Operators_Olattice__class_OSup__fin(X15405,hAPP(hAPP(c_Set_Oinsert(X15405),X15403),X15404))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oinsert__idem])])])). 4.05/4.30 fof(c_0_7761, plain, ![X3846, X3847, X3848, X3849]:(~class_Groups_Oordered__ab__semigroup__add(X3849)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3849),X3848),X3847))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3849),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3849),X3848),X3846)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3849),X3847),X3846))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])])). 4.05/4.30 fof(c_0_7762, plain, ![X11907, X11908, X11909, X11910]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11910),X11908),X11907))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11910),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11910),X11909),X11908)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11910),X11909),X11907)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X11910))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11910),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11910),X11909),X11908)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11910),X11909),X11907)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11910),X11908),X11907))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X11910))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__le__cancel__left])])])])). 4.05/4.30 fof(c_0_7763, plain, ![X6522, X6523, X6524, X6525]:(~class_Groups_Oordered__ab__semigroup__add(X6525)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6525),X6524),X6523))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6525),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6525),X6522),X6524)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6525),X6522),X6523))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])])). 4.05/4.30 fof(c_0_7764, plain, ![X8645, X8646, X8647]:(~class_Groups_Omonoid__mult(X8647)|hAPP(hAPP(c_Power_Opower__class_Opower(X8647),X8646),hAPP(c_Nat_OSuc,X8645))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8647),hAPP(hAPP(c_Power_Opower__class_Opower(X8647),X8646),X8645)),X8646)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__Suc2])])])). 4.05/4.30 fof(c_0_7765, plain, ![X6465, X6466, X6467, X6469, X6470, X6471, X6472]:(((hBOOL(hAPP(hAPP(c_member(X6467),esk194_3(X6465,X6466,X6467)),hAPP(c_List_Oset(X6467),X6466)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6467)),X6466),c_List_Olists(X6467,X6465))))&(~hBOOL(hAPP(hAPP(c_member(X6467),esk194_3(X6465,X6466,X6467)),X6465))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6467)),X6466),c_List_Olists(X6467,X6465)))))&(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6471)),X6470),c_List_Olists(X6471,X6469)))|(~hBOOL(hAPP(hAPP(c_member(X6471),X6472),hAPP(c_List_Oset(X6471),X6470)))|hBOOL(hAPP(hAPP(c_member(X6471),X6472),X6469))))), 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__lists__conv__set])])])])])])])). 4.05/4.30 fof(c_0_7766, plain, ![X2757, X2758, X2759]:(~class_Orderings_Olinorder(X2759)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2759),X2758))|(c_Orderings_Obot__class_Obot(tc_fun(X2759,tc_HOL_Obool))=X2758|c_Big__Operators_Olinorder__class_OMin(X2759,hAPP(hAPP(c_Set_Oinsert(X2759),X2757),X2758))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X2759),X2757),c_Big__Operators_Olinorder__class_OMin(X2759,X2758))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min__insert])])])). 4.05/4.30 fof(c_0_7767, plain, ![X12378, X12379, X12380]:(~class_Rings_Ocomm__semiring__1(X12380)|hAPP(hAPP(c_Power_Opower__class_Opower(X12380),X12379),hAPP(c_Nat_OSuc,X12378))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12380),hAPP(hAPP(c_Power_Opower__class_Opower(X12380),X12379),X12378)),X12379)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J])])])). 4.05/4.30 cnf(c_0_7768, plain, (X3=esk109_4(X1,X2,X4,X5)|X1!=hAPP(X2,X3)|~hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_Set_Oimage(X5,X4,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5412])). 4.05/4.30 cnf(c_0_7769, 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_5413]), ['final']). 4.05/4.30 fof(c_0_7770, plain, ![X5620, X5621, X5622]:((hBOOL(hAPP(hAPP(c_member(X5622),X5621),hAPP(c_List_Oset(X5622),X5620)))|hAPP(hAPP(c_List_Olist_OCons(X5622),X5621),c_List_Oremdups(X5622,X5620))=c_List_Oremdups(X5622,hAPP(hAPP(c_List_Olist_OCons(X5622),X5621),X5620)))&(~hBOOL(hAPP(hAPP(c_member(X5622),X5621),hAPP(c_List_Oset(X5622),X5620)))|c_List_Oremdups(X5622,hAPP(hAPP(c_List_Olist_OCons(X5622),X5621),X5620))=c_List_Oremdups(X5622,X5620))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remdups_Osimps_I2_J])])])). 4.05/4.30 fof(c_0_7771, plain, ![X16832, X16833, X16834, X16835]:(~class_Groups_Ocomm__monoid__mult(X16835)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16834),X16833))|hAPP(hAPP(c_Power_Opower__class_Opower(X16835),X16832),hAPP(c_Finite__Set_Ocard(X16834),X16833))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16834,X16835),hAPP(c_COMBK(X16835,X16834),X16832)),X16833))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__constant])])). 4.05/4.30 fof(c_0_7772, plain, ![X1634, X1635, X1636, X1637, X1638, X1639]:((~hBOOL(hAPP(c_List_Odistinct(X1635),X1634))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1636),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1635)),X1634)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1637),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1635)),X1634)))|(X1636=X1637|hAPP(hAPP(c_List_Onth(X1635),X1634),X1636)!=hAPP(hAPP(c_List_Onth(X1635),X1634),X1637)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk54_2(X1638,X1639)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1639)),X1638)))|hBOOL(hAPP(c_List_Odistinct(X1639),X1638)))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk55_2(X1638,X1639)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1639)),X1638)))|hBOOL(hAPP(c_List_Odistinct(X1639),X1638)))&((esk54_2(X1638,X1639)!=esk55_2(X1638,X1639)|hBOOL(hAPP(c_List_Odistinct(X1639),X1638)))&(hAPP(hAPP(c_List_Onth(X1639),X1638),esk54_2(X1638,X1639))=hAPP(hAPP(c_List_Onth(X1639),X1638),esk55_2(X1638,X1639))|hBOOL(hAPP(c_List_Odistinct(X1639),X1638))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__conv__nth])])])])])])])). 4.05/4.30 fof(c_0_7773, plain, ![X11823, X11824, X11825]:(~class_Orderings_Oorder(X11825)|c_Orderings_Obot__class_Obot(tc_fun(X11825,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11825,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X11825,X11824),X11823)),hAPP(c_SetInterval_Oord__class_OatLeast(X11825),X11823))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I8_J])])])). 4.05/4.30 fof(c_0_7774, plain, ![X13231, X13232, X13233]:(~class_Lattices_Olattice(X13233)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13233),X13232))|(c_Orderings_Obot__class_Obot(tc_fun(X13233,tc_HOL_Obool))=X13232|c_Big__Operators_Olattice__class_OInf__fin(X13233,hAPP(hAPP(c_Set_Oinsert(X13233),X13231),X13232))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13233),X13231),c_Big__Operators_Olattice__class_OInf__fin(X13233,X13232))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oinsert__idem])])])). 4.05/4.30 fof(c_0_7775, plain, ![X4758, X4759, X4760, X4761]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4761),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4760)),X4759)))|hBOOL(hAPP(hAPP(c_member(X4760),X4758),hAPP(c_List_Oset(X4760),hAPP(hAPP(c_List_Olist__update(X4760,X4759),X4761),X4758))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__update__memI])])). 4.05/4.30 fof(c_0_7776, plain, ![X5253, X5254, X5255]:(~class_Groups_Olinordered__ab__group__add(X5255)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X5255),hAPP(c_Groups_Ouminus__class_Ouminus(X5255),X5254)),hAPP(c_Groups_Ouminus__class_Ouminus(X5255),X5253))=hAPP(c_Groups_Ouminus__class_Ouminus(X5255),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5255),X5254),X5253))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__max__eq__min])])])). 4.05/4.30 fof(c_0_7777, plain, ![X3245, X3246, X3247]:(~class_Lattices_Oboolean__algebra(X3247)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3247),hAPP(c_Groups_Ouminus__class_Ouminus(X3247),X3246)),hAPP(c_Groups_Ouminus__class_Ouminus(X3247),X3245))=hAPP(c_Groups_Ouminus__class_Ouminus(X3247),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3247),X3246),X3245))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_compl__sup])])])). 4.05/4.30 fof(c_0_7778, plain, ![X8688, X8689, X8690]:(~class_Orderings_Oorder(X8690)|c_Orderings_Obot__class_Obot(tc_fun(X8690,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8690,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X8690),X8689)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X8690,X8689),X8688))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I2_J])])])). 4.05/4.30 fof(c_0_7779, plain, ![X2244, X2245, X2246, X2247]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2247),tc_List_Olist(X2247))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2247),tc_List_Olist(X2247)),X2246),X2245)),c_List_Olistrel1(X2247,X2244)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2247)),X2246)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2247)),X2245)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__eq__len])])). 4.05/4.30 fof(c_0_7780, plain, ![X12791, X12792, X12793]:(~class_Groups_Olinordered__ab__group__add(X12793)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X12793),hAPP(c_Groups_Ouminus__class_Ouminus(X12793),X12792)),hAPP(c_Groups_Ouminus__class_Ouminus(X12793),X12791))=hAPP(c_Groups_Ouminus__class_Ouminus(X12793),hAPP(hAPP(c_Orderings_Oord__class_Omin(X12793),X12792),X12791))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__min__eq__max])])). 4.05/4.30 fof(c_0_7781, plain, ![X10179, X10180, X10181]:(~class_Lattices_Oboolean__algebra(X10181)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10181),hAPP(c_Groups_Ouminus__class_Ouminus(X10181),X10180)),hAPP(c_Groups_Ouminus__class_Ouminus(X10181),X10179))=hAPP(c_Groups_Ouminus__class_Ouminus(X10181),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10181),X10180),X10179))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__inf])])). 4.05/4.30 fof(c_0_7782, plain, ![X16015, X16016, X16017]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16016),X16015))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16016),X16017)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16015),X16017)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16017),X16015))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16017),X16016)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16016),X16017)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16015),X16017)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16016),X16015))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16017),X16015))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16017),X16016)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__diff__iff])])])])). 4.05/4.30 fof(c_0_7783, plain, ![X5235, X5236, X5237]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5236),X5235))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5236),X5237)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5235),X5237)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5237),X5235))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5237),X5236)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5236),X5237)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5235),X5237)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5236),X5235))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5237),X5235))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5237),X5236)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__diff__iff])])])])). 4.05/4.30 fof(c_0_7784, plain, ![X6781, X6782]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X6782))|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(X6782),X6781))),X6782))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_range])])])). 4.05/4.30 fof(c_0_7785, plain, ![X13952, X13953, X13954]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13954),X13953))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13954,tc_HOL_Obool)),X13952),X13953))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X13954),X13952)),hAPP(c_Finite__Set_Ocard(X13954),X13953)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13954,tc_HOL_Obool)),X13952),X13953))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__psubset])])])). 4.05/4.30 fof(c_0_7786, plain, ![X9209, X9210, X9211]:(~class_Groups_Oab__group__add(X9211)|hAPP(c_Groups_Ouminus__class_Ouminus(X9211),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9211),X9210),X9209))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9211),hAPP(c_Groups_Ouminus__class_Ouminus(X9211),X9210)),hAPP(c_Groups_Ouminus__class_Ouminus(X9211),X9209))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__add__distrib])])])). 4.05/4.30 fof(c_0_7787, plain, ![X3733, X3734, X3735, X3736]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3736),X3734),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3736),X3733),X3735)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3736),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3736),X3734),X3735)),X3733))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3736),c_Groups_Ozero__class_Ozero(X3736)),X3735))|~class_Fields_Olinordered__field(X3736))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3736),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3736),X3734),X3735)),X3733))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3736),X3734),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3736),X3733),X3735)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3736),c_Groups_Ozero__class_Ozero(X3736)),X3735))|~class_Fields_Olinordered__field(X3736))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__divide__less__eq])])])])). 4.05/4.30 fof(c_0_7788, plain, ![X13434, X13435, X13436, X13437]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13437),X13435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13437),X13434),X13436)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13437),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13437),X13435),X13436)),X13434))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13437),c_Groups_Ozero__class_Ozero(X13437)),X13436))|~class_Fields_Olinordered__field(X13437))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13437),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13437),X13435),X13436)),X13434))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13437),X13435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13437),X13434),X13436)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13437),c_Groups_Ozero__class_Ozero(X13437)),X13436))|~class_Fields_Olinordered__field(X13437))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__divide__le__eq])])])])). 4.05/4.30 fof(c_0_7789, plain, ![X7452, X7453, X7454, X7455]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7455),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7455),X7453),X7454)),X7452))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7455),X7453),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7455),X7452),X7454)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7455),c_Groups_Ozero__class_Ozero(X7455)),X7454))|~class_Fields_Olinordered__field(X7455))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7455),X7453),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X7455),X7452),X7454)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7455),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7455),X7453),X7454)),X7452))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7455),c_Groups_Ozero__class_Ozero(X7455)),X7454))|~class_Fields_Olinordered__field(X7455))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq])])])). 4.05/4.30 fof(c_0_7790, plain, ![X8029, X8030, X8031, X8032, X8033]:(hBOOL(hAPP(hAPP(c_member(X8033),X8032),c_Map_Odom(X8033,X8031,X8030)))|hAPP(c_Map_Omap__add(X8033,X8031,X8029,X8030),X8032)=hAPP(X8029,X8032)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__add__dom__app__simps_I3_J])])])). 4.05/4.30 fof(c_0_7791, plain, ![X9119, X9120, X9121]:(~class_Groups_Ogroup__add(X9121)|hAPP(c_Groups_Ouminus__class_Ouminus(X9121),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9121),X9120),X9119))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9121),hAPP(c_Groups_Ouminus__class_Ouminus(X9121),X9119)),hAPP(c_Groups_Ouminus__class_Ouminus(X9121),X9120))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__add])])])). 4.05/4.30 fof(c_0_7792, plain, ![X4526, X4527, X4528, X4529, X4530]:(hBOOL(hAPP(hAPP(c_member(X4530),X4529),c_Map_Odom(X4530,X4528,X4527)))|hAPP(X4526,X4529)=hAPP(c_Map_Omap__add(X4530,X4528,X4527,X4526),X4529)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__add__dom__app__simps_I2_J])])])). 4.05/4.30 fof(c_0_7793, plain, ![X14131, X14132, X14133, X14134]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14134),X14132),X14133)),X14131))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14134),X14132),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14134),X14131),X14133)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14134),c_Groups_Ozero__class_Ozero(X14134)),X14133))|~class_Fields_Olinordered__field(X14134))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14134),X14132),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14134),X14131),X14133)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14134),X14132),X14133)),X14131))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14134),c_Groups_Ozero__class_Ozero(X14134)),X14133))|~class_Fields_Olinordered__field(X14134))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq])])])). 4.05/4.30 cnf(c_0_7794, plain, (X5=X4|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_5414])). 4.05/4.30 fof(c_0_7795, plain, ![X1642, X1643, X1644, X1645, X1646, X1647]:((~hBOOL(hAPP(hAPP(X1646,X1645),X1643))|~c_List_Olistrelp(X1647,X1646,X1644,X1642)|c_List_Olistrelp(X1647,X1646,hAPP(hAPP(c_List_Olist_OCons(X1647),X1645),X1644),hAPP(hAPP(c_List_Olist_OCons(X1647),X1643),X1642)))&((hBOOL(hAPP(hAPP(X1646,X1645),X1643))|~c_List_Olistrelp(X1647,X1646,hAPP(hAPP(c_List_Olist_OCons(X1647),X1645),X1644),hAPP(hAPP(c_List_Olist_OCons(X1647),X1643),X1642)))&(c_List_Olistrelp(X1647,X1646,X1644,X1642)|~c_List_Olistrelp(X1647,X1646,hAPP(hAPP(c_List_Olist_OCons(X1647),X1645),X1644),hAPP(hAPP(c_List_Olist_OCons(X1647),X1643),X1642))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_Oequations_I2_J])])])). 4.05/4.30 fof(c_0_7796, plain, ![X7252, X7253, X7254]:((~c_Fun_Oinj__on(tc_List_Olist(X7254),tc_List_Olist(X7253),hAPP(c_List_Omap(X7254,X7253),X7252),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X7254),tc_HOL_Obool)))|c_Fun_Oinj__on(X7254,X7253,X7252,c_Orderings_Otop__class_Otop(tc_fun(X7254,tc_HOL_Obool))))&(~c_Fun_Oinj__on(X7254,X7253,X7252,c_Orderings_Otop__class_Otop(tc_fun(X7254,tc_HOL_Obool)))|c_Fun_Oinj__on(tc_List_Olist(X7254),tc_List_Olist(X7253),hAPP(c_List_Omap(X7254,X7253),X7252),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X7254),tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__map])])). 4.05/4.30 cnf(c_0_7797, plain, (hAPP(X3,X5)=hAPP(X4,X5)|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X1,X2)),X3),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1))))|~class_Enum_Oenum(X1)|~class_HOL_Oequal(X2)), inference(split_conjunct,[status(thm)],[c_0_5415])). 4.05/4.30 cnf(c_0_7798, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1))))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_5416]), ['final']). 4.05/4.30 cnf(c_0_7799, 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_5417])). 4.05/4.30 cnf(c_0_7800, 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_5418]), ['final']). 4.05/4.30 cnf(c_0_7801, 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_5419])). 4.05/4.30 fof(c_0_7802, plain, ![X15649, X15650, X15651]:((~hBOOL(hAPP(hAPP(c_member(X15651),X15650),hAPP(c_List_Oset(X15651),X15649)))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15651)),X15649)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15651)),c_List_Oremove1(X15651,X15650,X15649)))&(hBOOL(hAPP(hAPP(c_member(X15651),X15650),hAPP(c_List_Oset(X15651),X15649)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15651)),c_List_Oremove1(X15651,X15650,X15649))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15651)),X15649))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_length__remove1])])])). 4.05/4.30 cnf(c_0_7803, 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(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(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_4670])). 4.05/4.30 cnf(c_0_7804, plain, (hAPP(c_Nat_OSuc,X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_5420]), ['final']). 4.05/4.30 cnf(c_0_7805, plain, (c_List_Olist_ONil(X3)=c_List_OdropWhile(X3,X1,X2)|~hBOOL(hAPP(X1,esk37_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_5332])). 4.05/4.30 cnf(c_0_7806, 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_5421])). 4.05/4.30 fof(c_0_7807, plain, ![X16923, X16924, X16925, X16926]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X16925,esk507_4(X16923,X16924,X16925,X16926))))|hAPP(c_Nat_OSuc,X16923)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16926,tc_Nat_Onat),X16925),X16924))&(hBOOL(hAPP(hAPP(c_member(X16926),esk507_4(X16923,X16924,X16925,X16926)),X16924))|hAPP(c_Nat_OSuc,X16923)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16926,tc_Nat_Onat),X16925),X16924))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__SucD])])])])])). 4.05/4.30 fof(c_0_7808, plain, ![X4344, X4345, X4346, X4347]:(~class_Rings_Odivision__ring(X4347)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4347),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4347),X4346),X4345)),X4344)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4347),X4346),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4347),X4345),X4344))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_times__divide__eq__right])])])). 4.05/4.30 fof(c_0_7809, plain, ![X4732, X4733, X4734]:(~class_Rings_Olinordered__idom(X4734)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4734),c_Groups_Ozero__class_Ozero(X4734)),X4733))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4734),hAPP(c_Groups_Oabs__class_Oabs(X4734),X4732)),X4733)=hAPP(c_Groups_Oabs__class_Oabs(X4734),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4734),X4732),X4733)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__mult__pos])])])). 4.05/4.30 fof(c_0_7810, plain, ![X4179, X4180, X4181, X4182, X4183]:(~c_Finite__Set_Ofun__left__comm(X4183,X4182,X4181)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4183),X4180))|hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4183,X4182,X4181,X4179,X4180),hAPP(hAPP(c_Finite__Set_Ofold(X4183,X4182,X4181),X4179),X4180))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__fold])])). 4.05/4.31 fof(c_0_7811, plain, ![X16373, X16374, X16375, X16376, X16377, X16378, X16379, X16380, X16381]:((hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16376,tc_fun(X16375,tc_HOL_Obool)),X16374),X16373)!=c_Orderings_Obot__class_Obot(tc_fun(X16375,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_member(X16376),X16377),X16374))|hAPP(X16373,X16377)=c_Orderings_Obot__class_Obot(tc_fun(X16375,tc_HOL_Obool))))&((hBOOL(hAPP(hAPP(c_member(X16381),esk491_4(X16378,X16379,X16380,X16381)),X16379))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16381,tc_fun(X16380,tc_HOL_Obool)),X16379),X16378)=c_Orderings_Obot__class_Obot(tc_fun(X16380,tc_HOL_Obool)))&(hAPP(X16378,esk491_4(X16378,X16379,X16380,X16381))!=c_Orderings_Obot__class_Obot(tc_fun(X16380,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16381,tc_fun(X16380,tc_HOL_Obool)),X16379),X16378)=c_Orderings_Obot__class_Obot(tc_fun(X16380,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UNION__empty__conv_I2_J])])])])])])). 4.05/4.31 fof(c_0_7812, plain, ![X618, X619, X620, X621]:(~class_Lattices_Olattice(X621)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X621),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X621),X620),X619)),X618)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X621),X620),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X621),X619),X618))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__aci_I2_J])])])). 4.05/4.31 fof(c_0_7813, plain, ![X13451, X13452, X13453]:(~class_Groups_Omonoid__mult(X13453)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13453),hAPP(hAPP(c_Power_Opower__class_Opower(X13453),X13452),X13451)),X13452)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13453),X13452),hAPP(hAPP(c_Power_Opower__class_Opower(X13453),X13452),X13451))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__commutes])])])). 4.05/4.31 fof(c_0_7814, plain, ![X12075, X12076, X12077, X12078]:(~class_Groups_Oab__semigroup__mult(X12078)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12078),X12077),X12076)),X12075)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12078),X12077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12078),X12076),X12075))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])])). 4.05/4.31 fof(c_0_7815, plain, ![X7068, X7069, X7070, X7071, X7073, X7074, X7075, X7076, X7077]:(((hBOOL(hAPP(hAPP(c_member(X7070),esk219_4(X7068,X7069,X7070,X7071)),X7069))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7070,tc_fun(X7071,tc_HOL_Obool)),X7069),X7068)=c_Orderings_Obot__class_Obot(tc_fun(X7071,tc_HOL_Obool)))&(hAPP(X7068,esk219_4(X7068,X7069,X7070,X7071))!=c_Orderings_Obot__class_Obot(tc_fun(X7071,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7070,tc_fun(X7071,tc_HOL_Obool)),X7069),X7068)=c_Orderings_Obot__class_Obot(tc_fun(X7071,tc_HOL_Obool))))&(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7075,tc_fun(X7076,tc_HOL_Obool)),X7074),X7073)!=c_Orderings_Obot__class_Obot(tc_fun(X7076,tc_HOL_Obool))|(~hBOOL(hAPP(hAPP(c_member(X7075),X7077),X7074))|hAPP(X7073,X7077)=c_Orderings_Obot__class_Obot(tc_fun(X7076,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UNION__empty__conv_I1_J])])])])])])])). 4.05/4.31 fof(c_0_7816, plain, ![X16171, X16172]:(~class_Rings_Osemiring__1(X16172)|c_Nat_Osemiring__1__class_Oof__nat__aux(X16172,hAPP(hAPP(c_COMBC(X16172,X16172,X16172),c_Groups_Oplus__class_Oplus(X16172)),c_Groups_Oone__class_Oone(X16172)),X16171,c_Groups_Ozero__class_Ozero(X16172))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16172),X16171)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__1__class_Oof__nat__code])])). 4.05/4.31 fof(c_0_7817, plain, ![X10050, X10051, X10052, X10053, X10054]:((((X10052=X10050|X10053=X10050|hAPP(hAPP(c_Set_Oinsert(X10054),X10053),hAPP(hAPP(c_Set_Oinsert(X10054),X10052),c_Orderings_Obot__class_Obot(tc_fun(X10054,tc_HOL_Obool))))!=hAPP(hAPP(c_Set_Oinsert(X10054),X10051),hAPP(hAPP(c_Set_Oinsert(X10054),X10050),c_Orderings_Obot__class_Obot(tc_fun(X10054,tc_HOL_Obool)))))&(X10051=X10053|X10053=X10050|hAPP(hAPP(c_Set_Oinsert(X10054),X10053),hAPP(hAPP(c_Set_Oinsert(X10054),X10052),c_Orderings_Obot__class_Obot(tc_fun(X10054,tc_HOL_Obool))))!=hAPP(hAPP(c_Set_Oinsert(X10054),X10051),hAPP(hAPP(c_Set_Oinsert(X10054),X10050),c_Orderings_Obot__class_Obot(tc_fun(X10054,tc_HOL_Obool))))))&((X10052=X10050|X10051=X10052|hAPP(hAPP(c_Set_Oinsert(X10054),X10053),hAPP(hAPP(c_Set_Oinsert(X10054),X10052),c_Orderings_Obot__class_Obot(tc_fun(X10054,tc_HOL_Obool))))!=hAPP(hAPP(c_Set_Oinsert(X10054),X10051),hAPP(hAPP(c_Set_Oinsert(X10054),X10050),c_Orderings_Obot__class_Obot(tc_fun(X10054,tc_HOL_Obool)))))&(X10051=X10053|X10051=X10052|hAPP(hAPP(c_Set_Oinsert(X10054),X10053),hAPP(hAPP(c_Set_Oinsert(X10054),X10052),c_Orderings_Obot__class_Obot(tc_fun(X10054,tc_HOL_Obool))))!=hAPP(hAPP(c_Set_Oinsert(X10054),X10051),hAPP(hAPP(c_Set_Oinsert(X10054),X10050),c_Orderings_Obot__class_Obot(tc_fun(X10054,tc_HOL_Obool)))))))&((X10053!=X10050|X10051!=X10052|hAPP(hAPP(c_Set_Oinsert(X10054),X10053),hAPP(hAPP(c_Set_Oinsert(X10054),X10052),c_Orderings_Obot__class_Obot(tc_fun(X10054,tc_HOL_Obool))))=hAPP(hAPP(c_Set_Oinsert(X10054),X10051),hAPP(hAPP(c_Set_Oinsert(X10054),X10050),c_Orderings_Obot__class_Obot(tc_fun(X10054,tc_HOL_Obool)))))&(X10052!=X10050|X10051!=X10053|hAPP(hAPP(c_Set_Oinsert(X10054),X10053),hAPP(hAPP(c_Set_Oinsert(X10054),X10052),c_Orderings_Obot__class_Obot(tc_fun(X10054,tc_HOL_Obool))))=hAPP(hAPP(c_Set_Oinsert(X10054),X10051),hAPP(hAPP(c_Set_Oinsert(X10054),X10050),c_Orderings_Obot__class_Obot(tc_fun(X10054,tc_HOL_Obool))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff])])])). 4.05/4.31 fof(c_0_7818, plain, ![X8883, X8884, X8885, X8886, X8888, X8889, X8890, X8891, X8892]:(((hBOOL(hAPP(hAPP(c_member(X8886),esk282_4(X8883,X8884,X8885,X8886)),X8884))|c_Orderings_Otop__class_Otop(tc_fun(X8885,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8886,tc_fun(X8885,tc_HOL_Obool)),X8884),X8883))&(hAPP(X8883,esk282_4(X8883,X8884,X8885,X8886))!=c_Orderings_Otop__class_Otop(tc_fun(X8885,tc_HOL_Obool))|c_Orderings_Otop__class_Otop(tc_fun(X8885,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8886,tc_fun(X8885,tc_HOL_Obool)),X8884),X8883)))&(c_Orderings_Otop__class_Otop(tc_fun(X8890,tc_HOL_Obool))!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8891,tc_fun(X8890,tc_HOL_Obool)),X8889),X8888)|(~hBOOL(hAPP(hAPP(c_member(X8891),X8892),X8889))|hAPP(X8888,X8892)=c_Orderings_Otop__class_Otop(tc_fun(X8890,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_INTER__UNIV__conv_I2_J])])])])])])])). 4.05/4.31 fof(c_0_7819, plain, ![X3963, X3964]:((c_Divides_Odiv__class_Omod(tc_Int_Oint,X3964,X3963)=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),X3964),X3963)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3963),c_Divides_Odiv__class_Omod(tc_Int_Oint,X3964,X3963)))&(c_Divides_Odiv__class_Omod(tc_Int_Oint,X3964,X3963)!=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),X3964),X3963)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmod__zminus1__eq__if])])])). 4.05/4.31 fof(c_0_7820, plain, ![X2661, X2662, X2663, X2664]:(~class_Lattices_Osemilattice__sup(X2664)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2664),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2664),X2663),X2662)),X2661)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2664),X2663),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2664),X2662),X2661))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__assoc])])])). 4.05/4.31 fof(c_0_7821, plain, ![X13410, X13411, X13412, X13413]:(~class_Lattices_Olattice(X13413)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13413),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13413),X13412),X13411)),X13410)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13413),X13412),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13413),X13411),X13410))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I6_J])])). 4.05/4.31 fof(c_0_7822, plain, ![X16701, X16702, X16703, X16704]:(~class_Lattices_Osemilattice__inf(X16704)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16704),X16703),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16704),X16702),X16701))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16704),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X16704),X16703),X16702)),X16701)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__assoc])])). 4.05/4.31 fof(c_0_7823, plain, ![X6498, X6499, X6500, X6501, X6502, X6503, X6504, X6505, X6506]:((c_Orderings_Otop__class_Otop(tc_fun(X6501,tc_HOL_Obool))!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6500,tc_fun(X6501,tc_HOL_Obool)),X6499),X6498)|(~hBOOL(hAPP(hAPP(c_member(X6500),X6502),X6499))|c_Orderings_Otop__class_Otop(tc_fun(X6501,tc_HOL_Obool))=hAPP(X6498,X6502)))&((hBOOL(hAPP(hAPP(c_member(X6505),esk196_4(X6503,X6504,X6505,X6506)),X6504))|c_Orderings_Otop__class_Otop(tc_fun(X6506,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6505,tc_fun(X6506,tc_HOL_Obool)),X6504),X6503))&(c_Orderings_Otop__class_Otop(tc_fun(X6506,tc_HOL_Obool))!=hAPP(X6503,esk196_4(X6503,X6504,X6505,X6506))|c_Orderings_Otop__class_Otop(tc_fun(X6506,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6505,tc_fun(X6506,tc_HOL_Obool)),X6504),X6503)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INTER__UNIV__conv_I1_J])])])])])])). 4.05/4.31 fof(c_0_7824, plain, ![X3912, X3913, X3914]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3914,tc_HOL_Obool)),X3913),X3912))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X3914),tc_HOL_Obool)),c_List_Olists(X3914,X3913)),c_List_Olists(X3914,X3912)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lists__mono])])])). 4.05/4.31 fof(c_0_7825, plain, ![X14679, X14680, X14681]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14681,tc_HOL_Obool)),X14680),X14679))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X14681),tc_HOL_Obool)),c_List_Olistsp(X14681,X14680)),c_List_Olistsp(X14681,X14679)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__mono])])). 4.05/4.31 fof(c_0_7826, plain, ![X8068, X8069, X8070, X8071, X8072]:(hBOOL(hAPP(X8072,X8071))|c_List_OtakeWhile(X8070,X8072,X8069)=c_List_OtakeWhile(X8070,X8072,hAPP(hAPP(c_List_Oappend(X8070),X8069),hAPP(hAPP(c_List_Olist_OCons(X8070),X8071),X8068)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile__tail])])])). 4.05/4.31 fof(c_0_7827, plain, ![X821, X822, X823, X824]:(~class_Rings_Ocomm__semiring__1(X824)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X824),X823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X824),X822),X821))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X824),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X824),X823),X822)),X821)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])])). 4.05/4.31 fof(c_0_7828, plain, ![X9400, X9401, X9402, X9403]:(~class_Groups_Oab__semigroup__add(X9403)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9403),X9402),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9403),X9401),X9400))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9403),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9403),X9402),X9401)),X9400)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])])])). 4.05/4.31 fof(c_0_7829, plain, ![X358, X359, X360, X361]:(~class_Rings_Ocomm__semiring__1(X361)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X361),X360),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X361),X359),X358))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X361),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X361),X360),X359)),X358)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])])). 4.05/4.31 cnf(c_0_7830, plain, (hAPP(c_List_Orotate(X1,X3),X2)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5422])). 4.05/4.31 fof(c_0_7831, plain, ![X16790, X16791, X16792, X16793, X16794, X16795]:(~class_Orderings_Olinorder(X16795)|(hBOOL(hAPP(X16794,X16793))|hAPP(c_List_Ofilter(X16792,X16794),X16790)=hAPP(c_List_Ofilter(X16792,X16794),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16792,X16795,X16791),X16793),X16790)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__insort__triv])])])). 4.05/4.31 cnf(c_0_7832, plain, (hAPP(X5,X4)=c_Map_Omap__comp(X3,X6,X7,X5,X1,X2)|hAPP(X1,X2)!=hAPP(c_Option_Ooption_OSome(X3),X4)), inference(split_conjunct,[status(thm)],[c_0_5423])). 4.05/4.31 fof(c_0_7833, plain, ![X12157, X12158, X12159, X12160, X12161]:((hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12161),X12158),X12160)!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12161),X12157),X12159)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12161),X12157),X12160)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12161),X12158),X12159)|c_Groups_Ozero__class_Ozero(X12161)=X12159|c_Groups_Ozero__class_Ozero(X12161)=X12160|~class_Fields_Ofield(X12161))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12161),X12157),X12160)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12161),X12158),X12159)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12161),X12158),X12160)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12161),X12157),X12159)|c_Groups_Ozero__class_Ozero(X12161)=X12159|c_Groups_Ozero__class_Ozero(X12161)=X12160|~class_Fields_Ofield(X12161))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_frac__eq__eq])])])])). 4.05/4.31 fof(c_0_7834, plain, ![X13339, X13340, X13341, X13342]:(~class_Rings_Ocomm__semiring__1(X13342)|hAPP(hAPP(c_Power_Opower__class_Opower(X13342),X13341),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13340),X13339))=hAPP(hAPP(c_Power_Opower__class_Opower(X13342),hAPP(hAPP(c_Power_Opower__class_Opower(X13342),X13341),X13340)),X13339)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])])). 4.05/4.31 fof(c_0_7835, plain, ![X14342, X14343, X14344, X14345]:(~class_Groups_Omonoid__mult(X14345)|hAPP(hAPP(c_Power_Opower__class_Opower(X14345),hAPP(hAPP(c_Power_Opower__class_Opower(X14345),X14344),X14343)),X14342)=hAPP(hAPP(c_Power_Opower__class_Opower(X14345),X14344),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14343),X14342))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])])). 4.05/4.31 cnf(c_0_7836, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[c_0_5424, c_0_4475])). 4.05/4.31 cnf(c_0_7837, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[c_0_5425, c_0_4475])). 4.05/4.31 cnf(c_0_7838, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5426, c_0_4475])). 4.05/4.31 cnf(c_0_7839, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[c_0_5427, c_0_4475])). 4.05/4.31 cnf(c_0_7840, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5428, c_0_4475])). 4.05/4.31 cnf(c_0_7841, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(rw,[status(thm)],[c_0_5429, c_0_4475])). 4.05/4.31 cnf(c_0_7842, plain, (c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2)))|~c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))), inference(rw,[status(thm)],[c_0_5430, c_0_5018])). 4.05/4.31 fof(c_0_7843, plain, ![X2349, X2350, X2351]:(~class_Fields_Olinordered__field__inverse__zero(X2351)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2351),c_Groups_Ozero__class_Ozero(X2351)),X2350))|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2351),hAPP(c_Groups_Oabs__class_Oabs(X2351),X2349)),X2350)=hAPP(c_Groups_Oabs__class_Oabs(X2351),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2351),X2349),X2350)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__div__pos])])). 4.05/4.31 fof(c_0_7844, plain, ![X11588, X11589, X11590, X11591]:(~hBOOL(hAPP(hAPP(c_member(X11591),X11590),c_Complete__Lattice_OInf__class_OInf(tc_fun(X11591,tc_HOL_Obool),X11589)))|(~hBOOL(hAPP(hAPP(c_member(tc_fun(X11591,tc_HOL_Obool)),X11588),X11589))|hBOOL(hAPP(hAPP(c_member(X11591),X11590),X11588)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_InterD])])])). 4.05/4.31 cnf(c_0_7845, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[c_0_5431, c_0_4475])). 4.05/4.31 cnf(c_0_7846, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[c_0_5432, c_0_4475])). 4.05/4.31 cnf(c_0_7847, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))), inference(rw,[status(thm)],[c_0_5433, c_0_4475])). 4.05/4.31 cnf(c_0_7848, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[c_0_5434, c_0_4475])). 4.05/4.31 fof(c_0_7849, plain, ![X6050, X6051, X6052]:(~class_Orderings_Olinorder(X6052)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6052),X6051))|(~hBOOL(hAPP(hAPP(c_member(X6052),X6050),X6051))|c_Big__Operators_Olattice_OInf__fin(X6052,c_Orderings_Oord__class_Omin(X6052),X6051)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X6052),X6050),c_Big__Operators_Olattice_OInf__fin(X6052,c_Orderings_Oord__class_Omin(X6052),X6051))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oin__idem])])])). 4.05/4.31 fof(c_0_7850, plain, ![X14790, X14791, X14792]:(~class_Orderings_Olinorder(X14792)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14792),X14791))|(~hBOOL(hAPP(hAPP(c_member(X14792),X14790),X14791))|c_Big__Operators_Olattice_OSup__fin(X14792,c_Orderings_Oord__class_Omax(X14792),X14791)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X14792),X14790),c_Big__Operators_Olattice_OSup__fin(X14792,c_Orderings_Oord__class_Omax(X14792),X14791))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oin__idem])])])). 4.05/4.31 cnf(c_0_7851, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(X1,esk24_4(X1,X2,X3,X4))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X3),X4),X2))|hAPP(X1,X4)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5275])). 4.05/4.31 fof(c_0_7852, plain, ![X14156, X14157, X14158, X14159, X14160, X14161, X14162]:(~c_Finite__Set_Ofolding__image__simple(X14162,X14161,X14160,X14159,X14158,X14157)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14161),X14156))|hAPP(X14157,X14156)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X14162,X14161,X14160),X14158),X14159),X14156))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g])])). 4.05/4.31 fof(c_0_7853, plain, ![X695, X696]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X696|X695=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X696),X695))&(X696=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X696),X695)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X696),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X695)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__eq__if])])])). 4.05/4.31 cnf(c_0_7854, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))), inference(rw,[status(thm)],[c_0_5435, c_0_4475])). 4.05/4.31 fof(c_0_7855, plain, ![X4574, X4575, X4576, X4577]:((~hBOOL(hAPP(hAPP(c_member(X4575),X4577),hAPP(c_List_Oset(X4575),c_List_Oremove1(X4575,X4576,X4574))))|hBOOL(hAPP(hAPP(c_member(X4575),X4577),hAPP(c_List_Oset(X4575),X4574)))|X4577=X4576)&(~hBOOL(hAPP(hAPP(c_member(X4575),X4577),hAPP(c_List_Oset(X4575),X4574)))|hBOOL(hAPP(hAPP(c_member(X4575),X4577),hAPP(c_List_Oset(X4575),c_List_Oremove1(X4575,X4576,X4574))))|X4577=X4576)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__set__remove1])])])])). 4.05/4.31 fof(c_0_7856, plain, ![X16150, X16151, X16152, X16153, X16154, X16156, X16157, X16158, X16159, X16160, X16161]:(((hBOOL(hAPP(hAPP(c_member(X16154),esk486_5(X16150,X16151,X16152,X16153,X16154)),X16152))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16154,tc_fun(X16153,tc_HOL_Obool)),X16152),X16151),X16150)))&(hBOOL(hAPP(hAPP(X16151,esk486_5(X16150,X16151,X16152,X16153,X16154)),X16150))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16154,tc_fun(X16153,tc_HOL_Obool)),X16152),X16151),X16150))))&(~hBOOL(hAPP(hAPP(c_member(X16160),X16161),X16158))|~hBOOL(hAPP(hAPP(X16157,X16161),X16156))|hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16160,tc_fun(X16159,tc_HOL_Obool)),X16158),X16157),X16156)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP1__iff])])])])])])). 4.05/4.31 cnf(c_0_7857, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)|~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5436, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.31 fof(c_0_7858, plain, ![X5883, X5884, X5885]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5885),X5884))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5885,tc_HOL_Obool)),X5884),X5883)=hAPP(hAPP(c_Finite__Set_Ofold(X5885,tc_fun(X5885,tc_HOL_Obool),c_Set_Oinsert(X5885)),X5883),X5884)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__fold__insert])])). 4.05/4.31 fof(c_0_7859, plain, ![X8635, X8636, X8637]:(~class_Orderings_Oorder(X8637)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8637,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X8637,X8636,X8635)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X8637),X8635))=c_Orderings_Obot__class_Obot(tc_fun(X8637,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I5_J])])). 4.05/4.31 fof(c_0_7860, plain, ![X3541, X3542, X3543]:(~class_Int_Onumber__ring(X3543)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3543),hAPP(c_Int_Onumber__class_Onumber__of(X3543),X3542)),hAPP(c_Int_Onumber__class_Onumber__of(X3543),X3541))=hAPP(c_Int_Onumber__class_Onumber__of(X3543),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3542),X3541))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_number__of__diff])])])). 4.05/4.31 cnf(c_0_7861, 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_5154])). 4.05/4.31 fof(c_0_7862, plain, ![X8471, X8472, X8473, X8474, X8475, X8476]:(~hBOOL(hAPP(hAPP(X8476,X8475),X8474))|(~hBOOL(hAPP(hAPP(X8473,X8475),X8474))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8472,tc_fun(X8471,tc_HOL_Obool))),X8476),X8473),X8475),X8474)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf2I])])])). 4.05/4.31 fof(c_0_7863, plain, ![X3646, X3647, X3648, X3649]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3649,tc_HOL_Obool)),X3647),hAPP(hAPP(c_Set_Oinsert(X3649),X3648),X3646)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3649,tc_HOL_Obool)),X3647),X3646))|hBOOL(hAPP(hAPP(c_member(X3649),X3648),X3647)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3649,tc_HOL_Obool)),X3647),X3646))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3649,tc_HOL_Obool)),X3647),hAPP(hAPP(c_Set_Oinsert(X3649),X3648),X3646)))|hBOOL(hAPP(hAPP(c_member(X3649),X3648),X3647)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__insert])])])])). 4.05/4.31 fof(c_0_7864, plain, ![X12054, X12055, X12056]:(~class_Orderings_Oorder(X12056)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12056,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X12056,X12055,X12054)),hAPP(c_SetInterval_Oord__class_OatLeast(X12056),X12054))=c_Orderings_Obot__class_Obot(tc_fun(X12056,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I6_J])])])). 4.05/4.31 fof(c_0_7865, plain, ![X15853, X15854, X15855, X15857]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15855),esk476_3(X15853,X15854,X15855)),X15853))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15855),c_Complete__Lattice_OInf__class_OInf(X15855,X15854)),X15853))|(~class_Complete__Lattice_Ocomplete__lattice(X15855)|~class_Orderings_Olinorder(X15855)))&(hBOOL(hAPP(hAPP(c_member(X15855),esk476_3(X15853,X15854,X15855)),X15854))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15855),c_Complete__Lattice_OInf__class_OInf(X15855,X15854)),X15853))|(~class_Complete__Lattice_Ocomplete__lattice(X15855)|~class_Orderings_Olinorder(X15855))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15855),X15857),X15853))|~hBOOL(hAPP(hAPP(c_member(X15855),X15857),X15854))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15855),c_Complete__Lattice_OInf__class_OInf(X15855,X15854)),X15853))|(~class_Complete__Lattice_Ocomplete__lattice(X15855)|~class_Orderings_Olinorder(X15855)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__less__iff])])])])])])). 4.05/4.31 fof(c_0_7866, plain, ![X15159, X15160, X15161, X15163]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15161),X15160),esk455_3(X15159,X15160,X15161)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15161),X15160),c_Complete__Lattice_OSup__class_OSup(X15161,X15159)))|(~class_Orderings_Olinorder(X15161)|~class_Complete__Lattice_Ocomplete__lattice(X15161)))&(hBOOL(hAPP(hAPP(c_member(X15161),esk455_3(X15159,X15160,X15161)),X15159))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15161),X15160),c_Complete__Lattice_OSup__class_OSup(X15161,X15159)))|(~class_Orderings_Olinorder(X15161)|~class_Complete__Lattice_Ocomplete__lattice(X15161))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15161),X15160),X15163))|~hBOOL(hAPP(hAPP(c_member(X15161),X15163),X15159))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15161),X15160),c_Complete__Lattice_OSup__class_OSup(X15161,X15159)))|(~class_Orderings_Olinorder(X15161)|~class_Complete__Lattice_Ocomplete__lattice(X15161)))), 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])])])])])])). 4.05/4.31 fof(c_0_7867, plain, ![X4737, X4738, X4739]:(~class_Orderings_Olinorder(X4739)|(~hBOOL(hAPP(hAPP(c_member(X4739),X4738),hAPP(c_List_Oset(X4739),X4737)))|(~c_List_Olinorder__class_Osorted(X4739,X4737)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4739,X4739,c_COMBI(X4739)),X4738),c_List_Oremove1(X4739,X4738,X4737))=X4737))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__remove1])])). 4.05/4.31 fof(c_0_7868, plain, ![X9196, X9197, X9198]:(~class_Orderings_Oorder(X9198)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9198,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X9198,X9197,X9196)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X9198),X9196))=c_Orderings_Obot__class_Obot(tc_fun(X9198,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I7_J])])). 4.05/4.31 fof(c_0_7869, plain, ![X2704, X2705, X2706, X2707, X2708, X2709]:(~c_Finite__Set_Ofun__left__comm(X2709,X2708,X2707)|hAPP(hAPP(X2707,X2706),hAPP(hAPP(X2707,X2705),X2704))=hAPP(hAPP(X2707,X2705),hAPP(hAPP(X2707,X2706),X2704))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofun__left__comm])])])). 4.05/4.31 fof(c_0_7870, plain, ![X1053, X1054, X1055]:(~class_Orderings_Oorder(X1055)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1055,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1055),X1054)),c_SetInterval_Oord__class_OatLeastAtMost(X1055,X1054,X1053))=c_Orderings_Obot__class_Obot(tc_fun(X1055,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I4_J])])])). 4.05/4.31 fof(c_0_7871, plain, ![X15185, X15186, X15187]:((hBOOL(hAPP(hAPP(c_member(X15187),esk456_3(X15185,X15186,X15187)),X15186))|(~hBOOL(hAPP(hAPP(c_member(X15187),X15185),X15186))|c_Big__Operators_Olinorder__class_OMax(X15187,X15186)=X15185)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15187),X15186))|~class_Orderings_Olinorder(X15187))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15187),esk456_3(X15185,X15186,X15187)),X15185))|(~hBOOL(hAPP(hAPP(c_member(X15187),X15185),X15186))|c_Big__Operators_Olinorder__class_OMax(X15187,X15186)=X15185)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15187),X15186))|~class_Orderings_Olinorder(X15187))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max__eqI])])])])])). 4.05/4.31 fof(c_0_7872, plain, ![X15756, X15757, X15758]:(~class_Orderings_Oorder(X15758)|c_Orderings_Obot__class_Obot(tc_fun(X15758,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15758,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X15758),X15757)),c_SetInterval_Oord__class_OgreaterThanAtMost(X15758,X15757,X15756))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I3_J])])])). 4.05/4.31 fof(c_0_7873, plain, ![X12349, X12350, X12351]:(~class_Rings_Osemiring__1(X12351)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X12351),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12350),X12349))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12351),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X12351),X12350)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X12351),X12349))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__mult])])). 4.05/4.31 cnf(c_0_7874, 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_5437])). 4.05/4.31 fof(c_0_7875, plain, ![X9651, X9652, X9653]:((hBOOL(hAPP(hAPP(c_member(X9653),X9651),X9652))|hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X9653),X9652))=hAPP(c_Finite__Set_Ocard(X9653),hAPP(hAPP(c_Set_Oinsert(X9653),X9651),X9652))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9653),X9652)))&(~hBOOL(hAPP(hAPP(c_member(X9653),X9651),X9652))|hAPP(c_Finite__Set_Ocard(X9653),X9652)=hAPP(c_Finite__Set_Ocard(X9653),hAPP(hAPP(c_Set_Oinsert(X9653),X9651),X9652))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9653),X9652)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__insert__if])])])])). 4.05/4.31 fof(c_0_7876, plain, ![X13692, X13693, X13694]:(~class_Orderings_Oorder(X13694)|c_Orderings_Obot__class_Obot(tc_fun(X13694,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13694,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X13694),X13693)),c_SetInterval_Oord__class_OgreaterThanLessThan(X13694,X13693,X13692))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I1_J])])])). 4.05/4.31 fof(c_0_7877, plain, ![X17514, X17515, X17516]:((hBOOL(hAPP(hAPP(c_member(X17516),esk524_3(X17514,X17515,X17516)),X17515))|(~hBOOL(hAPP(hAPP(c_member(X17516),X17514),X17515))|X17514=c_Big__Operators_Olinorder__class_OMin(X17516,X17515))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X17516),X17515))|~class_Orderings_Olinorder(X17516))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17516),X17514),esk524_3(X17514,X17515,X17516)))|(~hBOOL(hAPP(hAPP(c_member(X17516),X17514),X17515))|X17514=c_Big__Operators_Olinorder__class_OMin(X17516,X17515))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X17516),X17515))|~class_Orderings_Olinorder(X17516))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min__eqI])])])])])). 4.05/4.31 fof(c_0_7878, plain, ![X13852, X13853, X13854, X13855]:(~class_Divides_Oring__div(X13855)|c_Divides_Odiv__class_Omod(X13855,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13855),X13854),X13853),X13852)=c_Divides_Odiv__class_Omod(X13855,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13855),c_Divides_Odiv__class_Omod(X13855,X13854,X13852)),X13853),X13852)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__left__eq])])). 4.05/4.31 fof(c_0_7879, plain, ![X5407, X5408, X5409]:(~class_Rings_Osemiring__1(X5409)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5409),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5408),X5407))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5409),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5409),X5408)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5409),X5407))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__add])])])). 4.05/4.31 fof(c_0_7880, plain, ![X8330, X8331, X8332, X8333]:(~hBOOL(hAPP(hAPP(c_member(X8333),X8332),X8331))|(~hBOOL(hAPP(hAPP(c_member(X8333),X8332),X8330))|hBOOL(hAPP(hAPP(c_member(X8333),X8332),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8333,tc_HOL_Obool)),X8331),X8330))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_IntI])])])). 4.05/4.31 fof(c_0_7881, plain, ![X2282, X2283, X2284, X2285]:(~class_Divides_Osemiring__div(X2285)|c_Divides_Odiv__class_Omod(X2285,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2285),X2284),X2282),X2283)=c_Divides_Odiv__class_Omod(X2285,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2285),c_Divides_Odiv__class_Omod(X2285,X2284,X2283)),X2282),X2283)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmod__simps_I4_J])])])). 4.05/4.31 fof(c_0_7882, plain, ![X7886, X7887, X7888, X7889]:(~class_Divides_Osemiring__div(X7889)|c_Divides_Odiv__class_Omod(X7889,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7889),X7888),X7887),X7886)=c_Divides_Odiv__class_Omod(X7889,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7889),c_Divides_Odiv__class_Omod(X7889,X7888,X7886)),X7887),X7886)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__left__eq])])). 4.05/4.31 fof(c_0_7883, plain, ![X8518, X8519, X8520]:(~class_Int_Onumber__ring(X8520)|hAPP(c_Int_Onumber__class_Onumber__of(X8520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8519),X8518))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8520),hAPP(c_Int_Onumber__class_Onumber__of(X8520),X8519)),hAPP(c_Int_Onumber__class_Onumber__of(X8520),X8518))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__mult])])). 4.05/4.31 fof(c_0_7884, plain, ![X9488, X9489, X9490, X9491]:(~class_Divides_Osemiring__div(X9491)|c_Divides_Odiv__class_Omod(X9491,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9491),X9490),c_Divides_Odiv__class_Omod(X9491,X9489,X9488)),X9488)=c_Divides_Odiv__class_Omod(X9491,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9491),X9490),X9489),X9488)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__right__eq])])). 4.05/4.31 fof(c_0_7885, plain, ![X7319, X7320, X7321]:(~class_Rings_Olinordered__idom(X7321)|hAPP(c_Groups_Oabs__class_Oabs(X7321),hAPP(hAPP(c_Power_Opower__class_Opower(X7321),X7320),X7319))=hAPP(c_Groups_Oabs__class_Oabs(X7321),hAPP(hAPP(c_Power_Opower__class_Opower(X7321),hAPP(c_Groups_Ouminus__class_Ouminus(X7321),X7320)),X7319))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__power__minus])])])). 4.05/4.31 fof(c_0_7886, plain, ![X17463, X17464, X17465]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17465),X17464),X17463))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17465,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X17465),X17464)),hAPP(c_SetInterval_Oord__class_OlessThan(X17465),X17463)))|~class_Orderings_Olinorder(X17465))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17465,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X17465),X17464)),hAPP(c_SetInterval_Oord__class_OlessThan(X17465),X17463)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17465),X17464),X17463))|~class_Orderings_Olinorder(X17465))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lessThan__strict__subset__iff])])])])). 4.05/4.31 fof(c_0_7887, plain, ![X5341, X5342, X5343]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5343,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5343),X5342)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5343),X5341)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5343),X5341),X5342))|~class_Orderings_Olinorder(X5343))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5343),X5341),X5342))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5343,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5343),X5342)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5343),X5341)))|~class_Orderings_Olinorder(X5343))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_greaterThan__subset__iff])])])])). 4.05/4.31 fof(c_0_7888, plain, ![X5330, X5331, X5332, X5333]:(~class_Divides_Osemiring__div(X5333)|c_Divides_Odiv__class_Omod(X5333,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5333),X5332),c_Divides_Odiv__class_Omod(X5333,X5331,X5330)),X5330)=c_Divides_Odiv__class_Omod(X5333,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5333),X5332),X5331),X5330)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__right__eq])])). 4.05/4.31 fof(c_0_7889, plain, ![X17389, X17390, X17391, X17392]:(~class_Divides_Oring__div(X17392)|c_Divides_Odiv__class_Omod(X17392,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17392),X17391),X17390),X17389)=c_Divides_Odiv__class_Omod(X17392,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17392),X17391),c_Divides_Odiv__class_Omod(X17392,X17390,X17389)),X17389)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__right__eq])])). 4.05/4.31 fof(c_0_7890, plain, ![X12257, X12258, X12259, X12260, X12261, X12262]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12262,X12261),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X12260),X12259)))|(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X12262,X12261),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X12258),X12257)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X12261|X12260=X12258))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_unique__quotient])])])). 4.05/4.31 fof(c_0_7891, plain, ![X13684, X13685, X13686]:(~class_Fields_Olinordered__field__inverse__zero(X13686)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13686),hAPP(c_Groups_Oabs__class_Oabs(X13686),X13685)),hAPP(c_Groups_Oabs__class_Oabs(X13686),X13684))=hAPP(c_Groups_Oabs__class_Oabs(X13686),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X13686),X13685),X13684))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__divide])])). 4.05/4.31 fof(c_0_7892, plain, ![X7456, X7457, X7458]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7458),X7457),X7456))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7458,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X7458),X7457)),hAPP(c_SetInterval_Oord__class_OlessThan(X7458),X7456)))|~class_Orderings_Olinorder(X7458))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7458,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X7458),X7457)),hAPP(c_SetInterval_Oord__class_OlessThan(X7458),X7456)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7458),X7457),X7456))|~class_Orderings_Olinorder(X7458))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__subset__iff])])])). 4.05/4.31 fof(c_0_7893, plain, ![X2052, X2053, X2054]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2054),X2053),X2052))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2054,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X2054),X2053)),hAPP(c_SetInterval_Oord__class_OatMost(X2054),X2052)))|~class_Orderings_Oorder(X2054))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2054,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X2054),X2053)),hAPP(c_SetInterval_Oord__class_OatMost(X2054),X2052)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2054),X2053),X2052))|~class_Orderings_Oorder(X2054))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__subset__iff])])])). 4.05/4.31 fof(c_0_7894, plain, ![X16407, X16408, X16409]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16409,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X16409),X16408)),hAPP(c_SetInterval_Oord__class_OatLeast(X16409),X16407)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16409),X16407),X16408))|~class_Orderings_Oorder(X16409))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16409),X16407),X16408))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16409,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X16409),X16408)),hAPP(c_SetInterval_Oord__class_OatLeast(X16409),X16407)))|~class_Orderings_Oorder(X16409))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeast__subset__iff])])])])). 4.05/4.31 fof(c_0_7895, plain, ![X16661, X16662, X16663]:(~class_Groups_Omonoid__add(X16663)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16663),hAPP(c_List_Omonoid__add__class_Olistsum(X16663),X16662)),hAPP(c_List_Omonoid__add__class_Olistsum(X16663),X16661))=hAPP(c_List_Omonoid__add__class_Olistsum(X16663),hAPP(hAPP(c_List_Oappend(X16663),X16662),X16661))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__append])])])). 4.05/4.31 fof(c_0_7896, plain, ![X4902, X4903, X4904, X4905, X4906, X4907]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4907,X4906),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4905),X4904)))|(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4907,X4906),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4903),X4902)))|(X4906=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X4904=X4902))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_unique__remainder])])])). 4.05/4.31 fof(c_0_7897, plain, ![X2316, X2317]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2317))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2316))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2317),X2316)=hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X2317,X2316)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos])])). 4.05/4.31 fof(c_0_7898, plain, ![X9422, X9423]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9423),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)),X9422))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X9423),X9422)=hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X9423,X9422)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__neg__pos])])])). 4.05/4.31 fof(c_0_7899, plain, ![X11610, X11611, X11612]:(~class_Rings_Olinordered__idom(X11612)|hAPP(c_Groups_Oabs__class_Oabs(X11612),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11612),X11611),X11610))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11612),hAPP(c_Groups_Oabs__class_Oabs(X11612),X11611)),hAPP(c_Groups_Oabs__class_Oabs(X11612),X11610))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult])])). 4.05/4.31 fof(c_0_7900, plain, ![X532, X533, X534]:(~class_Int_Onumber__ring(X534)|hAPP(c_Int_Onumber__class_Onumber__of(X534),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X533),X532))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X534),hAPP(c_Int_Onumber__class_Onumber__of(X534),X533)),hAPP(c_Int_Onumber__class_Onumber__of(X534),X532))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_number__of__add])])])). 4.05/4.31 cnf(c_0_7901, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)!=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_5438])). 4.05/4.31 fof(c_0_7902, plain, ![X1047, X1048, X1049]:(~class_Rings_Oring__1(X1049)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1049),hAPP(c_Int_Oring__1__class_Oof__int(X1049),X1048)),hAPP(c_Int_Oring__1__class_Oof__int(X1049),X1047))=hAPP(c_Int_Oring__1__class_Oof__int(X1049),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1048),X1047))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__add])])). 4.05/4.31 fof(c_0_7903, plain, ![X7772, X7773, X7774]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7774,X7774),tc_HOL_Obool)),X7773),X7772))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7774,tc_HOL_Obool)),c_Wellfounded_Oacc(X7774,X7772)),c_Wellfounded_Oacc(X7774,X7773)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acc__subset])])])). 4.05/4.31 fof(c_0_7904, plain, ![X7790, X7791, X7792]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7792,tc_fun(X7792,tc_HOL_Obool))),X7791),X7790))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7792,tc_HOL_Obool)),c_Wellfounded_Oaccp(X7792,X7790)),c_Wellfounded_Oaccp(X7792,X7791)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__subset])])). 4.05/4.31 fof(c_0_7905, plain, ![X4144, X4145, X4146, X4147]:(~class_Orderings_Oorder(X4147)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4147,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4147,X4146,X4145)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4147,X4145,X4144))=c_Orderings_Obot__class_Obot(tc_fun(X4147,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I14_J])])])). 4.05/4.31 fof(c_0_7906, plain, ![X6477, X6478, X6479, X6480]:(~class_Orderings_Oorder(X6480)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6480,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X6480,X6479,X6478)),c_SetInterval_Oord__class_OgreaterThanLessThan(X6480,X6478,X6477))=c_Orderings_Obot__class_Obot(tc_fun(X6480,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I10_J])])). 4.05/4.31 fof(c_0_7907, plain, ![X12096, X12097, X12098]:(~class_Rings_Oring__1(X12098)|hAPP(c_Int_Oring__1__class_Oof__int(X12098),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X12097),X12096))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X12098),hAPP(c_Int_Oring__1__class_Oof__int(X12098),X12097)),hAPP(c_Int_Oring__1__class_Oof__int(X12098),X12096))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__diff])])])). 4.05/4.31 fof(c_0_7908, plain, ![X14673, X14674]:(~class_Fields_Ofield__inverse__zero(X14674)|~class_Int_Onumber__ring(X14674)|hAPP(c_Groups_Ouminus__class_Ouminus(X14674),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14674),c_Groups_Oone__class_Oone(X14674)),X14673))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X14674),hAPP(c_Int_Onumber__class_Onumber__of(X14674),c_Int_OMin)),X14673)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus1__divide])])). 4.05/4.31 fof(c_0_7909, plain, ![X8134, X8135, X8136]:(~class_Rings_Oring__1(X8136)|hAPP(c_Int_Oring__1__class_Oof__int(X8136),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8135),X8134))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8136),hAPP(c_Int_Oring__1__class_Oof__int(X8136),X8135)),hAPP(c_Int_Oring__1__class_Oof__int(X8136),X8134))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__mult])])])). 4.05/4.31 fof(c_0_7910, plain, ![X15901, X15902, X15903, X15904]:(~class_Orderings_Oorder(X15904)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15904,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X15904,X15903,X15902)),c_SetInterval_Oord__class_OgreaterThanAtMost(X15904,X15902,X15901))=c_Orderings_Obot__class_Obot(tc_fun(X15904,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I16_J])])). 4.05/4.31 fof(c_0_7911, plain, ![X6268, X6269, X6270, X6271]:(~class_Orderings_Oorder(X6271)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6271,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X6271,X6270,X6269)),c_SetInterval_Oord__class_OgreaterThanLessThan(X6271,X6269,X6268))=c_Orderings_Obot__class_Obot(tc_fun(X6271,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I12_J])])])). 4.05/4.31 fof(c_0_7912, plain, ![X2388, X2389, X2390, X2391]:(~class_Orderings_Oorder(X2391)|c_Orderings_Obot__class_Obot(tc_fun(X2391,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2391,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X2391,X2390,X2389)),c_SetInterval_Oord__class_OatLeastAtMost(X2391,X2389,X2388))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ivl__disj__int_I13_J])])])). 4.05/4.31 fof(c_0_7913, plain, ![X2075, X2076]:(~class_Lattices_Olattice(X2076)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2076),X2075))|(c_Orderings_Obot__class_Obot(tc_fun(X2076,tc_HOL_Obool))=X2075|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2076),c_Big__Operators_Olattice__class_OInf__fin(X2076,X2075)),c_Big__Operators_Olattice__class_OSup__fin(X2076,X2075)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__le__Sup])])])). 4.05/4.31 cnf(c_0_7914, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X3))))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)!=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))), inference(split_conjunct,[status(thm)],[c_0_5438])). 4.05/4.31 cnf(c_0_7915, 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))))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5439])). 4.05/4.31 cnf(c_0_7916, 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_5440, c_0_4427]), ['final']). 4.05/4.31 cnf(c_0_7917, 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_5441])). 4.05/4.31 cnf(c_0_7918, 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_5442, c_0_4427]), c_0_4427]), ['final']). 4.05/4.31 cnf(c_0_7919, 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_5443])). 4.05/4.31 cnf(c_0_7920, 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_5444]), ['final']). 4.05/4.31 fof(c_0_7921, plain, ![X17548, X17549, X17550, X17551, X17552]:(~class_Rings_Ocomm__semiring__1(X17551)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17550),X17549))|(~hBOOL(hAPP(hAPP(c_member(X17550),X17552),X17549))|c_Groups_Ozero__class_Ozero(X17551)!=hAPP(X17548,X17552)|c_Groups_Ozero__class_Ozero(X17551)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X17550,X17551),X17548),X17549)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__zero])])])])). 4.05/4.31 fof(c_0_7922, plain, ![X13186, X13187, X13188, X13189]:(~class_Rings_Olinordered__semiring(X13189)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13189),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13189),X13188),X13187)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13189),X13186),X13187)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13189),c_Groups_Ozero__class_Ozero(X13189)),X13187))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13189),X13188),X13186))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right__less__imp__less])])])). 4.05/4.31 fof(c_0_7923, plain, ![X14515, X14516, X14517, X14518]:(~class_Rings_Olinordered__semiring__strict(X14518)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14518),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14518),X14517),X14516)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14518),X14515),X14516)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14518),c_Groups_Ozero__class_Ozero(X14518)),X14516))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14518),X14517),X14515))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__imp__less__right])])])). 4.05/4.31 fof(c_0_7924, plain, ![X16511, X16512, X16513, X16514]:(~class_Rings_Olinordered__semiring(X16514)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16514),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16514),X16513),X16512)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16514),X16513),X16511)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16514),c_Groups_Ozero__class_Ozero(X16514)),X16513))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16514),X16512),X16511))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__left__less__imp__less])])])). 4.05/4.31 cnf(c_0_7925, 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))=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(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5445, c_0_4422])). 4.05/4.31 fof(c_0_7926, plain, ![X11110, X11111, X11112, X11114, X11115, X11116, X11117]:(((X11111=hAPP(hAPP(c_List_Onth(X11112),X11110),esk338_3(X11110,X11111,X11112))|~hBOOL(hAPP(hAPP(c_member(X11112),X11111),hAPP(c_List_Oset(X11112),X11110))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk338_3(X11110,X11111,X11112)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11112)),X11110)))|~hBOOL(hAPP(hAPP(c_member(X11112),X11111),hAPP(c_List_Oset(X11112),X11110)))))&(X11115!=hAPP(hAPP(c_List_Onth(X11116),X11114),X11117)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11117),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11116)),X11114)))|hBOOL(hAPP(hAPP(c_member(X11116),X11115),hAPP(c_List_Oset(X11116),X11114))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__conv__nth])])])])])])). 4.05/4.31 fof(c_0_7927, plain, ![X8974, X8975]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8974),X8975)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8974),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)),X8975)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8974),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),X8974),X8975)),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)),X8975)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff])])])). 4.05/4.31 fof(c_0_7928, plain, ![X7370, X7371]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X7370),X7371)),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)),X7370))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7371),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)),X7370))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X7370),X7371)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7371),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])])])). 4.05/4.31 fof(c_0_7929, plain, ![X6204, X6205, X6206, X6207]:(~class_Rings_Olinordered__semiring__strict(X6207)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6207),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6207),X6206),X6205)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6207),X6206),X6204)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6207),c_Groups_Ozero__class_Ozero(X6207)),X6206))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6207),X6205),X6204))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__imp__less__left])])])). 4.05/4.31 fof(c_0_7930, plain, ![X14169, X14170, X14171, X14172]:(~class_Rings_Olinordered__semiring__strict(X14172)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14172),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14172),X14171),X14170)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14172),X14169),X14170)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14172),c_Groups_Ozero__class_Ozero(X14172)),X14170))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14172),X14171),X14169))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__right__le__imp__le])])])). 4.05/4.31 fof(c_0_7931, plain, ![X17287, X17288]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17288))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17287),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),X17288),X17287)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__nonneg__neg__le0])])). 4.05/4.31 fof(c_0_7932, plain, ![X10538, X10539]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10539),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)),X10538))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X10539),X10538)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__nonpos__pos__le0])])])). 4.05/4.31 fof(c_0_7933, plain, ![X14357, X14358]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14358))|~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),X14358),X14357))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14357))|~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),X14358),X14357)))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14358))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14357))|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),X14358),X14357))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])])). 4.05/4.31 fof(c_0_7934, plain, ![X11397, X11398]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11398))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11397))|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),X11398),X11397))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])])])). 4.05/4.31 fof(c_0_7935, plain, ![X8464, X8465, X8466, X8467]:(~class_Rings_Olinordered__semiring__strict(X8467)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8467),X8466),X8465)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8467),X8466),X8464)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8467),c_Groups_Ozero__class_Ozero(X8467)),X8466))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8467),X8465),X8464))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le])])). 4.05/4.31 fof(c_0_7936, plain, ![X12239, X12240, X12241, X12242]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12242),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12242),X12241),X12240)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12242),X12241),X12239)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12242),X12239),X12240))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12242),X12241),c_Groups_Ozero__class_Ozero(X12242)))|~class_Rings_Olinordered__ring__strict(X12242))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12242),X12239),X12240))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12242),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12242),X12241),X12240)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12242),X12241),X12239)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12242),X12241),c_Groups_Ozero__class_Ozero(X12242)))|~class_Rings_Olinordered__ring__strict(X12242))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__less__cancel__left__neg])])])])). 4.05/4.31 cnf(c_0_7937, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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)),esk509_3(X2,X3,X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_5446])). 4.05/4.31 fof(c_0_7938, plain, ![X11014, X11015]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11015))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11014))|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),X11015),X11014))))), 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])])])). 4.05/4.31 fof(c_0_7939, plain, ![X14499, X14500]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14499))|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),X14499),X14500)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14500)))&(~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),X14499),X14500)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14499))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14500)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff])])])])). 4.05/4.31 fof(c_0_7940, plain, ![X9623, X9624]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9624))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9623))|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),X9624),X9623))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J])])])). 4.05/4.31 fof(c_0_7941, plain, ![X7217, X7218]:((~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),X7217),X7218)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7217),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7218),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X7217),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),X7217),X7218)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X7218),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__imp__zdiv__nonneg__iff])])])])). 4.05/4.31 fof(c_0_7942, plain, ![X11137, X11138]:((~hBOOL(hAPP(X11137,c_Option_Ooption_ONone(X11138)))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X11138),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X11138),tc_HOL_Obool,X11138),X11137),c_Option_Ooption_OSome(X11138))))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X11138)),X11137))|~class_Enum_Oenum(X11138))&((hBOOL(hAPP(X11137,c_Option_Ooption_ONone(X11138)))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X11138)),X11137))|~class_Enum_Oenum(X11138))&(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X11138),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X11138),tc_HOL_Obool,X11138),X11137),c_Option_Ooption_OSome(X11138))))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X11138)),X11137))|~class_Enum_Oenum(X11138)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__all__option__def])])])). 4.05/4.31 fof(c_0_7943, plain, ![X13029, X13030, X13031]:(~class_Orderings_Olinorder(X13031)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13031),X13030))|c_Big__Operators_Olattice_OInf__fin(X13031,c_Orderings_Oord__class_Omin(X13031),hAPP(hAPP(c_Set_Oinsert(X13031),X13029),X13030))=hAPP(hAPP(c_Finite__Set_Ofold(X13031,X13031,c_Orderings_Oord__class_Omin(X13031)),X13029),X13030))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold__idem_H])])])). 4.05/4.31 fof(c_0_7944, plain, ![X8824, X8825, X8826]:(~class_Orderings_Olinorder(X8826)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8826),X8825))|hAPP(hAPP(c_Finite__Set_Ofold(X8826,X8826,c_Orderings_Oord__class_Omax(X8826)),X8824),X8825)=c_Big__Operators_Olattice_OSup__fin(X8826,c_Orderings_Oord__class_Omax(X8826),hAPP(hAPP(c_Set_Oinsert(X8826),X8824),X8825)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold__idem_H])])])). 4.05/4.31 fof(c_0_7945, plain, ![X14431, X14432, X14433, X14434]:(~class_Divides_Osemiring__div(X14434)|c_Divides_Odiv__class_Omod(X14434,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14434),X14433),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X14434),X14432),X14431)),X14432)=c_Divides_Odiv__class_Omod(X14434,X14433,X14432)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__mult__self2])])])). 4.05/4.31 fof(c_0_7946, plain, ![X11764, X11765, X11766, X11767]:(~class_Groups_Oordered__comm__monoid__add(X11767)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11767),c_Groups_Ozero__class_Ozero(X11767)),X11766))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11767),X11765),X11764))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11767),X11765),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11767),X11766),X11764)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__increasing2])])])). 4.05/4.31 fof(c_0_7947, plain, ![X8774, X8775, X8776, X8777]:(~class_Groups_Oordered__comm__monoid__add(X8777)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8777),c_Groups_Ozero__class_Ozero(X8777)),X8776))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8777),X8775),X8774))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8777),X8775),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8777),X8776),X8774)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__strict__increasing])])])). 4.05/4.31 fof(c_0_7948, plain, ![X11407, X11408, X11409, X11410]:(~class_Rings_Olinordered__semidom(X11410)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11410),c_Groups_Ozero__class_Ozero(X11410)),X11409))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11410),X11408),X11407))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11410),X11408),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X11410),X11409),X11407)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__add__strict])])])). 4.05/4.31 fof(c_0_7949, plain, ![X1209, X1210, X1211, X1212]:(~class_Divides_Osemiring__div(X1212)|c_Divides_Odiv__class_Omod(X1212,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1212),X1211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1212),X1210),X1209)),X1209)=c_Divides_Odiv__class_Omod(X1212,X1211,X1209)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1])])). 4.05/4.31 fof(c_0_7950, plain, ![X9683, X9684, X9685, X9686, X9687, X9688]:(~c_List_Olist__all2(X9688,X9687,X9686,X9685,X9684)|c_List_Olist__all2(X9688,X9687,X9686,hAPP(hAPP(c_List_Odrop(X9688),X9683),X9685),hAPP(hAPP(c_List_Odrop(X9687),X9683),X9684))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2__dropI])])])). 4.05/4.31 fof(c_0_7951, plain, ![X17254, X17255, X17256, X17257, X17258, X17259]:(~c_List_Olist__all2(X17259,X17258,X17257,X17256,X17255)|c_List_Olist__all2(X17259,X17258,X17257,hAPP(hAPP(c_List_Otake(X17259),X17254),X17256),hAPP(hAPP(c_List_Otake(X17258),X17254),X17255))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2__takeI])])])). 4.05/4.31 fof(c_0_7952, plain, ![X2765, X2766, X2767, X2768]:(~class_Groups_Oordered__comm__monoid__add(X2768)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2768),c_Groups_Ozero__class_Ozero(X2768)),X2767))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2768),X2766),X2765))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2768),X2766),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2768),X2767),X2765)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__increasing])])])). 4.05/4.31 fof(c_0_7953, plain, ![X6211, X6212, X6213, X6214]:(~class_Groups_Oordered__comm__monoid__add(X6214)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6214),c_Groups_Ozero__class_Ozero(X6214)),X6213))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6214),X6212),X6211))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6214),X6212),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6214),X6211),X6213)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__increasing2])])])). 4.05/4.31 fof(c_0_7954, plain, ![X15459, X15460, X15461, X15462]:(~hBOOL(hAPP(c_List_Olistsp(X15462,X15461),X15460))|(~hBOOL(hAPP(c_List_Olistsp(X15462,X15459),X15460))|hBOOL(hAPP(c_List_Olistsp(X15462,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15462,tc_HOL_Obool)),X15461),X15459)),X15460)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsp__infI])])])). 4.05/4.31 fof(c_0_7955, plain, ![X1781]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1781),c_Orderings_Otop__class_Otop(tc_fun(X1781,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(X1781),c_Orderings_Otop__class_Otop(tc_fun(X1781,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])])). 4.05/4.31 cnf(c_0_7956, 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))))|X4!=X3), inference(split_conjunct,[status(thm)],[c_0_5447])). 4.05/4.31 fof(c_0_7957, plain, ![X13243, X13244, X13245, X13246]:(~class_Rings_Olinordered__semidom(X13246)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13246),c_Groups_Oone__class_Oone(X13246)),X13245))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13246),hAPP(hAPP(c_Power_Opower__class_Opower(X13246),X13245),X13244)),hAPP(hAPP(c_Power_Opower__class_Opower(X13246),X13245),X13243)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13244),X13243))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__less__imp__less__exp])])])). 4.05/4.31 fof(c_0_7958, plain, ![X5432, X5433, X5434, X5435]:(~class_Orderings_Olinorder(X5435)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X5435),X5434),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5435),X5433),X5432))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X5435),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5435),X5434),X5433)),X5432)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__assoc])])). 4.05/4.31 fof(c_0_7959, plain, ![X14330, X14331, X14332, X14333]:(~class_Rings_Olinordered__semidom(X14333)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14333),c_Groups_Oone__class_Oone(X14333)),X14332))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14333),hAPP(hAPP(c_Power_Opower__class_Opower(X14333),X14332),X14331)),hAPP(hAPP(c_Power_Opower__class_Opower(X14333),X14332),X14330)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14331),X14330))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__le__imp__le__exp])])])). 4.05/4.31 fof(c_0_7960, plain, ![X13443, X13444, X13445, X13446]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13446),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13445)),c_List_OtakeWhile(X13445,X13444,X13443))))|hAPP(hAPP(c_List_Onth(X13445),X13443),X13446)=hAPP(hAPP(c_List_Onth(X13445),c_List_OtakeWhile(X13445,X13444,X13443)),X13446)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__nth])])). 4.05/4.31 cnf(c_0_7961, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk482_4(X2,X3,X4,X1)),c_Option_Oset(X1,X4)))|hBOOL(hAPP(X3,X2))|X4!=hAPP(c_Option_Ooption_OSome(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5448])). 4.05/4.31 cnf(c_0_7962, plain, (c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X2))=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5449]), ['final']). 4.05/4.31 fof(c_0_7963, plain, ![X13140, X13141, X13142, X13143]:(~class_Orderings_Olinorder(X13143)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X13143),X13142),hAPP(hAPP(c_Orderings_Oord__class_Omax(X13143),X13141),X13140))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X13143),hAPP(hAPP(c_Orderings_Oord__class_Omax(X13143),X13142),X13141)),X13140)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__assoc])])])). 4.05/4.31 fof(c_0_7964, plain, ![X4389, X4390, X4391]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4391),X4390))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4391),X4390)),hAPP(c_Finite__Set_Ocard(X4391),hAPP(hAPP(c_Set_Oinsert(X4391),X4389),X4390))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__insert__le])])])). 4.05/4.31 fof(c_0_7965, plain, ![X14419, X14420, X14421, X14423]:(((hBOOL(hAPP(hAPP(c_member(X14421),esk441_3(X14419,X14420,X14421)),X14420))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14421,tc_Nat_Onat),X14419),X14420)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14421),X14420)))&(hAPP(X14419,esk441_3(X14419,X14420,X14421))!=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(X14421,tc_Nat_Onat),X14419),X14420)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14421),X14420))))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X14421,tc_Nat_Onat),X14419),X14420)|(~hBOOL(hAPP(hAPP(c_member(X14421),X14423),X14420))|hAPP(X14419,X14423)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X14421),X14420)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setsum__eq__0__iff])])])])])])). 4.05/4.31 fof(c_0_7966, plain, ![X9199, X9200, X9201, X9203]:(((hBOOL(hAPP(hAPP(c_member(X9201),esk285_3(X9199,X9200,X9201)),X9200))|c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9201,tc_Nat_Onat),X9199),X9200)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9201),X9200)))&(c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X9199,esk285_3(X9199,X9200,X9201))|c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9201,tc_Nat_Onat),X9199),X9200)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9201),X9200))))&(c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X9201,tc_Nat_Onat),X9199),X9200)|(~hBOOL(hAPP(hAPP(c_member(X9201),X9203),X9200))|c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(X9199,X9203))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9201),X9200)))), 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__eq__1__iff])])])])])). 4.05/4.31 fof(c_0_7967, plain, ![X3853, X3854, X3855, X3856, X3857, X3858]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3858)),X3857)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3856)),X3855)|c_Map_Omap__upds(X3858,X3856,X3854,X3857,X3855)=c_Map_Omap__upds(X3858,X3856,X3854,hAPP(hAPP(c_List_Oappend(X3858),X3857),X3853),X3855)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upds__append__drop])])). 4.05/4.31 fof(c_0_7968, plain, ![X7538, X7539, X7540, X7541, X7542, X7543]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7543)),X7542)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7541)),X7540)|c_Map_Omap__upds(X7543,X7541,X7539,X7542,X7540)=c_Map_Omap__upds(X7543,X7541,X7539,X7542,hAPP(hAPP(c_List_Oappend(X7541),X7540),X7538))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__upds__append2__drop])])])). 4.05/4.31 fof(c_0_7969, plain, ![X7592, X7593]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7593))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X7592))|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,X7593,X7592))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I2_J])])])). 4.05/4.31 cnf(c_0_7970, plain, (hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X1,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(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_5450])). 4.05/4.31 cnf(c_0_7971, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),X1))|~c_Com_OWT__bodies|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),X1),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))), inference(split_conjunct,[status(thm)],[c_0_5451])). 4.05/4.31 cnf(c_0_7972, hypothesis, (c_Com_OWT__bodies), inference(split_conjunct,[status(thm)],[conj_1]), ['final']). 4.05/4.31 fof(c_0_7973, plain, ![X15202, X15203, X15204, X15205, X15206]:(~class_Orderings_Olinorder(X15206)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X15205,X15206,X15204),X15203),c_List_Olinorder__class_Osort__key(X15205,X15206,X15204,X15202))=c_List_Olinorder__class_Osort__key(X15205,X15206,X15204,hAPP(hAPP(c_List_Olist_OCons(X15205),X15203),X15202))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__key__simps_I2_J])])). 4.05/4.31 fof(c_0_7974, plain, ![X6756, X6757, X6758]:((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6758))|c_List_Osublist(X6757,hAPP(hAPP(c_List_Olist_OCons(X6757),X6756),c_List_Olist_ONil(X6757)),X6758)=c_List_Olist_ONil(X6757))&(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6758))|hAPP(hAPP(c_List_Olist_OCons(X6757),X6756),c_List_Olist_ONil(X6757))=c_List_Osublist(X6757,hAPP(hAPP(c_List_Olist_OCons(X6757),X6756),c_List_Olist_ONil(X6757)),X6758))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sublist__singleton])])])). 4.05/4.31 cnf(c_0_7975, 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_5452])). 4.05/4.31 fof(c_0_7976, plain, ![X15776, X15777, X15778, X15779, X15780]:(~class_Complete__Lattice_Ocomplete__lattice(X15780)|(~hBOOL(hAPP(hAPP(c_member(X15779),X15778),X15777))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15780),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X15779,X15780),X15777),X15776)),hAPP(X15776,X15778))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF__leI])])])). 4.05/4.31 fof(c_0_7977, plain, ![X5868, X5869, X5870]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5870),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5869)),X5868)))|hBOOL(hAPP(hAPP(c_member(X5869),hAPP(hAPP(c_List_Onth(X5869),X5868),X5870)),hAPP(c_List_Oset(X5869),X5868)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__mem])])). 4.05/4.31 fof(c_0_7978, plain, ![X16422, X16423]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16423),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X16422)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X16422),X16423)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X16422)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__le__listsum__nat])])). 4.05/4.31 fof(c_0_7979, plain, ![X16087, X16088, X16089]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(X16089,tc_HOL_Obool)),X16088),X16087))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16089,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X16089,tc_HOL_Obool),X16087)),X16088))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__lower])])). 4.05/4.31 fof(c_0_7980, plain, ![X12318, X12319, X12320]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(X12320,tc_HOL_Obool)),X12319),X12318))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12320,tc_HOL_Obool)),X12319),c_Complete__Lattice_OSup__class_OSup(tc_fun(X12320,tc_HOL_Obool),X12318)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Union__upper])])])). 4.05/4.31 cnf(c_0_7981, 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_5453])). 4.05/4.31 fof(c_0_7982, plain, ![X16109, X16110, X16111, X16112, X16113]:(~class_Complete__Lattice_Ocomplete__lattice(X16113)|(~hBOOL(hAPP(hAPP(c_member(X16112),X16111),X16110))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16113),hAPP(X16109,X16111)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16112,X16113),X16110),X16109))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__SUPI])])])). 4.05/4.31 fof(c_0_7983, plain, ![X11959, X11960, X11961]:(~class_Rings_Olinordered__semidom(X11961)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11961),c_Groups_Oone__class_Oone(X11961)),X11960))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11961),c_Groups_Oone__class_Oone(X11961)),hAPP(hAPP(c_Power_Opower__class_Opower(X11961),X11960),hAPP(c_Nat_OSuc,X11959)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__gt1])])])). 4.05/4.31 fof(c_0_7984, plain, ![X8229, X8230, X8231, X8232]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X8232,X8231)),hAPP(hAPP(c_Product__Type_OSigma(X8232,X8231),X8230),hAPP(c_COMBK(tc_fun(X8231,tc_HOL_Obool),X8232),X8229))))|(c_Orderings_Obot__class_Obot(tc_fun(X8231,tc_HOL_Obool))=X8229|hBOOL(hAPP(c_Finite__Set_Ofinite(X8232),X8230)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__cartesian__productD1])])])). 4.05/4.31 fof(c_0_7985, plain, ![X4586, X4587, X4588, X4589]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4589,X4588)),hAPP(hAPP(c_Product__Type_OSigma(X4589,X4588),X4587),hAPP(c_COMBK(tc_fun(X4588,tc_HOL_Obool),X4589),X4586))))|(X4587=c_Orderings_Obot__class_Obot(tc_fun(X4589,tc_HOL_Obool))|hBOOL(hAPP(c_Finite__Set_Ofinite(X4588),X4586)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD2])])). 4.05/4.31 fof(c_0_7986, plain, ![X5325, X5326, X5327]:((hBOOL(hAPP(hAPP(c_member(X5327),esk166_3(X5325,X5326,X5327)),X5325))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5327,X5327)),X5326),c_Relation_OId__on(X5327,X5325))))&(X5326=hAPP(hAPP(c_Product__Type_OPair(X5327,X5327),esk166_3(X5325,X5326,X5327)),esk166_3(X5325,X5326,X5327))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5327,X5327)),X5326),c_Relation_OId__on(X5327,X5325))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Id__onE])])])])])). 4.05/4.31 fof(c_0_7987, plain, ![X10556, X10557]:((~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),X10556),X10557)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10557),X10556))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10557)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10557),X10556))|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),X10556),X10557)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10557)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff])])])). 4.05/4.31 cnf(c_0_7988, plain, (c_List_Olast(tc_Nat_Onat,c_List_Oupt(X1,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5454])). 4.05/4.31 fof(c_0_7989, plain, ![X3191, X3192, X3193, X3194]:(~class_Rings_Olinordered__semidom(X3194)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3194),hAPP(hAPP(c_Power_Opower__class_Opower(X3194),X3193),X3192)),hAPP(hAPP(c_Power_Opower__class_Opower(X3194),X3191),X3192)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3194),c_Groups_Ozero__class_Ozero(X3194)),X3191))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3194),X3193),X3191))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__less__imp__less__base])])])). 4.05/4.31 fof(c_0_7990, plain, ![X13456, X13457, X13458]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13458),c_Map_Odom(X13458,X13457,X13456)))|(hBOOL(hAPP(c_Finite__Set_Ofinite(X13458),c_Orderings_Otop__class_Otop(tc_fun(X13458,tc_HOL_Obool))))|c_Option_Ooption_ONone(X13457)=hAPP(X13456,esk418_3(X13456,X13457,X13458)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__map__freshness])])])])). 4.05/4.31 fof(c_0_7991, plain, ![X3477, X3478]:((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk113_2(X3477,X3478)),X3478))|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)),X3477),X3478))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3477),esk113_2(X3477,X3478)))|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)),X3477),X3478))), 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])])])])])). 4.05/4.31 fof(c_0_7992, plain, ![X12299, X12300, X12301, X12302, X12303]:(~class_Orderings_Olinorder(X12303)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12302)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X12302,X12303,X12301),X12300),X12299))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12302)),X12299))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__insort])])). 4.05/4.31 cnf(c_0_7993, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X5=X6|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)|X3!=X4|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X6))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5))), inference(split_conjunct,[status(thm)],[c_0_5455])). 4.05/4.31 cnf(c_0_7994, 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_5336])). 4.05/4.31 fof(c_0_7995, plain, ![X11714, X11715, X11716]:(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X11716)),X11715),c_Wellfounded_Oacc(tc_List_Olist(X11716),c_List_Olistrel1(X11716,X11714))))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X11716)),X11715),c_List_Olists(X11716,c_Wellfounded_Oacc(X11716,X11714))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accI])])). 4.05/4.31 fof(c_0_7996, plain, ![X6070, X6071, X6072, X6073]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6073),X6072))|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6071),X6072)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6073),X6070)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6071),X6070)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__add__eq__less])])])). 4.05/4.31 fof(c_0_7997, plain, ![X4970, X4971, X4972, X4973, X4974, X4975]:(~c_Finite__Set_Ofolding(X4975,X4974,X4973,X4972)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4975),X4971))|hAPP(hAPP(c_Finite__Set_Ofold(X4975,X4974,X4973),X4970),X4971)=hAPP(hAPP(X4972,X4971),X4970))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Oeq__fold])])])). 4.05/4.31 cnf(c_0_7998, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))=c_Divides_OnegDivAlg(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_4551])). 4.05/4.31 fof(c_0_7999, plain, ![X9453, X9454]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X9454),c_Orderings_Otop__class_Otop(tc_fun(X9454,tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X9454),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9454,tc_HOL_Obool)),X9453)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9454),X9453)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9454),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9454,tc_HOL_Obool)),X9453)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X9454),c_Orderings_Otop__class_Otop(tc_fun(X9454,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X9454),X9453)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__compl])])])])). 4.05/4.31 cnf(c_0_8000, 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_5456])). 4.05/4.31 cnf(c_0_8001, 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_5457]), ['final']). 4.05/4.31 fof(c_0_8002, plain, ![X2965, X2966]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2966))|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),X2966),X2965))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2965))|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),X2966),X2965)))))&(~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),X2966),X2965)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2966))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2965))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])])). 4.05/4.31 fof(c_0_8003, plain, ![X4924, X4925, X4926]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4926),X4925))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4926,tc_HOL_Obool)),X4924),X4925))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4926),X4924)),hAPP(c_Finite__Set_Ocard(X4926),X4925))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_psubset__card__mono])])])). 4.05/4.31 fof(c_0_8004, plain, ![X12904, X12905, X12906]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12906),X12905))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12906,tc_HOL_Obool)),X12904),X12905))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X12906),X12904)),hAPP(c_Finite__Set_Ocard(X12906),X12905))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__mono])])])). 4.05/4.31 fof(c_0_8005, plain, ![X16290, X16291, X16292, X16293, X16294, X16295, X16296, X16297, X16298]:(hAPP(c_Fun_Ocomp(X16298,X16297,X16296,X16295),X16294)!=hAPP(c_Fun_Ocomp(X16293,X16297,X16296,X16292),X16291)|hAPP(X16292,hAPP(X16291,X16290))=hAPP(X16295,hAPP(X16294,X16290))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_o__eq__dest])])])). 4.05/4.31 cnf(c_0_8006, 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_5458])). 4.05/4.31 fof(c_0_8007, plain, ![X15743, X15744, X15745, X15746]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15746),X15744),X15743))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15746),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15746),X15745),X15744)),X15743))|~class_Lattices_Osemilattice__sup(X15746))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15746),X15745),X15743))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15746),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15746),X15745),X15744)),X15743))|~class_Lattices_Osemilattice__sup(X15746)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15746),X15744),X15743))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15746),X15745),X15743))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15746),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15746),X15745),X15744)),X15743))|~class_Lattices_Osemilattice__sup(X15746))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__sup__iff])])])])). 4.05/4.31 fof(c_0_8008, plain, ![X7273, X7274, X7275]:(~class_Groups_Omonoid__add(X7275)|c_Groups_Ozero__class_Ozero(X7275)=hAPP(c_List_Omonoid__add__class_Olistsum(X7275),hAPP(hAPP(c_List_Omap(X7274,X7275),hAPP(c_COMBK(X7275,X7274),c_Groups_Ozero__class_Ozero(X7275))),X7273))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__0])])])). 4.05/4.31 fof(c_0_8009, plain, ![X13351, X13352, X13353, X13354, X13355]:(~c_Fun_Oinj__on(X13355,X13354,X13353,X13352)|(~hBOOL(hAPP(hAPP(c_member(X13354),X13351),hAPP(c_Set_Oimage(X13355,X13354,X13353),X13352)))|hAPP(X13353,hAPP(c_Fun_Othe__inv__into(X13355,X13354,X13352,X13353),X13351))=X13351)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_f__the__inv__into__f])])])). 4.05/4.31 fof(c_0_8010, plain, ![X3414, X3415, X3416, X3417]:(~class_Lattices_Osemilattice__inf(X3417)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3417),X3416),X3415))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3417),X3416),X3414))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3417),X3416),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3417),X3415),X3414)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__greatest])])])). 4.05/4.31 fof(c_0_8011, plain, ![X5929, X5930, X5931]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5931),hAPP(c_Int_Onumber__class_Onumber__of(X5931),X5930)),hAPP(c_Int_Onumber__class_Onumber__of(X5931),X5929)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5930),X5929))|(~class_Rings_Olinordered__idom(X5931)|~class_Int_Onumber__ring(X5931)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5930),X5929))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5931),hAPP(c_Int_Onumber__class_Onumber__of(X5931),X5930)),hAPP(c_Int_Onumber__class_Onumber__of(X5931),X5929)))|(~class_Rings_Olinordered__idom(X5931)|~class_Int_Onumber__ring(X5931)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of])])])). 4.05/4.31 cnf(c_0_8012, 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_5459, c_0_5049])). 4.05/4.31 cnf(c_0_8013, 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_5460, c_0_5049])). 4.05/4.31 fof(c_0_8014, plain, ![X3330, X3331, X3332, X3333, X3334]:(~class_Orderings_Olinorder(X3334)|(~c_List_Olinorder__class_Osorted(X3334,hAPP(hAPP(c_List_Omap(X3333,X3334),X3332),X3331))|c_List_Olinorder__class_Osorted(X3334,hAPP(hAPP(c_List_Omap(X3333,X3334),X3332),c_List_Olinorder__class_Oinsort__insert__key(X3333,X3334,X3332,X3330,X3331))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__insort__insert__key])])])). 4.05/4.31 fof(c_0_8015, plain, ![X4148, X4149, X4150, X4151, X4152, X4153, X4154, X4155, X4156, X4157, X4158]:((~hBOOL(hAPP(hAPP(c_member(X4150),X4152),X4148))|hAPP(X4149,X4152)!=X4151|hBOOL(hAPP(hAPP(c_member(X4153),X4151),hAPP(c_Set_Oimage(X4150,X4153,X4149),X4148))))&((hBOOL(hAPP(hAPP(c_member(X4156),esk128_4(X4154,X4155,X4156,X4157)),X4154))|~hBOOL(hAPP(hAPP(c_member(X4158),X4157),hAPP(c_Set_Oimage(X4156,X4158,X4155),X4154))))&(hAPP(X4155,esk128_4(X4154,X4155,X4156,X4157))=X4157|~hBOOL(hAPP(hAPP(c_member(X4158),X4157),hAPP(c_Set_Oimage(X4156,X4158,X4155),X4154)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__iff])])])])])])). 4.05/4.31 fof(c_0_8016, plain, ![X15456, X15457, X15458]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15457),X15456))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15458),hAPP(c_Int_Onumber__class_Onumber__of(X15458),X15457)),hAPP(c_Int_Onumber__class_Onumber__of(X15458),X15456)))|(~class_Int_Onumber__ring(X15458)|~class_Rings_Olinordered__idom(X15458)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15458),hAPP(c_Int_Onumber__class_Onumber__of(X15458),X15457)),hAPP(c_Int_Onumber__class_Onumber__of(X15458),X15456)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15457),X15456))|(~class_Int_Onumber__ring(X15458)|~class_Rings_Olinordered__idom(X15458)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__number__of])])])])). 4.05/4.31 fof(c_0_8017, plain, ![X8648, X8649, X8650]:(~class_Orderings_Olinorder(X8650)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X8650),X8649))|(~hBOOL(hAPP(hAPP(c_member(X8650),X8648),X8649))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8650),hAPP(c_Finite__Set_Ofold1(X8650,c_Orderings_Oord__class_Omin(X8650)),X8649)),X8648))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ofold1__belowI])])])). 4.05/4.31 fof(c_0_8018, plain, ![X6578, X6579, X6580]:(~class_Lattices_Osemilattice__inf(X6580)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X6580),X6579))|(~hBOOL(hAPP(hAPP(c_member(X6580),X6578),X6579))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6580),hAPP(c_Finite__Set_Ofold1(X6580,c_Lattices_Osemilattice__inf__class_Oinf(X6580)),X6579)),X6578))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fold1__belowI])])])). 4.05/4.31 fof(c_0_8019, plain, ![X13314, X13315, X13316]:(~hBOOL(hAPP(hAPP(c_member(X13316),X13315),hAPP(c_List_Oset(X13316),X13314)))|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(X13316)),X13314)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__pos__if__in__set])])). 4.05/4.31 cnf(c_0_8020, 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_5347])). 4.05/4.31 fof(c_0_8021, plain, ![X16018, X16019, X16020]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16020,tc_HOL_Obool)),X16018),X16019))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16020,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16020,tc_HOL_Obool)),X16019)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16020,tc_HOL_Obool)),X16018))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16020,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16020,tc_HOL_Obool)),X16019)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X16020,tc_HOL_Obool)),X16018)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16020,tc_HOL_Obool)),X16018),X16019)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__subset__Compl__iff])])). 4.05/4.31 fof(c_0_8022, plain, ![X12117, X12118, X12119, X12120]:((hAPP(hAPP(c_Set_Oinsert(X12120),X12119),X12118)!=hAPP(hAPP(c_Set_Oinsert(X12120),X12119),X12117)|X12117=X12118|hBOOL(hAPP(hAPP(c_member(X12120),X12119),X12117))|hBOOL(hAPP(hAPP(c_member(X12120),X12119),X12118)))&(X12117!=X12118|hAPP(hAPP(c_Set_Oinsert(X12120),X12119),X12118)=hAPP(hAPP(c_Set_Oinsert(X12120),X12119),X12117)|hBOOL(hAPP(hAPP(c_member(X12120),X12119),X12117))|hBOOL(hAPP(hAPP(c_member(X12120),X12119),X12118)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__ident])])])])). 4.05/4.31 fof(c_0_8023, plain, ![X12143, X12144, X12145]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12145),X12144))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12143),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12144),X12143)),X12145)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__add__diff])])])). 4.05/4.31 cnf(c_0_8024, plain, (X3=hAPP(c_List_Orotate(X2,X1),X3)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_5461])). 4.05/4.31 fof(c_0_8025, plain, ![X17339, X17340, X17341, X17342, X17343]:(~c_Finite__Set_Ofolding__one__idem(X17343,X17342,X17341)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17343),X17340))|(~hBOOL(hAPP(hAPP(c_member(X17343),X17339),X17340))|hAPP(X17341,X17340)=hAPP(hAPP(X17342,X17339),hAPP(X17341,X17340))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one__idem_Oin__idem])])])). 4.05/4.31 fof(c_0_8026, plain, ![X6405, X6406, X6407]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6407),X6406))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6407),X6405)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6406),X6405)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])])). 4.05/4.31 fof(c_0_8027, plain, ![X2805, X2806, X2807]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2807),X2806))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2807),X2805)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2806),X2805)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])])). 4.05/4.31 fof(c_0_8028, plain, ![X7950, X7951, X7952]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7952),X7951)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7952),X7950)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7951),X7950)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7951),X7950))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7952),X7951)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7952),X7950))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])])). 4.05/4.31 fof(c_0_8029, plain, ![X12471, X12472, X12473]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12473),X12472))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12471),X12473)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12471),X12472)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zadd__left__mono])])])). 4.05/4.31 fof(c_0_8030, plain, ![X10487, X10488, X10489, X10490, X10491, X10492]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X10492,X10491)),hAPP(hAPP(c_Product__Type_OPair(X10492,X10491),X10490),X10489)),hAPP(hAPP(c_Product__Type_OSigma(X10492,X10491),X10488),X10487)))|hBOOL(hAPP(hAPP(c_member(X10491),X10489),hAPP(X10487,X10490)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SigmaD2])])])). 4.05/4.31 fof(c_0_8031, plain, ![X528, X529, X530, X531]:((~hBOOL(hAPP(c_List_Odistinct(X530),X528))|~c_Fun_Oinj__on(X530,X531,X529,hAPP(c_List_Oset(X530),X528))|hBOOL(hAPP(c_List_Odistinct(X531),hAPP(hAPP(c_List_Omap(X530,X531),X529),X528))))&((hBOOL(hAPP(c_List_Odistinct(X530),X528))|~hBOOL(hAPP(c_List_Odistinct(X531),hAPP(hAPP(c_List_Omap(X530,X531),X529),X528))))&(c_Fun_Oinj__on(X530,X531,X529,hAPP(c_List_Oset(X530),X528))|~hBOOL(hAPP(c_List_Odistinct(X531),hAPP(hAPP(c_List_Omap(X530,X531),X529),X528)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__map])])])). 4.05/4.31 fof(c_0_8032, plain, ![X15469, X15470, X15471, X15472, X15474]:(((c_Groups_Ozero__class_Ozero(X15472)=hAPP(X15469,esk467_4(X15469,X15470,X15471,X15472))|c_Groups_Ozero__class_Ozero(X15472)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X15471,X15472),X15469),X15470)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15471),X15470))|(~class_Rings_Ono__zero__divisors(X15472)|~class_Rings_Ocomm__semiring__1(X15472)))&(hBOOL(hAPP(hAPP(c_member(X15471),esk467_4(X15469,X15470,X15471,X15472)),X15470))|c_Groups_Ozero__class_Ozero(X15472)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X15471,X15472),X15469),X15470)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15471),X15470))|(~class_Rings_Ono__zero__divisors(X15472)|~class_Rings_Ocomm__semiring__1(X15472))))&(c_Groups_Ozero__class_Ozero(X15472)!=hAPP(X15469,X15474)|~hBOOL(hAPP(hAPP(c_member(X15471),X15474),X15470))|c_Groups_Ozero__class_Ozero(X15472)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X15471,X15472),X15469),X15470)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X15471),X15470))|(~class_Rings_Ono__zero__divisors(X15472)|~class_Rings_Ocomm__semiring__1(X15472)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__zero__iff])])])])])])). 4.05/4.31 cnf(c_0_8033, 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_5462])). 4.05/4.31 fof(c_0_8034, plain, ![X15135, X15136, X15137]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15137),X15136))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15137),X15135)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15136),X15135)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__le__mono])])])). 4.05/4.31 fof(c_0_8035, plain, ![X11142, X11143, X11144]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11144),X11143))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11142),X11143)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11142),X11144)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__le__mono2])])])). 4.05/4.31 fof(c_0_8036, plain, ![X2618, X2619, X2620, X2621, X2622]:((c_List_Olist_ONil(tc_List_Olist(X2619))!=c_List_Otranspose(X2619,X2618)|(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2619)),X2620),hAPP(c_List_Oset(tc_List_Olist(X2619)),X2618)))|c_List_Olist_ONil(X2619)=X2620))&((hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2622)),esk91_2(X2621,X2622)),hAPP(c_List_Oset(tc_List_Olist(X2622)),X2621)))|c_List_Olist_ONil(tc_List_Olist(X2622))=c_List_Otranspose(X2622,X2621))&(c_List_Olist_ONil(X2622)!=esk91_2(X2621,X2622)|c_List_Olist_ONil(tc_List_Olist(X2622))=c_List_Otranspose(X2622,X2621)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_transpose__empty])])])])])])])). 4.05/4.31 fof(c_0_8037, plain, ![X15837, X15838, X15839, X15840]:(~c_Map_Omap__le(X15840,X15839,X15838,X15837)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15840,tc_HOL_Obool)),c_Map_Odom(X15840,X15839,X15838)),c_Map_Odom(X15840,X15839,X15837)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__le__implies__dom__le])])). 4.05/4.31 fof(c_0_8038, plain, ![X3022, X3023, X3024, X3025, X3026]:(~class_Orderings_Olinorder(X3026)|hAPP(hAPP(c_Set_Oinsert(X3025),X3023),hAPP(c_List_Oset(X3025),X3022))=hAPP(c_List_Oset(X3025),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3025,X3026,X3024),X3023),X3022))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__insort])])])). 4.05/4.31 fof(c_0_8039, plain, ![X5513, X5514, X5515]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5515),X5514))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5513),X5515)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5513),X5514)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__le__mono2])])])). 4.05/4.31 fof(c_0_8040, plain, ![X11672, X11673, X11674]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11674),X11673))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11674),X11672)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11673),X11672)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])])). 4.05/4.31 fof(c_0_8041, plain, ![X5177, X5178, X5179]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5179),X5178)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5179),X5177)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5178),X5177)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5178),X5177))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5179),X5178)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5179),X5177))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])])). 4.05/4.31 fof(c_0_8042, plain, ![X10747, X10748, X10749]:((hBOOL(hAPP(hAPP(c_member(X10749),X10748),hAPP(c_List_Oset(X10749),X10747)))|c_List_Oinsert(X10749,X10748,X10747)=hAPP(hAPP(c_List_Olist_OCons(X10749),X10748),X10747))&(~hBOOL(hAPP(hAPP(c_member(X10749),X10748),hAPP(c_List_Oset(X10749),X10747)))|X10747=c_List_Oinsert(X10749,X10748,X10747))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_List_Oinsert__def])])])). 4.05/4.31 fof(c_0_8043, plain, ![X7300, X7301, X7302, X7303]:(~c_Wellfounded_Owf(X7303,X7302)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X7303,X7303)),hAPP(hAPP(c_Product__Type_OPair(X7303,X7303),X7301),X7300)),X7302))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X7303,X7303)),hAPP(hAPP(c_Product__Type_OPair(X7303,X7303),X7300),X7301)),X7302)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__asym])])])). 4.05/4.31 fof(c_0_8044, plain, ![X4976, X4977, X4978]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4978),X4977))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X4978),X4976)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X4977),X4976)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono])])). 4.05/4.31 cnf(c_0_8045, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5463])). 4.05/4.31 cnf(c_0_8046, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=hAPP(hAPP(c_Power_Opower__class_Opower(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_5381])). 4.05/4.31 fof(c_0_8047, plain, ![X9060, X9061, X9062, X9063, X9064]:(~c_Relation_Orefl__on(X9064,X9063,X9062)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X9064,X9064)),hAPP(hAPP(c_Product__Type_OPair(X9064,X9064),X9061),X9060)),X9062))|hBOOL(hAPP(hAPP(c_member(X9064),X9061),X9063)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__onD1])])])). 4.05/4.31 fof(c_0_8048, plain, ![X7500, X7501, X7502, X7503, X7504]:(~c_Relation_Orefl__on(X7504,X7503,X7502)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X7504,X7504)),hAPP(hAPP(c_Product__Type_OPair(X7504,X7504),X7501),X7500)),X7502))|hBOOL(hAPP(hAPP(c_member(X7504),X7500),X7503)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_refl__onD2])])])). 4.05/4.31 cnf(c_0_8049, 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_5332])). 4.05/4.31 fof(c_0_8050, plain, ![X11783, X11784, X11785]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11785),X11784),X11783))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11785),hAPP(c_Groups_Ouminus__class_Ouminus(X11785),X11784)),X11783))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11785),hAPP(c_Groups_Oabs__class_Oabs(X11785),X11784)),X11783))|~class_Rings_Olinordered__idom(X11785))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11785),X11784),X11783))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11785),hAPP(c_Groups_Oabs__class_Oabs(X11785),X11784)),X11783))|~class_Rings_Olinordered__idom(X11785))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11785),hAPP(c_Groups_Ouminus__class_Ouminus(X11785),X11784)),X11783))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11785),hAPP(c_Groups_Oabs__class_Oabs(X11785),X11784)),X11783))|~class_Rings_Olinordered__idom(X11785)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__less__iff])])])). 4.05/4.31 fof(c_0_8051, plain, ![X4881, X4882, X4883]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4883),X4882),X4881))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4883),hAPP(c_Groups_Ouminus__class_Ouminus(X4883),X4882)),X4881))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4883),hAPP(c_Groups_Oabs__class_Oabs(X4883),X4882)),X4881))|~class_Groups_Oordered__ab__group__add__abs(X4883))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4883),X4882),X4881))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4883),hAPP(c_Groups_Oabs__class_Oabs(X4883),X4882)),X4881))|~class_Groups_Oordered__ab__group__add__abs(X4883))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4883),hAPP(c_Groups_Ouminus__class_Ouminus(X4883),X4882)),X4881))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4883),hAPP(c_Groups_Oabs__class_Oabs(X4883),X4882)),X4881))|~class_Groups_Oordered__ab__group__add__abs(X4883)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__iff])])])). 4.05/4.31 cnf(c_0_8052, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_5300])). 4.05/4.31 fof(c_0_8053, plain, ![X15606, X15607, X15608, X15609, X15611, X15612, X15613, X15614, X15615]:(((hBOOL(hAPP(hAPP(c_member(X15609),esk471_4(X15606,X15607,X15608,X15609)),c_Map_Odom(X15609,X15608,X15607)))|c_Map_Omap__le(X15609,X15608,X15607,X15606))&(hAPP(X15606,esk471_4(X15606,X15607,X15608,X15609))!=hAPP(X15607,esk471_4(X15606,X15607,X15608,X15609))|c_Map_Omap__le(X15609,X15608,X15607,X15606)))&(~c_Map_Omap__le(X15614,X15613,X15612,X15611)|(~hBOOL(hAPP(hAPP(c_member(X15614),X15615),c_Map_Odom(X15614,X15613,X15612)))|hAPP(X15611,X15615)=hAPP(X15612,X15615)))), 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_map__le__def])])])])])])])). 4.05/4.31 fof(c_0_8054, plain, ![X8682, X8683, X8684, X8685, X8686, X8687]:(((c_Option_Ooption_ONone(X8686)!=hAPP(X8684,X8683)|hAPP(c_Option_Ooption_OSome(X8686),X8682)!=hAPP(X8685,X8683)|hAPP(c_Option_Ooption_OSome(X8686),X8682)=hAPP(c_Map_Omap__add(X8687,X8686,X8685,X8684),X8683))&(hAPP(c_Option_Ooption_OSome(X8686),X8682)!=hAPP(X8684,X8683)|hAPP(c_Option_Ooption_OSome(X8686),X8682)=hAPP(c_Map_Omap__add(X8687,X8686,X8685,X8684),X8683)))&((c_Option_Ooption_ONone(X8686)=hAPP(X8684,X8683)|hAPP(c_Option_Ooption_OSome(X8686),X8682)=hAPP(X8684,X8683)|hAPP(c_Option_Ooption_OSome(X8686),X8682)!=hAPP(c_Map_Omap__add(X8687,X8686,X8685,X8684),X8683))&(hAPP(c_Option_Ooption_OSome(X8686),X8682)=hAPP(X8685,X8683)|hAPP(c_Option_Ooption_OSome(X8686),X8682)=hAPP(X8684,X8683)|hAPP(c_Option_Ooption_OSome(X8686),X8682)!=hAPP(c_Map_Omap__add(X8687,X8686,X8685,X8684),X8683)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__Some__iff])])])). 4.05/4.31 fof(c_0_8055, plain, ![X10663, X10664, X10665, X10666]:(((c_Groups_Ozero__class_Ozero(X10666)=X10663|X10664=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10666),hAPP(c_Int_Onumber__class_Onumber__of(X10666),X10665)),X10663)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10666),X10664),X10663)!=hAPP(c_Int_Onumber__class_Onumber__of(X10666),X10665)|(~class_Fields_Ofield__inverse__zero(X10666)|~class_Int_Onumber(X10666)))&(X10663!=c_Groups_Ozero__class_Ozero(X10666)|hAPP(c_Int_Onumber__class_Onumber__of(X10666),X10665)=c_Groups_Ozero__class_Ozero(X10666)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10666),X10664),X10663)!=hAPP(c_Int_Onumber__class_Onumber__of(X10666),X10665)|(~class_Fields_Ofield__inverse__zero(X10666)|~class_Int_Onumber(X10666))))&(((X10663=c_Groups_Ozero__class_Ozero(X10666)|c_Groups_Ozero__class_Ozero(X10666)!=X10663|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10666),X10664),X10663)=hAPP(c_Int_Onumber__class_Onumber__of(X10666),X10665)|(~class_Fields_Ofield__inverse__zero(X10666)|~class_Int_Onumber(X10666)))&(hAPP(c_Int_Onumber__class_Onumber__of(X10666),X10665)!=c_Groups_Ozero__class_Ozero(X10666)|c_Groups_Ozero__class_Ozero(X10666)!=X10663|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10666),X10664),X10663)=hAPP(c_Int_Onumber__class_Onumber__of(X10666),X10665)|(~class_Fields_Ofield__inverse__zero(X10666)|~class_Int_Onumber(X10666))))&((X10663=c_Groups_Ozero__class_Ozero(X10666)|X10664!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10666),hAPP(c_Int_Onumber__class_Onumber__of(X10666),X10665)),X10663)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10666),X10664),X10663)=hAPP(c_Int_Onumber__class_Onumber__of(X10666),X10665)|(~class_Fields_Ofield__inverse__zero(X10666)|~class_Int_Onumber(X10666)))&(hAPP(c_Int_Onumber__class_Onumber__of(X10666),X10665)!=c_Groups_Ozero__class_Ozero(X10666)|X10664!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10666),hAPP(c_Int_Onumber__class_Onumber__of(X10666),X10665)),X10663)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10666),X10664),X10663)=hAPP(c_Int_Onumber__class_Onumber__of(X10666),X10665)|(~class_Fields_Ofield__inverse__zero(X10666)|~class_Int_Onumber(X10666)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__divide__eq__number__of])])])])). 4.05/4.31 fof(c_0_8056, plain, ![X7156, X7157, X7158, X7159, X7160]:((~c_Nitpick_Orefl_H(X7157,X7156)|hBOOL(hAPP(hAPP(c_member(tc_prod(X7157,X7157)),hAPP(hAPP(c_Product__Type_OPair(X7157,X7157),X7158),X7158)),X7156)))&(~hBOOL(hAPP(hAPP(c_member(tc_prod(X7160,X7160)),hAPP(hAPP(c_Product__Type_OPair(X7160,X7160),esk221_2(X7159,X7160)),esk221_2(X7159,X7160))),X7159))|c_Nitpick_Orefl_H(X7160,X7159))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Orefl_H__def])])])])])). 4.05/4.31 cnf(c_0_8057, 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_5464])). 4.05/4.31 cnf(c_0_8058, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_5465, c_0_4475])). 4.05/4.31 fof(c_0_8059, plain, ![X17487, X17488, X17489, X17490]:(~c_Fun_Oinj__on(X17490,X17489,X17488,X17487)|X17487=hAPP(c_Set_Oimage(X17489,X17490,c_Fun_Othe__inv__into(X17490,X17489,X17487,X17488)),hAPP(c_Set_Oimage(X17490,X17489,X17488),X17487))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__onto])])). 4.05/4.31 fof(c_0_8060, plain, ![X13558, X13559, X13560]:(~class_Groups_Oordered__ab__group__add(X13560)|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X13560,hAPP(c_Groups_Ouminus__class_Ouminus(X13560),X13558)),hAPP(c_Groups_Ouminus__class_Ouminus(X13560),X13559))=hAPP(c_Set_Oimage(X13560,X13560,c_Groups_Ouminus__class_Ouminus(X13560)),c_SetInterval_Oord__class_OgreaterThanAtMost(X13560,X13559,X13558))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__uminus__greaterThanAtMost])])])). 4.05/4.31 cnf(c_0_8061, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_member(X2),X4),X3))|hAPP(c_Nat_OSuc,X1)=hAPP(c_Finite__Set_Ocard(X2),X5)|hAPP(c_Finite__Set_Ocard(X2),X3)!=X1|X5!=hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_5466])). 4.05/4.31 fof(c_0_8062, plain, ![X10544, X10545, X10546, X10547]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10546),c_Complete__Lattice_OSup__class_OSup(X10546,X10545)),X10544))|(~hBOOL(hAPP(hAPP(c_member(X10546),X10547),X10545))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10546),X10547),X10544)))|~class_Complete__Lattice_Ocomplete__lattice(X10546))&((hBOOL(hAPP(hAPP(c_member(X10546),esk320_3(X10544,X10545,X10546)),X10545))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10546),c_Complete__Lattice_OSup__class_OSup(X10546,X10545)),X10544))|~class_Complete__Lattice_Ocomplete__lattice(X10546))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10546),esk320_3(X10544,X10545,X10546)),X10544))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10546),c_Complete__Lattice_OSup__class_OSup(X10546,X10545)),X10544))|~class_Complete__Lattice_Ocomplete__lattice(X10546)))), 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])])])])])). 4.05/4.31 fof(c_0_8063, plain, ![X7308, X7309, X7310, X7311]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7310),X7309),c_Complete__Lattice_OInf__class_OInf(X7310,X7308)))|(~hBOOL(hAPP(hAPP(c_member(X7310),X7311),X7308))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7310),X7309),X7311)))|~class_Complete__Lattice_Ocomplete__lattice(X7310))&((hBOOL(hAPP(hAPP(c_member(X7310),esk229_3(X7308,X7309,X7310)),X7308))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7310),X7309),c_Complete__Lattice_OInf__class_OInf(X7310,X7308)))|~class_Complete__Lattice_Ocomplete__lattice(X7310))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7310),X7309),esk229_3(X7308,X7309,X7310)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7310),X7309),c_Complete__Lattice_OInf__class_OInf(X7310,X7308)))|~class_Complete__Lattice_Ocomplete__lattice(X7310)))), 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__Inf__iff])])])])])). 4.05/4.31 fof(c_0_8064, plain, ![X13326, X13327]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13327),X13326))|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),X13327),X13326)),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),X13327),X13326)),c_Wellfounded_Oless__than))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13327),X13326)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__than__iff])])). 4.05/4.31 fof(c_0_8065, plain, ![X8865, X8866, X8867]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk280_3(X8865,X8866,X8867)),X8867))|(~hBOOL(hAPP(X8866,X8865))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8865),X8867))|hBOOL(hAPP(X8866,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))&((hBOOL(hAPP(X8866,esk280_3(X8865,X8866,X8867)))|(~hBOOL(hAPP(X8866,X8865))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8865),X8867))|hBOOL(hAPP(X8866,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))&(~hBOOL(hAPP(X8866,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk280_3(X8865,X8866,X8867)),X8867)))|(~hBOOL(hAPP(X8866,X8865))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8865),X8867))|hBOOL(hAPP(X8866,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__induct__0])])])])])). 4.05/4.31 fof(c_0_8066, plain, ![X12921, X12922, X12923, X12924, X12925, X12926, X12927, X12929, X12930, X12931, X12932, X12933, X12934, X12935, X12936]:(((hBOOL(hAPP(hAPP(X12923,esk395_4(X12921,X12922,X12923,X12924)),X12921))|~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X12927,X12926,X12925,X12924,X12923),X12922),X12921)))&(hBOOL(hAPP(hAPP(X12924,X12922),esk395_4(X12921,X12922,X12923,X12924)))|~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X12927,X12926,X12925,X12924,X12923),X12922),X12921))))&(~hBOOL(hAPP(hAPP(X12931,X12933),X12929))|~hBOOL(hAPP(hAPP(X12932,X12930),X12933))|hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X12936,X12935,X12934,X12932,X12931),X12930),X12929)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__comp_Oequations])])])])])])). 4.05/4.31 fof(c_0_8067, plain, ![X11535, X11536, X11537, X11538, X11539]:((X11535=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11539)),X11538)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X11539),tc_List_Olist(X11539))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X11539),tc_List_Olist(X11539)),X11538),X11537)),hAPP(c_List_Olexn(X11539,X11536),X11535))))&(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11539)),X11537)=X11535|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X11539),tc_List_Olist(X11539))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X11539),tc_List_Olist(X11539)),X11538),X11537)),hAPP(c_List_Olexn(X11539,X11536),X11535))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lexn__length])])])])). 4.05/4.31 fof(c_0_8068, plain, ![X12149]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X12149|hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12149),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])])])). 4.05/4.31 fof(c_0_8069, plain, ![X13527, X13528, X13529]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13529))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X13529),X13528)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X13529),X13527)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13528),X13527)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__power__less__imp__less])])])). 4.05/4.31 fof(c_0_8070, plain, ![X11620, X11621, X11622, X11623, X11624]:(~class_Orderings_Olinorder(X11624)|(~c_List_Olinorder__class_Osorted(X11624,hAPP(hAPP(c_List_Omap(X11623,X11624),X11622),X11621))|c_List_Olinorder__class_Osorted(X11624,hAPP(hAPP(c_List_Omap(X11623,X11624),X11622),hAPP(c_List_Ofilter(X11623,X11620),X11621))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__filter])])])). 4.05/4.31 cnf(c_0_8071, 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_5290])). 4.05/4.31 cnf(c_0_8072, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X2),X3)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|X1!=esk24_4(X2,X3,X4,X1)|~hBOOL(hAPP(hAPP(c_member(X4),X1),X3))|hAPP(X2,X1)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_5275])). 4.05/4.31 fof(c_0_8073, plain, ![X4125, X4126]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4126))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4125))|hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X4126,X4125))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X4126,X4125))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos])])). 4.05/4.31 fof(c_0_8074, plain, ![X11708, X11709]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11709),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)),X11708))|hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X11709,X11708))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X11709,X11708))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__neg__pos])])])). 4.05/4.31 fof(c_0_8075, plain, ![X1330, X1331, X1332, X1333, X1334, X1335, X1336]:((~c_List_Olist__all(X1332,X1331,X1330)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1333),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1332)),X1330)))|hBOOL(hAPP(X1331,hAPP(hAPP(c_List_Onth(X1332),X1330),X1333)))))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk36_3(X1334,X1335,X1336)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1336)),X1334)))|c_List_Olist__all(X1336,X1335,X1334))&(~hBOOL(hAPP(X1335,hAPP(hAPP(c_List_Onth(X1336),X1334),esk36_3(X1334,X1335,X1336))))|c_List_Olist__all(X1336,X1335,X1334)))), 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__length])])])])])])])). 4.05/4.31 fof(c_0_8076, plain, ![X6885, X6886, X6887]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6887),X6886))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6887),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6886),X6885)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_start__le__sum])])). 4.05/4.31 cnf(c_0_8077, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_4966])). 4.05/4.31 cnf(c_0_8078, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_5325])). 4.05/4.31 fof(c_0_8079, plain, ![X15589, X15590, X15591, X15592]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15592,tc_HOL_Obool)),X15591),X15590))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15592,tc_HOL_Obool)),X15591),hAPP(hAPP(c_Set_Oinsert(X15592),X15589),X15590)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_subset__insertI2])])])). 4.05/4.31 fof(c_0_8080, plain, ![X2477, X2478, X2479, X2480, X2481, X2482, X2483]:((hAPP(c_List_Ofilter(X2479,X2478),X2477)!=c_List_Olist_ONil(X2479)|(~hBOOL(hAPP(hAPP(c_member(X2479),X2480),hAPP(c_List_Oset(X2479),X2477)))|~hBOOL(hAPP(X2478,X2480))))&((hBOOL(hAPP(hAPP(c_member(X2483),esk88_3(X2481,X2482,X2483)),hAPP(c_List_Oset(X2483),X2481)))|hAPP(c_List_Ofilter(X2483,X2482),X2481)=c_List_Olist_ONil(X2483))&(hBOOL(hAPP(X2482,esk88_3(X2481,X2482,X2483)))|hAPP(c_List_Ofilter(X2483,X2482),X2481)=c_List_Olist_ONil(X2483)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__empty__conv])])])])])])])). 4.05/4.31 fof(c_0_8081, plain, ![X7855, X7856, X7857, X7858]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7858),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7857)),X7856)))|X7855=hAPP(hAPP(c_List_Onth(X7857),hAPP(hAPP(c_List_Olist__update(X7857,X7856),X7858),X7855)),X7858)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update__eq])])). 4.05/4.31 fof(c_0_8082, plain, ![X15616, X15617, X15618, X15619, X15620]:(hAPP(X15620,X15619)!=hAPP(c_Option_Ooption_OSome(X15618),X15617)|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X15616,tc_Option_Ooption(X15618)),X15620),X15619),hAPP(c_Option_Ooption_OSome(X15618),X15617))=X15620), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__upd__triv])])])). 4.05/4.31 fof(c_0_8083, plain, ![X7050, X7051, X7052, X7053]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7053),X7052),X7050))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7053),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7053),X7052),X7051)),X7050))|~class_Orderings_Olinorder(X7053))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7053),X7051),X7050))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7053),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7053),X7052),X7051)),X7050))|~class_Orderings_Olinorder(X7053)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7053),X7052),X7050))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7053),X7051),X7050))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7053),hAPP(hAPP(c_Orderings_Oord__class_Omax(X7053),X7052),X7051)),X7050))|~class_Orderings_Olinorder(X7053))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__less__iff__conj])])])). 4.05/4.31 fof(c_0_8084, plain, ![X6436, X6437]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk192_2(X6436,X6437)),esk193_2(X6436,X6437)))|c_List_Olinorder__class_Osorted(X6437,X6436)|~class_Orderings_Olinorder(X6437))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk193_2(X6436,X6437)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6437)),X6436)))|c_List_Olinorder__class_Osorted(X6437,X6436)|~class_Orderings_Olinorder(X6437))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6437),hAPP(hAPP(c_List_Onth(X6437),X6436),esk192_2(X6436,X6437))),hAPP(hAPP(c_List_Onth(X6437),X6436),esk193_2(X6436,X6437))))|c_List_Olinorder__class_Osorted(X6437,X6436)|~class_Orderings_Olinorder(X6437)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__nth__monoI])])])])])). 4.05/4.31 fof(c_0_8085, plain, ![X6947, X6948, X6949]:((hBOOL(hAPP(hAPP(c_member(X6949),X6948),esk217_3(X6947,X6948,X6949)))|~hBOOL(hAPP(hAPP(c_member(X6949),X6948),c_Complete__Lattice_OSup__class_OSup(tc_fun(X6949,tc_HOL_Obool),X6947))))&(hBOOL(hAPP(hAPP(c_member(tc_fun(X6949,tc_HOL_Obool)),esk217_3(X6947,X6948,X6949)),X6947))|~hBOOL(hAPP(hAPP(c_member(X6949),X6948),c_Complete__Lattice_OSup__class_OSup(tc_fun(X6949,tc_HOL_Obool),X6947))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UnionE])])])])])). 4.05/4.31 cnf(c_0_8086, 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_5467])). 4.05/4.31 cnf(c_0_8087, 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_5468])). 4.05/4.31 fof(c_0_8088, plain, ![X5768, X5769, X5770, X5771]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5771),X5769),X5768))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5771),X5770),X5768))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5771),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5771),X5770),X5769)),X5768))|~class_Orderings_Olinorder(X5771))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5771),X5769),X5768))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5771),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5771),X5770),X5769)),X5768))|~class_Orderings_Olinorder(X5771))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5771),X5770),X5768))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5771),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5771),X5770),X5769)),X5768))|~class_Orderings_Olinorder(X5771)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__sup__iff])])])). 4.05/4.31 fof(c_0_8089, plain, ![X11432, X11433, X11434, X11435]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11435),X11434),X11433))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11435),X11434),X11432))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11435),X11434),hAPP(hAPP(c_Orderings_Oord__class_Omin(X11435),X11433),X11432)))|~class_Orderings_Olinorder(X11435))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11435),X11434),X11433))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11435),X11434),hAPP(hAPP(c_Orderings_Oord__class_Omin(X11435),X11433),X11432)))|~class_Orderings_Olinorder(X11435))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11435),X11434),X11432))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11435),X11434),hAPP(hAPP(c_Orderings_Oord__class_Omin(X11435),X11433),X11432)))|~class_Orderings_Olinorder(X11435)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__less__iff__conj])])])])). 4.05/4.31 cnf(c_0_8090, 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_5469])). 4.05/4.31 cnf(c_0_8091, 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_5470])). 4.05/4.31 fof(c_0_8092, plain, ![X7366, X7367, X7368, X7369]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7369)|hAPP(hAPP(c_List_Otake(X7368),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7369)),hAPP(hAPP(c_List_Olist_OCons(X7368),X7367),X7366))=c_List_Olist_ONil(X7368))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7369)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Otake(X7368),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7369)),hAPP(hAPP(c_List_Olist_OCons(X7368),X7367),X7366))=hAPP(hAPP(c_List_Olist_OCons(X7368),X7367),hAPP(hAPP(c_List_Otake(X7368),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7369)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X7366)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_take__Cons__number__of])])])). 4.05/4.31 fof(c_0_8093, plain, ![X5420, X5421, X5422, X5423]:(~class_Orderings_Olinorder(X5423)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5423),X5422),X5421))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5423),X5422),X5420))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5423),X5422),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5423),X5421),X5420)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ole__infI])])])). 4.05/4.31 fof(c_0_8094, plain, ![X4671, X4672]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4672))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X4671))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4672),X4671)),X4672)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__div__less__self])])). 4.05/4.31 fof(c_0_8095, plain, ![X14020, X14021]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14021))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14020))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14020),X14021)),X14020)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less])])). 4.05/4.31 fof(c_0_8096, plain, ![X10966, X10967, X10968]:(~class_Groups_Oordered__ab__group__add__abs(X10968)|hAPP(c_Groups_Oabs__class_Oabs(X10968),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10968),X10966),X10967))=hAPP(c_Groups_Oabs__class_Oabs(X10968),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10968),X10967),X10966))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__minus__commute])])])). 4.05/4.31 fof(c_0_8097, plain, ![X10568, X10569]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X10569))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10568))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X10568),X10569)),X10568)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less__dividend])])). 4.05/4.31 fof(c_0_8098, plain, ![X2171, X2172, X2173]:(~class_Rings_Olinordered__semiring__strict(X2173)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2173),c_Groups_Ozero__class_Ozero(X2173)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2173),X2172),X2171)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2173),c_Groups_Ozero__class_Ozero(X2173)),X2171))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2173),c_Groups_Ozero__class_Ozero(X2173)),X2172))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__mult__pos2])])])). 4.05/4.31 fof(c_0_8099, plain, ![X4332, X4333, X4334]:(~class_Rings_Olinordered__semiring__strict(X4334)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4334),c_Groups_Ozero__class_Ozero(X4334)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4334),X4333),X4332)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4334),c_Groups_Ozero__class_Ozero(X4334)),X4333))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4334),c_Groups_Ozero__class_Ozero(X4334)),X4332))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__mult__pos])])])). 4.05/4.31 fof(c_0_8100, plain, ![X4635, X4636, X4637]:(~class_Rings_Oring__1(X4637)|hAPP(c_Int_Oring__1__class_Oof__int(X4637),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4636),X4635))=hAPP(hAPP(c_Power_Opower__class_Opower(X4637),hAPP(c_Int_Oring__1__class_Oof__int(X4637),X4636)),X4635)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__power])])])). 4.05/4.31 fof(c_0_8101, plain, ![X7418, X7419, X7420]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7419),X7420))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X7419,tc_HOL_Obool)),X7420),X7418))|hBOOL(hAPP(c_Finite__Set_Ofinite(X7419),c_Complete__Lattice_OInf__class_OInf(tc_fun(X7419,tc_HOL_Obool),X7418)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Inter])])])])). 4.05/4.31 fof(c_0_8102, plain, ![X15785, X15786, X15787]:(~class_Rings_Osemiring__1(X15787)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15787),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15786),X15785))=hAPP(hAPP(c_Power_Opower__class_Opower(X15787),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15787),X15786)),X15785)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__power])])). 4.05/4.31 fof(c_0_8103, plain, ![X16767, X16768, X16769, X16770, X16771, X16772]:((~c_Fun_Oinj__on(X16772,X16768,hAPP(c_Fun_Ocomp(X16771,X16768,X16772,X16767),X16770),X16769)|c_Fun_Oinj__on(X16771,X16768,X16767,hAPP(c_Set_Oimage(X16772,X16771,X16770),X16769))|~c_Fun_Oinj__on(X16772,X16771,X16770,X16769))&(~c_Fun_Oinj__on(X16771,X16768,X16767,hAPP(c_Set_Oimage(X16772,X16771,X16770),X16769))|c_Fun_Oinj__on(X16772,X16768,hAPP(c_Fun_Ocomp(X16771,X16768,X16772,X16767),X16770),X16769)|~c_Fun_Oinj__on(X16772,X16771,X16770,X16769))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comp__inj__on__iff])])])])). 4.05/4.31 fof(c_0_8104, plain, ![X2278, X2279]:(~class_Complete__Lattice_Ocomplete__lattice(X2279)|hAPP(c_List_Ofoldl(X2279,X2279,c_Lattices_Osemilattice__sup__class_Osup(X2279),c_Orderings_Obot__class_Obot(X2279)),X2278)=c_Complete__Lattice_OSup__class_OSup(X2279,hAPP(c_List_Oset(X2279),X2278))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__set__fold])])). 4.05/4.31 cnf(c_0_8105, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|X2=X1|hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)), inference(split_conjunct,[status(thm)],[c_0_5380])). 4.05/4.31 fof(c_0_8106, plain, ![X14080, X14081]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14081),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14081),X14080),X14080)),c_Groups_Ozero__class_Ozero(X14081)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14081),X14080),c_Groups_Ozero__class_Ozero(X14081)))|~class_Groups_Olinordered__ab__group__add(X14081))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14081),X14080),c_Groups_Ozero__class_Ozero(X14081)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14081),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14081),X14080),X14080)),c_Groups_Ozero__class_Ozero(X14081)))|~class_Groups_Olinordered__ab__group__add(X14081))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero])])])). 4.05/4.31 fof(c_0_8107, plain, ![X14063, X14064]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14064),X14063),c_Groups_Ozero__class_Ozero(X14064)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14064),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14064),X14063),X14063)),c_Groups_Ozero__class_Ozero(X14064)))|~class_Rings_Olinordered__idom(X14064))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14064),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14064),X14063),X14063)),c_Groups_Ozero__class_Ozero(X14064)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14064),X14063),c_Groups_Ozero__class_Ozero(X14064)))|~class_Rings_Olinordered__idom(X14064))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_even__less__0__iff])])])])). 4.05/4.31 fof(c_0_8108, plain, ![X15682, X15683]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15683),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15683),X15682),X15682)),c_Groups_Ozero__class_Ozero(X15683)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15683),X15682),c_Groups_Ozero__class_Ozero(X15683)))|~class_Groups_Olinordered__ab__group__add(X15683))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15683),X15682),c_Groups_Ozero__class_Ozero(X15683)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15683),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15683),X15682),X15682)),c_Groups_Ozero__class_Ozero(X15683)))|~class_Groups_Olinordered__ab__group__add(X15683))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero])])])])). 4.05/4.31 fof(c_0_8109, plain, ![X1600, X1601]:(~class_Groups_Ocomm__monoid__add(X1601)|(~hBOOL(hAPP(c_List_Odistinct(X1601),X1600))|hAPP(c_List_Omonoid__add__class_Olistsum(X1601),X1600)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1601,X1601),c_COMBI(X1601)),hAPP(c_List_Oset(X1601),X1600)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__listsum__conv__Setsum])])])). 4.05/4.31 fof(c_0_8110, plain, ![X11995, X11996, X11997]:(~class_Rings_Olinordered__semidom(X11997)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11997),c_Groups_Ozero__class_Ozero(X11997)),X11996))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11997),c_Groups_Ozero__class_Ozero(X11997)),hAPP(hAPP(c_Power_Opower__class_Opower(X11997),X11996),X11995))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])])). 4.05/4.31 fof(c_0_8111, plain, ![X15781, X15782]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15782),c_Groups_Ozero__class_Ozero(X15782)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15782),X15781),X15781)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15782),c_Groups_Ozero__class_Ozero(X15782)),X15781))|~class_Groups_Olinordered__ab__group__add(X15782))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15782),c_Groups_Ozero__class_Ozero(X15782)),X15781))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15782),c_Groups_Ozero__class_Ozero(X15782)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15782),X15781),X15781)))|~class_Groups_Olinordered__ab__group__add(X15782))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add])])])])). 4.05/4.31 fof(c_0_8112, plain, ![X15197, X15198, X15199]:(~class_Rings_Olinordered__semidom(X15199)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15199),c_Groups_Ozero__class_Ozero(X15199)),X15198))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15199),c_Groups_Ozero__class_Ozero(X15199)),hAPP(hAPP(c_Power_Opower__class_Opower(X15199),X15198),X15197))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__power])])])). 4.05/4.31 fof(c_0_8113, plain, ![X3785, X3786]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3786),c_Groups_Ozero__class_Ozero(X3786)),X3785))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3786),c_Groups_Ozero__class_Ozero(X3786)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3786),X3785),X3785)))|~class_Groups_Olinordered__ab__group__add(X3786))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3786),c_Groups_Ozero__class_Ozero(X3786)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3786),X3785),X3785)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3786),c_Groups_Ozero__class_Ozero(X3786)),X3785))|~class_Groups_Olinordered__ab__group__add(X3786))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__double__add__iff__zero__le__single__add])])])). 4.05/4.31 fof(c_0_8114, plain, ![X7880, X7881, X7882, X7883, X7885]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7883),hAPP(X7881,esk251_4(X7880,X7881,X7882,X7883))),hAPP(X7880,esk251_4(X7880,X7881,X7882,X7883))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7882,X7883)),X7881),X7880))|~class_Orderings_Oord(X7883))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7882,X7883)),X7881),X7880))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7883),hAPP(X7881,X7885)),hAPP(X7880,X7885)))|~class_Orderings_Oord(X7883))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__fun__def])])])])])])). 4.05/4.31 fof(c_0_8115, plain, ![X11643, X11644, X11645, X11646, X11647, X11648]:(~c_Equiv__Relations_Ocongruent(X11648,X11647,X11646,X11645)|(~hBOOL(hAPP(hAPP(c_member(tc_prod(X11648,X11648)),hAPP(hAPP(c_Product__Type_OPair(X11648,X11648),X11644),X11643)),X11646))|hAPP(X11645,X11644)=hAPP(X11645,X11643))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_congruentD])])])). 4.05/4.31 fof(c_0_8116, plain, ![X15684, X15685, X15686]:(~class_Rings_Olinordered__semidom(X15686)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15686),c_Groups_Oone__class_Oone(X15686)),X15685))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15686),c_Groups_Oone__class_Oone(X15686)),hAPP(hAPP(c_Power_Opower__class_Opower(X15686),X15685),X15684))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])])). 4.05/4.31 cnf(c_0_8117, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5471])). 4.05/4.31 cnf(c_0_8118, 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_5472])). 4.05/4.31 fof(c_0_8119, plain, ![X1904, X1905, X1906, X1908, X1909, X1910, X1911]:(((hBOOL(hAPP(hAPP(c_member(X1906),esk67_3(X1904,X1905,X1906)),hAPP(c_List_Oset(X1906),X1904)))|hBOOL(hAPP(c_List_Olistsp(X1906,X1905),X1904)))&(~hBOOL(hAPP(X1905,esk67_3(X1904,X1905,X1906)))|hBOOL(hAPP(c_List_Olistsp(X1906,X1905),X1904))))&(~hBOOL(hAPP(c_List_Olistsp(X1910,X1909),X1908))|(~hBOOL(hAPP(hAPP(c_member(X1910),X1911),hAPP(c_List_Oset(X1910),X1908)))|hBOOL(hAPP(X1909,X1911))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__listsp__conv__set])])])])])])). 4.05/4.31 fof(c_0_8120, plain, ![X4954, X4955, X4956, X4957]:((hBOOL(hAPP(X4957,esk152_4(X4954,X4955,X4956,X4957)))|c_Wellfounded_Owf(tc_prod(X4954,X4956),c_Recdef_Osame__fst(X4954,X4956,X4957,X4955)))&(~c_Wellfounded_Owf(X4956,hAPP(X4955,esk152_4(X4954,X4955,X4956,X4957)))|c_Wellfounded_Owf(tc_prod(X4954,X4956),c_Recdef_Osame__fst(X4954,X4956,X4957,X4955)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__same__fst])])])])])). 4.05/4.31 fof(c_0_8121, plain, ![X6485, X6486, X6487, X6489, X6490, X6491, X6492]:(((hBOOL(hAPP(X6486,hAPP(hAPP(c_List_Onth(X6487),X6485),esk195_3(X6485,X6486,X6487))))|~c_List_Olist__ex(X6487,X6486,X6485))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk195_3(X6485,X6486,X6487)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6487)),X6485)))|~c_List_Olist__ex(X6487,X6486,X6485)))&(~hBOOL(hAPP(X6490,hAPP(hAPP(c_List_Onth(X6491),X6489),X6492)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6492),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6491)),X6489)))|c_List_Olist__ex(X6491,X6490,X6489))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__length])])])])])])). 4.05/4.31 fof(c_0_8122, plain, ![X10618, X10619, X10620]:(~class_Rings_Ocomm__semiring__1(X10620)|hAPP(hAPP(c_Power_Opower__class_Opower(X10620),X10619),hAPP(c_Nat_OSuc,X10618))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10620),X10619),hAPP(hAPP(c_Power_Opower__class_Opower(X10620),X10619),X10618))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J])])])). 4.05/4.31 fof(c_0_8123, plain, ![X972, X973]:(((X972!=c_Orderings_Obot__class_Obot(tc_fun(X973,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(X973),X972))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X973),X972))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X973),X972)))))&(X972=c_Orderings_Obot__class_Obot(tc_fun(X973,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X973),X972))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X973),X972))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff])])])). 4.05/4.31 fof(c_0_8124, plain, ![X9108, X9109, X9110]:((hBOOL(hAPP(hAPP(c_member(X9110),X9109),hAPP(c_List_Oset(X9110),X9108)))|~hBOOL(hAPP(c_List_Odistinct(X9110),X9108))|hBOOL(hAPP(c_List_Odistinct(X9110),hAPP(hAPP(c_List_Olist_OCons(X9110),X9109),X9108))))&((~hBOOL(hAPP(hAPP(c_member(X9110),X9109),hAPP(c_List_Oset(X9110),X9108)))|~hBOOL(hAPP(c_List_Odistinct(X9110),hAPP(hAPP(c_List_Olist_OCons(X9110),X9109),X9108))))&(hBOOL(hAPP(c_List_Odistinct(X9110),X9108))|~hBOOL(hAPP(c_List_Odistinct(X9110),hAPP(hAPP(c_List_Olist_OCons(X9110),X9109),X9108)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct_Osimps_I2_J])])])])). 4.05/4.31 cnf(c_0_8125, 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))|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)),X2))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X2),X1))), inference(split_conjunct,[status(thm)],[c_0_5084])). 4.05/4.31 fof(c_0_8126, plain, ![X1682, X1683, X1684, X1685, X1686, X1687, X1688]:((~hBOOL(hAPP(hAPP(c_member(X1686),X1687),hAPP(c_List_Oset(X1686),X1682)))|~hBOOL(hAPP(X1685,X1687))|hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1686),tc_List_Olist(X1686)),X1683),X1682)!=c_List_Opartition(X1686,X1685,X1684))&(~hBOOL(hAPP(hAPP(c_member(X1686),X1688),hAPP(c_List_Oset(X1686),X1683)))|hBOOL(hAPP(X1685,X1688))|hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1686),tc_List_Olist(X1686)),X1683),X1682)!=c_List_Opartition(X1686,X1685,X1684))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_partition__P])])])])])). 4.05/4.31 fof(c_0_8127, plain, ![X7224, X7225, X7226, X7227]:((hAPP(c_Nat_OSuc,esk225_4(X7224,X7225,X7226,X7227))=X7225|~c_Natural_Oevaln(c_Com_Ocom_OBODY(X7227),X7226,X7225,X7224))&(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X7227)),X7226,esk225_4(X7224,X7225,X7226,X7227),X7224)|~c_Natural_Oevaln(c_Com_Ocom_OBODY(X7227),X7226,X7225,X7224))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_evaln__elim__cases_I6_J])])])])])). 4.05/4.31 fof(c_0_8128, plain, ![X7974, X7975, X7976]:(~class_Power_Opower(X7976)|hAPP(hAPP(c_Power_Opower__class_Opower(X7976),X7975),hAPP(c_Nat_OSuc,X7974))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7976),X7975),hAPP(hAPP(c_Power_Opower__class_Opower(X7976),X7975),X7974))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc])])). 4.05/4.31 cnf(c_0_8129, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))), inference(split_conjunct,[status(thm)],[c_0_5354])). 4.05/4.31 fof(c_0_8130, plain, ![X9917, X9918, X9919, X9920]:(~hBOOL(hAPP(hAPP(c_member(X9920),X9919),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9920,tc_HOL_Obool)),X9918),X9917)))|(hBOOL(hAPP(hAPP(c_member(X9920),X9919),X9918))|hBOOL(hAPP(hAPP(c_member(X9920),X9919),X9917)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UnE])])])). 4.05/4.31 fof(c_0_8131, plain, ![X3072, X3073, X3074]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3074),c_Groups_Ozero__class_Ozero(X3074)),esk103_3(X3072,X3073,X3074)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3074),X3073),X3072))|~class_Fields_Olinordered__field__inverse__zero(X3074))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3074),esk103_3(X3072,X3073,X3074)),c_Groups_Oone__class_Oone(X3074)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3074),X3073),X3072))|~class_Fields_Olinordered__field__inverse__zero(X3074))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3074),esk103_3(X3072,X3073,X3074)),X3073)),X3072))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3074),X3073),X3072))|~class_Fields_Olinordered__field__inverse__zero(X3074)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_field__le__mult__one__interval])])])])])). 4.05/4.31 fof(c_0_8132, plain, ![X7763, X7764, X7765]:(~class_Groups_Oordered__ab__group__add(X7765)|c_SetInterval_Oord__class_OgreaterThanLessThan(X7765,hAPP(c_Groups_Ouminus__class_Ouminus(X7765),X7763),hAPP(c_Groups_Ouminus__class_Ouminus(X7765),X7764))=hAPP(c_Set_Oimage(X7765,X7765,c_Groups_Ouminus__class_Ouminus(X7765)),c_SetInterval_Oord__class_OgreaterThanLessThan(X7765,X7764,X7763))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__uminus__greaterThanLessThan])])])). 4.05/4.31 fof(c_0_8133, plain, ![X17069, X17070, X17071]:(~class_Groups_Oordered__ab__group__add(X17071)|hAPP(c_Set_Oimage(X17071,X17071,c_Groups_Ouminus__class_Ouminus(X17071)),c_SetInterval_Oord__class_OatLeastAtMost(X17071,X17070,X17069))=c_SetInterval_Oord__class_OatLeastAtMost(X17071,hAPP(c_Groups_Ouminus__class_Ouminus(X17071),X17069),hAPP(c_Groups_Ouminus__class_Ouminus(X17071),X17070))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__uminus__atLeastAtMost])])])). 4.05/4.31 cnf(c_0_8134, 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_5473])). 4.05/4.31 fof(c_0_8135, plain, ![X15849, X15850, X15851]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15851),c_Groups_Ozero__class_Ozero(X15851)),esk475_3(X15849,X15850,X15851)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15851),X15850),X15849))|~class_Fields_Olinordered__field(X15851))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15851),X15850),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15851),X15849),esk475_3(X15849,X15850,X15851))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15851),X15850),X15849))|~class_Fields_Olinordered__field(X15851))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_field__le__epsilon])])])])])). 4.05/4.31 fof(c_0_8136, plain, ![X5625, X5626, X5627]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5627,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5627,X5627,X5626),X5625)),X5625))|X5625=hAPP(c_Relation_OImage(X5627,X5627,c_Transitive__Closure_Ortrancl(X5627,X5626)),X5625)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__closed__trancl])])). 4.05/4.31 fof(c_0_8137, plain, ![X10493, X10494, X10495, X10496, X10497]:((~hBOOL(hAPP(hAPP(c_member(X10497),X10494),X10493))|hBOOL(hAPP(hAPP(c_member(X10496),hAPP(X10495,X10494)),hAPP(c_Set_Oimage(X10497,X10496,X10495),X10493)))|~c_Fun_Oinj__on(X10497,X10496,X10495,c_Orderings_Otop__class_Otop(tc_fun(X10497,tc_HOL_Obool))))&(~hBOOL(hAPP(hAPP(c_member(X10496),hAPP(X10495,X10494)),hAPP(c_Set_Oimage(X10497,X10496,X10495),X10493)))|hBOOL(hAPP(hAPP(c_member(X10497),X10494),X10493))|~c_Fun_Oinj__on(X10497,X10496,X10495,c_Orderings_Otop__class_Otop(tc_fun(X10497,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__image__mem__iff])])])])). 4.05/4.31 fof(c_0_8138, plain, ![X9559, X9560, X9561]:(~class_Rings_Odivision__ring(X9561)|(X9560=c_Groups_Ozero__class_Ozero(X9561)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9561),X9559),X9560)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9561),hAPP(c_Groups_Ouminus__class_Ouminus(X9561),X9559)),hAPP(c_Groups_Ouminus__class_Ouminus(X9561),X9560)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonzero__minus__divide__divide])])])). 4.05/4.31 fof(c_0_8139, plain, ![X16404, X16405, X16406]:(~class_Orderings_Olinorder(X16406)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16406),X16405))|hAPP(hAPP(c_Finite__Set_Ofold(X16406,X16406,c_Orderings_Oord__class_Omin(X16406)),X16404),X16405)=c_Big__Operators_Olinorder__class_OMin(X16406,hAPP(hAPP(c_Set_Oinsert(X16406),X16404),X16405)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Oeq__fold__idem_H])])])). 4.05/4.31 fof(c_0_8140, plain, ![X13427, X13428, X13429]:(~class_Orderings_Olinorder(X13429)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13429),X13428))|hAPP(hAPP(c_Finite__Set_Ofold(X13429,X13429,c_Orderings_Oord__class_Omax(X13429)),X13427),X13428)=c_Big__Operators_Olinorder__class_OMax(X13429,hAPP(hAPP(c_Set_Oinsert(X13429),X13427),X13428)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Oeq__fold__idem_H])])])). 4.05/4.31 fof(c_0_8141, plain, ![X7342, X7343, X7344]:(~class_Complete__Lattice_Ocomplete__lattice(X7344)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7344),X7343))|hAPP(hAPP(c_Finite__Set_Ofold(X7344,X7344,c_Lattices_Osemilattice__sup__class_Osup(X7344)),X7342),X7343)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7344),X7342),c_Complete__Lattice_OSup__class_OSup(X7344,X7343)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Sup__fold__sup])])). 4.05/4.31 fof(c_0_8142, plain, ![X16148, X16149]:((((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16149))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16149),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X16148=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16149),X16148)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16149),X16148))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16149),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X16148=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16149),X16148)!=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)),X16149))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16148),X16149))|X16148=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16149),X16148)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16149),X16148))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16148),X16149))|X16148=c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16149),X16148)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&(((X16148!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16149),X16148)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X16149),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16148),X16149))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16149),X16148)=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)),X16149))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16149),X16148))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X16149),X16148)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__eq__0__iff])])])). 4.05/4.31 fof(c_0_8143, plain, ![X11998, X11999, X12000, X12002, X12003, X12004, X12005]:(((hBOOL(hAPP(hAPP(c_member(X12000),esk373_3(X11998,X11999,X12000)),hAPP(c_List_Oset(X12000),X11998)))|hAPP(c_List_Ofilter(X12000,X11999),X11998)=X11998)&(~hBOOL(hAPP(X11999,esk373_3(X11998,X11999,X12000)))|hAPP(c_List_Ofilter(X12000,X11999),X11998)=X11998))&(hAPP(c_List_Ofilter(X12004,X12003),X12002)!=X12002|(~hBOOL(hAPP(hAPP(c_member(X12004),X12005),hAPP(c_List_Oset(X12004),X12002)))|hBOOL(hAPP(X12003,X12005))))), 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])])])])])])). 4.05/4.31 fof(c_0_8144, plain, ![X12882, X12883, X12884]:(~class_Orderings_Olinorder(X12884)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12884),X12883))|(~hBOOL(hAPP(hAPP(c_member(X12884),X12882),X12883))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X12884),X12882),c_Big__Operators_Olattice_OSup__fin(X12884,c_Orderings_Oord__class_Omax(X12884),X12883))=X12882))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__Sup__absorb])])])). 4.05/4.31 fof(c_0_8145, plain, ![X2655, X2656, X2657]:(~class_Orderings_Olinorder(X2657)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2657),X2656))|(~hBOOL(hAPP(hAPP(c_member(X2657),X2655),X2656))|X2655=hAPP(hAPP(c_Orderings_Oord__class_Omax(X2657),X2655),c_Big__Operators_Olattice_OInf__fin(X2657,c_Orderings_Oord__class_Omin(X2657),X2656))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__Inf__absorb])])])). 4.05/4.31 fof(c_0_8146, plain, ![X10849, X10850, X10851]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10851),hAPP(c_Groups_Ouminus__class_Ouminus(X10851),X10849)),X10850))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10851),hAPP(c_Groups_Ouminus__class_Ouminus(X10851),X10850)),X10849))|~class_Groups_Oordered__ab__group__add(X10851))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10851),hAPP(c_Groups_Ouminus__class_Ouminus(X10851),X10850)),X10849))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10851),hAPP(c_Groups_Ouminus__class_Ouminus(X10851),X10849)),X10850))|~class_Groups_Oordered__ab__group__add(X10851))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])])). 4.05/4.31 fof(c_0_8147, plain, ![X13611, X13612, X13613]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13613),hAPP(c_Groups_Ouminus__class_Ouminus(X13613),X13612)),X13611))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13613),hAPP(c_Groups_Ouminus__class_Ouminus(X13613),X13611)),X13612))|~class_Groups_Oordered__ab__group__add(X13613))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13613),hAPP(c_Groups_Ouminus__class_Ouminus(X13613),X13611)),X13612))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13613),hAPP(c_Groups_Ouminus__class_Ouminus(X13613),X13612)),X13611))|~class_Groups_Oordered__ab__group__add(X13613))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__le__iff])])])])). 4.05/4.31 fof(c_0_8148, plain, ![X5864, X5865, X5866]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5866),X5864),hAPP(c_Groups_Ouminus__class_Ouminus(X5866),X5865)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5866),X5865),hAPP(c_Groups_Ouminus__class_Ouminus(X5866),X5864)))|~class_Groups_Oordered__ab__group__add(X5866))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5866),X5865),hAPP(c_Groups_Ouminus__class_Ouminus(X5866),X5864)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5866),X5864),hAPP(c_Groups_Ouminus__class_Ouminus(X5866),X5865)))|~class_Groups_Oordered__ab__group__add(X5866))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__minus__iff])])])])). 4.05/4.31 fof(c_0_8149, plain, ![X5578, X5579, X5580]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5580),X5578),hAPP(c_Groups_Ouminus__class_Ouminus(X5580),X5579)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5580),X5579),hAPP(c_Groups_Ouminus__class_Ouminus(X5580),X5578)))|~class_Groups_Oordered__ab__group__add(X5580))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5580),X5579),hAPP(c_Groups_Ouminus__class_Ouminus(X5580),X5578)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5580),X5578),hAPP(c_Groups_Ouminus__class_Ouminus(X5580),X5579)))|~class_Groups_Oordered__ab__group__add(X5580))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__iff])])])). 4.05/4.31 cnf(c_0_8150, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|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_5474])). 4.05/4.31 fof(c_0_8151, plain, ![X6526, X6527, X6528, X6529]:(~c_Fun_Oinj__on(X6529,X6528,X6527,c_Orderings_Otop__class_Otop(tc_fun(X6529,tc_HOL_Obool)))|hAPP(c_Fun_Othe__inv__into(X6529,X6528,c_Orderings_Otop__class_Otop(tc_fun(X6529,tc_HOL_Obool)),X6527),hAPP(X6527,X6526))=X6526), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_the__inv__f__f])])])). 4.05/4.31 fof(c_0_8152, plain, ![X16765, X16766]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16766))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16766),X16765)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16766),X16765)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X16766,X16765))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__pos__neg__trivial])])])). 4.05/4.31 fof(c_0_8153, plain, ![X3137, X3138, X3139, X3140]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3140),X3139))|hAPP(hAPP(c_List_Onth(X3138),hAPP(hAPP(c_List_Otake(X3138),X3139),X3137)),X3140)=hAPP(hAPP(c_List_Onth(X3138),X3137),X3140)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__take])])). 4.05/4.31 fof(c_0_8154, plain, ![X10995, X10996]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10996))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10995))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X10996,X10995))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J])])])). 4.05/4.31 fof(c_0_8155, plain, ![X7636, X7637, X7638, X7639]:((hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7639)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X7637=hAPP(hAPP(c_List_Onth(X7638),hAPP(hAPP(c_List_Olist_OCons(X7638),X7637),X7636)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7639)))&(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7639)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Onth(X7638),hAPP(hAPP(c_List_Olist_OCons(X7638),X7637),X7636)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7639))=hAPP(hAPP(c_List_Onth(X7638),X7636),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X7639)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__Cons__number__of])])])). 4.05/4.31 fof(c_0_8156, plain, ![X4432, X4433, X4434, X4435, X4436, X4437]:((~hBOOL(hAPP(hAPP(X4434,X4436),X4432))|~hBOOL(hAPP(hAPP(X4435,X4433),X4436))|hBOOL(hAPP(hAPP(c_member(X4437),X4436),c_SetInterval_Oord_OatLeastLessThan(X4437,X4435,X4434,X4433,X4432))))&((hBOOL(hAPP(hAPP(X4434,X4436),X4432))|~hBOOL(hAPP(hAPP(c_member(X4437),X4436),c_SetInterval_Oord_OatLeastLessThan(X4437,X4435,X4434,X4433,X4432))))&(hBOOL(hAPP(hAPP(X4435,X4433),X4436))|~hBOOL(hAPP(hAPP(c_member(X4437),X4436),c_SetInterval_Oord_OatLeastLessThan(X4437,X4435,X4434,X4433,X4432)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastLessThan__iff])])])). 4.05/4.31 fof(c_0_8157, plain, ![X4703, X4704, X4705, X4706, X4707, X4708]:(((hBOOL(hAPP(hAPP(X4705,X4704),X4707))|~hBOOL(hAPP(hAPP(c_member(X4708),X4707),c_SetInterval_Oord_OgreaterThanAtMost(X4708,X4706,X4705,X4704,X4703))))&(hBOOL(hAPP(hAPP(X4706,X4707),X4703))|~hBOOL(hAPP(hAPP(c_member(X4708),X4707),c_SetInterval_Oord_OgreaterThanAtMost(X4708,X4706,X4705,X4704,X4703)))))&(~hBOOL(hAPP(hAPP(X4705,X4704),X4707))|~hBOOL(hAPP(hAPP(X4706,X4707),X4703))|hBOOL(hAPP(hAPP(c_member(X4708),X4707),c_SetInterval_Oord_OgreaterThanAtMost(X4708,X4706,X4705,X4704,X4703))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanAtMost__iff])])])). 4.05/4.31 fof(c_0_8158, plain, ![X11035, X11036, X11037]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11037),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11036)),X11035)))|hAPP(hAPP(c_List_Otake(X11036),X11037),c_List_Obutlast(X11036,X11035))=hAPP(hAPP(c_List_Otake(X11036),X11037),X11035)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__butlast])])). 4.05/4.31 fof(c_0_8159, plain, ![X9410, X9411, X9412, X9413, X9414, X9415]:((~hBOOL(hAPP(hAPP(X9415,X9414),X9413))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9411,tc_fun(X9410,tc_HOL_Obool))),X9412),X9415),X9414),X9413)))&(~hBOOL(hAPP(hAPP(X9412,X9414),X9413))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9411,tc_fun(X9410,tc_HOL_Obool))),X9412),X9415),X9414),X9413)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup2CI])])])])). 4.05/4.31 fof(c_0_8160, plain, ![X5063, X5064, X5065, X5066, X5067]:(~class_Orderings_Olinorder(X5067)|(~hBOOL(hAPP(hAPP(c_member(X5067),hAPP(X5066,X5065)),hAPP(c_Set_Oimage(X5064,X5067,X5066),hAPP(c_List_Oset(X5064),X5063))))|c_List_Olinorder__class_Oinsort__insert__key(X5064,X5067,X5066,X5065,X5063)=X5063)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__insert__key__triv])])])). 4.05/4.31 fof(c_0_8161, plain, ![X17223, X17224, X17225, X17226, X17227]:(X17227=X17226|hAPP(hAPP(c_List_Onth(X17225),hAPP(hAPP(c_List_Olist__update(X17225,X17224),X17227),X17223)),X17226)=hAPP(hAPP(c_List_Onth(X17225),X17224),X17226)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__list__update__neq])])])). 4.05/4.31 fof(c_0_8162, plain, ![X2058, X2059, X2060]:(~class_Rings_Oring(X2060)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2060),hAPP(c_Groups_Ouminus__class_Ouminus(X2060),X2059)),hAPP(c_Groups_Ouminus__class_Ouminus(X2060),X2058))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2060),X2059),X2058)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__minus])])). 4.05/4.31 fof(c_0_8163, plain, ![X1406, X1407, X1408, X1409, X1410, X1411]:(~hBOOL(hAPP(hAPP(X1411,X1410),X1409))|hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1408,tc_fun(X1407,tc_HOL_Obool))),X1406),X1411),X1410),X1409))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup2I2])])). 4.05/4.31 fof(c_0_8164, plain, ![X14346, X14347, X14348]:(~class_Orderings_Olinorder(X14348)|hAPP(c_List_Oset(X14348),c_List_Olinorder__class_Oinsort__insert__key(X14348,X14348,c_COMBI(X14348),X14347,X14346))=hAPP(hAPP(c_Set_Oinsert(X14348),X14347),hAPP(c_List_Oset(X14348),X14346))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__insort__insert])])). 4.05/4.31 fof(c_0_8165, plain, ![X6196, X6197, X6198]:(~class_Fields_Ofield__inverse__zero(X6198)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6198),X6197),X6196)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X6198),hAPP(c_Groups_Ouminus__class_Ouminus(X6198),X6197)),hAPP(c_Groups_Ouminus__class_Ouminus(X6198),X6196))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__divide__divide])])])). 4.05/4.31 fof(c_0_8166, plain, ![X16724, X16725]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X16725))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16725),X16724)),X16725)=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__times__mod__eq])])])). 4.05/4.31 fof(c_0_8167, plain, ![X12797, X12798]:(~class_Orderings_Olinorder(X12798)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12798),X12797))|(X12797=c_Orderings_Obot__class_Obot(tc_fun(X12798,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X12798),c_Big__Operators_Olinorder__class_OMax(X12798,X12797)),X12797))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__in])])). 4.05/4.31 fof(c_0_8168, plain, ![X11525, X11526]:(~class_Rings_Olinordered__idom(X11526)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11526),X11525),X11525)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X11526),hAPP(c_Groups_Oabs__class_Oabs(X11526),X11525)),hAPP(c_Groups_Oabs__class_Oabs(X11526),X11525))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__mult__self])])])). 4.05/4.31 cnf(c_0_8169, 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_5473])). 4.05/4.31 fof(c_0_8170, plain, ![X12296, X12297]:(~class_Orderings_Olinorder(X12297)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12297),X12296))|(X12296=c_Orderings_Obot__class_Obot(tc_fun(X12297,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X12297),c_Big__Operators_Olinorder__class_OMin(X12297,X12296)),X12296))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min__in])])])). 4.05/4.31 fof(c_0_8171, plain, ![X3439, X3440]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3440),X3439))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3440,X3439)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3440),X3439),X3439)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__geq])])])). 4.05/4.31 fof(c_0_8172, plain, ![X3141]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3141))|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)),X3141)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])])). 4.05/4.31 cnf(c_0_8173, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(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_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_5475])). 4.05/4.31 fof(c_0_8174, plain, ![X10552]:(~class_Rings_Olinordered__semidom(X10552)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10552),c_Groups_Ozero__class_Ozero(X10552)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10552),c_Groups_Oone__class_Oone(X10552)),c_Groups_Oone__class_Oone(X10552))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])])). 4.05/4.31 fof(c_0_8175, plain, ![X8217, X8218, X8219, X8220, X8221, X8222]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X8222,X8221)),hAPP(hAPP(c_Product__Type_OPair(X8222,X8221),X8220),X8219)),hAPP(hAPP(c_Product__Type_OSigma(X8222,X8221),X8218),X8217)))|hBOOL(hAPP(hAPP(c_member(X8222),X8220),X8218))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD1])])). 4.05/4.31 fof(c_0_8176, plain, ![X565, X566, X567]:(c_List_Olist_ONil(X566)=X567|hAPP(hAPP(c_List_Oappend(X566),hAPP(c_List_Otl(X566),X567)),X565)=hAPP(c_List_Otl(X566),hAPP(hAPP(c_List_Oappend(X566),X567),X565))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_tl__append2])])])). 4.05/4.31 cnf(c_0_8177, plain, (c_Fun_Oinj__on(X1,X2,esk212_4(X3,X2,X1,X4),X4)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X4|X4!=hAPP(c_Set_Oimage(X2,X1,X5),X3)), inference(split_conjunct,[status(thm)],[c_0_5258])). 4.05/4.31 fof(c_0_8178, plain, ![X5185, X5186, X5187, X5188, X5189, X5190]:(~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5190,tc_fun(X5189,tc_HOL_Obool)),X5188),X5187),X5186))|(hBOOL(hAPP(hAPP(X5187,X5185),X5186))|~hBOOL(hAPP(hAPP(c_member(X5190),X5185),X5188)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_INF1__E])])])). 4.05/4.31 fof(c_0_8179, plain, ![X13039, X13040, X13041, X13043, X13044, X13045, X13046]:(((hBOOL(hAPP(hAPP(c_member(X13041),esk397_3(X13039,X13040,X13041)),hAPP(c_List_Oset(X13041),X13039)))|c_List_OtakeWhile(X13041,X13040,X13039)=X13039)&(~hBOOL(hAPP(X13040,esk397_3(X13039,X13040,X13041)))|c_List_OtakeWhile(X13041,X13040,X13039)=X13039))&(c_List_OtakeWhile(X13045,X13044,X13043)!=X13043|(~hBOOL(hAPP(hAPP(c_member(X13045),X13046),hAPP(c_List_Oset(X13045),X13043)))|hBOOL(hAPP(X13044,X13046))))), 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])])])])])])])). 4.05/4.31 fof(c_0_8180, plain, ![X3085, X3086, X3087]:(~class_Rings_Odivision__ring(X3087)|(X3086=c_Groups_Ozero__class_Ozero(X3087)|hAPP(c_Groups_Ouminus__class_Ouminus(X3087),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3087),X3085),X3086))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3087),X3085),hAPP(c_Groups_Ouminus__class_Ouminus(X3087),X3086)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonzero__minus__divide__right])])])). 4.05/4.31 fof(c_0_8181, plain, ![X8906, X8907, X8908]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8908),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8908),X8907),X8906)),c_Groups_Ozero__class_Ozero(X8908)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8908),X8907),X8906))|~class_Groups_Oordered__ab__group__add(X8908))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8908),X8907),X8906))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8908),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8908),X8907),X8906)),c_Groups_Ozero__class_Ozero(X8908)))|~class_Groups_Oordered__ab__group__add(X8908))), 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])])])])). 4.05/4.31 fof(c_0_8182, plain, ![X10532, X10533, X10534]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10534),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10534),X10533),X10532)),c_Groups_Ozero__class_Ozero(X10534)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10534),X10533),X10532))|~class_Groups_Oordered__ab__group__add(X10534))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10534),X10533),X10532))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10534),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10534),X10533),X10532)),c_Groups_Ozero__class_Ozero(X10534)))|~class_Groups_Oordered__ab__group__add(X10534))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__iff__diff__le__0])])])])). 4.05/4.31 fof(c_0_8183, plain, ![X1451, X1452, X1453]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1453),hAPP(c_Groups_Ouminus__class_Ouminus(X1453),X1452)),hAPP(c_Groups_Ouminus__class_Ouminus(X1453),X1451)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1453),X1451),X1452))|~class_Groups_Oordered__ab__group__add(X1453))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1453),X1451),X1452))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1453),hAPP(c_Groups_Ouminus__class_Ouminus(X1453),X1452)),hAPP(c_Groups_Ouminus__class_Ouminus(X1453),X1451)))|~class_Groups_Oordered__ab__group__add(X1453))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])])). 4.05/4.31 fof(c_0_8184, plain, ![X1507, X1508, X1509, X1510, X1511, X1512]:((c_Option_Ooption_ONone(X1511)=hAPP(X1509,X1508)|hAPP(X1509,X1508)=hAPP(c_Option_Ooption_OSome(X1511),X1507)|hAPP(c_Map_Omap__add(X1512,X1511,X1510,X1509),X1508)!=hAPP(c_Option_Ooption_OSome(X1511),X1507))&(hAPP(c_Option_Ooption_OSome(X1511),X1507)=hAPP(X1510,X1508)|hAPP(X1509,X1508)=hAPP(c_Option_Ooption_OSome(X1511),X1507)|hAPP(c_Map_Omap__add(X1512,X1511,X1510,X1509),X1508)!=hAPP(c_Option_Ooption_OSome(X1511),X1507))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__add__SomeD])])])])). 4.05/4.31 cnf(c_0_8185, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5476, c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_8186, plain, (X1=c_List_Olist_ONil(X2)|X1=hAPP(hAPP(c_List_Oappend(X2),X4),hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)))|X3!=c_List_Olast(X2,X1)|c_List_Obutlast(X2,X1)!=X4), inference(split_conjunct,[status(thm)],[c_0_5477])). 4.05/4.31 fof(c_0_8187, plain, ![X3464, X3465, X3466]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3466),X3464),X3465))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3466),hAPP(c_Groups_Ouminus__class_Ouminus(X3466),X3465)),hAPP(c_Groups_Ouminus__class_Ouminus(X3466),X3464)))|~class_Lattices_Oboolean__algebra(X3466))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3466),hAPP(c_Groups_Ouminus__class_Ouminus(X3466),X3465)),hAPP(c_Groups_Ouminus__class_Ouminus(X3466),X3464)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3466),X3464),X3465))|~class_Lattices_Oboolean__algebra(X3466))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff])])])). 4.05/4.31 fof(c_0_8188, plain, ![X2740, X2741, X2742]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2742),X2740),X2741))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2742),hAPP(c_Groups_Ouminus__class_Ouminus(X2742),X2741)),hAPP(c_Groups_Ouminus__class_Ouminus(X2742),X2740)))|~class_Groups_Oordered__ab__group__add(X2742))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2742),hAPP(c_Groups_Ouminus__class_Ouminus(X2742),X2741)),hAPP(c_Groups_Ouminus__class_Ouminus(X2742),X2740)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2742),X2740),X2741))|~class_Groups_Oordered__ab__group__add(X2742))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__le__iff__le])])])])). 4.05/4.31 fof(c_0_8189, plain, ![X12346, X12347, X12348]:(~class_Rings_Odivision__ring(X12348)|hAPP(c_Groups_Ouminus__class_Ouminus(X12348),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12348),X12347),X12346))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X12348),hAPP(c_Groups_Ouminus__class_Ouminus(X12348),X12347)),X12346)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__left])])). 4.05/4.31 cnf(c_0_8190, 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_5349])). 4.05/4.31 cnf(c_0_8191, plain, (c_Divides_Odivmod__nat(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))), inference(split_conjunct,[status(thm)],[c_0_5478])). 4.05/4.31 fof(c_0_8192, plain, ![X1869, X1870, X1871, X1873, X1874, X1875, X1876]:(((hBOOL(hAPP(hAPP(c_member(X1871),esk66_3(X1869,X1870,X1871)),hAPP(c_List_Oset(X1871),X1870)))|c_List_Olist__all(X1871,X1869,X1870))&(~hBOOL(hAPP(X1869,esk66_3(X1869,X1870,X1871)))|c_List_Olist__all(X1871,X1869,X1870)))&(~c_List_Olist__all(X1875,X1873,X1874)|(~hBOOL(hAPP(hAPP(c_member(X1875),X1876),hAPP(c_List_Oset(X1875),X1874)))|hBOOL(hAPP(X1873,X1876))))), 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])])])])])])])). 4.05/4.31 fof(c_0_8193, plain, ![X13496, X13497, X13498]:(~class_Rings_Oring(X13498)|hAPP(c_Groups_Ouminus__class_Ouminus(X13498),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13498),X13497),X13496))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13498),hAPP(c_Groups_Ouminus__class_Ouminus(X13498),X13497)),X13496)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__mult__left])])])). 4.05/4.31 fof(c_0_8194, plain, ![X1366, X1367, X1368]:(~class_Rings_Oring(X1368)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1368),hAPP(c_Groups_Ouminus__class_Ouminus(X1368),X1367)),X1366)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1368),X1367),hAPP(c_Groups_Ouminus__class_Ouminus(X1368),X1366))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__mult__commute])])])). 4.05/4.31 fof(c_0_8195, plain, ![X4673, X4674, X4675]:(~class_Rings_Oring__1(X4675)|(~hBOOL(hAPP(hAPP(c_member(X4675),X4674),c_Int_Oring__1__class_OInts(X4675)))|hBOOL(hAPP(hAPP(c_member(X4675),hAPP(hAPP(c_Power_Opower__class_Opower(X4675),X4674),X4673)),c_Int_Oring__1__class_OInts(X4675))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__power])])). 4.05/4.31 fof(c_0_8196, plain, ![X11550, X11551, X11552, X11553]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11553),X11552),X11550))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11553),hAPP(hAPP(c_Orderings_Oord__class_Omin(X11553),X11552),X11551)),X11550))|~class_Orderings_Olinorder(X11553))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11553),X11551),X11550))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11553),hAPP(hAPP(c_Orderings_Oord__class_Omin(X11553),X11552),X11551)),X11550))|~class_Orderings_Olinorder(X11553)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11553),hAPP(hAPP(c_Orderings_Oord__class_Omin(X11553),X11552),X11551)),X11550))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11553),X11552),X11550))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11553),X11551),X11550)))|~class_Orderings_Olinorder(X11553))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__disj])])])). 4.05/4.31 fof(c_0_8197, plain, ![X4470, X4471, X4472, X4473, X4474, X4475, X4476]:((~c_List_Olist__all(X4472,X4471,X4470)|(~hBOOL(hAPP(hAPP(c_member(X4472),X4473),hAPP(c_List_Oset(X4472),X4470)))|hBOOL(hAPP(X4471,X4473))))&((hBOOL(hAPP(hAPP(c_member(X4476),esk138_3(X4474,X4475,X4476)),hAPP(c_List_Oset(X4476),X4474)))|c_List_Olist__all(X4476,X4475,X4474))&(~hBOOL(hAPP(X4475,esk138_3(X4474,X4475,X4476)))|c_List_Olist__all(X4476,X4475,X4474)))), 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])])])])])])). 4.05/4.31 fof(c_0_8198, plain, ![X865, X866, X867]:(X867=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Oreplicate(X866,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X867),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X865)=hAPP(c_List_Otl(X866),c_List_Oreplicate(X866,X867,X865))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_tl__replicate])])])). 4.05/4.31 cnf(c_0_8199, 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_5479])). 4.05/4.31 fof(c_0_8200, plain, ![X2647, X2648, X2649, X2650, X2651, X2652, X2653]:((~c_List_Olist__all(X2649,X2648,X2647)|(~hBOOL(hAPP(hAPP(c_member(X2649),X2650),hAPP(c_List_Oset(X2649),X2647)))|hBOOL(hAPP(X2648,X2650))))&((hBOOL(hAPP(hAPP(c_member(X2653),esk92_3(X2651,X2652,X2653)),hAPP(c_List_Oset(X2653),X2651)))|c_List_Olist__all(X2653,X2652,X2651))&(~hBOOL(hAPP(X2652,esk92_3(X2651,X2652,X2653)))|c_List_Olist__all(X2653,X2652,X2651)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__iff__raw])])])])])])). 4.05/4.31 fof(c_0_8201, plain, ![X11403, X11404, X11405, X11406]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11406),X11405),X11403))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11406),hAPP(hAPP(c_Orderings_Oord__class_Omin(X11406),X11405),X11404)),X11403))|~class_Orderings_Olinorder(X11406))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11406),X11404),X11403))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11406),hAPP(hAPP(c_Orderings_Oord__class_Omin(X11406),X11405),X11404)),X11403))|~class_Orderings_Olinorder(X11406)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11406),hAPP(hAPP(c_Orderings_Oord__class_Omin(X11406),X11405),X11404)),X11403))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11406),X11405),X11403))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11406),X11404),X11403)))|~class_Orderings_Olinorder(X11406))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__le__iff__disj])])])). 4.05/4.31 fof(c_0_8202, plain, ![X15946, X15947, X15948, X15949]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15949),X15948),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15949),X15947),X15946)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15949),X15948),X15947))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15949),X15948),X15946)))|~class_Orderings_Olinorder(X15949))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15949),X15948),X15947))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15949),X15948),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15949),X15947),X15946)))|~class_Orderings_Olinorder(X15949))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15949),X15948),X15946))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15949),X15948),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15949),X15947),X15946)))|~class_Orderings_Olinorder(X15949)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__max__iff__disj])])])). 4.05/4.31 fof(c_0_8203, plain, ![X17619, X17620, X17621, X17622]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17622),X17621),hAPP(hAPP(c_Orderings_Oord__class_Omax(X17622),X17620),X17619)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17622),X17621),X17620))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17622),X17621),X17619)))|~class_Orderings_Olinorder(X17622))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17622),X17621),X17620))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17622),X17621),hAPP(hAPP(c_Orderings_Oord__class_Omax(X17622),X17620),X17619)))|~class_Orderings_Olinorder(X17622))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17622),X17621),X17619))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17622),X17621),hAPP(hAPP(c_Orderings_Oord__class_Omax(X17622),X17620),X17619)))|~class_Orderings_Olinorder(X17622)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__max__iff__disj])])])])). 4.05/4.31 fof(c_0_8204, plain, ![X1808, X1809]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1809))|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1808),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1809)))=c_SMT_Oz3div(X1808,X1809))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1809))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1808),X1809)=c_SMT_Oz3div(X1808,X1809))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_z3div__def])])])). 4.05/4.31 fof(c_0_8205, plain, ![X6018, X6019, X6020]:(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6020)),X6019),c_List_Olists(X6020,c_Wellfounded_Oacc(X6020,X6018))))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6020)),X6019),c_Wellfounded_Oacc(tc_List_Olist(X6020),c_List_Olistrel1(X6020,X6018))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accD])])). 4.05/4.31 fof(c_0_8206, plain, ![X13910, X13911]:(~class_Orderings_Olinorder(X13911)|c_Big__Operators_Olattice_OSup__fin(X13911,c_Orderings_Oord__class_Omax(X13911),hAPP(hAPP(c_Set_Oinsert(X13911),X13910),c_Orderings_Obot__class_Obot(tc_fun(X13911,tc_HOL_Obool))))=X13910), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osingleton])])). 4.05/4.31 fof(c_0_8207, plain, ![X16497, X16498, X16499]:(~class_Fields_Ofield__inverse__zero(X16499)|hAPP(c_Groups_Ouminus__class_Ouminus(X16499),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16499),X16498),X16497))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X16499),X16498),hAPP(c_Groups_Ouminus__class_Ouminus(X16499),X16497))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__right])])). 4.05/4.31 fof(c_0_8208, plain, ![X7874, X7875]:(~class_Orderings_Olinorder(X7875)|X7874=c_Big__Operators_Olattice_OInf__fin(X7875,c_Orderings_Oord__class_Omin(X7875),hAPP(hAPP(c_Set_Oinsert(X7875),X7874),c_Orderings_Obot__class_Obot(tc_fun(X7875,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Osingleton])])])). 4.05/4.31 fof(c_0_8209, plain, ![X6928, X6929, X6930]:(~class_Rings_Olinordered__idom(X6930)|c_Groups_Osgn__class_Osgn(X6930,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6930),X6929),X6928))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6930),c_Groups_Osgn__class_Osgn(X6930,X6929)),c_Groups_Osgn__class_Osgn(X6930,X6928))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__times])])])). 4.05/4.31 fof(c_0_8210, plain, ![X7135, X7136, X7137, X7138, X7139]:(~class_Orderings_Olinorder(X7139)|(~c_List_Olinorder__class_Osorted(X7139,hAPP(hAPP(c_List_Omap(X7138,X7139),X7137),X7136))|c_List_Olinorder__class_Osorted(X7139,hAPP(hAPP(c_List_Omap(X7138,X7139),X7137),c_List_Oremove1(X7138,X7135,X7136))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__map__remove1])])])). 4.05/4.31 cnf(c_0_8211, plain, (X1=c_List_Oembed__list(c_List_Oreturn__list(X1))|~c_List_Onat__list(X1)), inference(split_conjunct,[status(thm)],[c_0_5480])). 4.05/4.31 cnf(c_0_8212, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)), inference(split_conjunct,[status(thm)],[c_0_5481])). 4.05/4.31 cnf(c_0_8213, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls))|~class_Int_Onumber__ring(X2)|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_5482])). 4.05/4.31 cnf(c_0_8214, 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_5483])). 4.05/4.31 cnf(c_0_8215, 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_5484])). 4.05/4.31 fof(c_0_8216, plain, ![X8201, X8202, X8203]:(~class_Rings_Oring(X8203)|hAPP(c_Groups_Ouminus__class_Ouminus(X8203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8203),X8202),X8201))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8203),X8202),hAPP(c_Groups_Ouminus__class_Ouminus(X8203),X8201))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__right])])). 4.05/4.31 fof(c_0_8217, plain, ![X2967, X2968]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2967))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2967),X2968))|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),X2968),X2967)))|~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)),X2967))|~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),X2968),X2967)))|~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__eq(tc_Int_Oint),X2967),X2968))|~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),X2968),X2967)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2968))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff])])])). 4.05/4.31 cnf(c_0_8218, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk25_3(X2,X3,X1)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5275])). 4.05/4.31 fof(c_0_8219, plain, ![X2221, X2222, X2223, X2224]:((~hBOOL(hAPP(X2224,X2223))|c_List_OtakeWhile(X2222,X2224,hAPP(hAPP(c_List_Olist_OCons(X2222),X2223),X2221))=hAPP(hAPP(c_List_Olist_OCons(X2222),X2223),c_List_OtakeWhile(X2222,X2224,X2221)))&(hBOOL(hAPP(X2224,X2223))|c_List_OtakeWhile(X2222,X2224,hAPP(hAPP(c_List_Olist_OCons(X2222),X2223),X2221))=c_List_Olist_ONil(X2222))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_takeWhile_Osimps_I2_J])])])). 4.05/4.31 cnf(c_0_8220, 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(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_5358])). 4.05/4.31 cnf(c_0_8221, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk50_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_5485])). 4.05/4.31 cnf(c_0_8222, 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_5239])). 4.05/4.31 cnf(c_0_8223, 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_5486])). 4.05/4.31 cnf(c_0_8224, 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_5487, c_0_4422])). 4.05/4.31 cnf(c_0_8225, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2))|~c_Wellfounded_Owf(X1,X2)), inference(rw,[status(thm)],[c_0_5488, c_0_5018])). 4.05/4.31 cnf(c_0_8226, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1))=c_Divides_OnegDivAlg(X2,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_4551])). 4.05/4.31 cnf(c_0_8227, 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),c_Transitive__Closure_Ortrancl(X1,X2)),X2)))), inference(rw,[status(thm)],[c_0_5489, c_0_5018])). 4.05/4.31 cnf(c_0_8228, 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),c_Transitive__Closure_Ortrancl(X1,X2)),X2)))), inference(rw,[status(thm)],[c_0_5490, c_0_5018])). 4.05/4.31 fof(c_0_8229, plain, ![X3430, X3431, X3432]:(~class_Rings_Olinordered__idom(X3432)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3432),c_Groups_Ozero__class_Ozero(X3432)),hAPP(hAPP(c_Power_Opower__class_Opower(X3432),hAPP(c_Groups_Oabs__class_Oabs(X3432),X3431)),X3430)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs])])). 4.05/4.31 fof(c_0_8230, plain, ![X9630, X9631, X9632]:(~class_Lattices_Osemilattice__inf(X9632)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9632),X9631),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9632),X9631),X9630))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9632),X9631),X9630)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__idem])])). 4.05/4.31 fof(c_0_8231, plain, ![X11501, X11502, X11503, X11504, X11505, X11506, X11507]:(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X11507,tc_Option_Ooption(X11506)),X11502),X11504),hAPP(c_Option_Ooption_OSome(X11506),X11501))!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X11507,tc_Option_Ooption(X11506)),X11505),X11504),hAPP(c_Option_Ooption_OSome(X11506),X11503))|X11501=X11503), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__upd__eqD1])])])). 4.05/4.31 fof(c_0_8232, plain, ![X11889, X11890, X11891, X11892, X11893, X11894, X11895]:(((c_List_Olist__all2(X11895,X11893,X11891,X11890,X11889)|~c_List_Olist__all2(X11895,X11893,X11891,hAPP(hAPP(c_List_Oappend(X11895),X11894),X11890),hAPP(hAPP(c_List_Oappend(X11893),X11892),X11889))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11893)),X11892)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11895)),X11894))&(c_List_Olist__all2(X11895,X11893,X11891,X11894,X11892)|~c_List_Olist__all2(X11895,X11893,X11891,hAPP(hAPP(c_List_Oappend(X11895),X11894),X11890),hAPP(hAPP(c_List_Oappend(X11893),X11892),X11889))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11893)),X11892)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11895)),X11894)))&(~c_List_Olist__all2(X11895,X11893,X11891,X11890,X11889)|~c_List_Olist__all2(X11895,X11893,X11891,X11894,X11892)|c_List_Olist__all2(X11895,X11893,X11891,hAPP(hAPP(c_List_Oappend(X11895),X11894),X11890),hAPP(hAPP(c_List_Oappend(X11893),X11892),X11889))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11893)),X11892)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X11895)),X11894))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2__append])])])])). 4.05/4.31 fof(c_0_8233, plain, ![X15808, X15809, X15810]:(~class_Lattices_Oab__semigroup__idem__mult(X15810)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15810),X15809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15810),X15809),X15808))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15810),X15809),X15808)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__idem])])). 4.05/4.31 fof(c_0_8234, plain, ![X15955, X15956, X15957]:(~class_Lattices_Olattice(X15957)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15957),X15956),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15957),X15956),X15955))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15957),X15956),X15955)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I8_J])])). 4.05/4.31 fof(c_0_8235, plain, ![X6716, X6717, X6718]:(~class_Lattices_Olattice(X6718)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6718),X6717),X6716)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6718),X6717),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6718),X6717),X6716))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__aci_I4_J])])])). 4.05/4.31 fof(c_0_8236, plain, ![X6009, X6010, X6011, X6012, X6013]:(~c_Map_Omap__le(X6013,X6012,X6011,X6010)|(~c_Map_Omap__le(X6013,X6012,X6009,X6010)|(~c_Map_Omap__le(X6013,X6012,X6011,c_Map_Omap__add(X6013,X6012,X6011,X6009))|c_Map_Omap__le(X6013,X6012,c_Map_Omap__add(X6013,X6012,X6011,X6009),X6010)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__add__le__mapI])])])). 4.05/4.31 fof(c_0_8237, plain, ![X14039, X14040, X14041, X14042, X14043]:(~c_Fun_Oinj__on(X14043,X14042,X14041,X14040)|(~c_Fun_Oinj__on(X14043,X14042,X14041,X14039)|c_Fun_Oinj__on(X14043,X14042,X14041,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14043,tc_HOL_Obool)),X14040),X14039)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__Int])])])). 4.05/4.31 fof(c_0_8238, plain, ![X9046, X9047]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9047),c_Orderings_Otop__class_Otop(tc_fun(X9047,tc_HOL_Obool))))|(~c_Fun_Oinj__on(X9047,X9047,X9046,c_Orderings_Otop__class_Otop(tc_fun(X9047,tc_HOL_Obool)))|hAPP(c_Set_Oimage(X9047,X9047,X9046),c_Orderings_Otop__class_Otop(tc_fun(X9047,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X9047,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])])). 4.05/4.31 fof(c_0_8239, plain, ![X15078, X15079]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15079),c_Orderings_Otop__class_Otop(tc_fun(X15079,tc_HOL_Obool))))|(c_Orderings_Otop__class_Otop(tc_fun(X15079,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X15079,X15079,X15078),c_Orderings_Otop__class_Otop(tc_fun(X15079,tc_HOL_Obool)))|c_Fun_Oinj__on(X15079,X15079,X15078,c_Orderings_Otop__class_Otop(tc_fun(X15079,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__UNIV__surj__inj])])])). 4.05/4.31 cnf(c_0_8240, 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_5491])). 4.05/4.31 fof(c_0_8241, plain, ![X17438, X17439, X17440]:(~class_Lattices_Osemilattice__sup(X17440)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17440),X17439),X17438)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17440),X17439),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17440),X17439),X17438))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__left__idem])])). 4.05/4.31 fof(c_0_8242, plain, ![X16363, X16364, X16365]:((hBOOL(hAPP(c_Finite__Set_Ofinite(X16365),esk490_3(X16363,X16364,X16365)))|hBOOL(hAPP(X16363,X16364))|~hBOOL(hAPP(X16363,c_Orderings_Obot__class_Obot(tc_fun(X16365,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16365),X16364)))&((~hBOOL(hAPP(hAPP(c_member(X16365),esk489_3(X16363,X16364,X16365)),esk490_3(X16363,X16364,X16365)))|hBOOL(hAPP(X16363,X16364))|~hBOOL(hAPP(X16363,c_Orderings_Obot__class_Obot(tc_fun(X16365,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16365),X16364)))&((hBOOL(hAPP(X16363,esk490_3(X16363,X16364,X16365)))|hBOOL(hAPP(X16363,X16364))|~hBOOL(hAPP(X16363,c_Orderings_Obot__class_Obot(tc_fun(X16365,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16365),X16364)))&(~hBOOL(hAPP(X16363,hAPP(hAPP(c_Set_Oinsert(X16365),esk489_3(X16363,X16364,X16365)),esk490_3(X16363,X16364,X16365))))|hBOOL(hAPP(X16363,X16364))|~hBOOL(hAPP(X16363,c_Orderings_Obot__class_Obot(tc_fun(X16365,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16365),X16364)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__induct])])])])])). 4.05/4.31 fof(c_0_8243, plain, ![X14902, X14903]:(~class_Rings_Olinordered__idom(X14903)|~class_Int_Onumber__ring(X14903)|c_Groups_Oone__class_Oone(X14903)=hAPP(c_Groups_Oabs__class_Oabs(X14903),hAPP(hAPP(c_Power_Opower__class_Opower(X14903),hAPP(c_Int_Onumber__class_Onumber__of(X14903),c_Int_OMin)),X14902))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus__one])])). 4.05/4.31 fof(c_0_8244, plain, ![X3043, X3044, X3045, X3046]:(~class_Orderings_Opreorder(X3046)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3046),X3045),X3044))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3046),X3044),X3043))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3046),X3045),X3043))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__trans])])])). 4.05/4.31 fof(c_0_8245, plain, ![X12574, X12575]:((hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk385_2(X12574,X12575)),c_Int_OInteg))|hBOOL(hAPP(X12575,X12574)))&(~hBOOL(hAPP(X12575,hAPP(c_Int_OAbs__Integ,esk385_2(X12574,X12575))))|hBOOL(hAPP(X12575,X12574)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Abs__Integ__induct])])])])])). 4.05/4.31 fof(c_0_8246, plain, ![X8046, X8047, X8048, X8049, X8050]:(hAPP(c_Option_Ooption_OSome(X8048),X8047)!=hAPP(X8050,X8049)|c_Map_Odom(X8046,X8048,X8050)=hAPP(hAPP(c_Set_Oinsert(X8046),X8049),c_Map_Odom(X8046,X8048,X8050))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insert__dom])])])). 4.05/4.31 fof(c_0_8247, plain, ![X8839, X8840]:(~class_Groups_Oordered__ab__group__add(X8840)|hAPP(c_Set_Oimage(X8840,X8840,c_Groups_Ouminus__class_Ouminus(X8840)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X8840),X8839))=hAPP(c_SetInterval_Oord__class_OlessThan(X8840),hAPP(c_Groups_Ouminus__class_Ouminus(X8840),X8839))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThan])])). 4.05/4.31 fof(c_0_8248, plain, ![X4952, X4953]:(~class_Groups_Oordered__ab__group__add(X4953)|hAPP(c_Set_Oimage(X4953,X4953,c_Groups_Ouminus__class_Ouminus(X4953)),hAPP(c_SetInterval_Oord__class_OlessThan(X4953),X4952))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X4953),hAPP(c_Groups_Ouminus__class_Ouminus(X4953),X4952))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__uminus__lessThan])])])). 4.05/4.31 fof(c_0_8249, plain, ![X6559, X6560, X6561, X6562]:(~class_Orderings_Opreorder(X6562)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6562),X6561),X6560))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6562),X6560),X6559))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6562),X6561),X6559))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__le__less__trans])])])). 4.05/4.31 fof(c_0_8250, plain, ![X8060, X8061, X8062, X8063]:(~class_Orderings_Opreorder(X8063)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8063),X8062),X8061))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8063),X8061),X8060))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8063),X8062),X8060))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__le__trans])])])). 4.05/4.31 fof(c_0_8251, plain, ![X16369, X16370, X16371, X16372]:(~class_Orderings_Oorder(X16372)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16372),X16371),X16370))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16372),X16369),X16371))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16372),X16369),X16370))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I10_J])])])). 4.05/4.31 fof(c_0_8252, plain, ![X10133, X10134, X10135, X10136]:(~class_Orderings_Oorder(X10136)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10136),X10135),X10134))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10136),X10133),X10135))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10136),X10133),X10134))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I8_J])])])). 4.05/4.31 fof(c_0_8253, plain, ![X6279, X6280]:(~class_Groups_Oordered__ab__group__add(X6280)|hAPP(c_Set_Oimage(X6280,X6280,c_Groups_Ouminus__class_Ouminus(X6280)),hAPP(c_SetInterval_Oord__class_OatMost(X6280),X6279))=hAPP(c_SetInterval_Oord__class_OatLeast(X6280),hAPP(c_Groups_Ouminus__class_Ouminus(X6280),X6279))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__uminus__atMost])])])). 4.05/4.31 fof(c_0_8254, plain, ![X2357, X2358]:(~class_Groups_Oordered__ab__group__add(X2358)|hAPP(c_SetInterval_Oord__class_OatMost(X2358),hAPP(c_Groups_Ouminus__class_Ouminus(X2358),X2357))=hAPP(c_Set_Oimage(X2358,X2358,c_Groups_Ouminus__class_Ouminus(X2358)),hAPP(c_SetInterval_Oord__class_OatLeast(X2358),X2357))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_image__uminus__atLeast])])])). 4.05/4.31 fof(c_0_8255, plain, ![X9548, X9549, X9550, X9551]:(~class_Complete__Lattice_Ocomplete__lattice(X9551)|(c_Orderings_Obot__class_Obot(tc_fun(X9549,tc_HOL_Obool))=X9550|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9549,X9551),X9550),hAPP(c_COMBK(X9551,X9549),X9548))=X9548)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__const])])). 4.05/4.31 fof(c_0_8256, plain, ![X8179, X8180, X8181, X8182]:(~class_Orderings_Oorder(X8182)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8182),X8181),X8180))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8182),X8179),X8181))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8182),X8179),X8180))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I7_J])])])). 4.05/4.31 fof(c_0_8257, plain, ![X16529, X16530, X16531, X16532]:(~class_Orderings_Opreorder(X16532)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16532),X16531),X16530))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16532),X16530),X16529))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16532),X16531),X16529))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__trans])])])). 4.05/4.31 fof(c_0_8258, plain, ![X1652, X1653, X1654, X1655]:(~class_Orderings_Oorder(X1655)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1655),X1654),X1653))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1655),X1652),X1654))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1655),X1652),X1653))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I6_J])])])). 4.05/4.31 fof(c_0_8259, plain, ![X3183, X3184, X3185, X3186, X3187, X3188, X3189, X3190]:(~c_Equiv__Relations_Oequiv(X3190,X3189,X3188)|(~c_Equiv__Relations_Ocongruent2(X3190,X3187,X3186,X3188,X3185,X3184)|(~hBOOL(hAPP(hAPP(c_member(X3190),X3183),X3189))|c_Equiv__Relations_Ocongruent(X3187,X3186,X3185,hAPP(X3184,X3183))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_congruent2__implies__congruent])])])). 4.05/4.31 fof(c_0_8260, plain, ![X4783, X4784, X4785]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X4785),X4784))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4785,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4785,X4785,X4783),X4784)),X4784))|(~c_Fun_Oinj__on(X4785,X4785,X4783,X4784)|X4784=hAPP(c_Set_Oimage(X4785,X4785,X4783),X4784)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_endo__inj__surj])])])). 4.05/4.31 fof(c_0_8261, plain, ![X16092, X16093, X16094]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X16094,X16094),tc_HOL_Obool)),X16093),X16092))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X16094,X16094),tc_HOL_Obool)),X16092),c_Transitive__Closure_Ortrancl(X16094,X16093)))|c_Transitive__Closure_Ortrancl(X16094,X16093)=c_Transitive__Closure_Ortrancl(X16094,X16092))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset])])). 4.05/4.31 fof(c_0_8262, plain, ![X4235, X4236, X4237, X4238]:((~c_Fun_Oinj__on(X4238,tc_Option_Ooption(X4237),X4235,c_Map_Odom(X4238,X4237,X4235))|c_Fun_Oinj__on(X4238,tc_Option_Ooption(X4237),c_Map_Omap__add(X4238,X4237,X4236,X4235),c_Map_Odom(X4238,X4237,X4235)))&(~c_Fun_Oinj__on(X4238,tc_Option_Ooption(X4237),c_Map_Omap__add(X4238,X4237,X4236,X4235),c_Map_Odom(X4238,X4237,X4235))|c_Fun_Oinj__on(X4238,tc_Option_Ooption(X4237),X4235,c_Map_Odom(X4238,X4237,X4235)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__map__add__dom])])). 4.05/4.31 fof(c_0_8263, plain, ![X4858, X4859, X4860, X4861]:(~class_Complete__Lattice_Ocomplete__lattice(X4861)|(X4860=c_Orderings_Obot__class_Obot(tc_fun(X4859,tc_HOL_Obool))|X4858=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4859,X4861),X4860),hAPP(c_COMBK(X4861,X4859),X4858)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SUP__const])])])). 4.05/4.31 fof(c_0_8264, plain, ![X16122, X16123, X16124]:((~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,X16124)),X16123)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X16124)),X16122)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16123),X16122)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16123),X16122))|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,X16124)),X16123)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X16124)),X16122))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1])])). 4.05/4.31 fof(c_0_8265, plain, ![X9089, X9090, X9091]:(~class_Groups_Ogroup__add(X9091)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9091),X9090),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9091),hAPP(c_Groups_Ouminus__class_Ouminus(X9091),X9090)),X9089))=X9089), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__minus__cancel])])])). 4.05/4.31 fof(c_0_8266, plain, ![X2904, X2905, X2906]:(~class_Groups_Ogroup__add(X2906)|X2904=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2906),hAPP(c_Groups_Ouminus__class_Ouminus(X2906),X2905)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2906),X2905),X2904))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__add__cancel])])])). 4.05/4.31 fof(c_0_8267, plain, ![X10508, X10509, X10510, X10511, X10512, X10513]:(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10513,tc_fun(X10512,tc_HOL_Obool))),X10511),X10510),X10509),X10508))|(hBOOL(hAPP(hAPP(X10511,X10509),X10508))|hBOOL(hAPP(hAPP(X10510,X10509),X10508)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup2E])])])). 4.05/4.31 fof(c_0_8268, plain, ![X16709, X16710, X16711]:(~class_Orderings_Olinorder(X16711)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16711),X16710))|(~hBOOL(hAPP(hAPP(c_member(X16711),X16709),X16710))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X16711),X16709),c_Big__Operators_Olinorder__class_OMin(X16711,X16710))=c_Big__Operators_Olinorder__class_OMin(X16711,X16710)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Oin__idem])])])). 4.05/4.31 fof(c_0_8269, plain, ![X5033, X5034, X5035]:(~class_Orderings_Olinorder(X5035)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5035),X5034))|(~hBOOL(hAPP(hAPP(c_member(X5035),X5033),X5034))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X5035),X5033),c_Big__Operators_Olinorder__class_OMax(X5035,X5034))=c_Big__Operators_Olinorder__class_OMax(X5035,X5034)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Oin__idem])])])). 4.05/4.31 cnf(c_0_8270, 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_5492])). 4.05/4.31 fof(c_0_8271, plain, ![X16483, X16484, X16485, X16486]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X16486,tc_HOL_Obool)),X16485),X16484))|(~hBOOL(hAPP(hAPP(c_member(X16486),X16483),X16485))|hBOOL(hAPP(hAPP(c_member(X16486),X16483),X16484)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_psubsetD])])])). 4.05/4.31 fof(c_0_8272, plain, ![X12266, X12267, X12268]:(~class_Lattices_Olattice(X12268)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12268),X12267))|(~hBOOL(hAPP(hAPP(c_member(X12268),X12266),X12267))|c_Big__Operators_Olattice__class_OInf__fin(X12268,X12267)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12268),X12266),c_Big__Operators_Olattice__class_OInf__fin(X12268,X12267))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oin__idem])])). 4.05/4.31 fof(c_0_8273, plain, ![X12233, X12234, X12235]:(~class_Lattices_Olattice(X12235)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12235),X12234))|(~hBOOL(hAPP(hAPP(c_member(X12235),X12233),X12234))|c_Big__Operators_Olattice__class_OSup__fin(X12235,X12234)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X12235),X12233),c_Big__Operators_Olattice__class_OSup__fin(X12235,X12234))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oin__idem])])])). 4.05/4.31 cnf(c_0_8274, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk254_2(X1,X2))=X1|hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1)))), inference(split_conjunct,[status(thm)],[c_0_5493])). 4.05/4.31 fof(c_0_8275, plain, ![X6461, X6462]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6462),X6461))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X6461,X6462)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6461),X6462),X6462)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__mod__geq])])])). 4.05/4.31 fof(c_0_8276, plain, ![X5676, X5677, X5678, X5679, X5680]:(~hBOOL(hAPP(hAPP(c_member(X5680),X5679),X5678))|hBOOL(hAPP(hAPP(c_member(X5677),hAPP(X5676,X5679)),hAPP(c_Set_Oimage(X5680,X5677,X5676),X5678)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_imageI])])])). 4.05/4.31 fof(c_0_8277, plain, ![X1689, X1690, X1691, X1692]:((~hBOOL(hAPP(hAPP(c_member(X1692),X1691),X1690))|hBOOL(hAPP(hAPP(c_member(X1692),X1691),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1692,tc_HOL_Obool)),X1689),X1690))))&(~hBOOL(hAPP(hAPP(c_member(X1692),X1691),X1689))|hBOOL(hAPP(hAPP(c_member(X1692),X1691),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1692,tc_HOL_Obool)),X1689),X1690))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_UnCI])])])])). 4.05/4.31 fof(c_0_8278, plain, ![X966, X967, X968, X969, X970, X971]:(~c_Map_Omap__le(X971,X970,X969,X968)|c_Map_Omap__le(X971,X970,c_Map_Omap__upds(X971,X970,X969,X967,X966),c_Map_Omap__upds(X971,X970,X968,X967,X966))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__le__upds])])])). 4.05/4.31 fof(c_0_8279, plain, ![X12548, X12549, X12550, X12551]:(c_Orderings_Obot__class_Obot(tc_fun(X12551,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12551,tc_HOL_Obool)),c_Map_Odom(X12551,X12550,X12549)),c_Map_Odom(X12551,X12550,X12548))|c_Map_Omap__add(X12551,X12550,X12548,X12549)=c_Map_Omap__add(X12551,X12550,X12549,X12548)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__comm])])). 4.05/4.31 fof(c_0_8280, plain, ![X5674, X5675]:((c_Groups_Ozero__class_Ozero(X5675)!=X5674|c_Groups_Ozero__class_Ozero(X5675)=c_Groups_Osgn__class_Osgn(X5675,X5674)|~class_Groups_Osgn__if(X5675))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5675),c_Groups_Ozero__class_Ozero(X5675)),X5674))|c_Groups_Osgn__class_Osgn(X5675,X5674)=hAPP(c_Groups_Ouminus__class_Ouminus(X5675),c_Groups_Oone__class_Oone(X5675))|c_Groups_Ozero__class_Ozero(X5675)=X5674|~class_Groups_Osgn__if(X5675))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5675),c_Groups_Ozero__class_Ozero(X5675)),X5674))|c_Groups_Oone__class_Oone(X5675)=c_Groups_Osgn__class_Osgn(X5675,X5674)|c_Groups_Ozero__class_Ozero(X5675)=X5674|~class_Groups_Osgn__if(X5675)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__if])])])])). 4.05/4.31 fof(c_0_8281, plain, ![X7682, X7683, X7684]:(~class_Divides_Osemiring__div(X7684)|(c_Groups_Ozero__class_Ozero(X7684)=X7683|X7682=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X7684),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7684),X7683),X7682)),X7683))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__mult__self1__is__id])])])). 4.05/4.31 fof(c_0_8282, plain, ![X5108, X5109, X5110]:(~class_Divides_Osemiring__div(X5110)|(X5109=c_Groups_Ozero__class_Ozero(X5110)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X5110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5110),X5108),X5109)),X5109)=X5108)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2__is__id])])). 4.05/4.31 fof(c_0_8283, plain, ![X14163, X14164, X14165]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14165)),c_List_OtakeWhile(X14165,X14164,X14163))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14165)),X14163)))|~hBOOL(hAPP(X14164,hAPP(hAPP(c_List_Onth(X14165),X14163),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14165)),c_List_OtakeWhile(X14165,X14164,X14163)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__length__takeWhile])])])). 4.05/4.31 fof(c_0_8284, plain, ![X9206, X9207, X9208]:(~class_Rings_Olinordered__idom(X9208)|(X9207=X9206|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9208),X9207),X9206))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9208),X9206),X9207))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom])])])). 4.05/4.31 fof(c_0_8285, plain, ![X13035, X13036, X13037, X13038]:(~class_Groups_Oordered__ab__semigroup__add__imp__le(X13038)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13038),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13038),X13037),X13036)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13038),X13037),X13035)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13038),X13036),X13035)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__less__imp__less__left])])])). 4.05/4.31 fof(c_0_8286, plain, ![X2857, X2860, X2861, X2862, X2863, X2864, X2865, X2866]:(((hAPP(X2857,esk98_1(X2857))!=hAPP(X2857,esk99_1(X2857))|~hBOOL(hAPP(hAPP(X2857,esk98_1(X2857)),esk99_1(X2857)))|c_Equiv__Relations_Oequivp(X2860,X2857))&(hAPP(X2857,esk98_1(X2857))=hAPP(X2857,esk99_1(X2857))|hBOOL(hAPP(hAPP(X2857,esk98_1(X2857)),esk99_1(X2857)))|c_Equiv__Relations_Oequivp(X2860,X2857)))&((hAPP(X2861,X2863)!=hAPP(X2861,X2864)|hBOOL(hAPP(hAPP(X2861,X2863),X2864))|~c_Equiv__Relations_Oequivp(X2862,X2861))&(~hBOOL(hAPP(hAPP(X2861,X2865),X2866))|hAPP(X2861,X2865)=hAPP(X2861,X2866)|~c_Equiv__Relations_Oequivp(X2862,X2861)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__def])])])])])])). 4.05/4.31 fof(c_0_8287, plain, ![X8002, X8003, X8004]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8004),X8002),X8003))|X8003=X8002|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8004),X8003),X8002))|~class_Orderings_Olinorder(X8004))&(X8003!=X8002|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8004),X8002),X8003))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8004),X8003),X8002))|~class_Orderings_Olinorder(X8004))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3])])])])). 4.05/4.31 fof(c_0_8288, plain, ![X17162, X17163, X17164, X17165, X17166]:(~c_Finite__Set_Ofolding__idem(X17166,X17165,X17164,X17163)|hAPP(X17164,X17162)=hAPP(c_Fun_Ocomp(X17165,X17165,X17165,hAPP(X17164,X17162)),hAPP(X17164,X17162))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__idem_Oidem__comp])])])). 4.05/4.31 fof(c_0_8289, plain, ![X14824, X14825, X14826]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14825),X14824))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14826),hAPP(c_Int_Oring__1__class_Oof__int(X14826),X14825)),hAPP(c_Int_Oring__1__class_Oof__int(X14826),X14824)))|~class_Rings_Olinordered__idom(X14826))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14826),hAPP(c_Int_Oring__1__class_Oof__int(X14826),X14825)),hAPP(c_Int_Oring__1__class_Oof__int(X14826),X14824)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14825),X14824))|~class_Rings_Olinordered__idom(X14826))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__less__iff])])])])). 4.05/4.31 fof(c_0_8290, plain, ![X9313, X9314, X9315]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9314),X9313))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9315),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X9315),X9314)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X9315),X9313)))|~class_Rings_Olinordered__semidom(X9315))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9315),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X9315),X9314)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X9315),X9313)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9314),X9313))|~class_Rings_Olinordered__semidom(X9315))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__iff])])])). 4.05/4.31 fof(c_0_8291, plain, ![X2687, X2688, X2689]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2689),hAPP(c_Int_Oring__1__class_Oof__int(X2689),X2688)),hAPP(c_Int_Oring__1__class_Oof__int(X2689),X2687)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2688),X2687))|~class_Rings_Olinordered__idom(X2689))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2688),X2687))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2689),hAPP(c_Int_Oring__1__class_Oof__int(X2689),X2688)),hAPP(c_Int_Oring__1__class_Oof__int(X2689),X2687)))|~class_Rings_Olinordered__idom(X2689))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__le__iff])])])])). 4.05/4.31 fof(c_0_8292, plain, ![X7895, X7896, X7897]:(~class_Divides_Oring__div(X7897)|c_Divides_Odiv__class_Omod(X7897,hAPP(c_Groups_Ouminus__class_Ouminus(X7897),c_Divides_Odiv__class_Omod(X7897,X7896,X7895)),X7895)=c_Divides_Odiv__class_Omod(X7897,hAPP(c_Groups_Ouminus__class_Ouminus(X7897),X7896),X7895)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__minus__eq])])])). 4.05/4.31 fof(c_0_8293, plain, ![X12613, X12614, X12615]:(~c_Wellfounded_Owf(X12615,X12614)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X12615,X12615)),hAPP(hAPP(c_Product__Type_OPair(X12615,X12615),hAPP(X12613,hAPP(c_Nat_OSuc,esk387_3(X12613,X12614,X12615)))),hAPP(X12613,esk387_3(X12613,X12614,X12615)))),X12614))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__no__infinite__down__chainE])])])). 4.05/4.31 fof(c_0_8294, plain, ![X5983, X5984, X5985]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5985),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5985),X5984)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5985),X5983)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5984),X5983))|~class_Rings_Olinordered__semidom(X5985))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5984),X5983))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5985),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5985),X5984)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5985),X5983)))|~class_Rings_Olinordered__semidom(X5985))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__le__iff])])])])). 4.05/4.31 fof(c_0_8295, plain, ![X10207, X10208, X10209]:(~class_Rings_Olinordered__idom(X10209)|hAPP(c_Groups_Oabs__class_Oabs(X10209),hAPP(hAPP(c_Power_Opower__class_Opower(X10209),X10208),X10207))=hAPP(hAPP(c_Power_Opower__class_Opower(X10209),hAPP(c_Groups_Oabs__class_Oabs(X10209),X10208)),X10207)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__abs])])])). 4.05/4.31 fof(c_0_8296, plain, ![X7685, X7686, X7687]:(~class_Groups_Omonoid__add(X7687)|hAPP(c_List_Omonoid__add__class_Olistsum(X7687),hAPP(hAPP(c_List_Olist_OCons(X7687),X7686),X7685))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7687),X7686),hAPP(c_List_Omonoid__add__class_Olistsum(X7687),X7685))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__simps_I2_J])])])). 4.05/4.31 fof(c_0_8297, plain, ![X8534, X8535, X8536, X8537, X8538]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8538),X8537),X8536))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8538),X8535),X8534))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8538),X8537),X8536)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8538),X8535),X8534)|~class_Groups_Oordered__ab__group__add(X8538))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8538),X8535),X8534))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8538),X8537),X8536))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8538),X8537),X8536)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8538),X8535),X8534)|~class_Groups_Oordered__ab__group__add(X8538))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__eq__diff__less])])])])). 4.05/4.31 fof(c_0_8298, plain, ![X882, X883, X884]:((~hBOOL(hAPP(hAPP(c_member(X884),X883),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X884,tc_HOL_Obool)),X882)))|~hBOOL(hAPP(hAPP(c_member(X884),X883),X882)))&(hBOOL(hAPP(hAPP(c_member(X884),X883),X882))|hBOOL(hAPP(hAPP(c_member(X884),X883),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X884,tc_HOL_Obool)),X882))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Compl__iff])])])). 4.05/4.31 fof(c_0_8299, plain, ![X4884, X4885, X4886, X4887, X4888]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4888),X4887),X4886))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4888),X4885),X4884))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4888),X4885),X4884)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4888),X4887),X4886)|~class_Groups_Oordered__ab__group__add(X4888))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4888),X4885),X4884))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4888),X4887),X4886))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4888),X4885),X4884)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4888),X4887),X4886)|~class_Groups_Oordered__ab__group__add(X4888))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__eq__diff__less__eq])])])])). 4.05/4.31 fof(c_0_8300, plain, ![X17542, X17543, X17544]:(~class_Lattices_Oboolean__algebra(X17544)|(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X17544),X17543),X17542)!=c_Orderings_Obot__class_Obot(X17544)|(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X17544),X17543),X17542)!=c_Orderings_Otop__class_Otop(X17544)|X17542=hAPP(c_Groups_Ouminus__class_Ouminus(X17544),X17543)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__unique])])). 4.05/4.31 fof(c_0_8301, plain, ![X4490, X4491, X4492, X4493]:(c_List_Olist_ONil(X4492)=X4493|hAPP(X4490,hAPP(c_List_Ohd(X4492),X4493))=hAPP(c_List_Ohd(X4491),hAPP(hAPP(c_List_Omap(X4492,X4491),X4490),X4493))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__map])])). 4.05/4.31 fof(c_0_8302, plain, ![X10418, X10419, X10420]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10420),X10419))|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10420),X10418))|hBOOL(hAPP(c_Finite__Set_Ofinite(X10420),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10420,tc_HOL_Obool)),X10419),X10418))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__UnI])])])). 4.05/4.31 fof(c_0_8303, plain, ![X9016, X9017, X9018, X9019, X9020]:(((hBOOL(hAPP(hAPP(X9018,X9019),X9016))|~hBOOL(hAPP(hAPP(c_member(X9020),X9019),c_SetInterval_Oord_OatLeastAtMost(X9020,X9018,X9017,X9016))))&(hBOOL(hAPP(hAPP(X9018,X9017),X9019))|~hBOOL(hAPP(hAPP(c_member(X9020),X9019),c_SetInterval_Oord_OatLeastAtMost(X9020,X9018,X9017,X9016)))))&(~hBOOL(hAPP(hAPP(X9018,X9019),X9016))|~hBOOL(hAPP(hAPP(X9018,X9017),X9019))|hBOOL(hAPP(hAPP(c_member(X9020),X9019),c_SetInterval_Oord_OatLeastAtMost(X9020,X9018,X9017,X9016))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastAtMost__iff])])])). 4.05/4.31 fof(c_0_8304, plain, ![X9678, X9679, X9680, X9681, X9682]:(((hBOOL(hAPP(hAPP(X9680,X9679),X9681))|~hBOOL(hAPP(hAPP(c_member(X9682),X9681),c_SetInterval_Oord_OgreaterThanLessThan(X9682,X9680,X9679,X9678))))&(hBOOL(hAPP(hAPP(X9680,X9681),X9678))|~hBOOL(hAPP(hAPP(c_member(X9682),X9681),c_SetInterval_Oord_OgreaterThanLessThan(X9682,X9680,X9679,X9678)))))&(~hBOOL(hAPP(hAPP(X9680,X9679),X9681))|~hBOOL(hAPP(hAPP(X9680,X9681),X9678))|hBOOL(hAPP(hAPP(c_member(X9682),X9681),c_SetInterval_Oord_OgreaterThanLessThan(X9682,X9680,X9679,X9678))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanLessThan__iff])])])). 4.05/4.31 fof(c_0_8305, plain, ![X16515, X16516, X16517, X16518]:(~class_Rings_Osemiring__1(X16518)|c_Nat_Osemiring__1__class_Oof__nat__aux(X16518,X16517,hAPP(c_Nat_OSuc,X16516),X16515)=c_Nat_Osemiring__1__class_Oof__nat__aux(X16518,X16517,X16516,hAPP(X16517,X16515))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I2_J])])). 4.05/4.31 fof(c_0_8306, plain, ![X12748, X12749, X12750, X12751, X12752, X12753, X12754]:(hAPP(hAPP(c_List_Omap(X12754,X12753),X12752),X12751)!=hAPP(hAPP(c_List_Omap(X12750,X12753),X12749),X12748)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12750)),X12748)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12754)),X12751)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__eq__imp__length__eq])])])). 4.05/4.31 fof(c_0_8307, plain, ![X1620, X1621, X1622, X1623, X1624, X1626, X1627, X1628, X1629, X1630, X1631]:(((((c_Natural_Oevaln(c_Com_Ocom_OWhile(X1624,X1623),esk53_5(X1620,X1621,X1622,X1623,X1624),X1621,X1620)|X1622=X1620|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X1624,X1623),X1622,X1621,X1620))&(c_Natural_Oevaln(X1623,X1622,X1621,esk53_5(X1620,X1621,X1622,X1623,X1624))|X1622=X1620|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X1624,X1623),X1622,X1621,X1620)))&(hBOOL(hAPP(X1624,X1622))|X1622=X1620|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X1624,X1623),X1622,X1621,X1620)))&(((c_Natural_Oevaln(c_Com_Ocom_OWhile(X1624,X1623),esk53_5(X1620,X1621,X1622,X1623,X1624),X1621,X1620)|~hBOOL(hAPP(X1624,X1622))|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X1624,X1623),X1622,X1621,X1620))&(c_Natural_Oevaln(X1623,X1622,X1621,esk53_5(X1620,X1621,X1622,X1623,X1624))|~hBOOL(hAPP(X1624,X1622))|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X1624,X1623),X1622,X1621,X1620)))&(hBOOL(hAPP(X1624,X1622))|~hBOOL(hAPP(X1624,X1622))|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X1624,X1623),X1622,X1621,X1620))))&((X1628!=X1626|hBOOL(hAPP(X1630,X1628))|c_Natural_Oevaln(c_Com_Ocom_OWhile(X1630,X1629),X1628,X1627,X1626))&(~c_Natural_Oevaln(c_Com_Ocom_OWhile(X1630,X1629),X1631,X1627,X1626)|~c_Natural_Oevaln(X1629,X1628,X1627,X1631)|~hBOOL(hAPP(X1630,X1628))|c_Natural_Oevaln(c_Com_Ocom_OWhile(X1630,X1629),X1628,X1627,X1626)))), 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_evaln_Oequations_I8_J])])])])])])])). 4.05/4.31 fof(c_0_8308, plain, ![X5389, X5390, X5391]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5391,tc_HOL_Obool)),X5390),X5389))|hBOOL(hAPP(hAPP(c_member(tc_fun(X5391,tc_HOL_Obool)),X5390),hAPP(c_Set_OPow(X5391),X5389)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_PowI])])). 4.05/4.31 fof(c_0_8309, plain, ![X13749, X13750]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13750))|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),X13750),X13749))))&(X13749!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X13750),X13749)))))&(~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),X13750),X13749)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13750))|X13749=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])])). 4.05/4.31 fof(c_0_8310, plain, ![X5815, X5816, X5817]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X5817|hAPP(c_List_Oset(X5816),c_List_Oreplicate(X5816,X5817,X5815))=c_Orderings_Obot__class_Obot(tc_fun(X5816,tc_HOL_Obool)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X5817|hAPP(c_List_Oset(X5816),c_List_Oreplicate(X5816,X5817,X5815))=hAPP(hAPP(c_Set_Oinsert(X5816),X5815),c_Orderings_Obot__class_Obot(tc_fun(X5816,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__replicate__conv__if])])])). 4.05/4.31 fof(c_0_8311, plain, ![X11147, X11148, X11149]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11149),X11148))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11148),X11147))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X11149)),X11147)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__trans__Suc])])])). 4.05/4.31 fof(c_0_8312, plain, ![X7010, X7011, X7012, X7013, X7014, X7015, X7016]:((~hBOOL(hAPP(hAPP(c_member(X7012),X7013),hAPP(c_List_Oset(X7012),X7010)))|~hBOOL(hAPP(X7011,X7013))|c_List_Olist__ex(X7012,X7011,X7010))&((hBOOL(hAPP(hAPP(c_member(X7016),esk218_3(X7014,X7015,X7016)),hAPP(c_List_Oset(X7016),X7014)))|~c_List_Olist__ex(X7016,X7015,X7014))&(hBOOL(hAPP(X7015,esk218_3(X7014,X7015,X7016)))|~c_List_Olist__ex(X7016,X7015,X7014)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__iff])])])])])])). 4.05/4.31 fof(c_0_8313, plain, ![X11133, X11134, X11135, X11136]:(((hBOOL(hAPP(c_List_Olistsp(X11136,X11135),X11133))|~hBOOL(hAPP(c_List_Olistsp(X11136,X11135),hAPP(hAPP(c_List_Oappend(X11136),X11134),X11133))))&(hBOOL(hAPP(c_List_Olistsp(X11136,X11135),X11134))|~hBOOL(hAPP(c_List_Olistsp(X11136,X11135),hAPP(hAPP(c_List_Oappend(X11136),X11134),X11133)))))&(~hBOOL(hAPP(c_List_Olistsp(X11136,X11135),X11133))|~hBOOL(hAPP(c_List_Olistsp(X11136,X11135),X11134))|hBOOL(hAPP(c_List_Olistsp(X11136,X11135),hAPP(hAPP(c_List_Oappend(X11136),X11134),X11133))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__listsp__conv])])])). 4.05/4.31 fof(c_0_8314, plain, ![X10969, X10970, X10971]:(~c_Equiv__Relations_Oequiv(X10971,X10970,X10969)|X10969=hAPP(hAPP(c_Relation_Orel__comp(X10971,X10971,X10971),hAPP(c_Relation_Oconverse(X10971,X10971),X10969)),X10969)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equiv__comp__eq])])])). 4.05/4.31 fof(c_0_8315, plain, ![X2415, X2416]:(~class_Complete__Lattice_Ocomplete__lattice(X2416)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2416),X2415))|c_Complete__Lattice_OSup__class_OSup(X2416,X2415)=hAPP(hAPP(c_Finite__Set_Ofold(X2416,X2416,c_Lattices_Osemilattice__sup__class_Osup(X2416)),c_Orderings_Obot__class_Obot(X2416)),X2415))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fold__sup])])])). 4.05/4.31 fof(c_0_8316, plain, ![X1989, X1990]:(~class_Complete__Lattice_Ocomplete__lattice(X1990)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X1990),X1989))|c_Complete__Lattice_OInf__class_OInf(X1990,X1989)=hAPP(hAPP(c_Finite__Set_Ofold(X1990,X1990,c_Lattices_Osemilattice__inf__class_Oinf(X1990)),c_Orderings_Otop__class_Otop(X1990)),X1989))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fold__inf])])])). 4.05/4.31 cnf(c_0_8317, 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_5494])). 4.05/4.31 fof(c_0_8318, plain, ![X1066, X1067]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1067),hAPP(c_Groups_Ouminus__class_Ouminus(X1067),X1066)),c_Groups_Ozero__class_Ozero(X1067)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1067),c_Groups_Ozero__class_Ozero(X1067)),X1066))|~class_Groups_Oordered__ab__group__add(X1067))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1067),c_Groups_Ozero__class_Ozero(X1067)),X1066))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1067),hAPP(c_Groups_Ouminus__class_Ouminus(X1067),X1066)),c_Groups_Ozero__class_Ozero(X1067)))|~class_Groups_Oordered__ab__group__add(X1067))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less])])])). 4.05/4.31 fof(c_0_8319, plain, ![X16666, X16667]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16667),hAPP(c_Groups_Ouminus__class_Ouminus(X16667),X16666)),c_Groups_Ozero__class_Ozero(X16667)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16667),c_Groups_Ozero__class_Ozero(X16667)),X16666))|~class_Groups_Oordered__ab__group__add(X16667))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16667),c_Groups_Ozero__class_Ozero(X16667)),X16666))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16667),hAPP(c_Groups_Ouminus__class_Ouminus(X16667),X16666)),c_Groups_Ozero__class_Ozero(X16667)))|~class_Groups_Oordered__ab__group__add(X16667))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le])])])). 4.05/4.31 fof(c_0_8320, plain, ![X12840, X12841]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12841),c_Groups_Ozero__class_Ozero(X12841)),hAPP(c_Groups_Ouminus__class_Ouminus(X12841),X12840)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12841),X12840),c_Groups_Ozero__class_Ozero(X12841)))|~class_Groups_Oordered__ab__group__add(X12841))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12841),X12840),c_Groups_Ozero__class_Ozero(X12841)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X12841),c_Groups_Ozero__class_Ozero(X12841)),hAPP(c_Groups_Ouminus__class_Ouminus(X12841),X12840)))|~class_Groups_Oordered__ab__group__add(X12841))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less])])])). 4.05/4.31 fof(c_0_8321, plain, ![X3052, X3053, X3054, X3055]:(~c_Finite__Set_Ofolding__one(X3055,X3054,X3053)|X3052=hAPP(X3053,hAPP(hAPP(c_Set_Oinsert(X3055),X3052),c_Orderings_Obot__class_Obot(tc_fun(X3055,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Osingleton])])). 4.05/4.31 fof(c_0_8322, plain, ![X12337, X12338, X12339, X12340, X12341, X12342, X12343]:((hAPP(X12340,X12338)!=hAPP(X12340,X12337)|X12337=X12338|~hBOOL(hAPP(hAPP(c_member(X12342),X12337),X12339))|~hBOOL(hAPP(hAPP(c_member(X12342),X12338),X12339))|~c_Typedef_Otype__definition(X12343,X12342,X12341,X12340,X12339))&(X12337!=X12338|hAPP(X12340,X12338)=hAPP(X12340,X12337)|~hBOOL(hAPP(hAPP(c_member(X12342),X12337),X12339))|~hBOOL(hAPP(hAPP(c_member(X12342),X12338),X12339))|~c_Typedef_Otype__definition(X12343,X12342,X12341,X12340,X12339))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_type__definition_OAbs__inject])])])])). 4.05/4.31 fof(c_0_8323, plain, ![X13747, X13748]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13748),X13747),c_Groups_Ozero__class_Ozero(X13748)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13748),c_Groups_Ozero__class_Ozero(X13748)),hAPP(c_Groups_Ouminus__class_Ouminus(X13748),X13747)))|~class_Groups_Oordered__ab__group__add(X13748))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13748),c_Groups_Ozero__class_Ozero(X13748)),hAPP(c_Groups_Ouminus__class_Ouminus(X13748),X13747)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13748),X13747),c_Groups_Ozero__class_Ozero(X13748)))|~class_Groups_Oordered__ab__group__add(X13748))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le])])])). 4.05/4.31 fof(c_0_8324, plain, ![X13414, X13415]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13415),c_Groups_Ozero__class_Ozero(X13415)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13415),X13414)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13414))|~class_Rings_Olinordered__semidom(X13415))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13414))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13415),c_Groups_Ozero__class_Ozero(X13415)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13415),X13414)))|~class_Rings_Olinordered__semidom(X13415))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0__less__iff])])])). 4.05/4.31 cnf(c_0_8325, 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_5495])). 4.05/4.31 fof(c_0_8326, plain, ![X11660, X11661, X11662, X11663, X11664, X11665]:(~hBOOL(hAPP(hAPP(X11665,X11664),X11663))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11662,tc_fun(X11661,tc_HOL_Obool))),X11665),X11660))|hBOOL(hAPP(hAPP(X11660,X11664),X11663)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rev__predicate2D])])])). 4.05/4.31 cnf(c_0_8327, 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_5443])). 4.05/4.31 fof(c_0_8328, plain, ![X8153, X8154, X8155, X8156]:(~c_Fun_Oinj__on(X8156,X8155,X8154,X8153)|c_Fun_Oinj__on(X8155,X8156,c_Fun_Othe__inv__into(X8156,X8155,X8153,X8154),hAPP(c_Set_Oimage(X8156,X8155,X8154),X8153))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__the__inv__into])])])). 4.05/4.31 fof(c_0_8329, plain, ![X15828, X15829, X15830, X15831]:(~hBOOL(hAPP(c_List_Odistinct(X15831),X15830))|(~hBOOL(hAPP(c_List_Odistinct(X15829),X15828))|hBOOL(hAPP(c_List_Odistinct(tc_prod(X15831,X15829)),c_Enum_Oproduct(X15831,X15829,X15830,X15828))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__product])])])). 4.05/4.31 fof(c_0_8330, plain, ![X7421, X7422, X7423]:(~class_Orderings_Olinorder(X7423)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X7423),X7422),X7421)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X7423),X7422),hAPP(hAPP(c_Orderings_Oord__class_Omin(X7423),X7422),X7421))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__left__idem])])])). 4.05/4.31 fof(c_0_8331, plain, ![X2392, X2393, X2394]:(~class_Orderings_Olinorder(X2394)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X2394),X2393),X2392)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X2394),X2393),hAPP(hAPP(c_Orderings_Oord__class_Omax(X2394),X2393),X2392))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup_Oleft__idem])])])). 4.05/4.31 fof(c_0_8332, plain, ![X14189, X14190]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14190))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X14190),hAPP(c_Nat_OSuc,X14189))),X14190))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__Suc__less])])])). 4.05/4.31 fof(c_0_8333, plain, ![X986, X987, X988, X989]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X988),X986))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X989),X987))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X989,X988)),c_Sum__Type_OPlus(X989,X988,X987,X986))))&((hBOOL(hAPP(c_Finite__Set_Ofinite(X988),X986))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X989,X988)),c_Sum__Type_OPlus(X989,X988,X987,X986))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X989),X987))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X989,X988)),c_Sum__Type_OPlus(X989,X988,X987,X986)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])])). 4.05/4.31 fof(c_0_8334, plain, ![X3752, X3753, X3754]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X3754,X3754)),X3753),X3752))|hBOOL(hAPP(hAPP(c_member(tc_prod(X3754,X3754)),X3753),c_Transitive__Closure_Ortrancl(X3754,X3752)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl])])). 4.05/4.31 cnf(c_0_8335, plain, (c_List_Oconcat(X2,X1)=c_List_Olist_ONil(X2)|esk117_2(X1,X2)!=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_5239])). 4.05/4.31 cnf(c_0_8336, plain, (c_List_Oconcat(X1,X2)=c_List_Olist_ONil(X1)|c_List_Olist_ONil(X1)!=esk116_2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5241])). 4.05/4.31 fof(c_0_8337, plain, ![X1554, X1555, X1556]:((c_List_Olist_ONil(X1555)!=X1556|c_List_Obutlast(X1555,X1554)=c_List_Obutlast(X1555,hAPP(hAPP(c_List_Oappend(X1555),X1554),X1556)))&(c_List_Olist_ONil(X1555)=X1556|hAPP(hAPP(c_List_Oappend(X1555),X1554),c_List_Obutlast(X1555,X1556))=c_List_Obutlast(X1555,hAPP(hAPP(c_List_Oappend(X1555),X1554),X1556)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__append])])). 4.05/4.31 fof(c_0_8338, plain, ![X8406, X8407, X8408, X8409, X8410, X8411]:(~c_Fun_Oinj__on(X8411,X8410,hAPP(c_Fun_Ocomp(X8409,X8410,X8411,X8408),X8407),X8406)|c_Fun_Oinj__on(X8409,X8410,X8408,hAPP(c_Set_Oimage(X8411,X8409,X8407),X8406))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__imageI])])])). 4.05/4.31 fof(c_0_8339, plain, ![X9244, X9245]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9245),X9244))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9244),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9245),X9244))=X9245), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__diff__inverse])])])). 4.05/4.31 fof(c_0_8340, plain, ![X16616, X16617]:(~class_Orderings_Oorder(X16617)|hAPP(hAPP(c_Set_Oinsert(X16617),X16616),c_Orderings_Obot__class_Obot(tc_fun(X16617,tc_HOL_Obool)))=c_SetInterval_Oord__class_OatLeastAtMost(X16617,X16616,X16616)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastAtMost__singleton])])])). 4.05/4.31 fof(c_0_8341, plain, ![X1201, X1202]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1202))|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),X1202),X1201)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])])). 4.05/4.31 fof(c_0_8342, plain, ![X8226, X8227, X8228]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8228),X8226)),X8227))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8228),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8227),X8226))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8228),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8227),X8226)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8228),X8226)),X8227)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])])). 4.05/4.31 fof(c_0_8343, plain, ![X15360, X15361, X15362]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15362),X15361)),X15360))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15362),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15360),X15361))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15362),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15360),X15361)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15362),X15361)),X15360)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])])). 4.05/4.31 fof(c_0_8344, plain, ![X6719, X6720, X6721, X6722]:(~c_Finite__Set_Ofun__left__comm__idem(X6722,X6721,X6720)|hAPP(c_Fun_Ocomp(X6721,X6721,X6721,hAPP(X6720,X6719)),hAPP(X6720,X6719))=hAPP(X6720,X6719)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__comp__idem])])). 4.05/4.31 cnf(c_0_8345, plain, (c_Option_Ooption_ONone(X4)=c_Map_Omap__comp(X3,X4,X5,X6,X1,X2)|hAPP(X1,X2)!=c_Option_Ooption_ONone(X3)), inference(split_conjunct,[status(thm)],[c_0_5338])). 4.05/4.31 fof(c_0_8346, plain, ![X15961, X15962, X15963, X15964]:(~hBOOL(hAPP(c_List_Odistinct(X15964),X15963))|hBOOL(hAPP(c_List_Odistinct(tc_prod(X15964,X15962)),hAPP(hAPP(c_List_Ozip(X15964,X15962),X15963),X15961)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__zipI1])])). 4.05/4.31 fof(c_0_8347, plain, ![X17077, X17078, X17079, X17080]:(~hBOOL(hAPP(c_List_Odistinct(X17080),X17079))|hBOOL(hAPP(c_List_Odistinct(tc_prod(X17078,X17080)),hAPP(hAPP(c_List_Ozip(X17078,X17080),X17077),X17079)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__zipI2])])). 4.05/4.31 fof(c_0_8348, plain, ![X10321, X10322, X10323, X10324, X10325]:((X10324!=X10322|X10321!=X10323|hAPP(hAPP(c_List_Oappend(X10325),X10322),hAPP(hAPP(c_List_Olist_OCons(X10325),X10321),c_List_Olist_ONil(X10325)))=hAPP(hAPP(c_List_Oappend(X10325),X10324),hAPP(hAPP(c_List_Olist_OCons(X10325),X10323),c_List_Olist_ONil(X10325))))&((X10324=X10322|hAPP(hAPP(c_List_Oappend(X10325),X10322),hAPP(hAPP(c_List_Olist_OCons(X10325),X10321),c_List_Olist_ONil(X10325)))!=hAPP(hAPP(c_List_Oappend(X10325),X10324),hAPP(hAPP(c_List_Olist_OCons(X10325),X10323),c_List_Olist_ONil(X10325))))&(X10321=X10323|hAPP(hAPP(c_List_Oappend(X10325),X10322),hAPP(hAPP(c_List_Olist_OCons(X10325),X10321),c_List_Olist_ONil(X10325)))!=hAPP(hAPP(c_List_Oappend(X10325),X10324),hAPP(hAPP(c_List_Olist_OCons(X10325),X10323),c_List_Olist_ONil(X10325)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append1__eq__conv])])])). 4.05/4.31 fof(c_0_8349, plain, ![X6074, X6075, X6076]:(~class_Groups_Ocomm__monoid__mult(X6076)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X6075,X6076),hAPP(c_COMBK(X6076,X6075),c_Groups_Oone__class_Oone(X6076))),X6074)=c_Groups_Oone__class_Oone(X6076)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_setprod__1])])])). 4.05/4.31 cnf(c_0_8350, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_5496])). 4.05/4.31 cnf(c_0_8351, 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_5497])). 4.05/4.31 fof(c_0_8352, plain, ![X2514, X2515, X2516]:(~class_Groups_Ocomm__monoid__add(X2516)|c_Groups_Ozero__class_Ozero(X2516)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2515,X2516),hAPP(c_COMBK(X2516,X2515),c_Groups_Ozero__class_Ozero(X2516))),X2514)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__0])])). 4.05/4.31 fof(c_0_8353, plain, ![X7612, X7613, X7614, X7615]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X7615,X7614),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X7613),X7612)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7614|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X7615),X7614)=X7613)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__div])])])). 4.05/4.31 cnf(c_0_8354, 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_5498])). 4.05/4.31 cnf(c_0_8355, 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_5499])). 4.05/4.31 fof(c_0_8356, plain, ![X2575, X2576]:(~class_Rings_Osemiring__1(X2576)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2576),hAPP(c_Nat_OSuc,X2575))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2576),c_Groups_Oone__class_Oone(X2576)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2576),X2575))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__Suc])])])). 4.05/4.31 fof(c_0_8357, plain, ![X14945, X14946, X14947, X14948]:(~class_Lattices_Osemilattice__inf(X14948)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14948),X14947),X14946))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14948),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X14948),X14947),X14945)),X14946)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI1])])). 4.05/4.31 fof(c_0_8358, plain, ![X3781, X3782, X3783, X3784]:(~class_Lattices_Osemilattice__inf(X3784)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3784),X3783),X3782))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3784),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3784),X3781),X3783)),X3782)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__infI2])])])). 4.05/4.31 fof(c_0_8359, plain, ![X8013, X8014]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8014))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8013))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X8014,X8013),c_Divides_OposDivAlg(X8014,X8013))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg__correct])])). 4.05/4.31 fof(c_0_8360, plain, ![X13147, X13148]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13148),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)),X13147))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X13148,X13147),c_Divides_OnegDivAlg(X13148,X13147))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_negDivAlg__correct])])])). 4.05/4.31 fof(c_0_8361, plain, ![X2725]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X2725),c_Orderings_Otop__class_Otop(tc_fun(X2725,tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X2725)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2725),tc_HOL_Obool)))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X2725)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2725),tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X2725),c_Orderings_Otop__class_Otop(tc_fun(X2725,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])])). 4.05/4.31 fof(c_0_8362, plain, ![X6453, X6454, X6455, X6456]:(~class_Lattices_Osemilattice__inf(X6456)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6456),X6455),X6454))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6456),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6456),X6455),X6453)),X6454)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__infI1])])])). 4.05/4.31 fof(c_0_8363, plain, ![X10893, X10894, X10895, X10896]:(~class_Lattices_Osemilattice__inf(X10896)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10896),X10895),X10894))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10896),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10896),X10893),X10895)),X10894)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__infI2])])])). 4.05/4.31 fof(c_0_8364, plain, ![X7335, X7336, X7337, X7338]:(~class_Lattices_Osemilattice__sup(X7338)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7338),X7337),X7336))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7338),X7337),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7338),X7336),X7335))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__supI1])])])). 4.05/4.31 fof(c_0_8365, plain, ![X391, X392, X393, X394]:(~class_Lattices_Osemilattice__sup(X394)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X394),X393),X392))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X394),X393),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X394),X391),X392))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__supI2])])])). 4.05/4.31 fof(c_0_8366, plain, ![X7352, X7353, X7354, X7355]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(X7355,X7355)),hAPP(hAPP(c_Product__Type_OPair(X7355,X7355),X7354),X7353)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7355,X7355),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7352)))|X7353=X7354), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rel__pow__0__E])])])). 4.05/4.31 fof(c_0_8367, plain, ![X7977, X7978, X7979, X7980]:(~class_Lattices_Osemilattice__sup(X7980)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7980),X7979),X7978))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7980),X7979),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7980),X7978),X7977))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__supI1])])])). 4.05/4.31 fof(c_0_8368, plain, ![X14016, X14017, X14018, X14019]:(~class_Lattices_Osemilattice__sup(X14019)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14019),X14018),X14017))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14019),X14018),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X14019),X14016),X14017))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__supI2])])])). 4.05/4.31 cnf(c_0_8369, 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(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(c_Int_Onat,X1))|~class_Rings_Oring__1(X2)), inference(split_conjunct,[status(thm)],[c_0_5421])). 4.05/4.31 cnf(c_0_8370, 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_5494])). 4.05/4.31 cnf(c_0_8371, plain, (hAPP(c_Int_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_Onat,X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5500])). 4.05/4.31 cnf(c_0_8372, plain, (X1=hAPP(c_List_Ohd(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_5501])). 4.05/4.31 fof(c_0_8373, plain, ![X7713, X7714, X7716, X7717, X7718]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk246_2(X7713,X7714)),X7713))|X7714=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7714),hAPP(c_Nat_OSuc,X7713))))&(hAPP(c_Nat_OSuc,esk246_2(X7713,X7714))=X7714|X7714=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7714),hAPP(c_Nat_OSuc,X7713)))))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7718),X7716))|hAPP(c_Nat_OSuc,X7718)!=X7717|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7717),hAPP(c_Nat_OSuc,X7716))))&(X7717!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7717),hAPP(c_Nat_OSuc,X7716)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__0__disj])])])])])])). 4.05/4.31 fof(c_0_8374, plain, ![X5842, X5843, X5844, X5845, X5846, X5847, X5848]:(~c_Big__Operators_Ocomm__monoid__big(X5848,X5847,X5846,X5845,X5844)|(hBOOL(hAPP(c_Finite__Set_Ofinite(X5847),X5843))|X5845=hAPP(hAPP(X5844,X5842),X5843))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__monoid__big_Oinfinite])])])). 4.05/4.31 cnf(c_0_8375, 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_5396])). 4.05/4.31 fof(c_0_8376, plain, ![X6321, X6322]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6322),X6321))|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6321),X6322))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X6321)),X6322)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__diff__le])])])). 4.05/4.31 cnf(c_0_8377, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk191_2(X2,X1)),X2))|hAPP(c_Finite__Set_Ocard(X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5502])). 4.05/4.31 cnf(c_0_8378, 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_5503]), ['final']). 4.05/4.31 fof(c_0_8379, plain, ![X15056, X15057]:(~class_Rings_Oring__1(X15057)|(~hBOOL(hAPP(hAPP(c_member(X15057),X15056),c_Int_Oring__1__class_OInts(X15057)))|hBOOL(hAPP(hAPP(c_member(X15057),hAPP(c_Groups_Ouminus__class_Ouminus(X15057),X15056)),c_Int_Oring__1__class_OInts(X15057))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__minus])])])). 4.05/4.31 fof(c_0_8380, plain, ![X8085, X8086]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8086),hAPP(c_Int_Oring__1__class_Oof__int(X8086),X8085)),c_Groups_Ozero__class_Ozero(X8086)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8085),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X8086))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8085),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8086),hAPP(c_Int_Oring__1__class_Oof__int(X8086),X8085)),c_Groups_Ozero__class_Ozero(X8086)))|~class_Rings_Olinordered__idom(X8086))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__less__0__iff])])])])). 4.05/4.31 fof(c_0_8381, plain, ![X6778, X6779, X6780]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6780),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6779)),X6778)))|c_List_Olast(X6779,hAPP(hAPP(c_List_Odrop(X6779),X6780),X6778))=c_List_Olast(X6779,X6778)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__drop])])). 4.05/4.31 fof(c_0_8382, plain, ![X10182, X10183]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10183),hAPP(c_Int_Oring__1__class_Oof__int(X10183),X10182)),c_Groups_Ozero__class_Ozero(X10183)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10182),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X10183))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10182),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10183),hAPP(c_Int_Oring__1__class_Oof__int(X10183),X10182)),c_Groups_Ozero__class_Ozero(X10183)))|~class_Rings_Olinordered__idom(X10183))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__le__0__iff])])])])). 4.05/4.31 fof(c_0_8383, plain, ![X3927, X3928]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3927))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3928),c_Groups_Ozero__class_Ozero(X3928)),hAPP(c_Int_Oring__1__class_Oof__int(X3928),X3927)))|~class_Rings_Olinordered__idom(X3928))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3928),c_Groups_Ozero__class_Ozero(X3928)),hAPP(c_Int_Oring__1__class_Oof__int(X3928),X3927)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3927))|~class_Rings_Olinordered__idom(X3928))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__0__less__iff])])])])). 4.05/4.31 fof(c_0_8384, plain, ![X14521, X14522]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14521))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14522),c_Groups_Ozero__class_Ozero(X14522)),hAPP(c_Int_Oring__1__class_Oof__int(X14522),X14521)))|~class_Rings_Olinordered__idom(X14522))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14522),c_Groups_Ozero__class_Ozero(X14522)),hAPP(c_Int_Oring__1__class_Oof__int(X14522),X14521)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14521))|~class_Rings_Olinordered__idom(X14522))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__le__iff])])])). 4.05/4.31 fof(c_0_8385, plain, ![X721, X722, X723, X724, X725, X726]:(~c_Fun_Oinj__on(X726,X725,X724,X723)|(X721=X722|(~hBOOL(hAPP(hAPP(c_member(X726),X722),X723))|(~hBOOL(hAPP(hAPP(c_member(X726),X721),X723))|hAPP(X724,X721)!=hAPP(X724,X722))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__contraD])])])). 4.05/4.31 cnf(c_0_8386, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))), inference(rw,[status(thm)],[c_0_5504, c_0_4475])). 4.05/4.31 cnf(c_0_8387, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))), inference(rw,[status(thm)],[c_0_5505, c_0_4475])). 4.05/4.31 cnf(c_0_8388, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5506, c_0_4475])). 4.05/4.31 cnf(c_0_8389, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5507, c_0_4475])). 4.05/4.31 fof(c_0_8390, plain, ![X7428, X7429]:((hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X7429,X7428))!=X7428|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X7429),X7428))&(hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X7429,X7428))=X7428|hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X7429,X7428))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X7429),X7428))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__Suc])])). 4.05/4.31 cnf(c_0_8391, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))), inference(rw,[status(thm)],[c_0_5508, c_0_4475])). 4.05/4.31 cnf(c_0_8392, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))))), inference(rw,[status(thm)],[c_0_5509, c_0_4475])). 4.05/4.31 cnf(c_0_8393, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))), inference(rw,[status(thm)],[c_0_5510, c_0_4475])). 4.05/4.31 cnf(c_0_8394, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))), inference(rw,[status(thm)],[c_0_5511, c_0_4475])). 4.05/4.31 cnf(c_0_8395, 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_5512, c_0_4519])). 4.05/4.31 cnf(c_0_8396, 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_5513])). 4.05/4.31 fof(c_0_8397, plain, ![X9921, X9922, X9923]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X9923),tc_List_Olist(X9923))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X9923),tc_List_Olist(X9923)),c_List_Olist_ONil(X9923)),X9922)),c_List_Olistrel(X9923,X9921)))|c_List_Olist_ONil(X9923)=X9922), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil1])])). 4.05/4.31 cnf(c_0_8398, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)!=X4|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_5514])). 4.05/4.31 cnf(c_0_8399, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))), inference(rw,[status(thm)],[c_0_5515, c_0_4475])). 4.05/4.31 cnf(c_0_8400, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))), inference(rw,[status(thm)],[c_0_5516, c_0_4475])). 4.05/4.31 cnf(c_0_8401, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))), inference(rw,[status(thm)],[c_0_5517, c_0_4475])). 4.05/4.31 fof(c_0_8402, plain, ![X10377, X10378, X10379, X10380]:(~hBOOL(hAPP(hAPP(c_member(X10380),X10379),hAPP(c_List_Oset(X10380),hAPP(hAPP(c_List_Odrop(X10380),X10378),X10377))))|hBOOL(hAPP(hAPP(c_member(X10380),X10379),hAPP(c_List_Oset(X10380),X10377)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__dropD])])). 4.05/4.31 fof(c_0_8403, plain, ![X4596, X4597, X4598]:(~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4598),tc_List_Olist(X4598))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4598),tc_List_Olist(X4598)),X4597),c_List_Olist_ONil(X4598))),c_List_Olistrel(X4598,X4596)))|X4597=c_List_Olist_ONil(X4598)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel__Nil2])])])). 4.05/4.31 fof(c_0_8404, plain, ![X13583, X13584, X13585, X13586, X13587]:(~class_Orderings_Olinorder(X13587)|c_List_Olinorder__class_Osort__key(X13586,X13587,X13584,hAPP(c_List_Ofilter(X13586,X13585),X13583))=hAPP(c_List_Ofilter(X13586,X13585),c_List_Olinorder__class_Osort__key(X13586,X13587,X13584,X13583))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__sort])])). 4.05/4.31 fof(c_0_8405, plain, ![X10791, X10792, X10793, X10794]:(~hBOOL(hAPP(hAPP(c_member(X10794),X10793),hAPP(c_List_Oset(X10794),hAPP(hAPP(c_List_Otake(X10794),X10792),X10791))))|hBOOL(hAPP(hAPP(c_member(X10794),X10793),hAPP(c_List_Oset(X10794),X10791)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__takeD])])). 4.05/4.31 cnf(c_0_8406, 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_5351])). 4.05/4.31 fof(c_0_8407, plain, ![X7142, X7143, X7144, X7145]:(~hBOOL(hAPP(hAPP(c_member(X7145),X7144),c_Map_Odom(X7145,X7143,X7142)))|hAPP(c_Option_Ooption_OSome(X7143),esk220_3(X7142,X7143,X7144))=hAPP(X7142,X7144)), 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_domD])])])])])). 4.05/4.31 cnf(c_0_8408, 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_5351])). 4.05/4.31 fof(c_0_8409, plain, ![X16090, X16091]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X16091),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,X16090,X16091)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__sign])])). 4.05/4.31 fof(c_0_8410, plain, ![X10026, X10027, X10028]:(~class_Lattices_Olattice(X10028)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10028),X10027))|(~hBOOL(hAPP(hAPP(c_member(X10028),X10026),X10027))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10028),X10026),c_Big__Operators_Olattice__class_OSup__fin(X10028,X10027))=X10026))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__Sup__absorb])])])). 4.05/4.31 fof(c_0_8411, plain, ![X15410, X15411, X15412]:(~class_Lattices_Olattice(X15412)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15412),X15411))|(~hBOOL(hAPP(hAPP(c_member(X15412),X15410),X15411))|X15410=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15412),X15410),c_Big__Operators_Olattice__class_OInf__fin(X15412,X15411))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__Inf__absorb])])])). 4.05/4.31 fof(c_0_8412, plain, ![X15418, X15419]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15419))|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,X15418,X15419)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__mod__sign])])])). 4.05/4.31 cnf(c_0_8413, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X1)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5518])). 4.05/4.31 fof(c_0_8414, plain, ![X3818, X3820, X3821, X3823]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk118_1(X3818)))|hBOOL(hAPP(X3818,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3820))))&(~hBOOL(hAPP(X3818,esk118_1(X3818)))|hBOOL(hAPP(X3818,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3820)))))&(~hBOOL(hAPP(X3821,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk119_1(X3821))))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3823))|hBOOL(hAPP(X3821,X3823))))), 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_transfer__int__nat__quantifiers_I1_J])])])])])])])). 4.05/4.31 fof(c_0_8415, plain, ![X15348, X15349, X15350, X15351, X15354, X15355, X15356, X15357, X15358, X15359]:(((hBOOL(hAPP(hAPP(c_member(X15351),esk462_4(X15348,X15349,X15350,X15351)),X15348))|c_Fun_Oinj__on(X15351,X15350,X15349,X15348))&((hBOOL(hAPP(hAPP(c_member(X15351),esk463_4(X15348,X15349,X15350,X15351)),X15348))|c_Fun_Oinj__on(X15351,X15350,X15349,X15348))&((hAPP(X15349,esk462_4(X15348,X15349,X15350,X15351))=hAPP(X15349,esk463_4(X15348,X15349,X15350,X15351))|c_Fun_Oinj__on(X15351,X15350,X15349,X15348))&(esk462_4(X15348,X15349,X15350,X15351)!=esk463_4(X15348,X15349,X15350,X15351)|c_Fun_Oinj__on(X15351,X15350,X15349,X15348)))))&(~c_Fun_Oinj__on(X15357,X15356,X15355,X15354)|(~hBOOL(hAPP(hAPP(c_member(X15357),X15358),X15354))|(~hBOOL(hAPP(hAPP(c_member(X15357),X15359),X15354))|(hAPP(X15355,X15358)!=hAPP(X15355,X15359)|X15358=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)],[inference(fof_simplification,[status(thm)],[fact_inj__on__def])])])])])])])). 4.05/4.31 cnf(c_0_8416, plain, (hAPP(X1,esk25_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)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5275])). 4.05/4.31 cnf(c_0_8417, 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_5519])). 4.05/4.31 fof(c_0_8418, plain, ![X15621, X15622, X15623]:(~class_Orderings_Olinorder(X15623)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15623),X15622))|(~hBOOL(hAPP(hAPP(c_member(X15623),X15621),X15622))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15623),c_Big__Operators_Olinorder__class_OMin(X15623,X15622)),X15621))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__le])])). 4.05/4.31 fof(c_0_8419, plain, ![X15769, X15770, X15771]:(~class_Orderings_Olinorder(X15771)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15771),X15770))|(~hBOOL(hAPP(hAPP(c_member(X15771),X15769),X15770))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15771),X15769),c_Big__Operators_Olinorder__class_OMax(X15771,X15770)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max__ge])])])). 4.05/4.31 fof(c_0_8420, plain, ![X8605, X8606, X8607, X8608, X8609]:(hAPP(c_Option_Ooption_OSome(X8607),X8606)!=hAPP(X8609,X8608)|hBOOL(hAPP(hAPP(c_member(X8605),X8608),c_Map_Odom(X8605,X8607,X8609)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_domI])])])). 4.05/4.31 fof(c_0_8421, plain, ![X2690, X2691, X2692, X2693, X2694]:(hAPP(X2694,X2693)!=hAPP(c_Option_Ooption_OSome(X2692),X2691)|hBOOL(hAPP(hAPP(c_member(X2692),X2691),c_Map_Oran(X2690,X2692,X2694)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ranI])])])). 4.05/4.31 fof(c_0_8422, plain, ![X16352, X16353, X16354, X16355]:(~class_Orderings_Olinorder(X16355)|hAPP(hAPP(c_List_Olist_OCons(X16354),X16352),c_List_Olist_ONil(X16354))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X16354,X16355,X16353),X16352),c_List_Olist_ONil(X16354))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insort__key_Osimps_I1_J])])])). 4.05/4.31 fof(c_0_8423, plain, ![X2328, X2329, X2330, X2331, X2332]:(~c_Finite__Set_Ofun__left__comm(X2332,X2331,X2330)|c_Finite__Set_Ofun__left__comm(X2329,X2331,hAPP(hAPP(c_COMBB(X2332,tc_fun(X2331,X2331),X2329),X2330),X2328))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm__apply])])). 4.05/4.31 fof(c_0_8424, plain, ![X9259, X9260]:(~class_Rings_Ocomm__ring__1(X9260)|hAPP(c_Groups_Ouminus__class_Ouminus(X9260),X9259)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9260),hAPP(c_Groups_Ouminus__class_Ouminus(X9260),c_Groups_Oone__class_Oone(X9260))),X9259)), 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])])])). 4.05/4.31 fof(c_0_8425, plain, ![X13022, X13023]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13023),c_Groups_Osgn__class_Osgn(X13023,X13022)),c_Groups_Ozero__class_Ozero(X13023)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13023),X13022),c_Groups_Ozero__class_Ozero(X13023)))|~class_Rings_Olinordered__idom(X13023))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13023),X13022),c_Groups_Ozero__class_Ozero(X13023)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13023),c_Groups_Osgn__class_Osgn(X13023,X13022)),c_Groups_Ozero__class_Ozero(X13023)))|~class_Rings_Olinordered__idom(X13023))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__less])])])])). 4.05/4.31 fof(c_0_8426, plain, ![X6160, X6161]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6161),c_Groups_Ozero__class_Ozero(X6161)),X6160))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6161),c_Groups_Ozero__class_Ozero(X6161)),c_Groups_Osgn__class_Osgn(X6161,X6160)))|~class_Rings_Olinordered__idom(X6161))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6161),c_Groups_Ozero__class_Ozero(X6161)),c_Groups_Osgn__class_Osgn(X6161,X6160)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6161),c_Groups_Ozero__class_Ozero(X6161)),X6160))|~class_Rings_Olinordered__idom(X6161))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__greater])])])). 4.05/4.31 fof(c_0_8427, plain, ![X6111, X6112, X6113, X6114, X6115]:(~c_Finite__Set_Ofun__left__comm__idem(X6115,X6114,X6113)|c_Finite__Set_Ofun__left__comm__idem(X6112,X6114,hAPP(hAPP(c_COMBB(X6115,tc_fun(X6114,X6114),X6112),X6113),X6111))), 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])])])). 4.05/4.31 fof(c_0_8428, plain, ![X2092, X2093, X2094]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2093,X2094)),X2092))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2094,X2093)),hAPP(c_Relation_Oconverse(X2093,X2094),X2092))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2094,X2093)),hAPP(c_Relation_Oconverse(X2093,X2094),X2092)))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2093,X2094)),X2092)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__converse])])). 4.05/4.31 fof(c_0_8429, plain, ![X5381, X5382, X5383, X5386]:(((hBOOL(hAPP(X5381,esk167_3(X5381,X5382,X5383)))|~hBOOL(hAPP(X5381,X5383))|c_List_Olist__ex1(X5382,X5381,c_Enum_Oenum__class_Oenum(X5382))|~class_Enum_Oenum(X5382))&(esk167_3(X5381,X5382,X5383)!=X5383|~hBOOL(hAPP(X5381,X5383))|c_List_Olist__ex1(X5382,X5381,c_Enum_Oenum__class_Oenum(X5382))|~class_Enum_Oenum(X5382)))&((~hBOOL(hAPP(X5381,X5386))|X5386=esk168_2(X5381,X5382)|~c_List_Olist__ex1(X5382,X5381,c_Enum_Oenum__class_Oenum(X5382))|~class_Enum_Oenum(X5382))&(hBOOL(hAPP(X5381,esk168_2(X5381,X5382)))|~c_List_Olist__ex1(X5382,X5381,c_Enum_Oenum__class_Oenum(X5382))|~class_Enum_Oenum(X5382)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_exists1__code])])])])])])). 4.05/4.31 fof(c_0_8430, plain, ![X4517, X4518, X4519, X4520, X4521, X4522]:((~hBOOL(hAPP(hAPP(c_member(X4522),X4521),X4520))|hAPP(X4517,X4521)=hAPP(c_Fun_Ooverride__on(X4522,X4519,X4518,X4517,X4520),X4521))&(hBOOL(hAPP(hAPP(c_member(X4522),X4521),X4520))|hAPP(X4518,X4521)=hAPP(c_Fun_Ooverride__on(X4522,X4519,X4518,X4517,X4520),X4521))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_override__on__def])])])). 4.05/4.31 fof(c_0_8431, plain, ![X7462, X7463]:((~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7463)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X7462)))|hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X7463),X7462)))&(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X7463),X7462))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7463)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X7462))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I2_J])])). 4.05/4.31 cnf(c_0_8432, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X1)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~hBOOL(hAPP(hAPP(c_member(X2),X1),c_Int_Oring__1__class_OInts(X2)))|~class_Int_Oring__char__0(X2)), inference(split_conjunct,[status(thm)],[c_0_5520])). 4.05/4.31 fof(c_0_8433, plain, ![X10705, X10706, X10707, X10708]:(hBOOL(hAPP(hAPP(c_member(X10708),X10707),hAPP(c_List_Oset(X10708),X10706)))|~hBOOL(hAPP(hAPP(c_member(X10708),X10707),hAPP(c_List_Oset(X10708),c_List_Oremove1(X10708,X10705,X10706))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_notin__set__remove1])])])). 4.05/4.31 fof(c_0_8434, plain, ![X13166, X13167, X13168, X13169]:(~hBOOL(hAPP(hAPP(c_member(X13169),X13168),hAPP(c_List_Oset(X13169),c_List_Osublist(X13169,X13167,X13166))))|hBOOL(hAPP(hAPP(c_member(X13169),X13168),hAPP(c_List_Oset(X13169),X13167)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__sublistD])])). 4.05/4.31 fof(c_0_8435, plain, ![X12690, X12691, X12692, X12693]:((hBOOL(hAPP(hAPP(c_member(X12693),X12692),hAPP(c_List_Oset(X12693),X12690)))|~hBOOL(hAPP(hAPP(c_member(X12693),X12692),hAPP(c_List_Oset(X12693),c_List_OtakeWhile(X12693,X12691,X12690)))))&(hBOOL(hAPP(X12691,X12692))|~hBOOL(hAPP(hAPP(c_member(X12693),X12692),hAPP(c_List_Oset(X12693),c_List_OtakeWhile(X12693,X12691,X12690)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__takeWhileD])])])])). 4.05/4.31 fof(c_0_8436, plain, ![X2259, X2260, X2261, X2262, X2263, X2264, X2265, X2266, X2267]:(((hBOOL(hAPP(X2262,X2260))|c_Natural_Oevaln(c_Com_Ocom_OWhile(X2262,X2261),X2260,X2259,X2260))&(~c_Natural_Oevaln(X2261,X2260,X2259,X2263)|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X2262,X2261),X2263,X2259,X2260)|c_Natural_Oevaln(c_Com_Ocom_OWhile(X2262,X2261),X2260,X2259,X2260)))&((c_Natural_Oevaln(X2266,X2265,X2264,esk84_4(X2264,X2265,X2266,X2267))|~hBOOL(hAPP(X2267,X2265))|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X2267,X2266),X2265,X2264,X2265))&(c_Natural_Oevaln(c_Com_Ocom_OWhile(X2267,X2266),esk84_4(X2264,X2265,X2266,X2267),X2264,X2265)|~hBOOL(hAPP(X2267,X2265))|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X2267,X2266),X2265,X2264,X2265)))), 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_evaln_Oequations_I7_J])])])])])])). 4.05/4.31 fof(c_0_8437, plain, ![X14602, X14603, X14604, X14605]:(c_List_Olist_ONil(X14604)=X14605|hAPP(X14602,c_List_Olast(X14604,X14605))=c_List_Olast(X14603,hAPP(hAPP(c_List_Omap(X14604,X14603),X14602),X14605))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_last__map])])])). 4.05/4.31 fof(c_0_8438, plain, ![X14728, X14729, X14730]:(((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14730),X14728),X14729))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14730),X14729),X14728))|~class_Orderings_Opreorder(X14730))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14730),X14729),X14728))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14730),X14729),X14728))|~class_Orderings_Opreorder(X14730)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14730),X14728),X14729))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14730),X14729),X14728))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14730),X14729),X14728))|~class_Orderings_Opreorder(X14730))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__le__not__le])])])])). 4.05/4.31 cnf(c_0_8439, 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_4686])). 4.05/4.31 fof(c_0_8440, plain, ![X9246, X9247, X9248]:(hBOOL(hAPP(hAPP(c_member(X9248),X9247),hAPP(c_List_Oset(X9248),X9246)))|c_List_Oremove1(X9248,X9247,X9246)=X9246), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remove1__idem])])])). 4.05/4.31 cnf(c_0_8441, 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_4713])). 4.05/4.31 fof(c_0_8442, plain, ![X8893, X8894, X8895, X8896, X8897]:(~c_Fun_Oinj__on(X8897,X8896,X8895,X8894)|c_Fun_Oinj__on(X8897,X8896,X8895,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8897,tc_HOL_Obool)),X8894),X8893))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__diff])])). 4.05/4.31 fof(c_0_8443, plain, ![X15217, X15218]:(X15218=c_List_Olist_ONil(X15217)|hBOOL(hAPP(hAPP(c_member(X15217),hAPP(c_List_Ohd(X15217),X15218)),hAPP(c_List_Oset(X15217),X15218)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__in__set])])). 4.05/4.31 fof(c_0_8444, plain, ![X9087, X9088]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9088),c_Groups_Oone__class_Oone(tc_Int_Oint))),X9087))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9088),X9087)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9088),X9087))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X9088),c_Groups_Oone__class_Oone(tc_Int_Oint))),X9087)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])])). 4.05/4.31 fof(c_0_8445, plain, ![X17419, X17420]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17420),X17419))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X17420),X17419)),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),X17420),X17419)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17420),X17419)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])])). 4.05/4.31 fof(c_0_8446, plain, ![X14661, X14662]:(~class_Rings_Olinordered__idom(X14662)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X14662),X14661),c_Groups_Ozero__class_Ozero(X14662)))|c_Groups_Osgn__class_Osgn(X14662,X14661)=hAPP(c_Groups_Ouminus__class_Ouminus(X14662),c_Groups_Oone__class_Oone(X14662)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__neg])])). 4.05/4.31 cnf(c_0_8447, plain, (c_Option_Ooption_ONone(X1)!=hAPP(hAPP(c_Map_Omap__of(X2,X1),X3),X4)|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Set_Oimage(tc_prod(X2,X1),X2,c_Product__Type_Ofst(X2,X1)),hAPP(c_List_Oset(tc_prod(X2,X1)),X3))))), inference(split_conjunct,[status(thm)],[c_0_5255])). 4.05/4.31 fof(c_0_8448, plain, ![X16523, X16524, X16525, X16526]:((X16525!=X16524|~hBOOL(hAPP(hAPP(c_member(X16526),X16525),X16523))|hBOOL(hAPP(hAPP(c_member(tc_prod(X16526,X16526)),hAPP(hAPP(c_Product__Type_OPair(X16526,X16526),X16525),X16524)),c_Relation_OId__on(X16526,X16523))))&((X16525=X16524|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16526,X16526)),hAPP(hAPP(c_Product__Type_OPair(X16526,X16526),X16525),X16524)),c_Relation_OId__on(X16526,X16523))))&(hBOOL(hAPP(hAPP(c_member(X16526),X16525),X16523))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X16526,X16526)),hAPP(hAPP(c_Product__Type_OPair(X16526,X16526),X16525),X16524)),c_Relation_OId__on(X16526,X16523)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__iff])])])). 4.05/4.31 fof(c_0_8449, plain, ![X8784, X8785]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8785),X8784))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X8785)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X8784))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X8785)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X8784)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8785),X8784)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__int])])). 4.05/4.31 fof(c_0_8450, plain, ![X7430, X7431, X7432]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7432),X7431))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7432,tc_HOL_Obool)),X7430),X7431))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X7432),X7431)),hAPP(c_Finite__Set_Ocard(X7432),X7430)))|X7430=X7431))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__seteq])])])). 4.05/4.31 fof(c_0_8451, plain, ![X10774, X10775, X10776, X10777, X10778]:(~hBOOL(hAPP(hAPP(c_member(X10778),X10777),c_Map_Odom(X10778,X10776,X10775)))|hAPP(X10775,X10777)=hAPP(c_Map_Omap__add(X10778,X10776,X10774,X10775),X10777)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__add__dom__app__simps_I1_J])])])). 4.05/4.31 cnf(c_0_8452, 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_5521])). 4.05/4.31 fof(c_0_8453, plain, ![X8778, X8779]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8779),X8778))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X8779)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X8778))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X8779)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X8778)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8779),X8778)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__int])])). 4.05/4.31 fof(c_0_8454, plain, ![X2090, X2091]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2090),X2091))|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),X2091),X2090))))&(~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),X2091),X2090)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2090),X2091)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])])). 4.05/4.31 fof(c_0_8455, plain, ![X8267, X8268]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8268),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8267),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8268),X8267)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8268),X8267))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X8268),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X8267),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le])])). 4.05/4.31 cnf(c_0_8456, 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_5522])). 4.05/4.31 cnf(c_0_8457, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)=X3|~class_Rings_Odivision__ring(X1)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)!=X4), inference(split_conjunct,[status(thm)],[c_0_5523])). 4.05/4.31 cnf(c_0_8458, 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_5492])). 4.05/4.31 fof(c_0_8459, plain, ![X10964, X10965]:(~class_Groups_Oordered__ab__group__add__abs(X10965)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10965),hAPP(c_Groups_Ouminus__class_Ouminus(X10965),hAPP(c_Groups_Oabs__class_Oabs(X10965),X10964))),c_Groups_Ozero__class_Ozero(X10965)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__minus__le__zero])])])). 4.05/4.31 fof(c_0_8460, plain, ![X338, X339, X340]:(~class_Groups_Oab__group__add(X340)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X340),X338),X339)=hAPP(c_Groups_Ouminus__class_Ouminus(X340),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X340),X339),X338))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__diff__eq])])). 4.05/4.31 fof(c_0_8461, plain, ![X11038, X11039, X11041, X11042]:(((hBOOL(hAPP(X11038,esk334_1(X11038)))|~hBOOL(hAPP(X11038,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X11039))))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk334_1(X11038)))|~hBOOL(hAPP(X11038,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X11039)))))&(~hBOOL(hAPP(X11041,X11042))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11042))|hBOOL(hAPP(X11041,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk335_1(X11041)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I2_J])])])])])])). 4.05/4.31 fof(c_0_8462, plain, ![X8391, X8392, X8393]:((hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X8393,X8392),X8391)!=c_Orderings_Obot__class_Obot(tc_fun(X8393,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8393),X8392),X8391))|~class_Orderings_Oorder(X8393))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8393),X8392),X8391))|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X8393,X8392),X8391)=c_Orderings_Obot__class_Obot(tc_fun(X8393,tc_HOL_Obool))|~class_Orderings_Oorder(X8393))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff2])])])])). 4.05/4.31 fof(c_0_8463, plain, ![X4936, X4937]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4937))|X4936=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4937),X4936)),X4937)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__m])])). 4.05/4.31 fof(c_0_8464, plain, ![X9366, X9367]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9367))|X9366=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9366),X9367)),X9367)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self__is__m])])). 4.05/4.31 fof(c_0_8465, plain, ![X7233, X7234]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7234),X7233),c_Groups_Ozero__class_Ozero(X7234)))|hAPP(c_Groups_Ouminus__class_Ouminus(X7234),c_Groups_Oone__class_Oone(X7234))=c_Groups_Osgn__class_Osgn(X7234,X7233)|~class_Rings_Olinordered__idom(X7234))&(hAPP(c_Groups_Ouminus__class_Ouminus(X7234),c_Groups_Oone__class_Oone(X7234))!=c_Groups_Osgn__class_Osgn(X7234,X7233)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7234),X7233),c_Groups_Ozero__class_Ozero(X7234)))|~class_Rings_Olinordered__idom(X7234))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__neg])])])). 4.05/4.31 fof(c_0_8466, plain, ![X9262, X9263, X9264, X9265, X9266]:((~c_List_Olist__all2(X9266,X9265,X9264,hAPP(c_List_Orev(X9266),X9263),hAPP(c_List_Orev(X9265),X9262))|c_List_Olist__all2(X9266,X9265,X9264,X9263,X9262))&(~c_List_Olist__all2(X9266,X9265,X9264,X9263,X9262)|c_List_Olist__all2(X9266,X9265,X9264,hAPP(c_List_Orev(X9266),X9263),hAPP(c_List_Orev(X9265),X9262)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__rev])])). 4.05/4.31 cnf(c_0_8467, 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_5524, c_0_4422])). 4.05/4.31 fof(c_0_8468, plain, ![X4918, X4919, X4920, X4921]:(~class_Orderings_Olinorder(X4921)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4921),X4920),X4919))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4921),hAPP(hAPP(c_Orderings_Oord__class_Omin(X4921),X4920),X4918)),X4919)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oless__infI1])])])). 4.05/4.31 fof(c_0_8469, plain, ![X13065, X13066, X13067]:(~c_Wellfounded_Owf(X13067,X13066)|c_Wellfounded_Owf(X13067,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X13067,X13067),tc_HOL_Obool)),X13066),X13065))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__Int1])])])). 4.05/4.31 fof(c_0_8470, plain, ![X5157, X5158, X5159]:(~c_Wellfounded_Owf(X5159,X5158)|c_Wellfounded_Owf(X5159,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5159,X5159),tc_HOL_Obool)),X5157),X5158))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int2])])). 4.05/4.31 fof(c_0_8471, plain, ![X3744, X3745, X3746, X3747, X3748]:(~c_Fun_Oinj__on(X3748,X3747,X3746,X3745)|(~hBOOL(hAPP(hAPP(c_member(X3748),X3744),X3745))|X3744=hAPP(c_Fun_Othe__inv__into(X3748,X3747,X3745,X3746),hAPP(X3746,X3744)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_the__inv__into__f__f])])])). 4.05/4.31 cnf(c_0_8472, plain, (X1=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X3)|X1!=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3)!=X4|~class_Fields_Ofield__inverse__zero(X2)), inference(split_conjunct,[status(thm)],[c_0_5514])). 4.05/4.31 fof(c_0_8473, plain, ![X2944, X2945, X2946, X2947]:(~class_Orderings_Olinorder(X2947)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2947),X2946),X2945))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2947),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2947),X2944),X2946)),X2945)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oless__infI2])])])). 4.05/4.31 fof(c_0_8474, plain, ![X341, X342, X343, X344]:(~class_Orderings_Olinorder(X344)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X344),X343),X342))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X344),hAPP(hAPP(c_Orderings_Oord__class_Omin(X344),X343),X341)),X342)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ole__infI1])])])). 4.05/4.31 fof(c_0_8475, plain, ![X14949, X14950, X14951]:(~class_Orderings_Olinorder(X14951)|c_List_Oremove1(X14951,X14950,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X14951,X14951,c_COMBI(X14951)),X14950),X14949))=X14949), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1__insort])])). 4.05/4.31 cnf(c_0_8476, plain, (hBOOL(hAPP(X1,X2))|hAPP(c_List_Ofilter(X3,X1),X4)=c_List_Oremove1(X3,X2,hAPP(c_List_Ofilter(X3,X1),X4))), inference(split_conjunct,[status(thm)],[c_0_5525])). 4.05/4.31 cnf(c_0_8477, 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_5526]), ['final']). 4.05/4.31 fof(c_0_8478, plain, ![X7864, X7865, X7866]:(~class_Complete__Lattice_Ocomplete__lattice(X7866)|c_Complete__Lattice_OSup__class_OSup(X7866,hAPP(hAPP(c_Set_Oinsert(X7866),X7865),X7864))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7866),X7865),c_Complete__Lattice_OSup__class_OSup(X7866,X7864))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__insert])])). 4.05/4.31 cnf(c_0_8479, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1)=X4|X3!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X4),X1)|~class_Fields_Ofield__inverse__zero(X2)), inference(split_conjunct,[status(thm)],[c_0_5514])). 4.05/4.31 fof(c_0_8480, plain, ![X13419, X13420, X13421, X13422]:(~class_Orderings_Olinorder(X13422)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13422),X13421),X13420))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13422),X13421),hAPP(hAPP(c_Orderings_Oord__class_Omax(X13422),X13420),X13419))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oless__supI1])])])). 4.05/4.31 fof(c_0_8481, plain, ![X12199, X12200, X12201]:(~class_Complete__Lattice_Ocomplete__lattice(X12201)|c_Complete__Lattice_OInf__class_OInf(X12201,hAPP(hAPP(c_Set_Oinsert(X12201),X12200),X12199))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X12201),X12200),c_Complete__Lattice_OInf__class_OInf(X12201,X12199))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__insert])])])). 4.05/4.31 fof(c_0_8482, plain, ![X7859, X7860, X7861]:((hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7860),X7861)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7859),X7861)|X7860=X7859|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7861),X7859))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7861),X7860)))&(X7860!=X7859|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7860),X7861)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7859),X7861)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7861),X7859))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7861),X7860)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__diff__iff])])])])). 4.05/4.31 cnf(c_0_8483, 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_5463])). 4.05/4.31 fof(c_0_8484, plain, ![X15728, X15729, X15730, X15731]:(~class_Orderings_Olinorder(X15731)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15731),X15730),X15729))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15731),X15730),hAPP(hAPP(c_Orderings_Oord__class_Omax(X15731),X15728),X15729))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oless__supI2])])])). 4.05/4.31 fof(c_0_8485, plain, ![X10684, X10685, X10686, X10687]:(~class_Orderings_Olinorder(X10687)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10687),X10686),X10685))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10687),X10686),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10687),X10685),X10684))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ole__supI1])])])). 4.05/4.31 fof(c_0_8486, plain, ![X425, X426, X427, X428, X429, X430, X431, X432, X433, X434, X435]:((hAPP(c_Option_Ooption_OSome(X429),X430)!=X426|X425!=hAPP(X427,X430)|hAPP(c_Option_Ooption_OSome(X428),X425)=hAPP(hAPP(c_Option_Omap(X429,X428),X427),X426))&((hAPP(c_Option_Ooption_OSome(X435),esk5_5(X431,X432,X433,X434,X435))=X432|hAPP(c_Option_Ooption_OSome(X434),X431)!=hAPP(hAPP(c_Option_Omap(X435,X434),X433),X432))&(X431=hAPP(X433,esk5_5(X431,X432,X433,X434,X435))|hAPP(c_Option_Ooption_OSome(X434),X431)!=hAPP(hAPP(c_Option_Omap(X435,X434),X433),X432)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option__map__eq__Some])])])])])])). 4.05/4.31 fof(c_0_8487, plain, ![X3218, X3219, X3220, X3221, X3222]:(~c_Typedef_Otype__definition(X3222,X3221,X3220,X3219,X3218)|X3218=hAPP(c_Set_Oimage(X3222,X3221,X3220),c_Orderings_Otop__class_Otop(tc_fun(X3222,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__range])])). 4.05/4.31 fof(c_0_8488, plain, ![X5788, X5789, X5790]:(~class_Rings_Ocomm__ring__1(X5790)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5790),X5789),hAPP(c_Groups_Ouminus__class_Ouminus(X5790),X5788))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5790),X5789),X5788)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J])])). 4.05/4.31 fof(c_0_8489, plain, ![X8638, X8639, X8640, X8641]:(~class_Orderings_Olinorder(X8641)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8641),X8640),X8639))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8641),X8640),hAPP(hAPP(c_Orderings_Oord__class_Omax(X8641),X8638),X8639))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ole__supI2])])])). 4.05/4.31 fof(c_0_8490, plain, ![X14633, X14635, X14636]:(((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk444_1(X14633)),hAPP(c_List_Oset(tc_Nat_Onat),X14633)))|hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X14633)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=esk444_1(X14633)|hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X14633)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X14635)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X14636),hAPP(c_List_Oset(tc_Nat_Onat),X14635)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X14636))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__eq__0__nat__iff__nat])])])])])])). 4.05/4.31 fof(c_0_8491, plain, ![X8515, X8516, X8517]:(~c_Relation_Osingle__valued(X8517,X8517,X8516)|c_Relation_Osingle__valued(X8517,X8517,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X8517,X8517),tc_HOL_Obool),X8515),X8516))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_single__valued__rel__pow])])])). 4.05/4.31 fof(c_0_8492, plain, ![X6208, X6209, X6210]:(~class_Groups_Ogroup__add(X6210)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6210),X6209),hAPP(c_Groups_Ouminus__class_Ouminus(X6210),X6208))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X6210),X6209),X6208)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__def])])). 4.05/4.31 fof(c_0_8493, plain, ![X16705, X16706, X16707, X16708]:(((hBOOL(hAPP(c_List_Olistsp(X16708,X16707),X16705))|~hBOOL(hAPP(c_List_Olistsp(X16708,X16707),hAPP(hAPP(c_List_Olist_OCons(X16708),X16706),X16705))))&(hBOOL(hAPP(X16707,X16706))|~hBOOL(hAPP(c_List_Olistsp(X16708,X16707),hAPP(hAPP(c_List_Olist_OCons(X16708),X16706),X16705)))))&(~hBOOL(hAPP(c_List_Olistsp(X16708,X16707),X16705))|~hBOOL(hAPP(X16707,X16706))|hBOOL(hAPP(c_List_Olistsp(X16708,X16707),hAPP(hAPP(c_List_Olist_OCons(X16708),X16706),X16705))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp_Oequations_I2_J])])])). 4.05/4.31 fof(c_0_8494, plain, ![X9848]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X9848),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|X9848=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk299_1(X9848))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negD])])])). 4.05/4.31 cnf(c_0_8495, 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_5519])). 4.05/4.31 cnf(c_0_8496, 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_5527])). 4.05/4.31 fof(c_0_8497, plain, ![X4074, X4075, X4076, X4077, X4078, X4079]:(~hBOOL(hAPP(X4079,X4078))|(~c_Natural_Oevaln(X4077,X4078,X4076,X4075)|(~c_Natural_Oevaln(c_Com_Ocom_OWhile(X4079,X4077),X4075,X4076,X4074)|c_Natural_Oevaln(c_Com_Ocom_OWhile(X4079,X4077),X4078,X4076,X4074)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_OWhileTrue])])). 4.05/4.31 fof(c_0_8498, plain, ![X9160, X9161, X9162]:(~class_Groups_Oab__group__add(X9162)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9162),X9161),hAPP(c_Groups_Ouminus__class_Ouminus(X9162),X9160))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X9162),X9161),X9160)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_ab__diff__minus])])])). 4.05/4.31 fof(c_0_8499, plain, ![X1722, X1723, X1724]:(~c_Fun_Oinj__on(tc_List_Olist(X1724),tc_List_Olist(X1723),hAPP(c_List_Omap(X1724,X1723),X1722),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1724),tc_HOL_Obool)))|c_Fun_Oinj__on(X1724,X1723,X1722,c_Orderings_Otop__class_Otop(tc_fun(X1724,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__mapD])])])). 4.05/4.31 fof(c_0_8500, plain, ![X1944, X1945, X1946]:(~class_Lattices_Oboolean__algebra(X1946)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1946),X1945),X1944)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1946),X1945),hAPP(c_Groups_Ouminus__class_Ouminus(X1946),X1944))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__eq])])])). 4.05/4.31 fof(c_0_8501, plain, ![X16320, X16321, X16322, X16323, X16324]:(~c_Finite__Set_Ofun__left__comm__idem(X16324,X16323,X16322)|hAPP(hAPP(X16322,X16321),hAPP(hAPP(X16322,X16321),X16320))=hAPP(hAPP(X16322,X16321),X16320)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__idem])])])). 4.05/4.31 fof(c_0_8502, plain, ![X17031, X17032]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17032),hAPP(c_Groups_Ouminus__class_Ouminus(X17032),X17031)),X17031))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17032),c_Groups_Ozero__class_Ozero(X17032)),X17031))|~class_Groups_Olinordered__ab__group__add(X17032))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17032),c_Groups_Ozero__class_Ozero(X17032)),X17031))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17032),hAPP(c_Groups_Ouminus__class_Ouminus(X17032),X17031)),X17031))|~class_Groups_Olinordered__ab__group__add(X17032))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg])])])). 4.05/4.31 fof(c_0_8503, plain, ![X12352, X12353]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12353),hAPP(c_Groups_Ouminus__class_Ouminus(X12353),X12352)),X12352))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12353),c_Groups_Ozero__class_Ozero(X12353)),X12352))|~class_Groups_Olinordered__ab__group__add(X12353))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12353),c_Groups_Ozero__class_Ozero(X12353)),X12352))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12353),hAPP(c_Groups_Ouminus__class_Ouminus(X12353),X12352)),X12352))|~class_Groups_Olinordered__ab__group__add(X12353))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])])). 4.05/4.31 fof(c_0_8504, plain, ![X12310, X12311, X12312, X12313]:(~class_Orderings_Olinorder(X12313)|c_List_Olinorder__class_Osorted(X12313,hAPP(hAPP(c_List_Omap(X12312,X12313),X12311),c_List_Olinorder__class_Osort__key(X12312,X12313,X12311,X12310)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__sort__key])])). 4.05/4.31 fof(c_0_8505, plain, ![X16162, X16163]:(~class_Complete__Lattice_Ocomplete__lattice(X16163)|hAPP(c_List_Ofoldl(X16163,X16163,c_Lattices_Osemilattice__inf__class_Oinf(X16163),c_Orderings_Otop__class_Otop(X16163)),X16162)=c_Complete__Lattice_OInf__class_OInf(X16163,hAPP(c_List_Oset(X16163),X16162))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__set__fold])])])). 4.05/4.31 fof(c_0_8506, plain, ![X2395, X2396, X2397]:(~class_Rings_Olinordered__ring(X2397)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2397),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2397),X2396),X2396)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2397),X2395),X2395))),c_Groups_Ozero__class_Ozero(X2397)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero])])])). 4.05/4.31 fof(c_0_8507, plain, ![X15192, X15193, X15194]:(~class_Groups_Ogroup__add(X15194)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X15194),X15193),X15192)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X15194),X15193),hAPP(c_Groups_Ouminus__class_Ouminus(X15194),X15192))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__minus__eq__add])])])). 4.05/4.31 fof(c_0_8508, plain, ![X4359, X4360]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4360),X4359),hAPP(c_Groups_Ouminus__class_Ouminus(X4360),X4359)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4360),X4359),c_Groups_Ozero__class_Ozero(X4360)))|~class_Rings_Olinordered__idom(X4360))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4360),X4359),c_Groups_Ozero__class_Ozero(X4360)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4360),X4359),hAPP(c_Groups_Ouminus__class_Ouminus(X4360),X4359)))|~class_Rings_Olinordered__idom(X4360))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])])). 4.05/4.31 fof(c_0_8509, plain, ![X5334, X5335]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5335),X5334),c_Groups_Ozero__class_Ozero(X5335)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5335),X5334),hAPP(c_Groups_Ouminus__class_Ouminus(X5335),X5334)))|~class_Groups_Olinordered__ab__group__add(X5335))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5335),X5334),hAPP(c_Groups_Ouminus__class_Ouminus(X5335),X5334)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5335),X5334),c_Groups_Ozero__class_Ozero(X5335)))|~class_Groups_Olinordered__ab__group__add(X5335))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__minus__self__iff])])])])). 4.05/4.31 fof(c_0_8510, plain, ![X9518, X9519, X9520, X9521, X9522, X9523, X9524]:((~hBOOL(hAPP(c_Predicate_OPowp(X9520,X9519),X9518))|(~hBOOL(hAPP(hAPP(c_member(X9520),X9521),X9518))|hBOOL(hAPP(X9519,X9521))))&((hBOOL(hAPP(hAPP(c_member(X9524),esk291_3(X9522,X9523,X9524)),X9522))|hBOOL(hAPP(c_Predicate_OPowp(X9524,X9523),X9522)))&(~hBOOL(hAPP(X9523,esk291_3(X9522,X9523,X9524)))|hBOOL(hAPP(c_Predicate_OPowp(X9524,X9523),X9522))))), 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])])])])])])). 4.05/4.31 fof(c_0_8511, plain, ![X8998, X8999, X9000]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9000),X8999))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X8999),X8998))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9000),X8998)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zle__trans])])])). 4.05/4.31 cnf(c_0_8512, plain, (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)),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_5528])). 4.05/4.31 cnf(c_0_8513, plain, (c_Equiv__Relations_Oequiv(X2,X3,X1)|X1!=hAPP(hAPP(c_Relation_Orel__comp(X2,X2,X2),hAPP(c_Relation_Oconverse(X2,X2),X1)),X1)|hAPP(c_Relation_ODomain(X2,X2),X1)!=X3), inference(split_conjunct,[status(thm)],[c_0_5529])). 4.05/4.31 fof(c_0_8514, plain, ![X4051, X4052, X4053]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4053),X4052))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4052),X4051))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4053),X4051)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__trans])])])). 4.05/4.31 cnf(c_0_8515, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_5530])). 4.05/4.31 fof(c_0_8516, plain, ![X16899, X16900]:(X16900=c_List_Olist_ONil(X16899)|hBOOL(hAPP(hAPP(c_member(X16899),c_List_Olast(X16899,X16900)),hAPP(c_List_Oset(X16899),X16900)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_last__in__set])])])). 4.05/4.31 fof(c_0_8517, plain, ![X9506, X9507]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9507),X9506),c_Groups_Ozero__class_Ozero(X9507)))|hAPP(c_Groups_Oabs__class_Oabs(X9507),X9506)=X9506|~class_Groups_Oabs__if(X9507))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9507),X9506),c_Groups_Ozero__class_Ozero(X9507)))|hAPP(c_Groups_Oabs__class_Oabs(X9507),X9506)=hAPP(c_Groups_Ouminus__class_Ouminus(X9507),X9506)|~class_Groups_Oabs__if(X9507))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__if])])])])). 4.05/4.31 fof(c_0_8518, plain, ![X2310, X2311, X2312]:(~class_Orderings_Olinorder(X2312)|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2312),X2310),X2311))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2312),X2311),X2310)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])])). 4.05/4.31 fof(c_0_8519, plain, ![X9515, X9516, X9517]:(~class_Groups_Ocomm__monoid__add(X9517)|c_Groups_Ozero__class_Ozero(X9517)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X9516,X9517),X9515),c_Orderings_Obot__class_Obot(tc_fun(X9516,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oempty])])). 4.05/4.31 fof(c_0_8520, plain, ![X16828, X16829, X16830, X16831]:((hAPP(hAPP(c_Power_Opower__class_Opower(X16831),X16830),X16828)!=hAPP(hAPP(c_Power_Opower__class_Opower(X16831),X16830),X16829)|X16828=X16829|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16831),c_Groups_Oone__class_Oone(X16831)),X16830))|~class_Rings_Olinordered__semidom(X16831))&(X16828!=X16829|hAPP(hAPP(c_Power_Opower__class_Opower(X16831),X16830),X16828)=hAPP(hAPP(c_Power_Opower__class_Opower(X16831),X16830),X16829)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X16831),c_Groups_Oone__class_Oone(X16831)),X16830))|~class_Rings_Olinordered__semidom(X16831))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__inject__exp])])])])). 4.05/4.31 fof(c_0_8521, plain, ![X16038, X16039]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16039),c_Orderings_Otop__class_Otop(tc_fun(X16039,tc_HOL_Obool))))|(hAPP(c_Finite__Set_Ocard(X16039),X16038)!=hAPP(c_Finite__Set_Ocard(X16039),c_Orderings_Otop__class_Otop(tc_fun(X16039,tc_HOL_Obool)))|c_Orderings_Otop__class_Otop(tc_fun(X16039,tc_HOL_Obool))=X16038)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])])])). 4.05/4.31 fof(c_0_8522, plain, ![X4914, X4915]:((~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(X4915)),X4914)))|c_List_Olist_ONil(X4915)!=X4914)&(c_List_Olist_ONil(X4915)=X4914|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(X4915)),X4914))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__greater__0__conv])])). 4.05/4.31 cnf(c_0_8523, 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_5531])). 4.05/4.31 fof(c_0_8524, plain, ![X14470, X14471, X14472, X14473]:(~c_Fun_Oinj__on(X14473,X14472,X14471,X14470)|hAPP(c_Finite__Set_Ocard(X14473),X14470)=hAPP(c_Finite__Set_Ocard(X14472),hAPP(c_Set_Oimage(X14473,X14472,X14471),X14470))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__image])])])). 4.05/4.31 fof(c_0_8525, plain, ![X4462, X4463]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4462),X4463))|X4462=X4463|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4463),X4462))), inference(variable_rename,[status(thm)],[fact_zless__linear])). 4.05/4.31 fof(c_0_8526, plain, ![X4599, X4600]:(X4600=X4599|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4600),X4599))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4599),X4600)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat])])])). 4.05/4.31 fof(c_0_8527, plain, ![X12050, X12051, X12052, X12053]:((X12051!=hAPP(hAPP(c_List_Olist__update(X12052,X12051),X12053),X12050)|X12050=hAPP(hAPP(c_List_Onth(X12052),X12051),X12053)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12053),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12052)),X12051))))&(X12050!=hAPP(hAPP(c_List_Onth(X12052),X12051),X12053)|X12051=hAPP(hAPP(c_List_Olist__update(X12052,X12051),X12053),X12050)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12053),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12052)),X12051))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__same__conv])])])). 4.05/4.31 fof(c_0_8528, plain, ![X8289, X8290]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8290),X8289))|X8290=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8289),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X8289),X8290))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__diff__cancel])])])). 4.05/4.31 fof(c_0_8529, plain, ![X12597, X12598]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12598),X12597))|X12597=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12598),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12597),X12598))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])])). 4.05/4.31 cnf(c_0_8530, 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_5323])). 4.05/4.31 fof(c_0_8531, plain, ![X6063, X6064, X6065, X6066, X6067]:(~c_Relation_Osingle__valued(X6067,X6066,X6065)|(~c_Relation_Osingle__valued(X6066,X6064,X6063)|c_Relation_Osingle__valued(X6067,X6064,hAPP(hAPP(c_Relation_Orel__comp(X6067,X6066,X6064),X6065),X6063)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_single__valued__rel__comp])])])). 4.05/4.31 fof(c_0_8532, plain, ![X3773, X3774]:(~class_Orderings_Olinorder(X3774)|c_Big__Operators_Olinorder__class_OMax(X3774,hAPP(hAPP(c_Set_Oinsert(X3774),X3773),c_Orderings_Obot__class_Obot(tc_fun(X3774,tc_HOL_Obool))))=X3773), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_Osingleton])])])). 4.05/4.31 fof(c_0_8533, plain, ![X15283, X15284]:(~class_Orderings_Olinorder(X15284)|X15283=c_Big__Operators_Olinorder__class_OMin(X15284,hAPP(hAPP(c_Set_Oinsert(X15284),X15283),c_Orderings_Obot__class_Obot(tc_fun(X15284,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_Osingleton])])])). 4.05/4.31 cnf(c_0_8534, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5481])). 4.05/4.31 cnf(c_0_8535, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Int_OPls))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_5482])). 4.05/4.31 cnf(c_0_8536, 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_5483])). 4.05/4.31 cnf(c_0_8537, 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_5484])). 4.05/4.31 fof(c_0_8538, plain, ![X8491, X8492]:(~class_Lattices_Olattice(X8492)|X8491=c_Big__Operators_Olattice__class_OInf__fin(X8492,hAPP(hAPP(c_Set_Oinsert(X8492),X8491),c_Orderings_Obot__class_Obot(tc_fun(X8492,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osingleton])])). 4.05/4.31 cnf(c_0_8539, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)!=X3|~class_Rings_Oidom(X1)), inference(split_conjunct,[status(thm)],[c_0_5532])). 4.05/4.31 fof(c_0_8540, plain, ![X675, X676, X677, X679, X680, X681, X682, X683, X686]:((~hBOOL(hAPP(X677,esk13_3(X675,X676,X677)))|hBOOL(hAPP(X677,hAPP(hAPP(c_Product__Type_OPair(X676,X675),X679),X680))))&(~hBOOL(hAPP(X683,hAPP(hAPP(c_Product__Type_OPair(X682,X681),esk14_3(X681,X682,X683)),esk15_3(X681,X682,X683))))|hBOOL(hAPP(X683,X686)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__paired__All])])])])])). 4.05/4.31 fof(c_0_8541, plain, ![X3756, X3757]:(~class_Complete__Lattice_Ocomplete__lattice(X3757)|X3756=c_Complete__Lattice_OSup__class_OSup(X3757,hAPP(hAPP(c_Set_Oinsert(X3757),X3756),c_Orderings_Obot__class_Obot(tc_fun(X3757,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__singleton])])])). 4.05/4.31 fof(c_0_8542, plain, ![X4607, X4608, X4609]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4609),X4607)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4609),X4608)|X4608=X4607|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4609)))&(X4608!=X4607|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4609),X4607)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4609),X4608)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4609)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])])). 4.05/4.31 fof(c_0_8543, plain, ![X7688, X7689]:(~class_Complete__Lattice_Ocomplete__lattice(X7689)|X7688=c_Complete__Lattice_OInf__class_OInf(X7689,hAPP(hAPP(c_Set_Oinsert(X7689),X7688),c_Orderings_Obot__class_Obot(tc_fun(X7689,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__singleton])])])). 4.05/4.31 fof(c_0_8544, plain, ![X665, X666, X667]:(~hBOOL(hAPP(hAPP(c_member(X667),X666),hAPP(c_List_Oset(X667),c_List_Obutlast(X667,X665))))|hBOOL(hAPP(hAPP(c_member(X667),X666),hAPP(c_List_Oset(X667),X665)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__set__butlastD])])])). 4.05/4.31 cnf(c_0_8545, 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_5533])). 4.05/4.31 fof(c_0_8546, plain, ![X8666, X8667]:(~class_Groups_Oordered__ab__group__add__abs(X8667)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8667),hAPP(c_Groups_Ouminus__class_Ouminus(X8667),X8666)),hAPP(c_Groups_Oabs__class_Oabs(X8667),X8666)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__ge__minus__self])])])). 4.05/4.31 fof(c_0_8547, plain, ![X5267, X5268]:(~class_Lattices_Olattice(X5268)|X5267=c_Big__Operators_Olattice__class_OSup__fin(X5268,hAPP(hAPP(c_Set_Oinsert(X5268),X5267),c_Orderings_Obot__class_Obot(tc_fun(X5268,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_Osingleton])])])). 4.05/4.31 fof(c_0_8548, plain, ![X14933, X14934, X14935]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X14935),X14934))|c_Random_Ominus__shift(X14933,X14935,X14934)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X14935),X14934))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X14935),X14934))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X14933),X14935)),X14934)=c_Random_Ominus__shift(X14933,X14935,X14934))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__shift__def])])])). 4.05/4.31 fof(c_0_8549, plain, ![X6519, X6520, X6521]:(~class_Lazy__Sequence_Osmall__lazy(X6521)|~class_Lazy__Sequence_Osmall__lazy(X6520)|c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X6521,X6520),X6519)=c_Lazy__Sequence_Oproduct(X6521,X6520,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X6521,X6519),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X6520,X6519))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_small__lazy__prod__def])])])). 4.05/4.31 fof(c_0_8550, plain, ![X17692, X17693, X17694]:(~class_Orderings_Olinorder(X17694)|(~c_List_Olinorder__class_Osorted(X17694,X17693)|(~hBOOL(hAPP(c_List_Odistinct(X17694),X17693))|(~c_List_Olinorder__class_Osorted(X17694,X17692)|(~hBOOL(hAPP(c_List_Odistinct(X17694),X17692))|(hAPP(c_List_Oset(X17694),X17692)!=hAPP(c_List_Oset(X17694),X17693)|X17692=X17693)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__distinct__set__unique])])])). 4.05/4.31 cnf(c_0_8551, 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_5534])). 4.05/4.31 fof(c_0_8552, plain, ![X5039, X5040]:(~class_Rings_Olinordered__ring(X5040)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5040),c_Groups_Ozero__class_Ozero(X5040)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5040),X5039),X5039)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])])). 4.05/4.31 fof(c_0_8553, plain, ![X4369, X4370]:(~class_Rings_Olinordered__semidom(X4370)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4370),X4369),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4370),X4369),c_Groups_Oone__class_Oone(X4370))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])])). 4.05/4.31 fof(c_0_8554, plain, ![X17027, X17028, X17029, X17030]:(~class_Orderings_Olinorder(X17030)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17029)),X17027)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17029)),c_List_Olinorder__class_Osort__key(X17029,X17030,X17028,X17027))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_length__sort])])])). 4.05/4.31 fof(c_0_8555, plain, ![X16465, X16466, X16467, X16468, X16469]:((~c_List_Olist__all2(X16469,X16468,X16467,hAPP(c_List_Orev(X16469),X16466),X16465)|c_List_Olist__all2(X16469,X16468,X16467,X16466,hAPP(c_List_Orev(X16468),X16465)))&(~c_List_Olist__all2(X16469,X16468,X16467,X16466,hAPP(c_List_Orev(X16468),X16465))|c_List_Olist__all2(X16469,X16468,X16467,hAPP(c_List_Orev(X16469),X16466),X16465))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__rev1])])). 4.05/4.31 fof(c_0_8556, plain, ![X5201, X5202, X5203]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5203),X5202))|hBOOL(hAPP(c_Finite__Set_Ofinite(X5203),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5203,tc_HOL_Obool)),X5202),X5201)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Diff])])])). 4.05/4.31 fof(c_0_8557, plain, ![X7840, X7841, X7842]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X7842),X7840))|hBOOL(hAPP(c_Finite__Set_Ofinite(X7842),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7842,tc_HOL_Obool)),X7841),X7840))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X7842),X7841))|hBOOL(hAPP(c_Finite__Set_Ofinite(X7842),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7842,tc_HOL_Obool)),X7841),X7840))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Int])])])). 4.05/4.31 fof(c_0_8558, plain, ![X9539, X9540, X9541, X9542, X9543]:(~c_Equiv__Relations_Oequivp(X9543,X9542)|(~hBOOL(hAPP(hAPP(X9542,X9541),X9540))|(~hBOOL(hAPP(hAPP(X9542,X9540),X9539))|hBOOL(hAPP(hAPP(X9542,X9541),X9539))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equivp__transp])])])). 4.05/4.31 cnf(c_0_8559, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|c_Groups_Ozero__class_Ozero(X1)!=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|c_Groups_Ozero__class_Ozero(X1)!=X3|~class_Int_Onumber(X1)|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_5371])). 4.05/4.31 fof(c_0_8560, plain, ![X10680, X10681, X10682]:((~hBOOL(hAPP(hAPP(c_member(tc_fun(X10682,tc_HOL_Obool)),X10681),hAPP(c_Set_OPow(X10682),X10680)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10682,tc_HOL_Obool)),X10681),X10680)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10682,tc_HOL_Obool)),X10681),X10680))|hBOOL(hAPP(hAPP(c_member(tc_fun(X10682,tc_HOL_Obool)),X10681),hAPP(c_Set_OPow(X10682),X10680))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pow__iff])])). 4.05/4.31 fof(c_0_8561, plain, ![X17540, X17541]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X17541))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17541),X17540))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X17541),X17540))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__pos__pos__trivial])])])). 4.05/4.31 fof(c_0_8562, plain, ![X5430, X5431]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5431),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5430),X5431))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X5431),X5430)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__neg__neg__trivial])])])). 4.05/4.31 fof(c_0_8563, plain, ![X6729]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6729))|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),X6729))))&(~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),X6729)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6729)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__int__conv])])). 4.05/4.31 fof(c_0_8564, plain, ![X1675, X1676, X1677]:(~c_Equiv__Relations_Oequiv(X1677,X1676,X1675)|c_Complete__Lattice_OSup__class_OSup(tc_fun(X1677,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1677),X1676),X1675))=X1676), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Union__quotient])])])). 4.05/4.31 cnf(c_0_8565, 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),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_5535])). 4.05/4.31 fof(c_0_8566, plain, ![X10772, X10773]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X10773))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X10772,X10773)),X10773))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pos__mod__bound])])])). 4.05/4.31 fof(c_0_8567, plain, ![X5259, X5260]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5260))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5259,X5260)),X5260))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__less__divisor])])])). 4.05/4.31 fof(c_0_8568, plain, ![X9949, X9950]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X9950))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X9950,X9949)),X9950))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmod__le__nonneg__dividend])])])). 4.05/4.31 fof(c_0_8569, plain, ![X17637, X17638]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17638))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17637,X17638)),X17638))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__le__divisor])])])). 4.05/4.31 fof(c_0_8570, plain, ![X9075, X9076, X9077, X9078]:(~class_Groups_Ouminus(X9078)|hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9077,X9078)),X9076),X9075)=hAPP(c_Groups_Ouminus__class_Ouminus(X9078),hAPP(X9076,X9075))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__Compl__def])])). 4.05/4.31 fof(c_0_8571, plain, ![X6339, X6340, X6341, X6342, X6343]:((hAPP(hAPP(c_List_Omap(X6343,X6342),X6341),X6340)!=hAPP(hAPP(c_List_Omap(X6343,X6342),X6341),X6339)|X6340=X6339|~c_Fun_Oinj__on(X6343,X6342,X6341,c_Orderings_Otop__class_Otop(tc_fun(X6343,tc_HOL_Obool))))&(X6340!=X6339|hAPP(hAPP(c_List_Omap(X6343,X6342),X6341),X6340)=hAPP(hAPP(c_List_Omap(X6343,X6342),X6341),X6339)|~c_Fun_Oinj__on(X6343,X6342,X6341,c_Orderings_Otop__class_Otop(tc_fun(X6343,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__map__eq__map])])])). 4.05/4.31 fof(c_0_8572, plain, ![X1400, X1401]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1401),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1401),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1400,X1401)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_neg__mod__bound])])])). 4.05/4.31 fof(c_0_8573, plain, ![X12994, X12995]:(~class_Int_Onumber__ring(X12995)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12995),hAPP(c_Int_Onumber__class_Onumber__of(X12995),c_Int_OMin)),X12994)=hAPP(c_Groups_Ouminus__class_Ouminus(X12995),X12994)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__minus1])])])). 4.05/4.31 fof(c_0_8574, plain, ![X5719, X5720, X5721, X5722, X5724, X5725, X5726, X5727, X5728]:(((((X5720=X5719|c_Natural_Oevalc(c_Com_Ocom_OWhile(X5722,X5721),esk179_4(X5719,X5720,X5721,X5722),X5719)|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X5722,X5721),X5720,X5719))&(~hBOOL(hAPP(X5722,X5720))|c_Natural_Oevalc(c_Com_Ocom_OWhile(X5722,X5721),esk179_4(X5719,X5720,X5721,X5722),X5719)|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X5722,X5721),X5720,X5719)))&((X5720=X5719|c_Natural_Oevalc(X5721,X5720,esk179_4(X5719,X5720,X5721,X5722))|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X5722,X5721),X5720,X5719))&(~hBOOL(hAPP(X5722,X5720))|c_Natural_Oevalc(X5721,X5720,esk179_4(X5719,X5720,X5721,X5722))|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X5722,X5721),X5720,X5719))))&((X5720=X5719|hBOOL(hAPP(X5722,X5720))|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X5722,X5721),X5720,X5719))&(~hBOOL(hAPP(X5722,X5720))|hBOOL(hAPP(X5722,X5720))|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X5722,X5721),X5720,X5719))))&((~c_Natural_Oevalc(c_Com_Ocom_OWhile(X5727,X5726),X5728,X5724)|~c_Natural_Oevalc(X5726,X5725,X5728)|~hBOOL(hAPP(X5727,X5725))|c_Natural_Oevalc(c_Com_Ocom_OWhile(X5727,X5726),X5725,X5724))&(X5725!=X5724|hBOOL(hAPP(X5727,X5725))|c_Natural_Oevalc(c_Com_Ocom_OWhile(X5727,X5726),X5725,X5724)))), 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_evalc_Oequations_I8_J])])])])])])])). 4.05/4.31 fof(c_0_8575, plain, ![X17481, X17482, X17483, X17484, X17485, X17486]:(X17486=X17485|hAPP(X17482,X17486)=hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X17484,X17483),X17482),X17485),X17481),X17486)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__other])])). 4.05/4.31 cnf(c_0_8576, 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_5536])). 4.05/4.31 fof(c_0_8577, plain, ![X9788, X9789, X9790]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9790,tc_HOL_Obool)),X9789),X9788))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9790,tc_HOL_Obool)),X9789),X9788)=X9789), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb2])])). 4.05/4.31 fof(c_0_8578, plain, ![X7826, X7827, X7828]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7828,tc_HOL_Obool)),X7827),X7826))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7828,tc_HOL_Obool)),X7826),X7827)=X7827), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Int__absorb1])])])). 4.05/4.31 fof(c_0_8579, plain, ![X16560, X16561, X16562, X16563]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X16563,X16562),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X16561),X16560)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X16562|c_Divides_Odiv__class_Omod(tc_Int_Oint,X16563,X16562)=X16560)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__mod])])])). 4.05/4.31 fof(c_0_8580, plain, ![X10924, X10925]:(~class_Int_Onumber__ring(X10925)|~class_Fields_Ofield__inverse__zero(X10925)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10925),X10924),hAPP(c_Int_Onumber__class_Onumber__of(X10925),c_Int_OMin))=hAPP(c_Groups_Ouminus__class_Ouminus(X10925),X10924)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__minus1])])])). 4.05/4.31 fof(c_0_8581, plain, ![X5081, X5082, X5083]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5083,tc_HOL_Obool)),X5082),X5081))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5083,tc_HOL_Obool)),X5082),X5081)=X5081)&(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5083,tc_HOL_Obool)),X5082),X5081)!=X5081|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5083,tc_HOL_Obool)),X5082),X5081)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Un__eq])])). 4.05/4.31 fof(c_0_8582, plain, ![X8352, X8353, X8354]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8354,tc_HOL_Obool)),X8353),X8352))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8354,tc_HOL_Obool)),X8352),X8353)=X8352), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb2])])). 4.05/4.31 cnf(c_0_8583, plain, (esk396_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_5537])). 4.05/4.31 cnf(c_0_8584, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_5538]), ['final']). 4.05/4.31 fof(c_0_8585, plain, ![X3584, X3585, X3586, X3587, X3588, X3589, X3590]:(~c_Finite__Set_Ofun__left__comm(X3590,X3589,X3588)|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X3590,X3589,X3588,X3587,X3586),X3585))|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X3590,X3589,X3588,X3587,X3586),X3584))|X3584=X3585))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__graph__determ])])])). 4.05/4.31 fof(c_0_8586, plain, ![X14044, X14045, X14046, X14047, X14048]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14048),X14047))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14046,tc_HOL_Obool)),X14045),hAPP(c_Set_Oimage(X14048,X14046,X14044),X14047)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X14046),X14045)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__surj])])])). 4.05/4.31 fof(c_0_8587, plain, ![X10336, X10337]:(~class_Rings_Oring__1(X10337)|hAPP(c_Groups_Ouminus__class_Ouminus(X10337),hAPP(c_Int_Oring__1__class_Oof__int(X10337),X10336))=hAPP(c_Int_Oring__1__class_Oof__int(X10337),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X10336))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__minus])])])). 4.05/4.31 fof(c_0_8588, plain, ![X2981, X2982, X2983]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2983),X2982))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2983,tc_HOL_Obool)),X2981),X2982))|hBOOL(hAPP(c_Finite__Set_Ofinite(X2983),X2981)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rev__finite__subset])])])). 4.05/4.31 fof(c_0_8589, plain, ![X8195, X8196, X8197]:((~c_List_Olinorder__class_Osorted(X8197,X8195)|c_List_Olinorder__class_Osorted(X8197,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8197,X8197,c_COMBI(X8197)),X8196),X8195))|~class_Orderings_Olinorder(X8197))&(~c_List_Olinorder__class_Osorted(X8197,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8197,X8197,c_COMBI(X8197)),X8196),X8195))|c_List_Olinorder__class_Osorted(X8197,X8195)|~class_Orderings_Olinorder(X8197))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort])])])). 4.05/4.31 cnf(c_0_8590, 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_5539])). 4.05/4.31 cnf(c_0_8591, 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_5539])). 4.05/4.31 cnf(c_0_8592, 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_4671])). 4.05/4.31 fof(c_0_8593, plain, ![X13471]:(~c_Nat__Transfer_Onat__set(X13471)|hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X13471)=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X13471))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J])])])). 4.05/4.31 fof(c_0_8594, plain, ![X7652, X7653]:(~class_Int_Onumber__ring(X7653)|hAPP(c_Groups_Ouminus__class_Ouminus(X7653),hAPP(c_Int_Onumber__class_Onumber__of(X7653),X7652))=hAPP(c_Int_Onumber__class_Onumber__of(X7653),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X7652))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I30_J])])). 4.05/4.31 fof(c_0_8595, plain, ![X2873, X2874, X2875]:((~c_Nat__Transfer_Onat__set(X2873)|(~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2874),X2873))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2874))))&((hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk100_1(X2875)),X2875))|c_Nat__Transfer_Onat__set(X2875))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk100_1(X2875)))|c_Nat__Transfer_Onat__set(X2875)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__set__def])])])])])])). 4.05/4.31 cnf(c_0_8596, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|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),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5535])). 4.05/4.31 fof(c_0_8597, plain, ![X14931, X14932]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14932))|c_SMT_Oz3mod(X14931,X14932)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X14931,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X14932)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14932))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X14931,X14932)=c_SMT_Oz3mod(X14931,X14932))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_z3mod__def])])])). 4.05/4.31 fof(c_0_8598, plain, ![X11922, X11923, X11924, X11925]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11925),X11924))|hAPP(hAPP(c_List_Onth(X11923),c_List_Oreplicate(X11923,X11924,X11922)),X11925)=X11922), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__replicate])])])). 4.05/4.31 cnf(c_0_8599, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|c_List_Oupt(X1,X2)!=c_List_Olist_ONil(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_5540])). 4.05/4.31 fof(c_0_8600, plain, ![X16182, X16183, X16184]:(~class_Groups_Ocomm__monoid__mult(X16184)|c_Groups_Oone__class_Oone(X16184)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16183,X16184),X16182),c_Orderings_Obot__class_Obot(tc_fun(X16183,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__empty])])). 4.05/4.31 fof(c_0_8601, plain, ![X8711, X8712]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X8712,X8711)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X8712,X8711),tc_HOL_Obool))))|hBOOL(hAPP(c_Finite__Set_Ofinite(X8711),c_Orderings_Otop__class_Otop(tc_fun(X8711,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2])])). 4.05/4.31 fof(c_0_8602, plain, ![X10485, X10486]:(~class_Orderings_Olinorder(X10486)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10486,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10486),X10485))=hAPP(c_SetInterval_Oord__class_OatMost(X10486),X10485)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__greaterThan])])). 4.05/4.31 cnf(c_0_8603, 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_5541, c_0_4434])). 4.05/4.31 fof(c_0_8604, plain, ![X4164, X4165, X4166]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4166),X4165))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4166),X4164)),X4165))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__imp__diff__less])])])). 4.05/4.31 fof(c_0_8605, plain, ![X5462, X5463]:(~class_Orderings_Olinorder(X5463)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5463,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5463),X5462))=hAPP(c_SetInterval_Oord__class_OatLeast(X5463),X5462)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Compl__lessThan])])])). 4.05/4.31 fof(c_0_8606, plain, ![X10108, X10109, X10110, X10111]:(~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10111)),X10110),hAPP(c_List_Oset(tc_List_Olist(X10111)),c_Enum_On__lists(X10111,X10109,X10108))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10111)),X10110)=X10109), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__n__lists__elem])])). 4.05/4.31 cnf(c_0_8607, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),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_5439])). 4.05/4.31 fof(c_0_8608, plain, ![X1656, X1657]:(~class_Orderings_Olinorder(X1657)|hAPP(c_SetInterval_Oord__class_OgreaterThan(X1657),X1656)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1657,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1657),X1656))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__atMost])])). 4.05/4.31 cnf(c_0_8609, plain, (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1|X1=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_5535])). 4.05/4.31 cnf(c_0_8610, 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_5542])). 4.05/4.31 fof(c_0_8611, plain, ![X6473, X6474, X6475, X6476]:((~hBOOL(hAPP(hAPP(c_member(X6476),X6475),X6474))|hBOOL(hAPP(hAPP(c_member(X6476),X6475),hAPP(hAPP(c_Set_Oinsert(X6476),X6473),X6474))))&(X6475!=X6473|hBOOL(hAPP(hAPP(c_member(X6476),X6475),hAPP(hAPP(c_Set_Oinsert(X6476),X6473),X6474))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_insertCI])])])])). 4.05/4.31 fof(c_0_8612, plain, ![X9890, X9891]:(~class_Orderings_Olinorder(X9891)|hAPP(c_SetInterval_Oord__class_OlessThan(X9891),X9890)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9891,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X9891),X9890))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Compl__atLeast])])])). 4.05/4.31 cnf(c_0_8613, 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_5441])). 4.05/4.31 fof(c_0_8614, plain, ![X535, X536, X537]:(~class_Divides_Osemiring__div(X537)|c_Divides_Odiv__class_Omod(X537,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X537),X536),X535),X536)=c_Divides_Odiv__class_Omod(X537,X535,X536)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self1])])). 4.05/4.31 fof(c_0_8615, plain, ![X7571, X7572, X7573]:(~class_Divides_Osemiring__div(X7573)|c_Divides_Odiv__class_Omod(X7573,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7573),X7572),X7571),X7571)=c_Divides_Odiv__class_Omod(X7573,X7572,X7571)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self2])])). 4.05/4.31 fof(c_0_8616, plain, ![X1059, X1060]:(~class_Int_Onumber__ring(X1060)|hAPP(c_Groups_Ouminus__class_Ouminus(X1060),X1059)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1060),X1059),hAPP(c_Int_Onumber__class_Onumber__of(X1060),c_Int_OMin))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__minus1__right])])). 4.05/4.31 fof(c_0_8617, plain, ![X11255, X11256, X11257]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11257),X11256))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11257),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11256),X11255)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_termination__basic__simps_I1_J])])])). 4.05/4.31 fof(c_0_8618, plain, ![X11463, X11464, X11465]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11465),X11464))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11465),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11463),X11464)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_trans__less__add2])])])). 4.05/4.31 fof(c_0_8619, plain, ![X11052, X11053, X11054]:((c_Orderings_Obot__class_Obot(tc_fun(X11054,tc_HOL_Obool))!=c_SetInterval_Oord__class_OatLeastAtMost(X11054,X11053,X11052)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11054),X11053),X11052))|~class_Orderings_Oorder(X11054))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11054),X11053),X11052))|c_Orderings_Obot__class_Obot(tc_fun(X11054,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastAtMost(X11054,X11053,X11052)|~class_Orderings_Oorder(X11054))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty__iff])])])])). 4.05/4.31 fof(c_0_8620, plain, ![X5952, X5953, X5954, X5955]:((~hBOOL(hAPP(hAPP(c_member(X5955),X5954),c_Map_Odom(X5955,X5953,X5952)))|c_Option_Ooption_ONone(X5953)!=hAPP(X5952,X5954))&(c_Option_Ooption_ONone(X5953)=hAPP(X5952,X5954)|hBOOL(hAPP(hAPP(c_member(X5955),X5954),c_Map_Odom(X5955,X5953,X5952))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_domIff])])). 4.05/4.31 fof(c_0_8621, plain, ![X5821, X5822, X5823]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5823),X5822))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5823),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5822),X5821)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])])). 4.05/4.31 fof(c_0_8622, plain, ![X3568, X3569, X3570]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3570),X3569))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3570),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3568),X3569)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_termination__basic__simps_I4_J])])])). 4.05/4.31 fof(c_0_8623, plain, ![X15561, X15562, X15563, X15564]:(~hBOOL(hAPP(X15564,X15563))|(~hBOOL(hAPP(X15562,X15563))|hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X15561,tc_HOL_Obool)),X15564),X15562),X15563)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf1I])])])). 4.05/4.31 fof(c_0_8624, plain, ![X6651, X6652, X6653, X6654]:(((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6654),X6653),X6652))|~c_List_Olinorder__class_Osorted(X6654,hAPP(hAPP(c_List_Olist_OCons(X6654),X6653),hAPP(hAPP(c_List_Olist_OCons(X6654),X6652),X6651)))|~class_Orderings_Olinorder(X6654))&(c_List_Olinorder__class_Osorted(X6654,hAPP(hAPP(c_List_Olist_OCons(X6654),X6652),X6651))|~c_List_Olinorder__class_Osorted(X6654,hAPP(hAPP(c_List_Olist_OCons(X6654),X6653),hAPP(hAPP(c_List_Olist_OCons(X6654),X6652),X6651)))|~class_Orderings_Olinorder(X6654)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6654),X6653),X6652))|~c_List_Olinorder__class_Osorted(X6654,hAPP(hAPP(c_List_Olist_OCons(X6654),X6652),X6651))|c_List_Olinorder__class_Osorted(X6654,hAPP(hAPP(c_List_Olist_OCons(X6654),X6653),hAPP(hAPP(c_List_Olist_OCons(X6654),X6652),X6651)))|~class_Orderings_Olinorder(X6654))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__many__eq])])])])). 4.05/4.31 fof(c_0_8625, plain, ![X7609, X7610, X7611]:(~class_Lattices_Osemilattice__inf(X7611)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7611),X7610),X7609)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7611),X7609),X7610)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__commute])])])). 4.05/4.31 fof(c_0_8626, plain, ![X8066, X8067]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8067),X8066))|(hAPP(c_Nat_OSuc,X8067)=X8066|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X8067)),X8066)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__lessI])])])). 4.05/4.31 cnf(c_0_8627, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk254_2(X2,X1))=X2|hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5493])). 4.05/4.31 fof(c_0_8628, plain, ![X7936, X7937, X7938]:(X7938=c_List_Olist_ONil(X7937)|hAPP(c_List_Ohd(X7937),hAPP(hAPP(c_List_Oappend(X7937),X7938),X7936))=hAPP(c_List_Ohd(X7937),X7938)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_hd__append2])])])). 4.05/4.31 fof(c_0_8629, plain, ![X6537, X6538, X6539, X6540, X6541]:(~class_Orderings_Olinorder(X6541)|(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X6541,X6540),X6539)!=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X6541,X6538),X6537)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6541),X6540),X6539))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6541),X6538),X6537))|X6540=X6538)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J])])). 4.05/4.31 fof(c_0_8630, plain, ![X8803, X8804, X8805, X8806, X8807]:(~class_Orderings_Olinorder(X8807)|(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X8807,X8804),X8803)!=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X8807,X8806),X8805)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8807),X8806),X8805))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8807),X8804),X8803))|X8803=X8805)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J])])). 4.05/4.31 fof(c_0_8631, plain, ![X13817, X13818, X13819]:(~class_Groups_Ogroup__add(X13819)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13819),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13819),X13818),X13817)),X13817)=X13818), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])])). 4.05/4.31 fof(c_0_8632, plain, ![X16221, X16222, X16223]:(~class_Groups_Ogroup__add(X16223)|X16222=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X16223),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X16223),X16222),X16221)),X16221)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])])). 4.05/4.31 fof(c_0_8633, plain, ![X9455, X9456, X9457]:(~class_Lattices_Olattice(X9457)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9457),X9456),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9457),X9456),X9455))=X9456), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__absorb])])). 4.05/4.31 fof(c_0_8634, plain, ![X2211, X2212, X2213, X2214, X2215, X2216]:(~c_Finite__Set_Ofun__left__comm(X2216,X2215,X2214)|(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X2216,X2215,X2214,X2213,X2212),X2211))|X2211=hAPP(hAPP(c_Finite__Set_Ofold(X2216,X2215,X2214),X2213),X2212))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__equality])])])). 4.05/4.31 fof(c_0_8635, plain, ![X8919, X8920, X8921, X8922, X8923]:(~class_Orderings_Olinorder(X8923)|(~hBOOL(hAPP(c_List_Odistinct(X8922),X8921))|hBOOL(hAPP(c_List_Odistinct(X8922),c_List_Olinorder__class_Oinsort__insert__key(X8922,X8923,X8920,X8919,X8921))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__insort__insert])])). 4.05/4.31 fof(c_0_8636, plain, ![X3108, X3109, X3110, X3111, X3112]:(hBOOL(hAPP(hAPP(c_member(X3112),X3111),X3110))|c_Option_Ooption_ONone(X3109)=hAPP(c_Map_Orestrict__map(X3112,X3109,X3108,X3110),X3111)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_restrict__out])])])). 4.05/4.31 fof(c_0_8637, plain, ![X2463, X2464, X2465]:(~class_Lattices_Olattice(X2465)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2465),X2464),X2463)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2465),X2463),X2464)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I1_J])])). 4.05/4.31 fof(c_0_8638, plain, ![X10812, X10813, X10814]:(~class_Lattices_Olattice(X10814)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10814),X10813),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10814),X10813),X10812))=X10813), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__inf__absorb])])])). 4.05/4.31 fof(c_0_8639, plain, ![X9953, X9954, X9955, X9956, X9957, X9958]:(~c_Typedef_Otype__definition(X9958,X9957,X9956,X9955,X9954)|(~hBOOL(hAPP(hAPP(c_member(X9957),X9953),X9954))|X9953=hAPP(X9956,hAPP(X9955,X9953)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_type__definition_OAbs__inverse])])])). 4.05/4.31 fof(c_0_8640, plain, ![X2107, X2108, X2109]:(~c_Wellfounded_Owf(X2109,X2108)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2109,tc_HOL_Obool)),X2107),hAPP(c_Relation_OImage(X2109,X2109,X2108),X2107)))|c_Orderings_Obot__class_Obot(tc_fun(X2109,tc_HOL_Obool))=X2107)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wfE__pf])])])). 4.05/4.31 cnf(c_0_8641, 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_5543])). 4.05/4.31 fof(c_0_8642, plain, ![X15726, X15727]:(~hBOOL(hAPP(c_List_Odistinct(X15727),X15726))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15727)),X15726)=hAPP(c_Finite__Set_Ocard(X15727),hAPP(c_List_Oset(X15727),X15726))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__card])])])). 4.05/4.31 cnf(c_0_8643, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|c_List_Oupt(X1,X2)=c_List_Olist_ONil(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_5544])). 4.05/4.31 fof(c_0_8644, plain, ![X705, X706]:(~class_Rings_Olinordered__idom(X706)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X706),c_Groups_Osgn__class_Osgn(X706,X705)),hAPP(c_Groups_Oabs__class_Oabs(X706),X705))=X705), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__sgn__abs])])])). 4.05/4.31 fof(c_0_8645, plain, ![X11243, X11244, X11245, X11246]:(~hBOOL(hAPP(c_Wellfounded_Oaccp(X11246,X11245),X11244))|(~hBOOL(hAPP(hAPP(X11245,X11243),X11244))|hBOOL(hAPP(c_Wellfounded_Oaccp(X11246,X11245),X11243)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_accp__downward])])])). 4.05/4.31 cnf(c_0_8646, 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_5540])). 4.05/4.31 cnf(c_0_8647, plain, (~hBOOL(hAPP(X1,X2))|c_List_OdropWhile(X3,X1,X4)!=hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5)), inference(split_conjunct,[status(thm)],[c_0_5169])). 4.05/4.31 fof(c_0_8648, plain, ![X12807, X12808, X12809]:(~class_Rings_Ocomm__semiring__1(X12809)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12809),X12807),X12808)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12809),X12808),X12807)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])])). 4.05/4.31 fof(c_0_8649, plain, ![X6624]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6624))|X6624=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6624),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred_H])])). 4.05/4.31 fof(c_0_8650, plain, ![X6386, X6387, X6388, X6389]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6389),X6388),X6386))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6389),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6389),X6388),X6387)),X6386))|~class_Lattices_Osemilattice__sup(X6389))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6389),X6387),X6386))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6389),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X6389),X6388),X6387)),X6386))|~class_Lattices_Osemilattice__sup(X6389))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__supE])])])])). 4.05/4.31 cnf(c_0_8651, 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_5452])). 4.05/4.31 fof(c_0_8652, plain, ![X13019, X13020, X13021]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13021),X13020))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13021,tc_HOL_Obool)),X13020),hAPP(c_Set_Oimage(X13021,X13021,X13019),X13020)))|c_Fun_Oinj__on(X13021,X13021,X13019,X13020))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__surj__inj])])])). 4.05/4.31 fof(c_0_8653, plain, ![X5091, X5092]:(~class_Int_Oring__char__0(X5092)|(~hBOOL(hAPP(hAPP(c_member(X5092),X5091),c_Int_Oring__1__class_OInts(X5092)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5092),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5092),c_Groups_Oone__class_Oone(X5092)),X5091)),X5091)!=c_Groups_Ozero__class_Ozero(X5092))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__odd__nonzero])])])). 4.05/4.31 fof(c_0_8654, plain, ![X11077, X11078, X11079]:(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11079,tc_HOL_Obool)),X11078),X11077)!=c_Orderings_Obot__class_Obot(tc_fun(X11079,tc_HOL_Obool))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11079,tc_HOL_Obool)),X11078),X11077)=X11078), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Diff__triv])])])). 4.05/4.31 fof(c_0_8655, plain, ![X1877, X1878]:(~class_Orderings_Olinorder(X1878)|c_List_Olinorder__class_Osorted__list__of__set(X1878,hAPP(c_List_Oset(X1878),X1877))=c_List_Olinorder__class_Osort__key(X1878,X1878,c_COMBI(X1878),c_List_Oremdups(X1878,X1877))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__sort__remdups])])). 4.05/4.31 fof(c_0_8656, plain, ![X8926, X8927, X8928]:(~class_Lattices_Osemilattice__sup(X8928)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8928),X8926),X8927)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8928),X8927),X8926)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__commute])])])). 4.05/4.31 fof(c_0_8657, plain, ![X1969, X1970, X1971, X1972]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1972),X1971),X1970))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1972),X1971),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1972),X1970),X1969)))|~class_Lattices_Osemilattice__inf(X1972))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1972),X1971),X1969))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1972),X1971),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1972),X1970),X1969)))|~class_Lattices_Osemilattice__inf(X1972))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__infE])])])])). 4.05/4.31 fof(c_0_8658, plain, ![X11290, X11291, X11292]:((~hBOOL(hAPP(hAPP(c_member(X11292),X11291),hAPP(c_SetInterval_Oord__class_OlessThan(X11292),X11290)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11292),X11291),X11290))|~class_Orderings_Oord(X11292))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11292),X11291),X11290))|hBOOL(hAPP(hAPP(c_member(X11292),X11291),hAPP(c_SetInterval_Oord__class_OlessThan(X11292),X11290)))|~class_Orderings_Oord(X11292))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lessThan__iff])])])])). 4.05/4.31 cnf(c_0_8659, 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_5545])). 4.05/4.31 fof(c_0_8660, plain, ![X4449, X4450, X4451]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4451),X4450),X4449))|c_SetInterval_Oord__class_OgreaterThanAtMost(X4451,X4450,X4449)=c_Orderings_Obot__class_Obot(tc_fun(X4451,tc_HOL_Obool))|~class_Orderings_Oorder(X4451))&(c_SetInterval_Oord__class_OgreaterThanAtMost(X4451,X4450,X4449)!=c_Orderings_Obot__class_Obot(tc_fun(X4451,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4451),X4450),X4449))|~class_Orderings_Oorder(X4451))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_greaterThanAtMost__empty__iff2])])])])). 4.05/4.31 fof(c_0_8661, plain, ![X10541, X10542, X10543]:(~class_Lattices_Olattice(X10543)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10543),X10542),X10541)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10543),X10541),X10542)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I5_J])])). 4.05/4.31 fof(c_0_8662, plain, ![X5714, X5715, X5716]:((~hBOOL(hAPP(hAPP(c_member(X5716),X5715),hAPP(c_SetInterval_Oord__class_OatMost(X5716),X5714)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5716),X5715),X5714))|~class_Orderings_Oord(X5716))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5716),X5715),X5714))|hBOOL(hAPP(hAPP(c_member(X5716),X5715),hAPP(c_SetInterval_Oord__class_OatMost(X5716),X5714)))|~class_Orderings_Oord(X5716))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__iff])])])). 4.05/4.31 fof(c_0_8663, plain, ![X15318, X15319, X15320]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15320),X15318),X15319))|hBOOL(hAPP(hAPP(c_member(X15320),X15319),hAPP(c_SetInterval_Oord__class_OgreaterThan(X15320),X15318)))|~class_Orderings_Oord(X15320))&(~hBOOL(hAPP(hAPP(c_member(X15320),X15319),hAPP(c_SetInterval_Oord__class_OgreaterThan(X15320),X15318)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15320),X15318),X15319))|~class_Orderings_Oord(X15320))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__iff])])])). 4.05/4.31 fof(c_0_8664, plain, ![X11350, X11351, X11352]:((~hBOOL(hAPP(hAPP(c_member(X11352),X11351),hAPP(c_SetInterval_Oord__class_OatLeast(X11352),X11350)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11352),X11350),X11351))|~class_Orderings_Oord(X11352))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11352),X11350),X11351))|hBOOL(hAPP(hAPP(c_member(X11352),X11351),hAPP(c_SetInterval_Oord__class_OatLeast(X11352),X11350)))|~class_Orderings_Oord(X11352))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeast__iff])])])])). 4.05/4.31 cnf(c_0_8665, 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_Int_Onumber(X2)|~class_Fields_Ofield__inverse__zero(X2)), inference(split_conjunct,[status(thm)],[c_0_5371])). 4.05/4.31 fof(c_0_8666, plain, ![X17284, X17285, X17286]:(~class_Rings_Ocomm__semiring__1(X17286)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17286),X17284),X17285)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17286),X17285),X17284)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])])])). 4.05/4.31 fof(c_0_8667, plain, ![X862, X863, X864]:(~class_Orderings_Olinorder(X864)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X864),X863),X862)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X864),X862),X863)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf_Ocommute])])])). 4.05/4.31 fof(c_0_8668, plain, ![X6031, X6032, X6033]:(~class_Orderings_Olinorder(X6033)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X6033),X6031),X6032)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X6033),X6032),X6031)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Osup__commute])])])). 4.05/4.31 fof(c_0_8669, plain, ![X6710, X6711, X6712, X6713, X6714, X6715]:(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6715,tc_fun(X6714,tc_HOL_Obool))),X6713),X6712),X6711),X6710))|hBOOL(hAPP(hAPP(X6713,X6711),X6710))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf2D1])])])). 4.05/4.31 fof(c_0_8670, plain, ![X12506, X12507, X12508, X12509, X12510, X12511]:(~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12511,tc_fun(X12510,tc_HOL_Obool))),X12509),X12508),X12507),X12506))|hBOOL(hAPP(hAPP(X12508,X12507),X12506))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf2D2])])])). 4.05/4.31 cnf(c_0_8671, 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_5546])). 4.05/4.31 fof(c_0_8672, plain, ![X4762, X4763, X4764, X4765]:(~hBOOL(hAPP(hAPP(c_member(X4765),X4764),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4765,tc_HOL_Obool)),X4763),X4762)))|hBOOL(hAPP(hAPP(c_member(X4765),X4764),X4763))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_DiffD1])])])). 4.05/4.31 fof(c_0_8673, plain, ![X16754, X16755, X16756, X16757, X16758, X16759]:(~c_Typedef_Otype__definition(X16759,X16758,X16757,X16756,X16755)|hBOOL(hAPP(hAPP(c_member(X16758),hAPP(X16757,X16754)),X16755))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep])])). 4.05/4.31 fof(c_0_8674, plain, ![X897, X898, X899, X900]:(~hBOOL(hAPP(hAPP(c_member(X900),X899),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X900,tc_HOL_Obool)),X898),X897)))|hBOOL(hAPP(hAPP(c_member(X900),X899),X898))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_IntD1])])])). 4.05/4.31 fof(c_0_8675, plain, ![X1185, X1186]:(~class_Power_Opower(X1186)|~class_Rings_Osemiring__0(X1186)|hAPP(hAPP(c_Power_Opower__class_Opower(X1186),c_Groups_Ozero__class_Ozero(X1186)),hAPP(c_Nat_OSuc,X1185))=c_Groups_Ozero__class_Ozero(X1186)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__Suc])])). 4.05/4.31 fof(c_0_8676, plain, ![X14487, X14488, X14489, X14490]:(~hBOOL(hAPP(hAPP(c_member(X14490),X14489),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14490,tc_HOL_Obool)),X14488),X14487)))|hBOOL(hAPP(hAPP(c_member(X14490),X14489),X14487))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_IntD2])])])). 4.05/4.31 cnf(c_0_8677, plain, (X1=hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X1))), inference(split_conjunct,[status(thm)],[c_0_5547])). 4.05/4.31 fof(c_0_8678, plain, ![X643, X644]:(~class_Groups_Oordered__ab__group__add__abs(X644)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X644),X643),c_Groups_Ozero__class_Ozero(X644)))|hAPP(c_Groups_Oabs__class_Oabs(X644),X643)=hAPP(c_Groups_Ouminus__class_Ouminus(X644),X643))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__of__neg])])])). 4.05/4.31 fof(c_0_8679, plain, ![X1920, X1921]:(~class_Groups_Oordered__ab__group__add__abs(X1921)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1921),X1920),c_Groups_Ozero__class_Ozero(X1921)))|hAPP(c_Groups_Ouminus__class_Ouminus(X1921),X1920)=hAPP(c_Groups_Oabs__class_Oabs(X1921),X1920))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__of__nonpos])])])). 4.05/4.31 fof(c_0_8680, plain, ![X7797, X7798, X7799, X7800]:((~hBOOL(hAPP(hAPP(c_member(X7800),X7799),hAPP(hAPP(c_Set_Oinsert(X7800),X7798),X7797)))|(X7799=X7798|hBOOL(hAPP(hAPP(c_member(X7800),X7799),X7797))))&((X7799!=X7798|hBOOL(hAPP(hAPP(c_member(X7800),X7799),hAPP(hAPP(c_Set_Oinsert(X7800),X7798),X7797))))&(~hBOOL(hAPP(hAPP(c_member(X7800),X7799),X7797))|hBOOL(hAPP(hAPP(c_member(X7800),X7799),hAPP(hAPP(c_Set_Oinsert(X7800),X7798),X7797)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])])). 4.05/4.31 cnf(c_0_8681, plain, (c_Divides_Odivmod__int(X2,X1)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X1!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_4499])). 4.05/4.31 fof(c_0_8682, plain, ![X13439, X13440, X13441, X13442]:(~c_Finite__Set_Ofolding__one(X13442,X13441,X13440)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X13442),X13439))|hAPP(c_Finite__Set_Ofold1(X13442,X13441),X13439)=hAPP(X13440,X13439))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding__one_Oeq__fold])])])). 4.05/4.31 cnf(c_0_8683, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls))|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5548])). 4.05/4.31 fof(c_0_8684, plain, ![X791, X792, X793, X794]:(~c_Big__Operators_Osemilattice__big(X794,X793,X792)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X794),X791))|hAPP(X792,X791)=hAPP(c_Finite__Set_Ofold1(X794,X793),X791))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_semilattice__big_OF__eq])])])). 4.05/4.31 cnf(c_0_8685, 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_5376])). 4.05/4.31 fof(c_0_8686, plain, ![X3929, X3930, X3931]:(~class_Complete__Lattice_Ocomplete__lattice(X3931)|(~hBOOL(hAPP(hAPP(c_member(X3931),X3930),X3929))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3931),c_Complete__Lattice_OInf__class_OInf(X3931,X3929)),X3930)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__lower])])])). 4.05/4.31 fof(c_0_8687, plain, ![X7078, X7079, X7080]:(~class_Complete__Lattice_Ocomplete__lattice(X7080)|(~hBOOL(hAPP(hAPP(c_member(X7080),X7079),X7078))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7080),X7079),c_Complete__Lattice_OSup__class_OSup(X7080,X7078))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__upper])])])). 4.05/4.31 fof(c_0_8688, plain, ![X14893, X14894, X14895, X14897, X14898, X14899, X14900]:(((hBOOL(hAPP(hAPP(X14894,esk447_3(X14893,X14894,X14895)),X14893))|hBOOL(hAPP(c_Wellfounded_Oaccp(X14895,X14894),X14893)))&(~hBOOL(hAPP(c_Wellfounded_Oaccp(X14895,X14894),esk447_3(X14893,X14894,X14895)))|hBOOL(hAPP(c_Wellfounded_Oaccp(X14895,X14894),X14893))))&(~hBOOL(hAPP(c_Wellfounded_Oaccp(X14899,X14898),X14897))|(~hBOOL(hAPP(hAPP(X14898,X14900),X14897))|hBOOL(hAPP(c_Wellfounded_Oaccp(X14899,X14898),X14900))))), 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])])])])])])])). 4.05/4.31 fof(c_0_8689, plain, ![X12451, X12452, X12453, X12455, X12456, X12457, X12458]:(((hBOOL(hAPP(hAPP(X12452,esk381_3(X12451,X12452,X12453)),X12451))|hBOOL(hAPP(c_Wellfounded_Oaccp(X12453,X12452),X12451)))&(~hBOOL(hAPP(c_Wellfounded_Oaccp(X12453,X12452),esk381_3(X12451,X12452,X12453)))|hBOOL(hAPP(c_Wellfounded_Oaccp(X12453,X12452),X12451))))&(~hBOOL(hAPP(c_Wellfounded_Oaccp(X12457,X12456),X12455))|(~hBOOL(hAPP(hAPP(X12456,X12458),X12455))|hBOOL(hAPP(c_Wellfounded_Oaccp(X12457,X12456),X12458))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_accp_Osimps])])])])])])])). 4.05/4.31 fof(c_0_8690, plain, ![X9973, X9974, X9975, X9976]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9976)),X9975)),X9974))|hAPP(hAPP(c_List_Olist__update(X9976,X9975),X9974),X9973)=X9975), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__update__beyond])])])). 4.05/4.31 fof(c_0_8691, plain, ![X1594, X1595, X1596, X1597, X1598]:((~hBOOL(hAPP(hAPP(c_member(X1595),X1596),X1594))|X1594!=c_Orderings_Obot__class_Obot(tc_fun(X1595,tc_HOL_Obool)))&(X1597=c_Orderings_Obot__class_Obot(tc_fun(X1598,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1598),esk51_2(X1597,X1598)),X1597)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__in__conv])])])])])). 4.05/4.31 fof(c_0_8692, plain, ![X753, X754, X755]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X755),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X755,tc_HOL_Obool)),X753),X754)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X755),X753))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X755),X754)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X755),X753))|hBOOL(hAPP(c_Finite__Set_Ofinite(X755),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X755,tc_HOL_Obool)),X753),X754)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X755),X754)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Diff2])])])])). 4.05/4.31 fof(c_0_8693, plain, ![X9672, X9673, X9674, X9675, X9676]:((X9672!=c_Orderings_Obot__class_Obot(tc_fun(X9673,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X9673),X9674),X9672)))&(hBOOL(hAPP(hAPP(c_member(X9676),esk294_2(X9675,X9676)),X9675))|X9675=c_Orderings_Obot__class_Obot(tc_fun(X9676,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])])])])])])). 4.05/4.31 fof(c_0_8694, plain, ![X6274, X6275, X6276]:((~hBOOL(hAPP(hAPP(c_member(X6276),X6275),hAPP(c_List_Oset(X6276),X6274)))|c_List_Omember(X6276,X6274,X6275))&(~c_List_Omember(X6276,X6274,X6275)|hBOOL(hAPP(hAPP(c_member(X6276),X6275),hAPP(c_List_Oset(X6276),X6274))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__member])])). 4.05/4.31 fof(c_0_8695, plain, ![X10431, X10432, X10433, X10434, X10435]:(((hAPP(X10432,X10431)=c_Option_Ooption_ONone(X10434)|c_Option_Ooption_ONone(X10434)!=hAPP(c_Map_Omap__add(X10435,X10434,X10433,X10432),X10431))&(hAPP(X10433,X10431)=c_Option_Ooption_ONone(X10434)|c_Option_Ooption_ONone(X10434)!=hAPP(c_Map_Omap__add(X10435,X10434,X10433,X10432),X10431)))&(hAPP(X10432,X10431)!=c_Option_Ooption_ONone(X10434)|hAPP(X10433,X10431)!=c_Option_Ooption_ONone(X10434)|c_Option_Ooption_ONone(X10434)=hAPP(c_Map_Omap__add(X10435,X10434,X10433,X10432),X10431))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__None])])])). 4.05/4.31 fof(c_0_8696, plain, ![X12015, X12016, X12017, X12018, X12019, X12020, X12021]:(((hBOOL(hAPP(X12017,X12015))|c_Natural_Oevalc(c_Com_Ocom_OWhile(X12017,X12016),X12015,X12015))&(~c_Natural_Oevalc(X12016,X12015,X12018)|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X12017,X12016),X12018,X12015)|c_Natural_Oevalc(c_Com_Ocom_OWhile(X12017,X12016),X12015,X12015)))&((c_Natural_Oevalc(X12020,X12019,esk374_3(X12019,X12020,X12021))|~hBOOL(hAPP(X12021,X12019))|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X12021,X12020),X12019,X12019))&(c_Natural_Oevalc(c_Com_Ocom_OWhile(X12021,X12020),esk374_3(X12019,X12020,X12021),X12019)|~hBOOL(hAPP(X12021,X12019))|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X12021,X12020),X12019,X12019)))), 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_evalc_Oequations_I7_J])])])])])])). 4.05/4.31 fof(c_0_8697, plain, ![X10830, X10831, X10832]:(~class_Orderings_Olinorder(X10832)|(~hBOOL(hAPP(hAPP(c_member(X10832),X10831),hAPP(c_List_Oset(X10832),X10830)))|c_List_Olinorder__class_Oinsort__insert__key(X10832,X10832,c_COMBI(X10832),X10831,X10830)=X10830)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__insert__triv])])). 4.05/4.31 fof(c_0_8698, plain, ![X4416, X4417, X4418]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4418),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4417)),X4416))|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4418,X4417),hAPP(c_Divides_OnegateSnd,X4416)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__neg])])])). 4.05/4.31 fof(c_0_8699, plain, ![X3833, X3834, X3835, X3836]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3836,X3835),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3834),X3833)))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3836),X3835)=X3834), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__eq])])])). 4.05/4.31 fof(c_0_8700, plain, ![X5639, X5640]:((X5639!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X5640!=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),X5640)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5639)))))&((X5639=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),X5640)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5639)))))&(X5640=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),X5640)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5639))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__zle__neg])])])). 4.05/4.31 fof(c_0_8701, plain, ![X5516, X5517, X5518, X5519, X5520]:(~hBOOL(hAPP(X5520,X5519))|(~c_Natural_Oevalc(X5518,X5519,X5517)|(~c_Natural_Oevalc(c_Com_Ocom_OWhile(X5520,X5518),X5517,X5516)|c_Natural_Oevalc(c_Com_Ocom_OWhile(X5520,X5518),X5519,X5516)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_evalc_OWhileTrue])])])). 4.05/4.31 fof(c_0_8702, plain, ![X11075, X11076]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11076,tc_HOL_Obool)),X11075),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11076,tc_HOL_Obool)),X11075)))|c_Orderings_Obot__class_Obot(tc_fun(X11076,tc_HOL_Obool))=X11075)&(c_Orderings_Obot__class_Obot(tc_fun(X11076,tc_HOL_Obool))!=X11075|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11076,tc_HOL_Obool)),X11075),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11076,tc_HOL_Obool)),X11075))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Compl__self__eq])])). 4.05/4.31 fof(c_0_8703, plain, ![X7741, X7742, X7743]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X7743,X7743),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X7742),X7741)))|(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7743|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X7741)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__remainder])])). 4.05/4.31 fof(c_0_8704, plain, ![X15121, X15122, X15123]:(~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X15123,X15123),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X15122),X15121)))|(X15123=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Oone__class_Oone(tc_Int_Oint)=X15122)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient])])). 4.05/4.31 cnf(c_0_8705, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1)=c_Groups_Ozero__class_Ozero(X2)|c_Groups_Ozero__class_Ozero(X2)!=X3|~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_5549])). 4.05/4.31 fof(c_0_8706, plain, ![X5977]:(~class_Orderings_Olinorder(X5977)|c_Orderings_Oord_Omin(X5977,hAPP(c_COMBC(X5977,X5977,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X5977)))=c_Orderings_Oord__class_Omax(X5977)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dual__min])])). 4.05/4.31 fof(c_0_8707, plain, ![X7482, X7483, X7484]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7484),X7483),X7482))|X7482=X7483|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7484),X7483),X7482))|~class_Orderings_Olinorder(X7484))&(X7482!=X7483|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7484),X7483),X7482))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7484),X7483),X7482))|~class_Orderings_Olinorder(X7484))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1])])])])). 4.05/4.31 fof(c_0_8708, plain, ![X3811, X3812, X3813]:(~class_Orderings_Oorder(X3813)|(X3812=X3811|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3813),X3811),X3812))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3813),X3811),X3812))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])])). 4.05/4.31 fof(c_0_8709, plain, ![X9751, X9752]:(~class_Lattices_Oboolean__algebra(X9752)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9752),hAPP(c_Groups_Ouminus__class_Ouminus(X9752),X9751)),X9751)=c_Orderings_Otop__class_Otop(X9752)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_compl__sup__top])])])). 4.05/4.31 fof(c_0_8710, plain, ![X1706, X1707]:(~class_Lattices_Oboolean__algebra(X1707)|c_Orderings_Obot__class_Obot(X1707)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1707),hAPP(c_Groups_Ouminus__class_Ouminus(X1707),X1706)),X1706)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__inf__bot])])). 4.05/4.31 fof(c_0_8711, plain, ![X1678]:(~class_Orderings_Olinorder(X1678)|c_Orderings_Oord__class_Omin(X1678)=c_Orderings_Oord_Omax(X1678,hAPP(c_COMBC(X1678,X1678,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1678)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dual__max])])). 4.05/4.31 fof(c_0_8712, plain, ![X3203, X3204]:(~class_Groups_Oab__group__add(X3204)|c_Groups_Ozero__class_Ozero(X3204)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3204),hAPP(c_Groups_Ouminus__class_Ouminus(X3204),X3203)),X3203)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])])). 4.05/4.31 fof(c_0_8713, plain, ![X17623, X17624, X17625]:(~class_Orderings_Olinorder(X17625)|X17624=hAPP(hAPP(c_Orderings_Oord__class_Omin(X17625),X17624),hAPP(hAPP(c_Orderings_Oord__class_Omax(X17625),X17624),X17623))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__absorb])])). 4.05/4.31 fof(c_0_8714, plain, ![X14744, X14745, X14746]:(~class_Orderings_Olinorder(X14746)|X14745=hAPP(hAPP(c_Orderings_Oord__class_Omax(X14746),X14745),hAPP(hAPP(c_Orderings_Oord__class_Omin(X14746),X14745),X14744))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__absorb])])). 4.05/4.31 fof(c_0_8715, plain, ![X10723, X10724, X10725]:(~class_Lattices_Osemilattice__inf(X10725)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10725),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10725),X10724),X10723)),X10724))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le1])])). 4.05/4.31 fof(c_0_8716, plain, ![X9831, X9832, X9833]:(~class_Lattices_Olattice(X9833)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9833),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9833),X9832),X9831)),X9832))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__ord_I1_J])])])). 4.05/4.31 fof(c_0_8717, plain, ![X14059, X14060]:(~class_Groups_Ogroup__add(X14060)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14060),X14059),hAPP(c_Groups_Ouminus__class_Ouminus(X14060),X14059))=c_Groups_Ozero__class_Ozero(X14060)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus])])). 4.05/4.31 fof(c_0_8718, plain, ![X17141, X17142, X17143, X17144, X17145]:((X17141!=X17142|hAPP(c_Set_Oimage(X17145,X17144,X17143),X17142)=hAPP(c_Set_Oimage(X17145,X17144,X17143),X17141)|~c_Fun_Oinj__on(X17145,X17144,X17143,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17145,tc_HOL_Obool)),X17142),X17141)))&(hAPP(c_Set_Oimage(X17145,X17144,X17143),X17142)!=hAPP(c_Set_Oimage(X17145,X17144,X17143),X17141)|X17141=X17142|~c_Fun_Oinj__on(X17145,X17144,X17143,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17145,tc_HOL_Obool)),X17142),X17141)))), 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])])])])). 4.05/4.31 fof(c_0_8719, plain, ![X16260, X16261]:(~class_Lattices_Oboolean__algebra(X16261)|c_Orderings_Otop__class_Otop(X16261)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X16261),X16260),hAPP(c_Groups_Ouminus__class_Ouminus(X16261),X16260))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__compl__top])])). 4.05/4.31 cnf(c_0_8720, plain, (X1=c_Groups_Oone__class_Oone(tc_Int_Oint)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X1|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5550])). 4.05/4.31 fof(c_0_8721, plain, ![X7760, X7761, X7762]:(~class_Lattices_Osemilattice__inf(X7762)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7762),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7762),X7761),X7760)),X7760))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__le2])])])). 4.05/4.31 fof(c_0_8722, plain, ![X6193, X6194, X6195]:(~class_Lattices_Olattice(X6195)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6195),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6195),X6194),X6193)),X6193))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I2_J])])). 4.05/4.31 fof(c_0_8723, plain, ![X8903, X8904, X8905]:(~class_Lattices_Osemilattice__sup(X8905)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8905),X8904),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8905),X8904),X8903)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge1])])). 4.05/4.31 fof(c_0_8724, plain, ![X3211, X3212, X3213]:(~class_Lattices_Olattice(X3213)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3213),X3212),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3213),X3212),X3211)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__sup__ord_I3_J])])])). 4.05/4.31 fof(c_0_8725, plain, ![X10809, X10810]:(~class_Lattices_Oboolean__algebra(X10810)|c_Orderings_Obot__class_Obot(X10810)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10810),X10809),hAPP(c_Groups_Ouminus__class_Ouminus(X10810),X10809))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__compl__bot])])). 4.05/4.31 fof(c_0_8726, plain, ![X11387, X11388, X11389, X11390, X11391]:(~c_Fun_Oinj__on(X11391,X11390,X11389,X11388)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11391,tc_HOL_Obool)),X11387),X11388))|c_Fun_Oinj__on(X11391,X11390,X11389,X11387))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])])). 4.05/4.31 fof(c_0_8727, plain, ![X10254, X10255, X10256]:(~class_Divides_Osemiring__div(X10256)|c_Groups_Ozero__class_Ozero(X10256)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10256),c_Divides_Odiv__class_Omod(X10256,X10255,X10254)),X10254)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__div__trivial])])])). 4.05/4.31 fof(c_0_8728, plain, ![X17332, X17333, X17334, X17335]:((~hBOOL(hAPP(X17335,X17334))|hAPP(c_List_Ofilter(X17333,X17335),c_List_Oreplicate(X17333,X17332,X17334))=c_List_Oreplicate(X17333,X17332,X17334))&(hBOOL(hAPP(X17335,X17334))|hAPP(c_List_Ofilter(X17333,X17335),c_List_Oreplicate(X17333,X17332,X17334))=c_List_Olist_ONil(X17333))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_filter__replicate])])])). 4.05/4.31 cnf(c_0_8729, plain, (X1=c_Groups_Oone__class_Oone(tc_Int_Oint)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X1|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_5550])). 4.05/4.31 fof(c_0_8730, plain, ![X12102, X12103, X12104]:(~class_Lattices_Osemilattice__sup(X12104)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12104),X12103),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X12104),X12102),X12103)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge2])])). 4.05/4.31 fof(c_0_8731, plain, ![X16890, X16891, X16892]:(~class_Lattices_Olattice(X16892)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16892),X16891),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X16892),X16890),X16891)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I4_J])])). 4.05/4.31 fof(c_0_8732, plain, ![X15983, X15984, X15985, X15986, X15988, X15989, X15990, X15991, X15992]:((~hBOOL(hAPP(c_Predicate_ORangeP(X15986,X15985,X15984),X15983))|hBOOL(hAPP(hAPP(X15984,esk478_2(X15983,X15984)),X15983)))&(~hBOOL(hAPP(hAPP(X15989,X15990),X15988))|hBOOL(hAPP(c_Predicate_ORangeP(X15992,X15991,X15989),X15988)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP_Oequations])])])])])). 4.05/4.31 fof(c_0_8733, plain, ![X4962, X4963, X4964]:(~class_Divides_Osemiring__div(X4964)|c_Groups_Ozero__class_Ozero(X4964)=c_Divides_Odiv__class_Omod(X4964,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4964),X4963),X4962),X4963)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1__is__0])])). 4.05/4.31 fof(c_0_8734, plain, ![X2302, X2303, X2304]:(~class_Divides_Osemiring__div(X2304)|c_Groups_Ozero__class_Ozero(X2304)=c_Divides_Odiv__class_Omod(X2304,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2304),X2303),X2302),X2302)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2__is__0])])). 4.05/4.31 fof(c_0_8735, plain, ![X17010, X17011, X17012, X17013, X17014]:((X17010!=X17011|hAPP(c_Set_Oimage(X17014,X17013,X17012),X17011)=hAPP(c_Set_Oimage(X17014,X17013,X17012),X17010)|~c_Fun_Oinj__on(X17014,X17013,X17012,c_Orderings_Otop__class_Otop(tc_fun(X17014,tc_HOL_Obool))))&(hAPP(c_Set_Oimage(X17014,X17013,X17012),X17011)!=hAPP(c_Set_Oimage(X17014,X17013,X17012),X17010)|X17010=X17011|~c_Fun_Oinj__on(X17014,X17013,X17012,c_Orderings_Otop__class_Otop(tc_fun(X17014,tc_HOL_Obool))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__image__eq__iff])])])])). 4.05/4.31 fof(c_0_8736, plain, ![X904, X905, X906]:(hAPP(hAPP(c_Set_Oinsert(X906),X904),c_Orderings_Obot__class_Obot(tc_fun(X906,tc_HOL_Obool)))!=hAPP(hAPP(c_Set_Oinsert(X906),X905),c_Orderings_Obot__class_Obot(tc_fun(X906,tc_HOL_Obool)))|X904=X905), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__inject])])). 4.05/4.31 cnf(c_0_8737, plain, (c_List_Olinorder__class_Osorted(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk400_4(X3,X1,X4,X2)))|X3!=hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)|~c_List_Olinorder__class_Osorted(X1,X4)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5366])). 4.05/4.31 fof(c_0_8738, plain, ![X12823, X12824, X12825, X12826, X12827, X12828, X12829, X12830, X12831]:((~hBOOL(hAPP(hAPP(X12824,X12823),X12825))|hBOOL(hAPP(c_Predicate_ODomainP(X12827,X12826,X12824),X12823)))&(~hBOOL(hAPP(c_Predicate_ODomainP(X12831,X12830,X12829),X12828))|hBOOL(hAPP(hAPP(X12829,X12828),esk393_2(X12828,X12829))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP_Oequations])])])])])). 4.05/4.31 cnf(c_0_8739, 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_5551])). 4.05/4.31 cnf(c_0_8740, plain, (X1=c_Groups_Oone__class_Oone(tc_Int_Oint)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X2|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5550])). 4.05/4.31 fof(c_0_8741, plain, ![X631, X632, X633, X634, X635, X636]:(((~c_Natural_Oevaln(X634,X633,X632,X631)|hBOOL(hAPP(X636,X633))|c_Natural_Oevaln(c_Com_Ocom_OCond(X636,X635,X634),X633,X632,X631))&(~c_Natural_Oevaln(X635,X633,X632,X631)|~hBOOL(hAPP(X636,X633))|c_Natural_Oevaln(c_Com_Ocom_OCond(X636,X635,X634),X633,X632,X631)))&(((c_Natural_Oevaln(X635,X633,X632,X631)|c_Natural_Oevaln(X634,X633,X632,X631)|~c_Natural_Oevaln(c_Com_Ocom_OCond(X636,X635,X634),X633,X632,X631))&(hBOOL(hAPP(X636,X633))|c_Natural_Oevaln(X634,X633,X632,X631)|~c_Natural_Oevaln(c_Com_Ocom_OCond(X636,X635,X634),X633,X632,X631)))&((c_Natural_Oevaln(X635,X633,X632,X631)|~hBOOL(hAPP(X636,X633))|~c_Natural_Oevaln(c_Com_Ocom_OCond(X636,X635,X634),X633,X632,X631))&(hBOOL(hAPP(X636,X633))|~hBOOL(hAPP(X636,X633))|~c_Natural_Oevaln(c_Com_Ocom_OCond(X636,X635,X634),X633,X632,X631))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_evaln_Oequations_I5_J])])])])). 4.05/4.31 fof(c_0_8742, plain, ![X17615, X17616, X17617, X17618]:(((hBOOL(hAPP(X17617,X17616))|~c_List_Olist__all(X17618,X17617,hAPP(hAPP(c_List_Olist_OCons(X17618),X17616),X17615)))&(c_List_Olist__all(X17618,X17617,X17615)|~c_List_Olist__all(X17618,X17617,hAPP(hAPP(c_List_Olist_OCons(X17618),X17616),X17615))))&(~hBOOL(hAPP(X17617,X17616))|~c_List_Olist__all(X17618,X17617,X17615)|c_List_Olist__all(X17618,X17617,hAPP(hAPP(c_List_Olist_OCons(X17618),X17616),X17615)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__simps_I1_J])])])). 4.05/4.31 fof(c_0_8743, plain, ![X8569, X8570]:(~c_Nat__Transfer_Onat__set(X8570)|(~c_Nat__Transfer_Onat__set(X8569)|c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X8570),X8569)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J])])). 4.05/4.31 cnf(c_0_8744, plain, (X1=c_Groups_Oone__class_Oone(tc_Int_Oint)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)=X2|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_5550])). 4.05/4.31 fof(c_0_8745, plain, ![X9153, X9154, X9155, X9156]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9156),X9155),X9154))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9156),X9155),X9153))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9156),X9155),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9156),X9154),X9153)))|~class_Orderings_Olinorder(X9156))&((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9156),X9155),X9154))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9156),X9155),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9156),X9154),X9153)))|~class_Orderings_Olinorder(X9156))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9156),X9155),X9153))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9156),X9155),hAPP(hAPP(c_Orderings_Oord__class_Omin(X9156),X9154),X9153)))|~class_Orderings_Olinorder(X9156)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ole__inf__iff])])])])). 4.05/4.31 fof(c_0_8746, plain, ![X16338, X16339]:(~c_Nat__Transfer_Onat__set(X16339)|(~c_Nat__Transfer_Onat__set(X16338)|c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X16339),X16338)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J])])). 4.05/4.31 fof(c_0_8747, plain, ![X10815, X10816]:(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),X10816),X10815)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X10816,X10815)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zmod__zminus1__not__zero])])])). 4.05/4.31 cnf(c_0_8748, plain, (c_Groups_Ozero__class_Ozero(X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)|X1!=hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)|~class_Groups_Ogroup__add(X2)), inference(split_conjunct,[status(thm)],[c_0_5552])). 4.05/4.31 fof(c_0_8749, plain, ![X8321, X8322, X8323, X8324]:((~hBOOL(hAPP(hAPP(X8322,X8323),X8321))|hBOOL(hAPP(hAPP(c_member(X8324),X8323),c_SetInterval_Oord_OatMost(X8324,X8322,X8321))))&(~hBOOL(hAPP(hAPP(c_member(X8324),X8323),c_SetInterval_Oord_OatMost(X8324,X8322,X8321)))|hBOOL(hAPP(hAPP(X8322,X8323),X8321)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatMost__iff])])). 4.05/4.31 fof(c_0_8750, plain, ![X4160, X4161, X4162, X4163]:((~hBOOL(hAPP(hAPP(X4161,X4162),X4160))|hBOOL(hAPP(hAPP(c_member(X4163),X4162),c_SetInterval_Oord_OlessThan(X4163,X4161,X4160))))&(~hBOOL(hAPP(hAPP(c_member(X4163),X4162),c_SetInterval_Oord_OlessThan(X4163,X4161,X4160)))|hBOOL(hAPP(hAPP(X4161,X4162),X4160)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OlessThan__iff])])). 4.05/4.31 fof(c_0_8751, plain, ![X10046, X10047, X10048, X10049]:((~hBOOL(hAPP(hAPP(c_member(X10049),X10048),c_SetInterval_Oord_OatLeast(X10049,X10047,X10046)))|hBOOL(hAPP(hAPP(X10047,X10046),X10048)))&(~hBOOL(hAPP(hAPP(X10047,X10046),X10048))|hBOOL(hAPP(hAPP(c_member(X10049),X10048),c_SetInterval_Oord_OatLeast(X10049,X10047,X10046))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeast__iff])])). 4.05/4.31 fof(c_0_8752, plain, ![X7132, X7133, X7134]:((X7134!=c_List_Olist_ONil(X7133)|c_List_Olast(X7133,X7132)=c_List_Olast(X7133,hAPP(hAPP(c_List_Oappend(X7133),X7132),X7134)))&(X7134=c_List_Olist_ONil(X7133)|c_List_Olast(X7133,X7134)=c_List_Olast(X7133,hAPP(hAPP(c_List_Oappend(X7133),X7132),X7134)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_last__append])])])). 4.05/4.31 fof(c_0_8753, plain, ![X14779, X14780, X14781]:(X14781=c_List_Olist_ONil(X14780)|c_List_Olast(X14780,X14781)=c_List_Olast(X14780,hAPP(hAPP(c_List_Olist_OCons(X14780),X14779),X14781))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsR])])). 4.05/4.31 fof(c_0_8754, plain, ![X9012, X9013, X9014, X9015]:((~hBOOL(hAPP(hAPP(X9013,X9012),X9014))|hBOOL(hAPP(hAPP(c_member(X9015),X9014),c_SetInterval_Oord_OgreaterThan(X9015,X9013,X9012))))&(~hBOOL(hAPP(hAPP(c_member(X9015),X9014),c_SetInterval_Oord_OgreaterThan(X9015,X9013,X9012)))|hBOOL(hAPP(hAPP(X9013,X9012),X9014)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThan__iff])])). 4.05/4.31 fof(c_0_8755, plain, ![X6082, X6083, X6084]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6084)),X6083)),X6082))|c_List_Olist_ONil(X6084)=hAPP(hAPP(c_List_Odrop(X6084),X6082),X6083)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__all])])). 4.05/4.31 cnf(c_0_8756, 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_5553])). 4.05/4.31 cnf(c_0_8757, 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_5554])). 4.05/4.31 fof(c_0_8758, plain, ![X17273, X17274]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17274),c_Groups_Ozero__class_Ozero(X17274)),X17273))|c_Groups_Osgn__class_Osgn(X17274,X17273)=c_Groups_Oone__class_Oone(X17274)|~class_Rings_Olinordered__idom(X17274))&(c_Groups_Osgn__class_Osgn(X17274,X17273)!=c_Groups_Oone__class_Oone(X17274)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17274),c_Groups_Ozero__class_Ozero(X17274)),X17273))|~class_Rings_Olinordered__idom(X17274))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__1__pos])])])])). 4.05/4.31 fof(c_0_8759, plain, ![X17709, X17710]:(~class_Rings_Olinordered__idom(X17710)|hAPP(c_Groups_Oabs__class_Oabs(X17710),X17709)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17710),X17709),c_Groups_Osgn__class_Osgn(X17710,X17709))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__sgn])])])). 4.05/4.31 fof(c_0_8760, plain, ![X12760, X12761]:(~class_Groups_Oordered__ab__group__add__abs(X12761)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X12761),c_Groups_Ozero__class_Ozero(X12761)),hAPP(c_Groups_Oabs__class_Oabs(X12761),X12760)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__zero])])). 4.05/4.31 fof(c_0_8761, plain, ![X11722, X11723]:(~class_Rings_Olinordered__semidom(X11723)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11723),c_Groups_Ozero__class_Ozero(X11723)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X11723),X11722)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__0__le__iff])])])). 4.05/4.31 fof(c_0_8762, plain, ![X2601, X2602, X2603, X2604]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2604),X2603))|hBOOL(hAPP(c_Finite__Set_Ofinite(X2602),hAPP(c_Set_Oimage(X2604,X2602,X2601),X2603)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__imageI])])])). 4.05/4.31 fof(c_0_8763, plain, ![X8334, X8335]:((X8334!=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oone__class_Oone(tc_Int_Oint)!=X8335|c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8335),X8334)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8335)))&((X8334=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8335),X8334)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8335)))&(c_Groups_Oone__class_Oone(tc_Int_Oint)=X8335|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X8335),X8334)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X8335))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])])). 4.05/4.31 fof(c_0_8764, plain, ![X16586, X16587, X16588, X16589, X16590]:(hAPP(hAPP(c_List_Olist_OCons(X16590),X16587),X16586)!=hAPP(hAPP(c_List_Odrop(X16590),X16589),X16588)|X16587=hAPP(hAPP(c_List_Onth(X16590),X16588),X16589)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nth__via__drop])])])). 4.05/4.31 fof(c_0_8765, plain, ![X15652, X15653, X15654, X15655]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15655,X15654),tc_HOL_Obool)),X15653),X15652))|(~c_Relation_Osingle__valued(X15655,X15654,X15652)|c_Relation_Osingle__valued(X15655,X15654,X15653))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_single__valued__subset])])])). 4.05/4.31 fof(c_0_8766, plain, ![X16078, X16079]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X16079,tc_HOL_Obool)),hAPP(c_Set_OPow(X16079),X16078)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X16079),X16078)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X16079),X16078))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X16079,tc_HOL_Obool)),hAPP(c_Set_OPow(X16079),X16078))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Pow__iff])])). 4.05/4.31 fof(c_0_8767, plain, ![X1483, X1484, X1486, X1487, X1488]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1484),X1483))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1484),esk47_2(X1483,X1484))=X1483)&(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1487),X1488)!=X1486|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1487),X1486)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__add])])])])])). 4.05/4.31 cnf(c_0_8768, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1))=hAPP(c_Int_Onat,X2)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(split_conjunct,[status(thm)],[c_0_5022])). 4.05/4.31 fof(c_0_8769, plain, ![X13269, X13270, X13271, X13272]:((~hBOOL(hAPP(c_List_Odistinct(X13271),c_List_Olinorder__class_Osort__key(X13271,X13272,X13270,X13269)))|hBOOL(hAPP(c_List_Odistinct(X13271),X13269))|~class_Orderings_Olinorder(X13272))&(~hBOOL(hAPP(c_List_Odistinct(X13271),X13269))|hBOOL(hAPP(c_List_Odistinct(X13271),c_List_Olinorder__class_Osort__key(X13271,X13272,X13270,X13269)))|~class_Orderings_Olinorder(X13272))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__sort])])])])). 4.05/4.31 fof(c_0_8770, plain, ![X2377, X2378, X2379, X2380]:(((c_List_Olist__all(X2380,X2379,X2377)|~c_List_Olist__all(X2380,X2379,hAPP(hAPP(c_List_Oappend(X2380),X2378),X2377)))&(c_List_Olist__all(X2380,X2379,X2378)|~c_List_Olist__all(X2380,X2379,hAPP(hAPP(c_List_Oappend(X2380),X2378),X2377))))&(~c_List_Olist__all(X2380,X2379,X2377)|~c_List_Olist__all(X2380,X2379,X2378)|c_List_Olist__all(X2380,X2379,hAPP(hAPP(c_List_Oappend(X2380),X2378),X2377)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__append])])])). 4.05/4.31 fof(c_0_8771, plain, ![X17678, X17679, X17681, X17683]:(((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk528_2(X17678,X17679)),X17678))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X17678)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk528_2(X17678,X17679)),X17679))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X17678))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X17681))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X17683),X17681))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17683),esk529_1(X17681)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__nat__set__iff__bounded])])])])])])])). 4.05/4.31 fof(c_0_8772, plain, ![X4293, X4294, X4296, X4298]:(((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk132_2(X4293,X4294)),X4293))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X4293)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk132_2(X4293,X4294)),X4294))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X4293))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X4296))|(~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4298),X4296))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4298),esk133_1(X4296)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__nat__set__iff__bounded__le])])])])])])])). 4.05/4.31 fof(c_0_8773, plain, ![X10313, X10314, X10315, X10316]:((~c_Map_Omap__le(X10316,X10315,X10314,c_Map_Omap__add(X10316,X10315,X10314,X10313))|c_Map_Omap__add(X10316,X10315,X10314,X10313)=c_Map_Omap__add(X10316,X10315,X10313,X10314))&(c_Map_Omap__add(X10316,X10315,X10314,X10313)!=c_Map_Omap__add(X10316,X10315,X10313,X10314)|c_Map_Omap__le(X10316,X10315,X10314,c_Map_Omap__add(X10316,X10315,X10314,X10313)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__le__iff__map__add__commute])])). 4.05/4.31 fof(c_0_8774, plain, ![X14228, X14229]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X14229),c_Int_OInteg))|(~hBOOL(hAPP(X14228,hAPP(c_Int_ORep__Integ,esk435_2(X14228,X14229))))|hBOOL(hAPP(X14228,X14229)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__induct])])])). 4.05/4.31 fof(c_0_8775, plain, ![X12006, X12007, X12008, X12009]:((~c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X12009)),X12008,X12007,X12006)|c_Natural_Oevaln(c_Com_Ocom_OBODY(X12009),X12008,hAPP(c_Nat_OSuc,X12007),X12006))&(~c_Natural_Oevaln(c_Com_Ocom_OBODY(X12009),X12008,hAPP(c_Nat_OSuc,X12007),X12006)|c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X12009)),X12008,X12007,X12006))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I9_J])])). 4.05/4.31 fof(c_0_8776, plain, ![X1414]:((X1414=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk42_1(X1414))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1414)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk42_1(X1414)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1414)))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__less__imp__eq__int])])])])])). 4.05/4.31 fof(c_0_8777, plain, ![X10926, X10927]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10927),X10926))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10926),X10927))), inference(variable_rename,[status(thm)],[fact_zle__linear])). 4.05/4.31 fof(c_0_8778, plain, ![X10661, X10662]:(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10662),X10661))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X10661),X10662))), inference(variable_rename,[status(thm)],[fact_nat__le__linear])). 4.05/4.31 fof(c_0_8779, plain, ![X16740, X16741]:(c_List_Olist_ONil(X16740)=X16741|(~hBOOL(hAPP(c_List_Odistinct(X16740),X16741))|hBOOL(hAPP(c_List_Odistinct(X16740),c_List_Obutlast(X16740,X16741))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__butlast])])])). 4.05/4.31 fof(c_0_8780, plain, ![X4535, X4536, X4537]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4537,X4536)),X4535))|hBOOL(hAPP(c_Finite__Set_Ofinite(X4537),hAPP(c_Relation_ODomain(X4537,X4536),X4535)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Domain])])])). 4.05/4.31 fof(c_0_8781, plain, ![X5485, X5486, X5487]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5487,X5486)),X5485))|hBOOL(hAPP(c_Finite__Set_Ofinite(X5486),hAPP(c_Relation_ORange(X5487,X5486),X5485)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Range])])])). 4.05/4.31 cnf(c_0_8782, 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_5555])). 4.05/4.31 cnf(c_0_8783, plain, (X3=c_Groups_Ozero__class_Ozero(X1)|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))!=X3|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber(X1)), inference(split_conjunct,[status(thm)],[c_0_5556])). 4.05/4.31 fof(c_0_8784, plain, ![X525, X526, X527]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X527,tc_HOL_Obool)),X526),X525))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X527,tc_HOL_Obool)),X525),X526))|X525=X526)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equalityI])])])). 4.05/4.31 fof(c_0_8785, plain, ![X582, X583]:(~class_Complete__Lattice_Ocomplete__lattice(X583)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X583),X582))|(X582=c_Orderings_Obot__class_Obot(tc_fun(X583,tc_HOL_Obool))|c_Complete__Lattice_OInf__class_OInf(X583,X582)=c_Big__Operators_Olattice__class_OInf__fin(X583,X582)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin__Inf])])])). 4.05/4.31 fof(c_0_8786, plain, ![X14519, X14520]:(~class_Complete__Lattice_Ocomplete__lattice(X14520)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X14520),X14519))|(X14519=c_Orderings_Obot__class_Obot(tc_fun(X14520,tc_HOL_Obool))|c_Big__Operators_Olattice__class_OSup__fin(X14520,X14519)=c_Complete__Lattice_OSup__class_OSup(X14520,X14519)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin__Sup])])])). 4.05/4.31 fof(c_0_8787, plain, ![X15031, X15032, X15033]:((hAPP(hAPP(c_List_Odrop(X15033),X15032),X15031)!=c_List_Olist_ONil(X15033)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15033)),X15031)),X15032)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15033)),X15031)),X15032))|hAPP(hAPP(c_List_Odrop(X15033),X15032),X15031)=c_List_Olist_ONil(X15033))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__eq__Nil])])). 4.05/4.31 cnf(c_0_8788, 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,esk254_2(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_5493])). 4.05/4.31 fof(c_0_8789, plain, ![X3180, X3181, X3182]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3182),X3180),X3181))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3182),X3181),X3180))|~class_Orderings_Olinorder(X3182))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3182),X3181),X3180))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3182),X3180),X3181))|~class_Orderings_Olinorder(X3182))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__not__less])])])])). 4.05/4.31 fof(c_0_8790, plain, ![X10421, X10422, X10423]:(~class_Orderings_Oorder(X10423)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10423),X10422),X10421))|c_Orderings_Obot__class_Obot(tc_fun(X10423,tc_HOL_Obool))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10423,X10421),X10422))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty])])])). 4.05/4.31 fof(c_0_8791, plain, ![X2935, X2936]:(((c_Wellfounded_Oacyclic(X2936,X2935)|~c_Nitpick_Owf_H(X2936,X2935))&(c_Nitpick_Ounknown(tc_HOL_Obool)|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2936,X2936)),X2935))|~c_Nitpick_Owf_H(X2936,X2935)))&((~c_Nitpick_Ounknown(tc_HOL_Obool)|~c_Wellfounded_Oacyclic(X2936,X2935)|c_Nitpick_Owf_H(X2936,X2935))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2936,X2936)),X2935))|~c_Wellfounded_Oacyclic(X2936,X2935)|c_Nitpick_Owf_H(X2936,X2935)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Owf_H__def])])])). 4.05/4.31 cnf(c_0_8792, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|X2=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_5535])). 4.05/4.31 fof(c_0_8793, plain, ![X6969, X6970]:(~class_Groups_Ogroup__add(X6970)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X6970),c_Groups_Ozero__class_Ozero(X6970)),X6969)=hAPP(c_Groups_Ouminus__class_Ouminus(X6970),X6969)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__0])])])). 4.05/4.31 fof(c_0_8794, plain, ![X1466, X1467, X1468, X1469, X1470, X1471, X1472, X1473, X1474, X1475, X1476]:((~c_Natural_Oevaln(X1470,X1468,X1467,X1471)|~c_Natural_Oevaln(X1469,X1471,X1467,X1466)|c_Natural_Oevaln(c_Com_Ocom_OSemi(X1470,X1469),X1468,X1467,X1466))&((c_Natural_Oevaln(X1476,X1474,X1473,esk46_5(X1472,X1473,X1474,X1475,X1476))|~c_Natural_Oevaln(c_Com_Ocom_OSemi(X1476,X1475),X1474,X1473,X1472))&(c_Natural_Oevaln(X1475,esk46_5(X1472,X1473,X1474,X1475,X1476),X1473,X1472)|~c_Natural_Oevaln(c_Com_Ocom_OSemi(X1476,X1475),X1474,X1473,X1472)))), 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_evaln_Oequations_I4_J])])])])])])). 4.05/4.31 fof(c_0_8795, plain, ![X10875, X10876, X10877]:(~hBOOL(hAPP(c_List_Odistinct(X10877),X10876))|hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X10877)),c_Enum_On__lists(X10877,X10875,X10876)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__n__lists])])])). 4.05/4.31 fof(c_0_8796, plain, ![X2877, X2878, X2879, X2880]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2880),hAPP(c_Set_Oimage(X2879,X2880,X2878),X2877))),hAPP(c_Finite__Set_Ocard(X2879),X2877)))|~c_Fun_Oinj__on(X2879,X2880,X2878,X2877)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_pigeonhole])])])). 4.05/4.31 fof(c_0_8797, plain, ![X4374, X4375, X4376, X4377]:(~class_Orderings_Olinorder(X4377)|hAPP(c_List_Oset(X4376),X4374)=hAPP(c_List_Oset(X4376),c_List_Olinorder__class_Osort__key(X4376,X4377,X4375,X4374))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_set__sort])])])). 4.05/4.31 cnf(c_0_8798, 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_5522])). 4.05/4.31 cnf(c_0_8799, 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_5533])). 4.05/4.31 fof(c_0_8800, plain, ![X4557, X4558]:((X4557!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(X4558),c_Groups_Ozero__class_Ozero(X4558)),X4557)=c_Groups_Oone__class_Oone(X4558)|(~class_Rings_Osemiring__0(X4558)|~class_Power_Opower(X4558)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X4557|c_Groups_Ozero__class_Ozero(X4558)=hAPP(hAPP(c_Power_Opower__class_Opower(X4558),c_Groups_Ozero__class_Ozero(X4558)),X4557)|(~class_Rings_Osemiring__0(X4558)|~class_Power_Opower(X4558)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__0__left])])])])). 4.05/4.31 fof(c_0_8801, plain, ![X4287, X4288]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4288),hAPP(c_Nat_OSuc,X4287)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4288),X4287))|X4288=hAPP(c_Nat_OSuc,X4287))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__SucE])])])). 4.05/4.31 fof(c_0_8802, plain, ![X6223, X6224, X6225, X6226, X6227]:((hBOOL(hAPP(hAPP(c_member(X6227),X6226),X6225))|hAPP(c_Map_Orestrict__map(X6227,X6224,X6223,X6225),X6226)=c_Option_Ooption_ONone(X6224))&(~hBOOL(hAPP(hAPP(c_member(X6227),X6226),X6225))|hAPP(c_Map_Orestrict__map(X6227,X6224,X6223,X6225),X6226)=hAPP(X6223,X6226))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_restrict__map__def])])])). 4.05/4.31 fof(c_0_8803, plain, ![X2413, X2414]:(~class_Orderings_Olinorder(X2414)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X2414),X2413))|c_Big__Operators_Olattice_OInf__fin(X2414,c_Orderings_Oord__class_Omin(X2414),X2413)=hAPP(c_Finite__Set_Ofold1(X2414,c_Orderings_Oord__class_Omin(X2414)),X2413))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_OF__eq])])). 4.05/4.31 fof(c_0_8804, plain, ![X10873, X10874]:(~class_Orderings_Olinorder(X10874)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10874),X10873))|c_Big__Operators_Olattice_OSup__fin(X10874,c_Orderings_Oord__class_Omax(X10874),X10873)=hAPP(c_Finite__Set_Ofold1(X10874,c_Orderings_Oord__class_Omax(X10874)),X10873))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_OF__eq])])])). 4.05/4.31 cnf(c_0_8805, plain, (~class_Int_Onumber__ring(X1)|~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))), inference(rw,[status(thm)],[c_0_5557, c_0_4475])). 4.05/4.31 fof(c_0_8806, plain, ![X14595, X14596]:(~class_Enum_Oenum(X14596)|~class_Enum_Oenum(X14595)|c_Enum_Oenum__class_Oenum(tc_prod(X14596,X14595))=c_Enum_Oproduct(X14596,X14595,c_Enum_Oenum__class_Oenum(X14596),c_Enum_Oenum__class_Oenum(X14595))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_enum__prod__def])])])). 4.05/4.31 fof(c_0_8807, plain, ![X9183, X9184, X9185]:(~hBOOL(hAPP(c_List_Odistinct(X9185),X9184))|c_List_Oremdups(X9185,c_List_Oremove1(X9185,X9183,X9184))=c_List_Oremove1(X9185,X9183,c_List_Oremdups(X9185,X9184))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_remove1__remdups])])])). 4.05/4.31 cnf(c_0_8808, plain, (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)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=esk60_2(X1,X2)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X2), inference(split_conjunct,[status(thm)],[c_0_5372])). 4.05/4.31 fof(c_0_8809, plain, ![X8357, X8358, X8359]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8359),X8358)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8357),X8358)|(X8358=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X8359=X8357))&((X8358!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8359),X8358)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8357),X8358))&(X8359!=X8357|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8359),X8358)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8357),X8358)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])])). 4.05/4.31 fof(c_0_8810, plain, ![X3565, X3566, X3567]:((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3567),X3565)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3567),X3566)|(X3567=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X3566=X3565))&((X3567!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3567),X3565)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3567),X3566))&(X3566!=X3565|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3567),X3565)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3567),X3566)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])])). 4.05/4.31 cnf(c_0_8811, 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_5410])). 4.05/4.31 cnf(c_0_8812, plain, (c_List_Oremdups(X1,X2)=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_5558])). 4.05/4.31 cnf(c_0_8813, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremdups(X1,X2))=hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5559]), ['final']). 4.05/4.31 cnf(c_0_8814, 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_5560])). 4.05/4.31 fof(c_0_8815, plain, ![X16021, X16022]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X16022)),hAPP(c_Code__Numeral_Onat__of,X16021)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X16022),X16021)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X16022),X16021))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X16022)),hAPP(c_Code__Numeral_Onat__of,X16021))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__def])])). 4.05/4.31 fof(c_0_8816, plain, ![X12768]:(~class_Nat_Osemiring__char__0(X12768)|c_Fun_Oinj__on(tc_Nat_Onat,X12768,c_Nat_Osemiring__1__class_Oof__nat(X12768),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__of__nat])])). 4.05/4.31 fof(c_0_8817, plain, ![X10267, X10268]:(~class_Groups_Oordered__ab__group__add__abs(X10268)|hAPP(c_Groups_Oabs__class_Oabs(X10268),X10267)=hAPP(c_Groups_Oabs__class_Oabs(X10268),hAPP(c_Groups_Ouminus__class_Ouminus(X10268),X10267))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel])])). 4.05/4.31 fof(c_0_8818, plain, ![X5857, X5858]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5858),X5857))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X5858)),hAPP(c_Nat_OSuc,X5857))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X5858)),hAPP(c_Nat_OSuc,X5857)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5858),X5857)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])])). 4.05/4.31 cnf(c_0_8819, 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_5561])). 4.05/4.31 fof(c_0_8820, plain, ![X3057, X3058]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X3058),X3057))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X3058)),hAPP(c_Code__Numeral_Onat__of,X3057))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X3058)),hAPP(c_Code__Numeral_Onat__of,X3057)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X3058),X3057)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__def])])). 4.05/4.31 cnf(c_0_8821, plain, (hBOOL(hAPP(X1,esk292_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_5562])). 4.05/4.31 fof(c_0_8822, plain, ![X451, X452]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X452))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X452),X451))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X452,X451)=X452)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__pos__pos__trivial])])])). 4.05/4.31 fof(c_0_8823, plain, ![X4874, 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),X4874),X4875))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X4875,X4874)=X4875)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__neg__neg__trivial])])])). 4.05/4.31 fof(c_0_8824, plain, ![X8137, X8138]:((hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X8138)!=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X8137)|X8137=X8138|~c_Nat__Transfer_Onat__set(X8137)|~c_Nat__Transfer_Onat__set(X8138))&(X8137!=X8138|hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X8138)=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X8137)|~c_Nat__Transfer_Onat__set(X8137)|~c_Nat__Transfer_Onat__set(X8138))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I3_J])])])). 4.05/4.31 cnf(c_0_8825, plain, (hBOOL(hAPP(X1,esk58_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_5563])). 4.05/4.31 cnf(c_0_8826, 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_5536])). 4.05/4.31 fof(c_0_8827, plain, ![X3650, X3651]:((~c_Wellfounded_Owf(X3651,X3650)|c_Wellfounded_Owf(X3651,hAPP(hAPP(c_Relation_Orel__comp(X3651,X3651,X3651),X3650),X3650)))&(~c_Wellfounded_Owf(X3651,hAPP(hAPP(c_Relation_Orel__comp(X3651,X3651,X3651),X3650),X3650))|c_Wellfounded_Owf(X3651,X3650))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__comp__self])])). 4.05/4.31 cnf(c_0_8828, plain, (~class_Int_Onumber__ring(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))), inference(rw,[status(thm)],[c_0_5564, c_0_4475])). 4.05/4.31 fof(c_0_8829, plain, ![X13915, X13916, X13917]:(~class_Orderings_Olinorder(X13917)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13917),hAPP(hAPP(c_Orderings_Oord__class_Omin(X13917),X13916),X13915)),X13916))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le1])])). 4.05/4.31 fof(c_0_8830, plain, ![X16251, X16252]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16252,tc_HOL_Obool)),X16251),c_Orderings_Obot__class_Obot(tc_fun(X16252,tc_HOL_Obool))))|c_Orderings_Obot__class_Obot(tc_fun(X16252,tc_HOL_Obool))=X16251)&(c_Orderings_Obot__class_Obot(tc_fun(X16252,tc_HOL_Obool))!=X16251|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16252,tc_HOL_Obool)),X16251),c_Orderings_Obot__class_Obot(tc_fun(X16252,tc_HOL_Obool)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__empty])])). 4.05/4.31 fof(c_0_8831, plain, ![X14399, X14400, X14401, X14402, X14403]:(~c_Natural_Oevaln(X14403,X14402,X14401,X14400)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X14401),X14399))|c_Natural_Oevaln(X14403,X14402,X14399,X14400))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_evaln__nonstrict])])])). 4.05/4.31 fof(c_0_8832, plain, ![X11211, X11212, X11213]:(~class_Orderings_Olinorder(X11213)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11213),hAPP(hAPP(c_Orderings_Oord__class_Omin(X11213),X11212),X11211)),X11211))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__le2])])])). 4.05/4.31 fof(c_0_8833, plain, ![X13468, X13469, X13470]:(~class_Orderings_Olinorder(X13470)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13470),X13469),hAPP(hAPP(c_Orderings_Oord__class_Omax(X13470),X13469),X13468)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__maxI1])])])). 4.05/4.31 fof(c_0_8834, plain, ![X1134, X1135, X1136]:(~class_Orderings_Olinorder(X1136)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1136),X1135),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1136),X1134),X1135)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__maxI2])])])). 4.05/4.31 fof(c_0_8835, plain, ![X3223]:(~class_Groups_Omonoid__add(X3223)|c_List_Ofoldl(X3223,X3223,c_Groups_Oplus__class_Oplus(X3223),c_Groups_Ozero__class_Ozero(X3223))=c_List_Omonoid__add__class_Olistsum(X3223)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listsum__foldl])])])). 4.05/4.31 fof(c_0_8836, plain, ![X11371, X11372, X11373, X11374]:(~hBOOL(hAPP(X11374,X11373))|hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11372,tc_HOL_Obool)),X11374),X11371),X11373))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup1I1])])])). 4.05/4.31 fof(c_0_8837, plain, ![X5041, X5042, X5043, X5044]:(~hBOOL(hAPP(X5044,X5043))|hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5042,tc_HOL_Obool)),X5041),X5044),X5043))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup1I2])])). 4.05/4.31 fof(c_0_8838, plain, ![X15783, X15784]:(~class_Orderings_Olinorder(X15784)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X15784),X15783))|hAPP(c_Finite__Set_Ofold1(X15784,c_Orderings_Oord__class_Omin(X15784)),X15783)=c_Big__Operators_Olinorder__class_OMin(X15784,X15783))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Min_OF__eq])])])). 4.05/4.31 fof(c_0_8839, plain, ![X12503, X12504]:(~class_Orderings_Olinorder(X12504)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X12504),X12503))|hAPP(c_Finite__Set_Ofold1(X12504,c_Orderings_Oord__class_Omax(X12504)),X12503)=c_Big__Operators_Olinorder__class_OMax(X12504,X12503))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Max_OF__eq])])])). 4.05/4.31 fof(c_0_8840, plain, ![X10517, X10518]:(~class_Lattices_Olattice(X10518)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X10518),X10517))|c_Big__Operators_Olattice__class_OInf__fin(X10518,X10517)=hAPP(c_Finite__Set_Ofold1(X10518,c_Lattices_Osemilattice__inf__class_Oinf(X10518)),X10517))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_OF__eq])])])). 4.05/4.31 fof(c_0_8841, plain, ![X5881, X5882]:(~class_Lattices_Olattice(X5882)|(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5882),X5881))|c_Big__Operators_Olattice__class_OSup__fin(X5882,X5881)=hAPP(c_Finite__Set_Ofold1(X5882,c_Lattices_Osemilattice__sup__class_Osup(X5882)),X5881))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__fin_OF__eq])])])). 4.05/4.31 cnf(c_0_8842, plain, (c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=esk49_3(X1,X3,X2)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|hAPP(c_Nat_OSuc,X1)!=hAPP(c_Finite__Set_Ocard(X2),X3)), inference(split_conjunct,[status(thm)],[c_0_5466])). 4.05/4.31 fof(c_0_8843, plain, ![X17560, X17561, X17562, X17563]:((~c_Fun_Oinj__on(X17563,X17561,X17560,X17562)|hAPP(c_Finite__Set_Ocard(X17561),hAPP(c_Set_Oimage(X17563,X17561,X17560),X17562))=hAPP(c_Finite__Set_Ocard(X17563),X17562)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X17563),X17562)))&(hAPP(c_Finite__Set_Ocard(X17561),hAPP(c_Set_Oimage(X17563,X17561,X17560),X17562))!=hAPP(c_Finite__Set_Ocard(X17563),X17562)|c_Fun_Oinj__on(X17563,X17561,X17560,X17562)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X17563),X17562)))), 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])])])])). 4.05/4.31 fof(c_0_8844, plain, ![X3634, X3635, X3636]:((X3634!=X3635|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3636)),X3635)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3636)),X3634))&(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3636)),X3635)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3636)),X3634)|X3634=X3635)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1])])). 4.05/4.31 fof(c_0_8845, plain, ![X13677, X13678]:(~class_Rings_Oring__1(X13678)|hBOOL(hAPP(hAPP(c_member(X13678),hAPP(c_Int_Oring__1__class_Oof__int(X13678),X13677)),c_Int_Oring__1__class_OInts(X13678)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__of__int])])])). 4.05/4.31 fof(c_0_8846, plain, ![X3444, X3445]:(~class_Rings_Osemiring__1(X3445)|hBOOL(hAPP(hAPP(c_member(X3445),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3445),X3444)),c_Nat_Osemiring__1__class_ONats(X3445)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__in__Nats])])])). 4.05/4.31 fof(c_0_8847, plain, ![X5549, X5550, X5551, X5552]:(~c_Wellfounded_Owf(X5552,X5551)|(~c_Wellfounded_Owf(X5550,X5549)|c_Wellfounded_Owf(tc_prod(X5552,X5550),c_Wellfounded_Olex__prod(X5552,X5550,X5551,X5549)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__lex__prod])])])). 4.05/4.31 fof(c_0_8848, plain, ![X12321, X12322]:(~class_Rings_Oring__1(X12322)|hBOOL(hAPP(hAPP(c_member(X12322),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X12322),X12321)),c_Int_Oring__1__class_OInts(X12322)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__of__nat])])). 4.05/4.31 fof(c_0_8849, plain, ![X5786, X5787]:(~class_Int_Onumber__ring(X5787)|hBOOL(hAPP(hAPP(c_member(X5787),hAPP(c_Int_Onumber__class_Onumber__of(X5787),X5786)),c_Int_Oring__1__class_OInts(X5787)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__number__of])])])). 4.05/4.31 cnf(c_0_8850, 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_5565])). 4.05/4.31 fof(c_0_8851, plain, ![X12865, X12866, X12867, X12868, X12869]:(((~hBOOL(hAPP(X12869,X12866))|~c_Natural_Oevalc(X12868,X12866,X12865)|c_Natural_Oevalc(c_Com_Ocom_OCond(X12869,X12868,X12867),X12866,X12865))&(~c_Natural_Oevalc(X12867,X12866,X12865)|hBOOL(hAPP(X12869,X12866))|c_Natural_Oevalc(c_Com_Ocom_OCond(X12869,X12868,X12867),X12866,X12865)))&(((c_Natural_Oevalc(X12867,X12866,X12865)|hBOOL(hAPP(X12869,X12866))|~c_Natural_Oevalc(c_Com_Ocom_OCond(X12869,X12868,X12867),X12866,X12865))&(~hBOOL(hAPP(X12869,X12866))|hBOOL(hAPP(X12869,X12866))|~c_Natural_Oevalc(c_Com_Ocom_OCond(X12869,X12868,X12867),X12866,X12865)))&((c_Natural_Oevalc(X12867,X12866,X12865)|c_Natural_Oevalc(X12868,X12866,X12865)|~c_Natural_Oevalc(c_Com_Ocom_OCond(X12869,X12868,X12867),X12866,X12865))&(~hBOOL(hAPP(X12869,X12866))|c_Natural_Oevalc(X12868,X12866,X12865)|~c_Natural_Oevalc(c_Com_Ocom_OCond(X12869,X12868,X12867),X12866,X12865))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_evalc_Oequations_I6_J])])])])). 4.05/4.31 fof(c_0_8852, plain, ![X766, X767]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X766),hAPP(c_Nat_OSuc,X767)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X767),X766)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X767),X766))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X766),hAPP(c_Nat_OSuc,X767))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__less__eq])])])). 4.05/4.31 cnf(c_0_8853, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)),X2)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_5566])). 4.05/4.31 fof(c_0_8854, plain, ![X7719, X7720]:(~class_Groups_Oordered__ab__group__add__abs(X7720)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7720),c_Groups_Ozero__class_Ozero(X7720)),X7719))|X7719=hAPP(c_Groups_Oabs__class_Oabs(X7720),X7719))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__of__pos])])])). 4.05/4.31 fof(c_0_8855, plain, ![X5314, X5315]:(~class_Groups_Oordered__ab__group__add__abs(X5315)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5315),c_Groups_Ozero__class_Ozero(X5315)),X5314))|X5314=hAPP(c_Groups_Oabs__class_Oabs(X5315),X5314))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__of__nonneg])])])). 4.05/4.31 cnf(c_0_8856, 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_5567])). 4.05/4.31 cnf(c_0_8857, 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_5568])). 4.05/4.31 cnf(c_0_8858, plain, (hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|~hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5569])). 4.05/4.31 fof(c_0_8859, plain, ![X6854, X6855, X6856]:(~class_Groups_Ogroup__add(X6856)|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6856),X6855),X6854)!=c_Groups_Ozero__class_Ozero(X6856)|X6854=hAPP(c_Groups_Ouminus__class_Ouminus(X6856),X6855))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__unique])])])). 4.05/4.31 fof(c_0_8860, plain, ![X4316, X4317, X4318]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4318)),X4317)),X4316))|hAPP(hAPP(c_List_Otake(X4318),X4316),X4317)=X4317), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_take__all])])])). 4.05/4.31 fof(c_0_8861, plain, ![X10205, X10206]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10206,X10206)),X10205))|(~c_Wellfounded_Oacyclic(X10206,X10205)|c_Wellfounded_Owf(X10206,hAPP(c_Relation_Oconverse(X10206,X10206),X10205)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__acyclic__wf__converse])])])). 4.05/4.31 fof(c_0_8862, plain, ![X4224, X4225, X4226, X4227]:((~c_List_Olist__ex(X4227,X4226,hAPP(hAPP(c_List_Olist_OCons(X4227),X4225),X4224))|(hBOOL(hAPP(X4226,X4225))|c_List_Olist__ex(X4227,X4226,X4224)))&((~hBOOL(hAPP(X4226,X4225))|c_List_Olist__ex(X4227,X4226,hAPP(hAPP(c_List_Olist_OCons(X4227),X4225),X4224)))&(~c_List_Olist__ex(X4227,X4226,X4224)|c_List_Olist__ex(X4227,X4226,hAPP(hAPP(c_List_Olist_OCons(X4227),X4225),X4224))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__simps_I1_J])])])). 4.05/4.31 cnf(c_0_8863, plain, (X1=c_Int_OMin|c_Int_OMin!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)), inference(rw,[status(thm)],[c_0_5570, c_0_4475])). 4.05/4.31 fof(c_0_8864, plain, ![X15675, X15676, X15677]:(~class_Lattices_Osemilattice__inf(X15677)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15677),X15676),X15675))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15677),X15675),X15676)=X15676)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__absorb2])])])). 4.05/4.31 fof(c_0_8865, plain, ![X14491, X14492, X14493]:(~class_Orderings_Olinorder(X14493)|(~c_List_Olinorder__class_Osorted(X14493,X14492)|c_List_Olinorder__class_Osorted(X14493,c_List_Olinorder__class_Oinsort__insert__key(X14493,X14493,c_COMBI(X14493),X14491,X14492)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__insort__insert])])])). 4.05/4.31 fof(c_0_8866, plain, ![X10475, X10476, X10477]:(~c_Wellfounded_Oacyclic(X10477,X10476)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10477,X10477),tc_HOL_Obool)),X10475),X10476))|c_Wellfounded_Oacyclic(X10477,X10475))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_acyclic__subset])])])). 4.05/4.31 fof(c_0_8867, plain, ![X7339, X7340, X7341]:(~c_Wellfounded_Owf(X7341,X7340)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7341,X7341),tc_HOL_Obool)),X7339),X7340))|c_Wellfounded_Owf(X7341,X7339))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__subset])])])). 4.05/4.31 fof(c_0_8868, plain, ![X2013, X2014, X2015]:((hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2015),X2014),X2013)!=X2013|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2015),X2014),X2013))|~class_Lattices_Osemilattice__sup(X2015))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2015),X2014),X2013))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2015),X2014),X2013)=X2013|~class_Lattices_Osemilattice__sup(X2015))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__sup])])])). 4.05/4.31 fof(c_0_8869, plain, ![X13650, X13651, X13652]:(~class_Lattices_Osemilattice__sup(X13652)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13652),X13651),X13650))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13652),X13650),X13651)=X13650)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__absorb1])])])). 4.05/4.31 fof(c_0_8870, plain, ![X15177, X15178, X15179]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15179),X15178),X15177))|X15178=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15179),X15178),X15177)|~class_Lattices_Osemilattice__inf(X15179))&(X15178!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X15179),X15178),X15177)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15179),X15178),X15177))|~class_Lattices_Osemilattice__inf(X15179))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__inf])])])). 4.05/4.31 fof(c_0_8871, plain, ![X13657, X13658]:(~class_Groups_Ocomm__monoid__add(X13658)|hAPP(c_List_Omonoid__add__class_Olistsum(X13658),hAPP(c_List_Orev(X13658),X13657))=hAPP(c_List_Omonoid__add__class_Olistsum(X13658),X13657)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__rev])])). 4.05/4.31 fof(c_0_8872, plain, ![X4141, X4142]:(~class_Groups_Oordered__ab__group__add__abs(X4142)|hAPP(c_Groups_Oabs__class_Oabs(X4142),X4141)=hAPP(c_Groups_Oabs__class_Oabs(X4142),hAPP(c_Groups_Oabs__class_Oabs(X4142),X4141))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__idempotent])])])). 4.05/4.31 fof(c_0_8873, plain, ![X2817, X2818, X2819]:(~c_Wellfounded_OwfP(X2819,X2818)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2819,tc_fun(X2819,tc_HOL_Obool))),X2817),X2818))|c_Wellfounded_OwfP(X2819,X2817))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__subset])])). 4.05/4.31 fof(c_0_8874, plain, ![X6919, X6920]:(~class_Rings_Olinordered__idom(X6920)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X6920),X6919)=hAPP(c_Groups_Oabs__class_Oabs(X6920),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X6920),X6919))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nat])])). 4.05/4.31 fof(c_0_8875, plain, ![X4139, X4140]:(c_List_Olist_ONil(X4139)=X4140|c_List_Olast(X4139,X4140)=hAPP(c_List_Ohd(X4139),hAPP(c_List_Orev(X4139),X4140))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__rev])])). 4.05/4.31 fof(c_0_8876, plain, ![X17429, X17430]:(~class_Rings_Oring__1(X17430)|hAPP(c_Int_Oring__1__class_Oof__int(X17430),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17429))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X17430),X17429)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__of__nat__eq])])])). 4.05/4.31 fof(c_0_8877, plain, ![X9959, X9960, X9961, X9962]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X9962,X9961),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X9960),X9959)))|X9959=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X9962,X9961)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__eq])])])). 4.05/4.31 fof(c_0_8878, plain, ![X17477, X17478, X17479, X17480]:(((~c_List_Olist__ex(X17480,X17479,X17477)|c_List_Olist__ex(X17480,X17479,hAPP(hAPP(c_List_Oappend(X17480),X17478),X17477)))&(~c_List_Olist__ex(X17480,X17479,X17478)|c_List_Olist__ex(X17480,X17479,hAPP(hAPP(c_List_Oappend(X17480),X17478),X17477))))&(~c_List_Olist__ex(X17480,X17479,hAPP(hAPP(c_List_Oappend(X17480),X17478),X17477))|(c_List_Olist__ex(X17480,X17479,X17477)|c_List_Olist__ex(X17480,X17479,X17478)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__append])])])). 4.05/4.31 fof(c_0_8879, plain, ![X11425, X11426, X11427]:(~c_Relation_Orefl__on(X11427,X11426,X11425)|c_Relation_Orefl__on(tc_List_Olist(X11427),c_List_Olists(X11427,X11426),c_List_Olistrel(X11427,X11425))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_listrel__refl__on])])])). 4.05/4.31 fof(c_0_8880, plain, ![X8429, X8430, X8431]:(~c_Equiv__Relations_Oequiv(X8431,X8430,X8429)|c_Equiv__Relations_Oequiv(tc_List_Olist(X8431),c_List_Olists(X8431,X8430),c_List_Olistrel(X8431,X8429))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equiv__listrel])])])). 4.05/4.31 fof(c_0_8881, plain, ![X345, X346, X347, X348]:(hAPP(c_Product__Type_Ofst(X348,X347),X345)!=hAPP(c_Product__Type_Ofst(X348,X347),X346)|(hAPP(c_Product__Type_Osnd(X348,X347),X345)!=hAPP(c_Product__Type_Osnd(X348,X347),X346)|X346=X345)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_prod__eqI])])])). 4.05/4.31 fof(c_0_8882, plain, ![X11192, X11193]:(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),X11193),X11192))|c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X11193)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__zmult__eq__1])])])). 4.05/4.31 fof(c_0_8883, plain, ![X8834, X8835, X8836, X8837, X8838]:(~c_List_Olist__all2(X8838,X8837,X8836,X8835,X8834)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8837)),X8834)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8838)),X8835)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__all2__lengthD])])])). 4.05/4.31 fof(c_0_8884, plain, ![X5316, X5317, X5318, X5319]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X5319),hAPP(c_Set_Oimage(X5318,X5319,X5317),X5316)))|(~c_Fun_Oinj__on(X5318,X5319,X5317,X5316)|hBOOL(hAPP(c_Finite__Set_Ofinite(X5318),X5316)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__imageD])])])). 4.05/4.31 fof(c_0_8885, plain, ![X1728, X1729, X1730, X1731]:(~hBOOL(hAPP(X1731,X1730))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1729,tc_HOL_Obool)),X1731),X1728))|hBOOL(hAPP(X1728,X1730)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])])). 4.05/4.31 fof(c_0_8886, plain, ![X8183]:(~class_Int_Onumber__ring(X8183)|~class_Rings_Olinordered__idom(X8183)|c_Groups_Oone__class_Oone(X8183)=hAPP(c_Groups_Oabs__class_Oabs(X8183),hAPP(c_Int_Onumber__class_Onumber__of(X8183),c_Int_OMin))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__one])])). 4.05/4.31 fof(c_0_8887, plain, ![X17234]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X17234)))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X17234))|~c_Nat__Transfer_Onat__set(X17234))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X17234))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X17234)))|~c_Nat__Transfer_Onat__set(X17234))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I1_J])])])). 4.05/4.31 fof(c_0_8888, plain, ![X2409, X2410, X2411, X2412]:(~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2412,tc_HOL_Obool)),X2411),X2410),X2409))|(hBOOL(hAPP(X2411,X2409))|hBOOL(hAPP(X2410,X2409)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup1E])])])). 4.05/4.31 cnf(c_0_8889, 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_5571, c_0_4434])). 4.05/4.31 fof(c_0_8890, plain, ![X4188, X4189, X4190]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4190),X4189)),X4188))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4190),X4188))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])])). 4.05/4.31 fof(c_0_8891, plain, ![X6643, X6644]:(~class_Orderings_Olinorder(X6644)|c_List_Olinorder__class_Osorted(X6644,hAPP(hAPP(c_List_Olist_OCons(X6644),X6643),c_List_Olist_ONil(X6644)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__single])])). 4.05/4.31 fof(c_0_8892, plain, ![X17446, X17447, X17448]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17448),X17447)),X17446))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17448),X17446))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])])). 4.05/4.31 fof(c_0_8893, plain, ![X14987, X14988]:(X14988=c_List_Olist_ONil(X14987)|c_List_Olast(X14987,hAPP(c_List_Orev(X14987),X14988))=hAPP(c_List_Ohd(X14987),X14988)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__rev])])). 4.05/4.31 cnf(c_0_8894, 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_5542])). 4.05/4.31 cnf(c_0_8895, 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_5496])). 4.05/4.31 cnf(c_0_8896, 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_5568])). 4.05/4.31 cnf(c_0_8897, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))|~hBOOL(hAPP(X1,esk156_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_5572])). 4.05/4.31 fof(c_0_8898, plain, ![X3593, X3594, X3595, X3596]:(~hBOOL(hAPP(hAPP(c_member(X3596),X3595),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3596,tc_HOL_Obool)),X3594),X3593)))|~hBOOL(hAPP(hAPP(c_member(X3596),X3595),X3593))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_DiffD2])])])). 4.05/4.31 fof(c_0_8899, plain, ![X7660, X7661, X7662]:(~hBOOL(hAPP(c_List_Odistinct(X7662),X7661))|hBOOL(hAPP(c_List_Odistinct(X7662),hAPP(hAPP(c_List_Odrop(X7662),X7660),X7661)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__drop])])])). 4.05/4.31 fof(c_0_8900, plain, ![X4660, X4661, X4662]:(~hBOOL(hAPP(c_List_Odistinct(X4662),X4661))|hBOOL(hAPP(c_List_Odistinct(X4662),hAPP(hAPP(c_List_Otake(X4662),X4660),X4661)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__take])])). 4.05/4.31 fof(c_0_8901, plain, ![X9703, X9704, X9705]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(X9705),X9704))|hBOOL(hAPP(c_Finite__Set_Ofinite(X9705),hAPP(hAPP(c_Set_Oinsert(X9705),X9703),X9704)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite_OinsertI])])])). 4.05/4.31 fof(c_0_8902, plain, ![X4299, X4300, X4301]:(~class_Orderings_Oorder(X4301)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4301),X4300),X4299))|c_SetInterval_Oord__class_OatLeastAtMost(X4301,X4299,X4300)=c_Orderings_Obot__class_Obot(tc_fun(X4301,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty])])). 4.05/4.31 fof(c_0_8903, plain, ![X14579, X14580, X14581]:(~class_Divides_Osemiring__div(X14581)|c_Divides_Odiv__class_Omod(X14581,X14580,X14579)=c_Divides_Odiv__class_Omod(X14581,c_Divides_Odiv__class_Omod(X14581,X14580,X14579),X14579)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__trivial])])). 4.05/4.31 cnf(c_0_8904, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)=c_Groups_Oone__class_Oone(X1)|c_Groups_Oone__class_Oone(X1)!=X2|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_5546])). 4.05/4.31 cnf(c_0_8905, plain, (hBOOL(hAPP(X1,esk332_1(X1)))|~hBOOL(hAPP(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_5573])). 4.05/4.31 cnf(c_0_8906, 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_5553])). 4.05/4.31 fof(c_0_8907, plain, ![X7165, X7166]:((hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X7165)!=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X7166)|X7166=X7165)&(X7166!=X7165|hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X7165)=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X7166))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I3_J])])). 4.05/4.31 fof(c_0_8908, plain, ![X10170, X10171, X10172, X10173]:(~c_FunDef_Oreduction__pair(X10173,X10172)|c_FunDef_Oreduction__pair(X10171,hAPP(hAPP(c_FunDef_Orp__inv__image(X10173,X10171),X10172),X10170))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp])])). 4.05/4.31 fof(c_0_8909, plain, ![X10575, X10576, X10577, X10578]:(~c_Wellfounded_Owf(X10578,X10577)|c_Wellfounded_Owf(X10576,hAPP(hAPP(c_Relation_Oinv__image(X10578,X10576),X10577),X10575))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__inv__image])])). 4.05/4.31 fof(c_0_8910, plain, ![X3015, X3016]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3016),hAPP(c_Nat_OSuc,X3015)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3016),X3015))|X3015=X3016)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__SucE])])])). 4.05/4.31 fof(c_0_8911, plain, ![X9283, X9284, X9285, X9286, X9287]:(~c_Typedef_Otype__definition(X9287,X9286,X9285,X9284,X9283)|c_Orderings_Otop__class_Otop(tc_fun(X9287,tc_HOL_Obool))=hAPP(c_Set_Oimage(X9286,X9287,X9284),X9283)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_type__definition_OAbs__image])])])). 4.05/4.31 fof(c_0_8912, plain, ![X3943, X3944, X3945, X3946, X3947]:((~hBOOL(hAPP(hAPP(X3945,X3943),X3944))|hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X3947,X3946,X3945),X3944),X3943)))&(~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X3947,X3946,X3945),X3944),X3943))|hBOOL(hAPP(hAPP(X3945,X3943),X3944)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep_Oequations])])). 4.05/4.31 fof(c_0_8913, plain, ![X1228, X1229, X1230]:(~class_Orderings_Oorder(X1230)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1230),X1229),X1228))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1230),X1228),X1229))|X1228=X1229))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I5_J])])])). 4.05/4.31 fof(c_0_8914, plain, ![X15119, X15120]:(~class_Groups_Oordered__ab__group__add__abs(X15120)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X15120),X15119),hAPP(c_Groups_Oabs__class_Oabs(X15120),X15119)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__self])])). 4.05/4.31 fof(c_0_8915, plain, ![X13775, X13776]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13776),X13775)|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13775),X13776)|X13775=X13776)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diffs0__imp__equal])])])). 4.05/4.31 cnf(c_0_8916, 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_5574])). 4.05/4.31 fof(c_0_8917, plain, ![X16185, X16186, X16187]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X16187),X16186))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16187),X16185))|hBOOL(hAPP(c_Finite__Set_Ofinite(X16187),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16187,tc_HOL_Obool)),X16186),X16185))))&((hBOOL(hAPP(c_Finite__Set_Ofinite(X16187),X16186))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16187),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16187,tc_HOL_Obool)),X16186),X16185))))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X16187),X16185))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X16187),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16187,tc_HOL_Obool)),X16186),X16185)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Un])])])). 4.05/4.31 fof(c_0_8918, plain, ![X7985, X7986, X7987]:(~class_Orderings_Olinorder(X7987)|(~c_List_Olinorder__class_Osorted(X7987,X7986)|c_List_Olinorder__class_Osorted(X7987,hAPP(hAPP(c_List_Odrop(X7987),X7985),X7986)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__drop])])])). 4.05/4.31 fof(c_0_8919, plain, ![X5232, X5233, X5234]:(~class_Orderings_Olinorder(X5234)|(~c_List_Olinorder__class_Osorted(X5234,X5233)|c_List_Olinorder__class_Osorted(X5234,hAPP(hAPP(c_List_Otake(X5234),X5232),X5233)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__take])])])). 4.05/4.31 fof(c_0_8920, plain, ![X17056, X17057, X17058]:(~hBOOL(hAPP(c_List_Odistinct(X17058),X17057))|hBOOL(hAPP(c_List_Odistinct(X17058),hAPP(c_List_Ofilter(X17058,X17056),X17057)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_distinct__filter])])])). 4.05/4.31 fof(c_0_8921, plain, ![X5305]:((~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)),X5305)))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X5305)))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X5305))|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)),X5305))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I1_J])])). 4.05/4.31 cnf(c_0_8922, plain, (X3=X4|X1!=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X1),X2)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X3),X4)|~class_Groups_Oab__group__add(X5)), inference(split_conjunct,[status(thm)],[c_0_5575])). 4.05/4.31 cnf(c_0_8923, 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_5576])). 4.05/4.31 fof(c_0_8924, plain, ![X5347]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5347))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X5347)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X5347))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5347)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])])). 4.05/4.31 fof(c_0_8925, plain, ![X9741]:(~class_Rings_Olinordered__semidom(X9741)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9741),c_Groups_Ozero__class_Ozero(X9741)),c_Groups_Oone__class_Oone(X9741)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])])). 4.05/4.31 fof(c_0_8926, plain, ![X4931]:(~class_Rings_Olinordered__semidom(X4931)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4931),c_Groups_Ozero__class_Ozero(X4931)),c_Groups_Oone__class_Oone(X4931)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__le__one])])])). 4.05/4.31 fof(c_0_8927, plain, ![X7690, X7691, X7692, X7693, X7694, X7695]:(((~hBOOL(hAPP(X7695,X7692))|hBOOL(hAPP(X7695,X7692))|~c_Natural_Oevaln(c_Com_Ocom_OCond(X7695,X7694,X7693),X7692,X7691,X7690))&(c_Natural_Oevaln(X7693,X7692,X7691,X7690)|hBOOL(hAPP(X7695,X7692))|~c_Natural_Oevaln(c_Com_Ocom_OCond(X7695,X7694,X7693),X7692,X7691,X7690)))&((~hBOOL(hAPP(X7695,X7692))|c_Natural_Oevaln(X7694,X7692,X7691,X7690)|~c_Natural_Oevaln(c_Com_Ocom_OCond(X7695,X7694,X7693),X7692,X7691,X7690))&(c_Natural_Oevaln(X7693,X7692,X7691,X7690)|c_Natural_Oevaln(X7694,X7692,X7691,X7690)|~c_Natural_Oevaln(c_Com_Ocom_OCond(X7695,X7694,X7693),X7692,X7691,X7690)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_evaln__elim__cases_I5_J])])])])). 4.05/4.31 fof(c_0_8928, plain, ![X11364, X11365, X11366]:((~hBOOL(hAPP(hAPP(c_member(X11366),X11365),hAPP(hAPP(c_Set_Oinsert(X11366),X11364),c_Orderings_Obot__class_Obot(tc_fun(X11366,tc_HOL_Obool)))))|X11364=X11365)&(X11364!=X11365|hBOOL(hAPP(hAPP(c_member(X11366),X11365),hAPP(hAPP(c_Set_Oinsert(X11366),X11364),c_Orderings_Obot__class_Obot(tc_fun(X11366,tc_HOL_Obool))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__iff])])). 4.05/4.31 fof(c_0_8929, plain, ![X7594, X7595, X7596, X7597, X7598]:((~c_Wellfounded_Owf(X7595,X7594)|hBOOL(hAPP(hAPP(c_member(X7595),X7596),c_Wellfounded_Oacc(X7595,X7594))))&(~hBOOL(hAPP(hAPP(c_member(X7598),esk241_2(X7597,X7598)),c_Wellfounded_Oacc(X7598,X7597)))|c_Wellfounded_Owf(X7598,X7597))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__acc__iff])])])])])). 4.05/4.31 fof(c_0_8930, plain, ![X7706, X7707, X7708]:(~class_Orderings_Olinorder(X7708)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7708),X7707),X7706))|X7707=hAPP(hAPP(c_Orderings_Oord__class_Omin(X7708),X7707),X7706))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Oinf__absorb1])])])). 4.05/4.31 fof(c_0_8931, plain, ![X4945, X4946, X4947]:(((c_Orderings_Obot__class_Obot(tc_fun(X4947,tc_HOL_Obool))=X4945|c_Orderings_Obot__class_Obot(tc_fun(X4947,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4947,tc_HOL_Obool)),X4946),X4945))&(c_Orderings_Obot__class_Obot(tc_fun(X4947,tc_HOL_Obool))=X4946|c_Orderings_Obot__class_Obot(tc_fun(X4947,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4947,tc_HOL_Obool)),X4946),X4945)))&(c_Orderings_Obot__class_Obot(tc_fun(X4947,tc_HOL_Obool))!=X4945|c_Orderings_Obot__class_Obot(tc_fun(X4947,tc_HOL_Obool))!=X4946|c_Orderings_Obot__class_Obot(tc_fun(X4947,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4947,tc_HOL_Obool)),X4946),X4945))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__empty])])])). 4.05/4.31 fof(c_0_8932, plain, ![X14693, X14694, X14695]:(~class_Orderings_Olinorder(X14695)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X14695),X14694),X14693))|X14694=hAPP(hAPP(c_Orderings_Oord__class_Omin(X14695),X14693),X14694))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb2])])). 4.05/4.31 fof(c_0_8933, plain, ![X4723, X4724, X4725]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4725),X4724),X4723))|X4723=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4725),X4724),X4723)|~class_Orderings_Olinorder(X4725))&(X4723!=hAPP(hAPP(c_Orderings_Oord__class_Omax(X4725),X4724),X4723)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4725),X4724),X4723))|~class_Orderings_Olinorder(X4725))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ole__iff__sup])])])])). 4.05/4.31 fof(c_0_8934, plain, ![X11156, X11157, X11158]:(~class_Orderings_Olinorder(X11158)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X11158),X11157),X11156))|X11156=hAPP(hAPP(c_Orderings_Oord__class_Omax(X11158),X11156),X11157))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb1])])). 4.05/4.31 fof(c_0_8935, plain, ![X9221, X9222, X9223]:(~hBOOL(hAPP(c_List_Odistinct(X9223),X9222))|hBOOL(hAPP(c_List_Odistinct(X9223),c_List_Oremove1(X9223,X9221,X9222)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remove1])])). 4.05/4.31 fof(c_0_8936, plain, ![X3000, X3001, X3002]:(~class_Orderings_Oorder(X3002)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3002),X3001),X3000))|c_Orderings_Obot__class_Obot(tc_fun(X3002,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanAtMost(X3002,X3000,X3001))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty])])). 4.05/4.31 fof(c_0_8937, plain, ![X17184, X17185, X17186]:(~class_Orderings_Oorder(X17186)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17186),X17185),X17184))|c_SetInterval_Oord__class_OgreaterThanLessThan(X17186,X17184,X17185)=c_Orderings_Obot__class_Obot(tc_fun(X17186,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_greaterThanLessThan__empty])])])). 4.05/4.31 fof(c_0_8938, plain, ![X7081]:(~class_Orderings_Olinorder(X7081)|c_Finite__Set_Ofun__left__comm(X7081,tc_List_Olist(X7081),c_List_Olinorder__class_Oinsort__key(X7081,X7081,c_COMBI(X7081)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__insort])])])). 4.05/4.31 fof(c_0_8939, plain, ![X9204, X9205]:(~class_Groups_Omonoid__mult(X9205)|hAPP(hAPP(c_Power_Opower__class_Opower(X9205),c_Groups_Oone__class_Oone(X9205)),X9204)=c_Groups_Oone__class_Oone(X9205)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])])). 4.05/4.31 cnf(c_0_8940, 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_5577])). 4.05/4.31 fof(c_0_8941, plain, ![X12552, X12553, X12554]:(~hBOOL(hAPP(c_List_Odistinct(X12554),X12553))|hBOOL(hAPP(c_List_Odistinct(X12554),c_List_Osublist(X12554,X12553,X12552)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__sublistI])])). 4.05/4.31 fof(c_0_8942, plain, ![X6239, X6240, X6241]:(~hBOOL(hAPP(c_List_Odistinct(X6241),X6240))|hBOOL(hAPP(c_List_Odistinct(X6241),c_List_Oinsert(X6241,X6239,X6240)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__insert])])). 4.05/4.31 fof(c_0_8943, plain, ![X5348, X5349, X5350]:(~hBOOL(hAPP(c_List_Odistinct(X5350),X5349))|hBOOL(hAPP(c_List_Odistinct(X5350),c_List_OtakeWhile(X5350,X5348,X5349)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__takeWhile])])). 4.05/4.31 fof(c_0_8944, plain, ![X3178, X3179]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X3179,X3179)),X3178))|hBOOL(hAPP(c_Finite__Set_Ofinite(X3179),hAPP(c_Relation_OField(X3179),X3178)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__Field])])])). 4.05/4.31 fof(c_0_8945, plain, ![X2668, X2669]:(~class_Rings_Odivision__ring(X2669)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2669),c_Groups_Ozero__class_Ozero(X2669)),X2668)=c_Groups_Ozero__class_Ozero(X2669)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__zero__left])])])). 4.05/4.31 fof(c_0_8946, plain, ![X16312, X16313]:(~class_Rings_Omult__zero(X16313)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16313),c_Groups_Ozero__class_Ozero(X16313)),X16312)=c_Groups_Ozero__class_Ozero(X16313)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])])). 4.05/4.31 fof(c_0_8947, plain, ![X16819, X16820, X16821, X16822]:(~c_Equiv__Relations_Oequivp(X16822,X16821)|(~hBOOL(hAPP(hAPP(X16821,X16820),X16819))|hBOOL(hAPP(hAPP(X16821,X16819),X16820)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equivp__symp])])])). 4.05/4.31 fof(c_0_8948, plain, ![X1680, X1681]:(~class_Rings_Ocomm__semiring__1(X1681)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1681),c_Groups_Ozero__class_Ozero(X1681)),X1680)=c_Groups_Ozero__class_Ozero(X1681)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])])])). 4.05/4.31 fof(c_0_8949, plain, ![X2141, X2142]:(((c_List_Olinorder__class_Osorted(X2142,c_List_Olinorder__class_Osorted__list__of__set(X2142,X2141))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2142),X2141))|~class_Orderings_Olinorder(X2142))&(hBOOL(hAPP(c_List_Odistinct(X2142),c_List_Olinorder__class_Osorted__list__of__set(X2142,X2141)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2142),X2141))|~class_Orderings_Olinorder(X2142)))&(X2141=hAPP(c_List_Oset(X2142),c_List_Olinorder__class_Osorted__list__of__set(X2142,X2141))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2142),X2141))|~class_Orderings_Olinorder(X2142))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set])])])). 4.05/4.31 fof(c_0_8950, plain, ![X15521, X15522, X15523, X15524]:((X15522!=X15521|X15523!=X15522|c_SetInterval_Oord__class_OatLeastAtMost(X15524,X15523,X15522)=hAPP(hAPP(c_Set_Oinsert(X15524),X15521),c_Orderings_Obot__class_Obot(tc_fun(X15524,tc_HOL_Obool)))|~class_Orderings_Oorder(X15524))&((X15522=X15521|c_SetInterval_Oord__class_OatLeastAtMost(X15524,X15523,X15522)!=hAPP(hAPP(c_Set_Oinsert(X15524),X15521),c_Orderings_Obot__class_Obot(tc_fun(X15524,tc_HOL_Obool)))|~class_Orderings_Oorder(X15524))&(X15523=X15522|c_SetInterval_Oord__class_OatLeastAtMost(X15524,X15523,X15522)!=hAPP(hAPP(c_Set_Oinsert(X15524),X15521),c_Orderings_Obot__class_Obot(tc_fun(X15524,tc_HOL_Obool)))|~class_Orderings_Oorder(X15524)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atLeastAtMost__singleton__iff])])])])). 4.05/4.31 fof(c_0_8951, plain, ![X3041, X3042]:(~class_Lattices_Obounded__lattice__top(X3042)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3042),c_Orderings_Otop__class_Otop(X3042)),X3041)=c_Orderings_Otop__class_Otop(X3042)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__left])])). 4.05/4.31 fof(c_0_8952, plain, ![X13737, X13738]:(((X13737!=X13738|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13738),X13737)))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13738),X13737))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13738),X13737))))&(X13737=X13738|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13738),X13737))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13738),X13737)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])])). 4.05/4.31 fof(c_0_8953, plain, ![X7292, X7293]:(~class_Divides_Osemiring__div(X7293)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X7293),c_Groups_Ozero__class_Ozero(X7293)),X7292)=c_Groups_Ozero__class_Ozero(X7293)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__0])])). 4.05/4.31 fof(c_0_8954, plain, ![X3356, X3357, X3358]:(~class_Rings_Ono__zero__divisors(X3358)|(c_Groups_Ozero__class_Ozero(X3358)=X3357|(X3356=c_Groups_Ozero__class_Ozero(X3358)|c_Groups_Ozero__class_Ozero(X3358)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3358),X3357),X3356)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_no__zero__divisors])])])). 4.05/4.31 fof(c_0_8955, plain, ![X9100, X9101]:(~class_Lattices_Obounded__lattice__bot(X9101)|c_Orderings_Obot__class_Obot(X9101)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9101),c_Orderings_Obot__class_Obot(X9101)),X9100)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__bot__left])])])). 4.05/4.31 cnf(c_0_8956, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)))|~hBOOL(hAPP(X1,X2))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X3), inference(split_conjunct,[status(thm)],[c_0_5288])). 4.05/4.31 cnf(c_0_8957, plain, (X3=c_List_Olist_ONil(X1)|c_List_Olist_ONil(X1)!=hAPP(c_List_Orotate(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_4841])). 4.05/4.31 fof(c_0_8958, plain, ![X5061, X5062]:(c_List_Olist_ONil(X5061)=X5062|hAPP(hAPP(c_List_Onth(X5061),X5062),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_List_Ohd(X5061),X5062)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__conv__nth])])). 4.05/4.31 cnf(c_0_8959, 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_5574])). 4.05/4.31 fof(c_0_8960, plain, ![X1693, X1694]:(~class_Rings_Olinordered__idom(X1694)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1694),c_Groups_Ozero__class_Ozero(X1694)),X1693))|c_Groups_Oone__class_Oone(X1694)=c_Groups_Osgn__class_Osgn(X1694,X1693))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sgn__pos])])])). 4.05/4.31 fof(c_0_8961, plain, ![X8735, X8736]:(X8736=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X8735,X8736),c_Divides_Odivmod__int(X8735,X8736)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__correct])])). 4.05/4.31 fof(c_0_8962, plain, ![X10064, X10065]:(~class_Lattices_Obounded__lattice__bot(X10065)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10065),X10064),c_Orderings_Obot__class_Obot(X10065))=c_Orderings_Obot__class_Obot(X10065)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__bot__right])])])). 4.05/4.31 fof(c_0_8963, plain, ![X14719]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14719),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X14719)=hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X14719))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14719),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X14719)=X14719)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zabs__def])])])). 4.05/4.31 fof(c_0_8964, plain, ![X15385, X15386, X15387, X15388, X15390, X15391, X15392, X15393, X15394]:(((c_Natural_Oevalc(X15387,esk466_4(X15385,X15386,X15387,X15388),X15385)|~c_Natural_Oevalc(c_Com_Ocom_OSemi(X15388,X15387),X15386,X15385))&(c_Natural_Oevalc(X15388,X15386,esk466_4(X15385,X15386,X15387,X15388))|~c_Natural_Oevalc(c_Com_Ocom_OSemi(X15388,X15387),X15386,X15385)))&(~c_Natural_Oevalc(X15392,X15394,X15390)|~c_Natural_Oevalc(X15393,X15391,X15394)|c_Natural_Oevalc(c_Com_Ocom_OSemi(X15393,X15392),X15391,X15390))), 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_evalc_Oequations_I4_J])])])])])])). 4.05/4.31 cnf(c_0_8965, 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_5084])). 4.05/4.31 fof(c_0_8966, plain, ![X5871, X5872]:(~class_Rings_Ocomm__semiring__1(X5872)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5872),X5871),c_Groups_Ozero__class_Ozero(X5872))=c_Groups_Ozero__class_Ozero(X5872)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])])). 4.05/4.31 fof(c_0_8967, plain, ![X10021, X10022]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10022)),X10021)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|X10021=hAPP(c_List_Orotate1(X10022),X10021)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_rotate1__length01])])])). 4.05/4.31 fof(c_0_8968, plain, ![X9526, X9527, X9528, X9529, X9530]:(~hBOOL(hAPP(hAPP(X9530,X9529),X9528))|hBOOL(hAPP(c_Predicate_ORangeP(X9527,X9526,X9530),X9528))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_RangeP_Ointros])])])). 4.05/4.31 fof(c_0_8969, plain, ![X15369, X15370]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15370),X15369)|(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X15370|X15369=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X15370|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15370),X15369))&(X15369!=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),X15370),X15369)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__is__0])])])). 4.05/4.31 fof(c_0_8970, plain, ![X9806, X9807]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X9807),X9806))|c_Nat__Transfer_Otsub(X9806,X9807)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X9806),X9807)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_tsub__eq])])])). 4.05/4.31 fof(c_0_8971, plain, ![X1029, X1030]:(~class_Divides_Osemiring__div(X1030)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1030),X1029),c_Groups_Ozero__class_Ozero(X1030))=c_Groups_Ozero__class_Ozero(X1030)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__by__0])])])). 4.05/4.31 fof(c_0_8972, plain, ![X2495, X2496, X2497, X2498, X2499]:(~hBOOL(hAPP(hAPP(X2499,X2498),X2497))|hBOOL(hAPP(c_Predicate_ODomainP(X2496,X2495,X2499),X2498))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_DomainP_Ointros])])])). 4.05/4.31 fof(c_0_8973, plain, ![X3997]:(~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X3997),c_Int_OInteg))|hAPP(c_Int_ORep__Integ,esk123_1(X3997))=X3997), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Rep__Integ__cases])])])])). 4.05/4.31 fof(c_0_8974, plain, ![X5924, X5925]:(~class_Lattices_Obounded__lattice__top(X5925)|c_Orderings_Otop__class_Otop(X5925)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5925),X5924),c_Orderings_Otop__class_Otop(X5925))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__right])])). 4.05/4.31 fof(c_0_8975, plain, ![X13713, X13714]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13714),X13713)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13714),X13713)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13714),X13713))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13714),X13713))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq])])). 4.05/4.31 fof(c_0_8976, plain, ![X4538, X4539]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4539),X4538))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X4539),X4538)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less])])). 4.05/4.31 fof(c_0_8977, plain, ![X2745, X2746]:(~class_Rings_Odivision__ring__inverse__zero(X2746)|c_Groups_Ozero__class_Ozero(X2746)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2746),X2745),c_Groups_Ozero__class_Ozero(X2746))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero])])). 4.05/4.31 fof(c_0_8978, plain, ![X10116, X10117]:(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X10117|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10117))!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10116))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X10116|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10117))!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10116)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X10117|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X10116|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10117))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10116))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negative__eq__positive])])])). 4.05/4.31 fof(c_0_8979, plain, ![X6361, X6362, X6363]:(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X6363|hAPP(c_List_Ohd(X6362),c_List_Oreplicate(X6362,X6363,X6361))=X6361), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__replicate])])). 4.05/4.31 fof(c_0_8980, plain, ![X12344, X12345]:(~class_Rings_Omult__zero(X12345)|c_Groups_Ozero__class_Ozero(X12345)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12345),X12344),c_Groups_Ozero__class_Ozero(X12345))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])])). 4.05/4.31 fof(c_0_8981, plain, ![X9022, X9023]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9023),hAPP(c_Nat_OSuc,X9022)))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9023),X9022))|X9023=X9022))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9023),X9022))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9023),hAPP(c_Nat_OSuc,X9022))))&(X9023!=X9022|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9023),hAPP(c_Nat_OSuc,X9022)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])])). 4.05/4.31 fof(c_0_8982, plain, ![X2774, X2775, X2776]:(~c_Wellfounded_Owf(X2776,X2775)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2776,X2776)),hAPP(hAPP(c_Product__Type_OPair(X2776,X2776),X2774),X2774)),X2775))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__not__refl])])])). 4.05/4.31 cnf(c_0_8983, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X3),X1)=X3|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)), inference(split_conjunct,[status(thm)],[c_0_5578])). 4.05/4.31 fof(c_0_8984, plain, ![X8505, X8506]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8506),hAPP(c_Nat_OSuc,X8505)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8506),X8505)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8506),X8505))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8506),hAPP(c_Nat_OSuc,X8505))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])])). 4.05/4.31 fof(c_0_8985, plain, ![X6068, X6069]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6069),X6068))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6069),hAPP(c_Nat_OSuc,X6068)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])])). 4.05/4.31 fof(c_0_8986, plain, ![X1164, X1165]:(~class_Divides_Osemiring__div(X1165)|(c_Groups_Ozero__class_Ozero(X1165)=X1164|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1165),X1164),X1164)=c_Groups_Oone__class_Oone(X1165))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_div__self])])])). 4.05/4.31 fof(c_0_8987, plain, ![X9874, X9875]:((X9874!=c_Groups_Ozero__class_Ozero(X9875)|c_Groups_Ozero__class_Ozero(X9875)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9875),X9874),X9874)|~class_Rings_Odivision__ring__inverse__zero(X9875))&(c_Groups_Ozero__class_Ozero(X9875)=X9874|c_Groups_Oone__class_Oone(X9875)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X9875),X9874),X9874)|~class_Rings_Odivision__ring__inverse__zero(X9875))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__self__if])])])])). 4.05/4.31 cnf(c_0_8988, 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_5496])). 4.05/4.31 cnf(c_0_8989, 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_5560])). 4.05/4.31 fof(c_0_8990, plain, ![X3422, X3423, X3424, X3425, X3426]:(~hBOOL(hAPP(X3426,X3425))|(~c_Natural_Oevalc(X3424,X3425,X3423)|c_Natural_Oevalc(c_Com_Ocom_OCond(X3426,X3424,X3422),X3425,X3423))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_evalc_OIfTrue])])])). 4.05/4.31 fof(c_0_8991, plain, ![X1816, X1817, X1818]:(~c_Wellfounded_Owf(X1818,X1817)|c_Wellfounded_Owf(tc_List_Olist(X1818),hAPP(c_List_Olexn(X1818,X1817),X1816))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lexn])])). 4.05/4.31 cnf(c_0_8992, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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_5502])). 4.05/4.31 fof(c_0_8993, plain, ![X9165, X9166]:((X9166=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Olist_ONil(tc_List_Olist(X9165))=c_Enum_On__lists(X9165,X9166,c_List_Olist_ONil(X9165)))&(X9166!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X9165)),c_List_Olist_ONil(X9165)),c_List_Olist_ONil(tc_List_Olist(X9165)))=c_Enum_On__lists(X9165,X9166,c_List_Olist_ONil(X9165)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_n__lists__Nil])])])). 4.05/4.31 fof(c_0_8994, plain, ![X17104, X17105]:(~class_Rings_Odivision__ring(X17105)|(c_Groups_Ozero__class_Ozero(X17105)=X17104|c_Groups_Oone__class_Oone(X17105)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X17105),X17104),X17104))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divide__self])])])). 4.05/4.31 cnf(c_0_8995, 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_5561])). 4.05/4.31 fof(c_0_8996, plain, ![X13820, X13821, X13822, X13823]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X13823,X13822)),c_Sum__Type_OPlus(X13823,X13822,X13821,X13820)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X13823),X13821))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J])])). 4.05/4.31 fof(c_0_8997, plain, ![X3967, X3968, X3969, X3970]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X3970,X3969)),c_Sum__Type_OPlus(X3970,X3969,X3968,X3967)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X3969),X3967))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J])])). 4.05/4.31 fof(c_0_8998, plain, ![X1056]:(~class_Rings_Osemiring__1(X1056)|hBOOL(hAPP(hAPP(c_member(X1056),c_Groups_Ozero__class_Ozero(X1056)),c_Nat_Osemiring__1__class_ONats(X1056)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nats__0])])])). 4.05/4.31 fof(c_0_8999, plain, ![X8958]:(~class_Rings_Oring__1(X8958)|hBOOL(hAPP(hAPP(c_member(X8958),c_Groups_Ozero__class_Ozero(X8958)),c_Int_Oring__1__class_OInts(X8958)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__0])])). 4.05/4.31 fof(c_0_9000, plain, ![X8317]:(~class_Rings_Osemiring__1(X8317)|hBOOL(hAPP(hAPP(c_member(X8317),c_Groups_Oone__class_Oone(X8317)),c_Nat_Osemiring__1__class_ONats(X8317)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nats__1])])])). 4.05/4.31 fof(c_0_9001, plain, ![X3839, X3840, X3841, X3842, X3843, X3844, X3845]:(~c_Finite__Set_Ofolding__image__simple__idem(X3845,X3844,X3843,X3842,X3841,X3840)|X3839=hAPP(hAPP(X3843,X3839),X3839)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem])])). 4.05/4.31 fof(c_0_9002, plain, ![X6788, X6789, X6790, X6791, X6792]:(~c_Map_Omap__le(X6792,X6791,X6790,X6789)|(~c_Map_Omap__le(X6792,X6791,X6789,X6788)|c_Map_Omap__le(X6792,X6791,X6790,X6788))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__le__trans])])])). 4.05/4.31 fof(c_0_9003, plain, ![X5859]:(~class_Rings_Oring__1(X5859)|hBOOL(hAPP(hAPP(c_member(X5859),c_Groups_Oone__class_Oone(X5859)),c_Int_Oring__1__class_OInts(X5859)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Ints__1])])])). 4.05/4.31 cnf(c_0_9004, 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_5579])). 4.05/4.31 cnf(c_0_9005, 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_5580])). 4.05/4.31 fof(c_0_9006, plain, ![X14327, X14328, X14329]:((~c_Relation_Ototal__on(X14329,X14328,hAPP(c_Relation_Oconverse(X14329,X14329),X14327))|c_Relation_Ototal__on(X14329,X14328,X14327))&(~c_Relation_Ototal__on(X14329,X14328,X14327)|c_Relation_Ototal__on(X14329,X14328,hAPP(c_Relation_Oconverse(X14329,X14329),X14327)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__converse])])). 4.05/4.31 fof(c_0_9007, plain, ![X5336, X5337, X5338]:((~c_Relation_Orefl__on(X5338,X5337,hAPP(c_Relation_Oconverse(X5338,X5338),X5336))|c_Relation_Orefl__on(X5338,X5337,X5336))&(~c_Relation_Orefl__on(X5338,X5337,X5336)|c_Relation_Orefl__on(X5338,X5337,hAPP(c_Relation_Oconverse(X5338,X5338),X5336)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__converse])])). 4.05/4.31 cnf(c_0_9008, plain, (X1=X2|hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),X3)!=c_List_Oupt(X1,X4)), inference(split_conjunct,[status(thm)],[c_0_4671])). 4.05/4.31 fof(c_0_9009, plain, ![X16622, X16623]:(~class_Rings_Ocomm__semiring__1(X16623)|hAPP(hAPP(c_Power_Opower__class_Opower(X16623),X16622),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X16623)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])])])). 4.05/4.31 cnf(c_0_9010, plain, (X1=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_5554])). 4.05/4.31 fof(c_0_9011, plain, ![X4619, X4620, X4621, X4622]:(~class_Groups_Ocancel__semigroup__add(X4622)|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4622),X4619),X4620)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4622),X4621),X4620)|X4619=X4621)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__right__imp__eq])])])). 4.05/4.31 fof(c_0_9012, plain, ![X9458, X9459, X9460, X9461]:(~class_Groups_Ocancel__ab__semigroup__add(X9461)|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9461),X9460),X9458)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9461),X9460),X9459)|X9459=X9458)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])])). 4.05/4.31 fof(c_0_9013, plain, ![X1083, X1084, X1085, X1086]:(~class_Groups_Ocancel__semigroup__add(X1086)|(hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1086),X1085),X1083)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1086),X1085),X1084)|X1083=X1084)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__left__imp__eq])])])). 4.05/4.31 fof(c_0_9014, plain, ![X8318, X8319]:(~class_Power_Opower(X8319)|c_Groups_Oone__class_Oone(X8319)=hAPP(hAPP(c_Power_Opower__class_Opower(X8319),X8318),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__0])])])). 4.05/4.31 fof(c_0_9015, plain, ![X5474, X5475]:(~class_Groups_Omonoid__mult(X5475)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5475),c_Groups_Oone__class_Oone(X5475)),X5474)=X5474), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__1__left])])])). 4.05/4.31 fof(c_0_9016, plain, ![X4030, X4031]:(~class_Groups_Ocomm__monoid__mult(X4031)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4031),c_Groups_Oone__class_Oone(X4031)),X4030)=X4030), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__1])])])). 4.05/4.31 fof(c_0_9017, plain, ![X12738, X12739]:(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12739),X12738)!=X12739|(X12739=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X12738=c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__self__implies__10])])). 4.05/4.31 fof(c_0_9018, plain, ![X2670, X2671]:(~class_Rings_Ocomm__semiring__1(X2671)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2671),c_Groups_Oone__class_Oone(X2671)),X2670)=X2670), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])])). 4.05/4.31 fof(c_0_9019, plain, ![X9181, X9182]:(~class_Lattices_Obounded__lattice__bot(X9182)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9182),c_Orderings_Obot__class_Obot(X9182)),X9181)=X9181), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__bot__left])])])). 4.05/4.31 fof(c_0_9020, plain, ![X14849, X14850]:(~class_Groups_Ocomm__monoid__add(X14850)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14850),c_Groups_Ozero__class_Ozero(X14850)),X14849)=X14849), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])])). 4.05/4.31 fof(c_0_9021, plain, ![X8703, X8704]:(~class_Rings_Ocomm__semiring__1(X8704)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8704),c_Groups_Ozero__class_Ozero(X8704)),X8703)=X8703), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])])). 4.05/4.31 fof(c_0_9022, plain, ![X7261, X7262]:(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7262)),X7261)!=hAPP(c_Finite__Set_Ocard(X7262),hAPP(c_List_Oset(X7262),X7261))|hBOOL(hAPP(c_List_Odistinct(X7262),X7261))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__distinct])])])). 4.05/4.31 fof(c_0_9023, plain, ![X1369]:(~class_Orderings_Olinorder(X1369)|c_List_Olinorder__class_Osorted__list__of__set(X1369,c_Orderings_Obot__class_Obot(tc_fun(X1369,tc_HOL_Obool)))=c_List_Olist_ONil(X1369)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__empty])])). 4.05/4.31 fof(c_0_9024, plain, ![X4546]:(~class_Complete__Lattice_Ocomplete__lattice(X4546)|c_Complete__Lattice_OSup__class_OSup(X4546,c_Orderings_Obot__class_Obot(tc_fun(X4546,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(X4546)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__empty])])])). 4.05/4.31 fof(c_0_9025, plain, ![X6585]:(~class_Complete__Lattice_Ocomplete__lattice(X6585)|c_Complete__Lattice_OInf__class_OInf(X6585,c_Orderings_Otop__class_Otop(tc_fun(X6585,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(X6585)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__UNIV])])). 4.05/4.31 fof(c_0_9026, plain, ![X7397, X7398]:(~class_Lattices_Obounded__lattice__top(X7398)|X7397=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X7398),c_Orderings_Otop__class_Otop(X7398)),X7397)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__top__left])])). 4.05/4.31 fof(c_0_9027, plain, ![X14417, X14418]:(~class_Groups_Omonoid__add(X14418)|X14417=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X14418),c_Groups_Ozero__class_Ozero(X14418)),X14417)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])])). 4.05/4.31 fof(c_0_9028, plain, ![X17518, X17519]:(~class_Rings_Ocomm__semiring__1(X17519)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17519),X17518),c_Groups_Oone__class_Oone(X17519))=X17518), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])])). 4.05/4.31 fof(c_0_9029, plain, ![X12197, X12198]:(~class_Lattices_Obounded__lattice__bot(X12198)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X12198),X12197),c_Orderings_Obot__class_Obot(X12198))=X12197), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__bot__right])])])). 4.05/4.31 fof(c_0_9030, plain, ![X1419]:(~class_Complete__Lattice_Ocomplete__lattice(X1419)|c_Orderings_Otop__class_Otop(X1419)=c_Complete__Lattice_OSup__class_OSup(X1419,c_Orderings_Otop__class_Otop(tc_fun(X1419,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Sup__UNIV])])])). 4.05/4.31 fof(c_0_9031, plain, ![X7879]:(~class_Complete__Lattice_Ocomplete__lattice(X7879)|c_Orderings_Otop__class_Otop(X7879)=c_Complete__Lattice_OInf__class_OInf(X7879,c_Orderings_Obot__class_Obot(tc_fun(X7879,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__empty])])])). 4.05/4.31 fof(c_0_9032, plain, ![X10528, X10529]:(~class_Orderings_Olinorder(X10529)|(c_List_Olist_ONil(X10529)=X10528|(~c_List_Olinorder__class_Osorted(X10529,X10528)|c_List_Olinorder__class_Osorted(X10529,c_List_Obutlast(X10529,X10528))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__butlast])])])). 4.05/4.31 fof(c_0_9033, plain, ![X3704, X3705]:(~class_Groups_Omonoid__add(X3705)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3705),X3704),c_Groups_Ozero__class_Ozero(X3705))=X3704), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__0__right])])])). 4.05/4.31 fof(c_0_9034, plain, ![X13058, X13059]:(~class_Rings_Ocomm__semiring__1(X13059)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13059),X13058),c_Groups_Ozero__class_Ozero(X13059))=X13058), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])])])). 4.05/4.31 fof(c_0_9035, plain, ![X14558, X14559]:(~class_Divides_Osemiring__div(X14559)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X14559),X14558),c_Groups_Oone__class_Oone(X14559))=X14558), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__1])])). 4.05/4.31 fof(c_0_9036, plain, ![X15022, X15023]:(~class_Rings_Odivision__ring(X15023)|X15022=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X15023),X15022),c_Groups_Oone__class_Oone(X15023))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__1])])). 4.05/4.31 fof(c_0_9037, plain, ![X14085, X14086, X14087]:(X14087=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X14085=c_List_Olast(X14086,c_List_Oreplicate(X14086,X14087,X14085))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__replicate])])). 4.05/4.31 fof(c_0_9038, plain, ![X6433, X6434, X6435]:(((X6434!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_List_Otake(X6435),X6434),X6433)=c_List_Olist_ONil(X6435))&(c_List_Olist_ONil(X6435)!=X6433|hAPP(hAPP(c_List_Otake(X6435),X6434),X6433)=c_List_Olist_ONil(X6435)))&(hAPP(hAPP(c_List_Otake(X6435),X6434),X6433)!=c_List_Olist_ONil(X6435)|(X6434=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Olist_ONil(X6435)=X6433))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__eq__Nil])])])). 4.05/4.31 fof(c_0_9039, plain, ![X11652, X11653, X11654]:(~class_Orderings_Otop(X11654)|hAPP(c_Orderings_Otop__class_Otop(tc_fun(X11653,X11654)),X11652)=c_Orderings_Otop__class_Otop(X11654)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_top__apply])])])). 4.05/4.31 fof(c_0_9040, plain, ![X2937, X2938]:(~class_Groups_Ogroup__add(X2938)|X2937=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2938),X2937),c_Groups_Ozero__class_Ozero(X2938))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0__right])])). 4.05/4.31 fof(c_0_9041, plain, ![X8521, X8522]:(~class_Lattices_Obounded__lattice__top(X8522)|X8521=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8522),X8521),c_Orderings_Otop__class_Otop(X8522))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__top__right])])). 4.05/4.31 fof(c_0_9042, plain, ![X16443, X16444]:(~class_Groups_Omonoid__mult(X16444)|X16443=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X16444),X16443),c_Groups_Oone__class_Oone(X16444))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mult__1__right])])])). 4.05/4.31 fof(c_0_9043, plain, ![X17475, X17476]:(~class_Groups_Ocomm__monoid__mult(X17476)|X17475=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X17476),X17475),c_Groups_Oone__class_Oone(X17476))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])])). 4.05/4.31 fof(c_0_9044, plain, ![X4113, X4114, X4115]:(~class_Orderings_Obot(X4115)|c_Orderings_Obot__class_Obot(X4115)=hAPP(c_Orderings_Obot__class_Obot(tc_fun(X4114,X4115)),X4113)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bot__apply])])])). 4.05/4.31 fof(c_0_9045, plain, ![X1602, X1603, X1604, X1605, X1606]:(~c_Fun_Oinj__on(X1606,X1605,X1604,c_Orderings_Otop__class_Otop(tc_fun(X1606,tc_HOL_Obool)))|(hAPP(X1604,X1602)!=hAPP(X1604,X1603)|X1602=X1603)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_injD])])])). 4.05/4.31 fof(c_0_9046, plain, ![X5323, X5324]:(~class_Groups_Ocomm__monoid__add(X5324)|X5323=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5324),X5323),c_Groups_Ozero__class_Ozero(X5324))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add_Ocomm__neutral])])])). 4.05/4.31 fof(c_0_9047, plain, ![X9323, X9324]:(~class_Lattices_Oboolean__algebra(X9324)|X9323=hAPP(c_Groups_Ouminus__class_Ouminus(X9324),hAPP(c_Groups_Ouminus__class_Ouminus(X9324),X9323))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__compl])])). 4.05/4.31 fof(c_0_9048, plain, ![X12815, X12816]:(~class_Rings_Ocomm__semiring__1(X12816)|hAPP(hAPP(c_Power_Opower__class_Opower(X12816),X12815),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X12815), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])])])). 4.05/4.31 fof(c_0_9049, plain, ![X1695, X1696, X1697, X1698, X1699, X1700]:((X1698=X1696|hAPP(hAPP(c_Product__Type_OPair(X1700,X1699),X1696),X1695)!=hAPP(hAPP(c_Product__Type_OPair(X1700,X1699),X1698),X1697))&(X1695=X1697|hAPP(hAPP(c_Product__Type_OPair(X1700,X1699),X1696),X1695)!=hAPP(hAPP(c_Product__Type_OPair(X1700,X1699),X1698),X1697))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Pair__inject])])])])). 4.05/4.31 cnf(c_0_9050, 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_5581])). 4.05/4.31 fof(c_0_9051, plain, ![X2365, X2366]:(~class_Groups_Omonoid__mult(X2366)|X2365=hAPP(hAPP(c_Power_Opower__class_Opower(X2366),X2365),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])])). 4.05/4.31 fof(c_0_9052, plain, ![X13286, X13287, X13288]:(~class_Orderings_Opreorder(X13288)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13288),X13287),X13286))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13288),X13287),X13286)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__imp__le])])])). 4.05/4.31 fof(c_0_9053, plain, ![X3131, X3132, X3133]:((X3132!=X3131|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3133),X3131),X3132)=c_Groups_Oone__class_Oone(X3133)|c_Groups_Ozero__class_Ozero(X3133)=X3132|~class_Rings_Odivision__ring(X3133))&(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3133),X3131),X3132)!=c_Groups_Oone__class_Oone(X3133)|X3132=X3131|c_Groups_Ozero__class_Ozero(X3133)=X3132|~class_Rings_Odivision__ring(X3133))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_right__inverse__eq])])])])). 4.05/4.31 fof(c_0_9054, plain, ![X7066, X7067]:(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7067,X7067),tc_HOL_Obool))!=hAPP(hAPP(c_Relation_Orel__comp(X7067,X7067,X7067),X7066),X7066)|c_Wellfounded_Owf(X7067,X7066)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__no__loop])])])). 4.05/4.31 fof(c_0_9055, plain, ![X10023, X10024]:(((X10023!=c_Orderings_Obot__class_Obot(tc_fun(X10024,tc_HOL_Obool))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X10024),X10023))&(hBOOL(hAPP(c_Finite__Set_Ofinite(X10024),X10023))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(X10024),X10023)))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Finite__Set_Ocard(X10024),X10023)|(X10023=c_Orderings_Obot__class_Obot(tc_fun(X10024,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X10024),X10023))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__eq__0__iff])])])])). 4.05/4.31 cnf(c_0_9056, 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_5499])). 4.05/4.31 fof(c_0_9057, plain, ![X16644, X16645, X16646, X16647, X16648, X16649]:(~c_Typedef_Otype__definition(X16649,X16648,X16647,X16646,X16645)|X16644=hAPP(X16646,hAPP(X16647,X16644))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_type__definition_ORep__inverse])])])). 4.05/4.31 fof(c_0_9058, plain, ![X2973, X2974, X2975, X2977, X2978, X2979, X2980]:((~c_Natural_Oevalc(X2975,X2974,X2973)|c_Natural_Oevaln(X2975,X2974,esk101_3(X2973,X2974,X2975),X2973))&(~c_Natural_Oevaln(X2979,X2978,X2980,X2977)|c_Natural_Oevalc(X2979,X2978,X2977))), 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_eval__eq])])])])])). 4.05/4.31 cnf(c_0_9059, plain, (hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))), inference(split_conjunct,[status(thm)],[c_0_5265])). 4.05/4.31 cnf(c_0_9060, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,esk482_4(X2,X1,X3,X4)))|X3!=hAPP(c_Option_Ooption_OSome(X4),X2)), inference(split_conjunct,[status(thm)],[c_0_5448])). 4.05/4.31 fof(c_0_9061, plain, ![X2586, X2587, X2588, X2589]:(~c_Natural_Oevaln(X2589,X2588,X2587,X2586)|c_Natural_Oevaln(X2589,X2588,hAPP(c_Nat_OSuc,X2587),X2586)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_evaln__Suc])])])). 4.05/4.31 fof(c_0_9062, plain, ![X3375, X3376]:(~class_Orderings_Olinorder(X3376)|c_List_Olinorder__class_Osorted(X3376,c_List_Olinorder__class_Osort__key(X3376,X3376,c_COMBI(X3376),X3375))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__sort])])). 4.05/4.31 fof(c_0_9063, plain, ![X17676, X17677]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17677),X17676))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17676),X17677))|X17677=X17676)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zle__antisym])])])). 4.05/4.31 fof(c_0_9064, plain, ![X7819, X7820]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7820),X7819))|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X7819),X7820))|X7820=X7819)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__antisym])])])). 4.05/4.31 fof(c_0_9065, plain, ![X12608, X12609, X12610, X12611, X12612]:(((hBOOL(hAPP(X12612,X12609))|~c_Natural_Oevalc(X12610,X12609,X12608)|c_Natural_Oevalc(c_Com_Ocom_OCond(X12612,X12611,X12610),X12609,X12608))&(~hBOOL(hAPP(X12612,X12609))|~c_Natural_Oevalc(X12611,X12609,X12608)|c_Natural_Oevalc(c_Com_Ocom_OCond(X12612,X12611,X12610),X12609,X12608)))&(((hBOOL(hAPP(X12612,X12609))|~hBOOL(hAPP(X12612,X12609))|~c_Natural_Oevalc(c_Com_Ocom_OCond(X12612,X12611,X12610),X12609,X12608))&(c_Natural_Oevalc(X12611,X12609,X12608)|~hBOOL(hAPP(X12612,X12609))|~c_Natural_Oevalc(c_Com_Ocom_OCond(X12612,X12611,X12610),X12609,X12608)))&((hBOOL(hAPP(X12612,X12609))|c_Natural_Oevalc(X12610,X12609,X12608)|~c_Natural_Oevalc(c_Com_Ocom_OCond(X12612,X12611,X12610),X12609,X12608))&(c_Natural_Oevalc(X12611,X12609,X12608)|c_Natural_Oevalc(X12610,X12609,X12608)|~c_Natural_Oevalc(c_Com_Ocom_OCond(X12612,X12611,X12610),X12609,X12608))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_evalc_Oequations_I5_J])])])])). 4.05/4.31 fof(c_0_9066, plain, ![X16591, X16592]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16592))|c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X16592,X16591))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__function__closures])])])). 4.05/4.31 fof(c_0_9067, plain, ![X549]:(~class_Power_Opower(X549)|c_Power_Opower__class_Opower(X549)=c_Power_Opower_Opower(X549,c_Groups_Oone__class_Oone(X549),c_Groups_Otimes__class_Otimes(X549))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_power__power__power])])])). 4.05/4.31 fof(c_0_9068, plain, ![X956, X957, X958, X959, X960, X961]:(~c_Finite__Set_Ofolding__image__simple(X961,X960,X959,X958,X957,X956)|X958=hAPP(X956,c_Orderings_Obot__class_Obot(tc_fun(X960,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oempty])])). 4.05/4.31 fof(c_0_9069, plain, ![X4336, X4337]:(~c_Nat__Transfer_Ois__nat(X4337)|(~c_Nat__Transfer_Ois__nat(X4336)|c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4337),X4336)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J])])])). 4.05/4.31 fof(c_0_9070, plain, ![X6676, X6677]:(~c_Nat__Transfer_Ois__nat(X6677)|(~c_Nat__Transfer_Ois__nat(X6676)|c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6677),X6676)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J])])])). 4.05/4.31 fof(c_0_9071, plain, ![X5572, X5573]:(~c_Nat__Transfer_Ois__nat(X5573)|(~c_Nat__Transfer_Ois__nat(X5572)|c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X5573),X5572)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I1_J])])])). 4.05/4.31 fof(c_0_9072, plain, ![X8114, X8115, X8116, X8117]:(~c_Finite__Set_Ofolding(X8117,X8116,X8115,X8114)|c_Fun_Oid(X8116)=hAPP(X8114,c_Orderings_Obot__class_Obot(tc_fun(X8117,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_folding_Oempty])])])). 4.05/4.31 fof(c_0_9073, plain, ![X4503]:(~class_Enum_Oenum(X4503)|c_Orderings_Otop__class_Otop(tc_fun(X4503,tc_HOL_Obool))=hAPP(c_List_Oset(X4503),c_Enum_Oenum__class_Oenum(X4503))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_enum__UNIV])])])). 4.05/4.31 fof(c_0_9074, plain, ![X6697, X6698, X6699]:((hAPP(hAPP(c_Orderings_Oord__class_Omin(X6699),X6698),X6697)!=X6698|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6699),X6698),X6697))|~class_Orderings_Olinorder(X6699))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X6699),X6698),X6697))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X6699),X6698),X6697)=X6698|~class_Orderings_Olinorder(X6699))), 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])])])])). 4.05/4.31 cnf(c_0_9075, 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_5582, c_0_5583]), c_0_5583])). 4.05/4.31 fof(c_0_9076, plain, ![X10962, X10963]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10963),X10962))|c_Nat__Transfer_Otsub(X10962,X10963)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X10962),X10963))&(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X10963),X10962))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Nat__Transfer_Otsub(X10962,X10963))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_tsub__def])])])). 4.05/4.31 fof(c_0_9077, plain, ![X3631, X3632, X3633]:(~class_Orderings_Opreorder(X3633)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3633),X3632),X3631))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3633),X3631),X3632)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__not__sym])])])). 4.05/4.31 fof(c_0_9078, plain, ![X2118, X2119, X2120]:(~class_Orderings_Oorder(X2120)|(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2120),X2119),X2118))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2120),X2118),X2119)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_xt1_I9_J])])])). 4.05/4.31 fof(c_0_9079, plain, ![X8934, X8935, X8936]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8936),X8935),X8934))|(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8936),X8934),X8935))|X8934=X8935)|~class_Orderings_Olinorder(X8936))&((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8936),X8934),X8935))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8936),X8935),X8934))|~class_Orderings_Olinorder(X8936))&(X8934!=X8935|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8936),X8935),X8934))|~class_Orderings_Olinorder(X8936)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq])])])])). 4.05/4.31 fof(c_0_9080, plain, ![X9591]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X9591)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X9591)&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X9591|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X9591)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__le__0__conv])])). 4.05/4.31 fof(c_0_9081, plain, ![X5084, X5085, X5086]:((X5084!=hAPP(c_Option_Ooption_OSome(X5086),X5085)|hBOOL(hAPP(hAPP(c_member(X5086),X5085),c_Option_Oset(X5086,X5084))))&(~hBOOL(hAPP(hAPP(c_member(X5086),X5085),c_Option_Oset(X5086,X5084)))|X5084=hAPP(c_Option_Ooption_OSome(X5086),X5085))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__set])])). 4.05/4.31 fof(c_0_9082, plain, ![X6915, X6916, X6917, X6918]:(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6918,X6917),X6916))|(~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X6918,X6917),X6915))|X6916=X6915)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_divmod__nat__rel__unique])])])). 4.05/4.31 fof(c_0_9083, plain, ![X3259, X3260, X3261]:((X3259!=X3260|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3261,tc_HOL_Obool)),X3259)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3261,tc_HOL_Obool)),X3260))&(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3261,tc_HOL_Obool)),X3259)!=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3261,tc_HOL_Obool)),X3260)|X3259=X3260)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__eq__Compl__iff])])). 4.05/4.31 fof(c_0_9084, plain, ![X16631, X16632, X16633]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16631),X16632)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16633),X16632)|X16631=X16633)&(X16631!=X16633|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16631),X16632)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16633),X16632))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])])). 4.05/4.31 fof(c_0_9085, plain, ![X1810, X1811, X1812]:((hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1812),X1810)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1812),X1811)|X1811=X1810)&(X1811!=X1810|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1812),X1810)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1812),X1811))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])])). 4.05/4.31 fof(c_0_9086, plain, ![X8355, X8356]:((X8356!=X8355|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8355),hAPP(c_Nat_OSuc,X8356)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8356),X8355)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8355),hAPP(c_Nat_OSuc,X8356)))|X8356=X8355|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X8356),X8355)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_le__less__Suc__eq])])])])). 4.05/4.31 fof(c_0_9087, plain, ![X13224, X13225]:(~class_Groups_Ogroup__add(X13225)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13225),X13224),X13224)=c_Groups_Ozero__class_Ozero(X13225)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_diff__self])])])). 4.05/4.31 fof(c_0_9088, plain, ![X16071, X16072]:(~c_Wellfounded_Owf(X16072,X16071)|c_Wellfounded_Owf(tc_fun(X16072,tc_HOL_Obool),c_Wellfounded_Omin__ext(X16072,X16071))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__ext__wf])])])). 4.05/4.31 fof(c_0_9089, plain, ![X15761, X15762]:(~c_Wellfounded_Owf(X15762,X15761)|c_Wellfounded_Owf(tc_fun(X15762,tc_HOL_Obool),c_Wellfounded_Omax__ext(X15762,X15761))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_max__ext__wf])])])). 4.05/4.31 cnf(c_0_9090, plain, (X3=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=X2|X3!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_5514])). 4.05/4.31 fof(c_0_9091, plain, ![X11677, X11678]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X11678),X11677)|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X11678),X11677)))&(~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X11678),X11677))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X11678),X11677))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__int__def])])). 4.05/4.31 fof(c_0_9092, plain, ![X4638, X4639, X4640]:(~c_Natural_Oevalc(c_Com_Ocom_OBODY(X4640),X4639,X4638)|c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4640)),X4639,X4638)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_evalc__elim__cases_I6_J])])])). 4.05/4.31 fof(c_0_9093, plain, ![X1348, X1349]:((~hBOOL(hAPP(c_List_Odistinct(X1349),X1348))|hBOOL(hAPP(c_List_Odistinct(X1349),hAPP(c_List_Orotate1(X1349),X1348))))&(~hBOOL(hAPP(c_List_Odistinct(X1349),hAPP(c_List_Orotate1(X1349),X1348)))|hBOOL(hAPP(c_List_Odistinct(X1349),X1348)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct1__rotate])])). 4.05/4.31 fof(c_0_9094, plain, ![X12224, X12225]:((~hBOOL(hAPP(c_List_Odistinct(X12225),hAPP(c_List_Orev(X12225),X12224)))|hBOOL(hAPP(c_List_Odistinct(X12225),X12224)))&(~hBOOL(hAPP(c_List_Odistinct(X12225),X12224))|hBOOL(hAPP(c_List_Odistinct(X12225),hAPP(c_List_Orev(X12225),X12224))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__rev])])). 4.05/4.31 fof(c_0_9095, plain, ![X16475, X16476]:(~hBOOL(hAPP(c_List_Odistinct(X16476),X16475))|hBOOL(hAPP(c_List_Odistinct(X16476),hAPP(c_List_Otl(X16476),X16475)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__tl])])). 4.05/4.31 cnf(c_0_9096, 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_5493])). 4.05/4.31 cnf(c_0_9097, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|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_5549])). 4.05/4.31 fof(c_0_9098, plain, ![X3639, X3640, X3641]:(~hBOOL(hAPP(hAPP(c_member(X3641),X3640),X3639))|hAPP(hAPP(c_Set_Oinsert(X3641),X3640),X3639)=X3639), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])])). 4.05/4.31 fof(c_0_9099, plain, ![X16397, X16398]:(~class_Orderings_Obot(X16398)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16398),c_Orderings_Obot__class_Obot(X16398)),X16397))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__least])])). 4.05/4.31 fof(c_0_9100, plain, ![X1268, X1269]:(~class_Orderings_Otop(X1269)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1269),X1268),c_Orderings_Otop__class_Otop(X1269)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_top__greatest])])])). 4.05/4.31 fof(c_0_9101, plain, ![X16901, X16902, X16903]:((~hBOOL(hAPP(X16901,X16903))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X16902),X16901))|~class_Enum_Oenum(X16902))&(~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X16902),X16901))|hBOOL(hAPP(X16901,esk506_2(X16901,X16902)))|~class_Enum_Oenum(X16902))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exists__code])])])])])). 4.05/4.31 fof(c_0_9102, plain, ![X12599, X12600, X12602]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X12600),X12599))|hBOOL(hAPP(X12599,esk386_2(X12599,X12600)))|~class_Enum_Oenum(X12600))&(~hBOOL(hAPP(X12599,X12602))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X12600),X12599))|~class_Enum_Oenum(X12600))), 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__ex])])])])])])). 4.05/4.31 fof(c_0_9103, plain, ![X11460, X11461, X11462]:((~c_List_Olist__ex(X11462,X11461,X11460)|c_List_Olist__ex(X11462,X11461,hAPP(c_List_Orev(X11462),X11460)))&(~c_List_Olist__ex(X11462,X11461,hAPP(c_List_Orev(X11462),X11460))|c_List_Olist__ex(X11462,X11461,X11460))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__rev])])). 4.05/4.31 fof(c_0_9104, plain, ![X10381, X10382, X10383]:((~c_List_Olist__all(X10383,X10382,X10381)|c_List_Olist__all(X10383,X10382,hAPP(c_List_Orev(X10383),X10381)))&(~c_List_Olist__all(X10383,X10382,hAPP(c_List_Orev(X10383),X10381))|c_List_Olist__all(X10383,X10382,X10381))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__rev])])). 4.05/4.31 fof(c_0_9105, plain, ![X17574, X17575, X17576, X17577, X17578, X17579]:(~c_Fun_Oinj__on(X17579,X17578,hAPP(c_Fun_Ocomp(X17577,X17578,X17579,X17576),X17575),X17574)|c_Fun_Oinj__on(X17579,X17577,X17575,X17574)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inj__on__imageI2])])])). 4.05/4.31 cnf(c_0_9106, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),X1))|X1!=X2|~class_Orderings_Oorder(X3)), inference(split_conjunct,[status(thm)],[c_0_5254])). 4.05/4.31 cnf(c_0_9107, 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_5584])). 4.05/4.31 fof(c_0_9108, plain, ![X5355, X5356, X5357, X5358, X5359]:(((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X5358|X5358!=X5356|c_List_Oreplicate(X5359,X5356,X5355)=c_List_Oreplicate(X5359,X5358,X5357))&(X5355!=X5357|X5358!=X5356|c_List_Oreplicate(X5359,X5356,X5355)=c_List_Oreplicate(X5359,X5358,X5357)))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X5358|X5355=X5357|c_List_Oreplicate(X5359,X5356,X5355)!=c_List_Oreplicate(X5359,X5358,X5357))&(X5358=X5356|c_List_Oreplicate(X5359,X5356,X5355)!=c_List_Oreplicate(X5359,X5358,X5357)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_replicate__eq__replicate])])])])). 4.05/4.31 fof(c_0_9109, plain, ![X6795]:(X6795=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6795),X6795)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zdiv__self])])])). 4.05/4.31 cnf(c_0_9110, 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_4719])). 4.05/4.31 fof(c_0_9111, plain, ![X8079, X8080, X8082, X8083, X8084]:((c_Option_Ooption_ONone(X8079)=X8080|X8080=hAPP(c_Option_Ooption_OSome(X8079),esk256_2(X8079,X8080)))&(X8083!=hAPP(c_Option_Ooption_OSome(X8082),X8084)|c_Option_Ooption_ONone(X8082)!=X8083)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_not__None__eq])])])])])). 4.05/4.31 fof(c_0_9112, plain, ![X416, X417, X418, X419, X420]:((X417!=c_Option_Ooption_ONone(X416)|hAPP(c_Option_Ooption_OSome(X416),X418)!=X417)&(hAPP(c_Option_Ooption_OSome(X419),esk4_2(X419,X420))=X420|X420=c_Option_Ooption_ONone(X419))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_not__Some__eq])])])])])). 4.05/4.31 fof(c_0_9113, plain, ![X2073, X2074]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2074)),X2073))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2074),X2073))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Suc__lessD])])])). 4.05/4.31 fof(c_0_9114, plain, ![X7007, X7008, X7009]:(~class_Orderings_Olinorder(X7009)|c_List_Olinorder__class_Osort__key(X7008,X7009,X7007,c_List_Olist_ONil(X7008))=c_List_Olist_ONil(X7008)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__key__simps_I1_J])])). 4.05/4.31 fof(c_0_9115, plain, ![X1899, X1900]:(~class_Rings_Olinordered__ring(X1900)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1900),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1900),X1899),X1899)),c_Groups_Ozero__class_Ozero(X1900)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__square__less__zero])])])). 4.05/4.31 fof(c_0_9116, plain, ![X9358, X9359, X9360, X9361, X9362]:((X9359!=X9361|X9360!=X9358|hAPP(hAPP(c_List_Olist_OCons(X9362),X9361),X9360)=hAPP(hAPP(c_List_Olist_OCons(X9362),X9359),X9358))&((X9359=X9361|hAPP(hAPP(c_List_Olist_OCons(X9362),X9361),X9360)!=hAPP(hAPP(c_List_Olist_OCons(X9362),X9359),X9358))&(X9360=X9358|hAPP(hAPP(c_List_Olist_OCons(X9362),X9361),X9360)!=hAPP(hAPP(c_List_Olist_OCons(X9362),X9359),X9358)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list_Oinject])])])). 4.05/4.31 cnf(c_0_9117, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,esk254_2(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_5493])). 4.05/4.31 fof(c_0_9118, plain, ![X852, X853, X854, X855]:((hAPP(hAPP(c_List_Oappend(X855),X852),X853)!=hAPP(hAPP(c_List_Oappend(X855),X854),X853)|X854=X852)&(X854!=X852|hAPP(hAPP(c_List_Oappend(X855),X852),X853)=hAPP(hAPP(c_List_Oappend(X855),X854),X853))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__same__eq])])). 4.05/4.31 fof(c_0_9119, plain, ![X1997, X1998, X1999, X2000]:((hAPP(hAPP(c_List_Oappend(X2000),X1999),X1998)!=hAPP(hAPP(c_List_Oappend(X2000),X1999),X1997)|X1997=X1998)&(X1997!=X1998|hAPP(hAPP(c_List_Oappend(X2000),X1999),X1998)=hAPP(hAPP(c_List_Oappend(X2000),X1999),X1997))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__append__eq])])). 4.05/4.31 fof(c_0_9120, plain, ![X4454, X4455, X4456, X4457]:(~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4457,tc_HOL_Obool)),X4456),X4455),X4454))|hBOOL(hAPP(X4456,X4454))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D1])])). 4.05/4.31 fof(c_0_9121, plain, ![X8532, X8533]:((~c_Wellfounded_Oacyclic(X8533,hAPP(c_Relation_Oconverse(X8533,X8533),X8532))|c_Wellfounded_Oacyclic(X8533,X8532))&(~c_Wellfounded_Oacyclic(X8533,X8532)|c_Wellfounded_Oacyclic(X8533,hAPP(c_Relation_Oconverse(X8533,X8533),X8532)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__converse])])). 4.05/4.31 fof(c_0_9122, plain, ![X514, X515, X516, X517]:(~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X517,tc_HOL_Obool)),X516),X515),X514))|hBOOL(hAPP(X515,X514))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D2])])). 4.05/4.31 fof(c_0_9123, plain, ![X4401, X4402, X4403, X4404, X4405]:((hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4405,X4404),X4403),X4402),X4401)!=X4403|hAPP(X4403,X4402)=X4401)&(hAPP(X4403,X4402)!=X4401|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4405,X4404),X4403),X4402),X4401)=X4403)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff])])). 4.05/4.31 fof(c_0_9124, plain, ![X7126, X7127, X7128, X7129, X7130, X7131]:(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7131,X7130,X7129,X7128,X7127),X7126))|hBOOL(hAPP(c_Finite__Set_Ofinite(X7131),X7127))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph__imp__finite])])). 4.05/4.31 fof(c_0_9125, plain, ![X15307, X15308, X15309]:(~class_Rings_Osemiring__1(X15309)|X15307=c_Nat_Osemiring__1__class_Oof__nat__aux(X15309,X15308,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15307)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I1_J])])). 4.05/4.31 fof(c_0_9126, plain, ![X12384, X12385, X12386, X12387]:(~c_Finite__Set_Ofolding__one__idem(X12387,X12386,X12385)|hAPP(hAPP(X12386,X12384),X12384)=X12384), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oidem])])). 4.05/4.31 fof(c_0_9127, plain, ![X17130, X17131]:(~class_Orderings_Olinorder(X17131)|(~c_List_Olinorder__class_Osorted(X17131,X17130)|c_List_Olinorder__class_Osorted(X17131,hAPP(c_List_Otl(X17131),X17130)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__tl])])])). 4.05/4.31 fof(c_0_9128, plain, ![X17400, X17401, X17402]:((~hBOOL(hAPP(c_Finite__Set_Ofinite(X17402),X17400))|hBOOL(hAPP(c_Finite__Set_Ofinite(X17402),hAPP(hAPP(c_Set_Oinsert(X17402),X17401),X17400))))&(~hBOOL(hAPP(c_Finite__Set_Ofinite(X17402),hAPP(hAPP(c_Set_Oinsert(X17402),X17401),X17400)))|hBOOL(hAPP(c_Finite__Set_Ofinite(X17402),X17400)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])])). 4.05/4.31 fof(c_0_9129, plain, ![X9043, X9044, X9045]:(((c_Orderings_Otop__class_Otop(X9045)=X9043|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9045),X9044),X9043)!=c_Orderings_Otop__class_Otop(X9045)|~class_Lattices_Obounded__lattice__top(X9045))&(c_Orderings_Otop__class_Otop(X9045)=X9044|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9045),X9044),X9043)!=c_Orderings_Otop__class_Otop(X9045)|~class_Lattices_Obounded__lattice__top(X9045)))&(c_Orderings_Otop__class_Otop(X9045)!=X9043|c_Orderings_Otop__class_Otop(X9045)!=X9044|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X9045),X9044),X9043)=c_Orderings_Otop__class_Otop(X9045)|~class_Lattices_Obounded__lattice__top(X9045))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__eq__top__iff])])])])). 4.05/4.31 fof(c_0_9130, plain, ![X1740, X1741]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1741),X1740))|X1741=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1741,X1740)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less])])). 4.05/4.31 fof(c_0_9131, plain, ![X7314]:(~class_Int_Onumber__ring(X7314)|hAPP(c_Int_Onumber__class_Onumber__of(X7314),c_Int_OMin)=hAPP(c_Groups_Ouminus__class_Ouminus(X7314),c_Groups_Oone__class_Oone(X7314))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Min])])). 4.05/4.31 fof(c_0_9132, plain, ![X3749, X3750, X3751]:(~c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X3751)),X3750,X3749)|c_Natural_Oevalc(c_Com_Ocom_OBODY(X3751),X3750,X3749)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_OBody])])). 4.05/4.31 fof(c_0_9133, plain, ![X7890, X7891, X7892, X7893, X7894]:(~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7894,X7893,X7892,X7891,c_Orderings_Obot__class_Obot(tc_fun(X7894,tc_HOL_Obool))),X7890))|X7890=X7891), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__fold__graphE])])). 4.05/4.31 fof(c_0_9134, plain, ![X7523, X7524, X7525]:(~c_Wellfounded_Owf(X7525,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7525,X7525),tc_HOL_Obool),X7524),X7523))|c_Wellfounded_Owf(X7525,X7523)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__exp])])). 4.05/4.31 fof(c_0_9135, plain, ![X17194, X17195]:(~class_Rings_Olinordered__idom(X17195)|c_Groups_Osgn__class_Osgn(X17195,c_Groups_Osgn__class_Osgn(X17195,X17194))=c_Groups_Osgn__class_Osgn(X17195,X17194)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__sgn])])). 4.05/4.31 cnf(c_0_9136, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X1))=X1), inference(split_conjunct,[status(thm)],[c_0_5585])). 4.05/4.31 fof(c_0_9137, plain, ![X13144, X13145, X13146]:((hAPP(c_Int_Onumber__class_Onumber__of(X13146),X13145)!=hAPP(c_Int_Onumber__class_Onumber__of(X13146),X13144)|X13144=X13145|(~class_Int_Onumber__ring(X13146)|~class_Int_Oring__char__0(X13146)))&(X13144!=X13145|hAPP(c_Int_Onumber__class_Onumber__of(X13146),X13145)=hAPP(c_Int_Onumber__class_Onumber__of(X13146),X13144)|(~class_Int_Onumber__ring(X13146)|~class_Int_Oring__char__0(X13146)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__number__of])])])])). 4.05/4.31 fof(c_0_9138, plain, ![X14913, X14914]:(~class_Divides_Osemiring__div(X14914)|c_Groups_Ozero__class_Ozero(X14914)=c_Divides_Odiv__class_Omod(X14914,c_Groups_Ozero__class_Ozero(X14914),X14913)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__0])])])). 4.05/4.31 fof(c_0_9139, plain, ![X9717, X9718]:(~class_Divides_Osemiring__div(X9718)|c_Groups_Ozero__class_Ozero(X9718)=c_Divides_Odiv__class_Omod(X9718,X9717,c_Groups_Oone__class_Oone(X9718))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__1])])). 4.05/4.31 cnf(c_0_9140, plain, (hBOOL(hAPP(X2,X3))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1|~hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5288])). 4.05/4.31 fof(c_0_9141, plain, ![X10779, X10780, X10781]:(~class_Orderings_Olinorder(X10781)|(~c_List_Olinorder__class_Osorted(X10781,X10780)|c_List_Olinorder__class_Osorted(X10781,c_List_Oremove1(X10781,X10779,X10780)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__remove1])])])). 4.05/4.31 fof(c_0_9142, plain, ![X15174, X15175, X15176]:(~class_Orderings_Olinorder(X15176)|(~c_List_Olinorder__class_Osorted(X15176,X15175)|c_List_Olinorder__class_Osorted(X15176,c_List_OtakeWhile(X15176,X15174,X15175)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__takeWhile])])])). 4.05/4.31 cnf(c_0_9143, 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_5586])). 4.05/4.31 fof(c_0_9144, plain, ![X4172, X4173, X4174, X4175, X4176]:((~c_Wellfounded_OwfP(X4173,X4172)|hBOOL(hAPP(c_Wellfounded_Oaccp(X4173,X4172),X4174)))&(~hBOOL(hAPP(c_Wellfounded_Oaccp(X4176,X4175),esk129_2(X4175,X4176)))|c_Wellfounded_OwfP(X4176,X4175))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__accp__iff])])])])])). 4.05/4.31 fof(c_0_9145, plain, ![X4425, X4426, X4427, X4428, X4429, X4430, X4431]:((X4426!=X4425|hAPP(X4429,X4425)=hAPP(X4429,X4426)|~c_Typedef_Otype__definition(X4431,X4430,X4429,X4428,X4427))&(hAPP(X4429,X4425)!=hAPP(X4429,X4426)|X4426=X4425|~c_Typedef_Otype__definition(X4431,X4430,X4429,X4428,X4427))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_type__definition_ORep__inject])])])])). 4.05/4.31 fof(c_0_9146, plain, ![X2723, X2724]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2724),X2723))|c_List_Oupto(X2723,X2724)=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])])])). 4.05/4.31 cnf(c_0_9147, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk331_1(X1))))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5573])). 4.05/4.31 fof(c_0_9148, plain, ![X15541, X15542, X15543]:((c_Orderings_Obot__class_Obot(X15543)!=X15541|X15542!=c_Orderings_Obot__class_Obot(X15543)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15543),X15542),X15541)=c_Orderings_Obot__class_Obot(X15543)|~class_Lattices_Obounded__lattice__bot(X15543))&((c_Orderings_Obot__class_Obot(X15543)=X15541|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15543),X15542),X15541)!=c_Orderings_Obot__class_Obot(X15543)|~class_Lattices_Obounded__lattice__bot(X15543))&(X15542=c_Orderings_Obot__class_Obot(X15543)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X15543),X15542),X15541)!=c_Orderings_Obot__class_Obot(X15543)|~class_Lattices_Obounded__lattice__bot(X15543)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sup__eq__bot__iff])])])])). 4.05/4.31 fof(c_0_9149, plain, ![X5392, X5393, X5394]:(~class_Rings_Oring__1__no__zero__divisors(X5394)|(c_Groups_Ozero__class_Ozero(X5394)=X5393|c_Groups_Ozero__class_Ozero(X5394)!=hAPP(hAPP(c_Power_Opower__class_Opower(X5394),X5393),X5392))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_field__power__not__zero])])])). 4.05/4.31 cnf(c_0_9150, 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_5587])). 4.05/4.31 fof(c_0_9151, plain, ![X13328, X13329, X13330, X13331, X13332]:(~c_Map_Omap__le(X13332,X13331,c_Map_Omap__add(X13332,X13331,X13330,X13329),X13328)|c_Map_Omap__le(X13332,X13331,X13329,X13328)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__add__le__mapE])])). 4.05/4.31 cnf(c_0_9152, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk157_1(X1))))), inference(split_conjunct,[status(thm)],[c_0_5572])). 4.05/4.31 fof(c_0_9153, plain, ![X14585, X14586]:(~c_Wellfounded_Owf(X14586,X14585)|c_Wellfounded_Owf(tc_List_Olist(X14586),c_List_Olenlex(X14586,X14585))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__lenlex])])])). 4.05/4.31 fof(c_0_9154, plain, ![X5370, X5371]:(~c_Wellfounded_Owf(X5371,X5370)|c_Wellfounded_Owf(tc_List_Olist(X5371),c_List_Olex(X5371,X5370))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__lex])])])). 4.05/4.31 fof(c_0_9155, plain, ![X3730, X3731]:(~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X3731,X3731)),X3730))|(~c_Wellfounded_Oacyclic(X3731,X3730)|c_Wellfounded_Owf(X3731,X3730))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite__acyclic__wf])])])). 4.05/4.31 cnf(c_0_9156, 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_5565])). 4.05/4.31 fof(c_0_9157, plain, ![X422, X423]:(~class_Lattices_Osemilattice__inf(X423)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X423),X422),X422)=X422), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_inf__idem])])])). 4.05/4.31 fof(c_0_9158, plain, ![X15604, X15605]:(~class_Rings_Olinordered__semidom(X15605)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X15605),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X15605),X15604)),c_Groups_Ozero__class_Ozero(X15605)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__less__0__iff])])])). 4.05/4.31 fof(c_0_9159, plain, ![X10688, X10689]:(~class_Groups_Oordered__ab__group__add__abs(X10689)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10689),hAPP(c_Groups_Oabs__class_Oabs(X10689),X10688)),c_Groups_Ozero__class_Ozero(X10689)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__not__less__zero])])])). 4.05/4.31 fof(c_0_9160, plain, ![X807, X808]:(~class_Lattices_Olattice(X808)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X808),X807),X807)=X807), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oidem])])])). 4.05/4.31 fof(c_0_9161, plain, ![X2237, X2238]:(~class_Lattices_Osemilattice__sup(X2238)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2238),X2237),X2237)=X2237), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__idem])])). 4.05/4.31 fof(c_0_9162, plain, ![X9085, X9086]:(~class_Lattices_Oab__semigroup__idem__mult(X9086)|X9085=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9086),X9085),X9085)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times_Oidem])])). 4.05/4.31 fof(c_0_9163, plain, ![X9621, X9622]:(~class_Lattices_Olattice(X9622)|X9621=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X9622),X9621),X9621)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oidem])])). 4.05/4.31 fof(c_0_9164, plain, ![X2635, X2636]:(~class_Divides_Osemiring__div(X2636)|c_Divides_Odiv__class_Omod(X2636,X2635,c_Groups_Ozero__class_Ozero(X2636))=X2635), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__0])])). 4.05/4.31 fof(c_0_9165, plain, ![X5926, X5927, X5928]:((hAPP(c_Int_Oring__1__class_Oof__int(X5928),X5926)!=hAPP(c_Int_Oring__1__class_Oof__int(X5928),X5927)|X5927=X5926|~class_Int_Oring__char__0(X5928))&(X5927!=X5926|hAPP(c_Int_Oring__1__class_Oof__int(X5928),X5926)=hAPP(c_Int_Oring__1__class_Oof__int(X5928),X5927)|~class_Int_Oring__char__0(X5928))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__eq__iff])])])])). 4.05/4.31 fof(c_0_9166, plain, ![X9742, X9743, X9744]:((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9744),X9743),X9742))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9744),X9742),X9743))|~class_Orderings_Olinorder(X9744))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9744),X9742),X9743))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X9744),X9743),X9742))|~class_Orderings_Olinorder(X9744))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_linorder__not__le])])])])). 4.05/4.31 fof(c_0_9167, plain, ![X16845, X16846, X16847]:((X16845!=X16846|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16847),X16845)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16847),X16846)|~class_Nat_Osemiring__char__0(X16847))&(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16847),X16845)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16847),X16846)|X16845=X16846|~class_Nat_Osemiring__char__0(X16847))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__eq__iff])])])])). 4.05/4.31 fof(c_0_9168, plain, ![X1826, X1827, X1828]:((X1827!=X1826|hAPP(c_Groups_Ouminus__class_Ouminus(X1828),X1826)=hAPP(c_Groups_Ouminus__class_Ouminus(X1828),X1827)|~class_Lattices_Oboolean__algebra(X1828))&(hAPP(c_Groups_Ouminus__class_Ouminus(X1828),X1826)!=hAPP(c_Groups_Ouminus__class_Ouminus(X1828),X1827)|X1827=X1826|~class_Lattices_Oboolean__algebra(X1828))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff])])])). 4.05/4.31 fof(c_0_9169, plain, ![X3128, X3129, X3130]:((X3128!=X3129|hAPP(c_Groups_Ouminus__class_Ouminus(X3130),X3128)=hAPP(c_Groups_Ouminus__class_Ouminus(X3130),X3129)|~class_Groups_Ogroup__add(X3130))&(hAPP(c_Groups_Ouminus__class_Ouminus(X3130),X3128)!=hAPP(c_Groups_Ouminus__class_Ouminus(X3130),X3129)|X3128=X3129|~class_Groups_Ogroup__add(X3130))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal])])])). 4.05/4.31 fof(c_0_9170, plain, ![X7753, X7754]:(~c_Nat__Transfer_Ois__nat(X7754)|c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X7754),X7753))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J])])). 4.05/4.31 fof(c_0_9171, plain, ![X10683]:(~class_Groups_Ogroup__add(X10683)|hAPP(c_Groups_Ouminus__class_Ouminus(X10683),c_Groups_Ozero__class_Ozero(X10683))=c_Groups_Ozero__class_Ozero(X10683)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_minus__zero])])])). 4.05/4.31 fof(c_0_9172, plain, ![X9381, X9382, X9384, X9385, X9386]:((~hBOOL(hAPP(X9382,c_Hilbert__Choice_OEps(X9381,X9382)))|hBOOL(hAPP(X9382,esk288_2(X9381,X9382))))&(~hBOOL(hAPP(X9385,X9386))|hBOOL(hAPP(X9385,c_Hilbert__Choice_OEps(X9384,X9385))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_some__eq__ex])])])])])). 4.05/4.31 fof(c_0_9173, plain, ![X501, X503, X504]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X501))|X501=hAPP(c_Nat_OSuc,esk8_1(X501)))&(X503!=hAPP(c_Nat_OSuc,X504)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X503)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc])])])])])). 4.05/4.31 cnf(c_0_9174, 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_5588])). 4.05/4.31 fof(c_0_9175, plain, ![X1922, X1923]:(~class_Groups_Oordered__ab__group__add(X1923)|c_Fun_Oinj__on(X1923,X1923,c_Groups_Ouminus__class_Ouminus(X1923),X1922)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__uminus])])). 4.05/4.31 fof(c_0_9176, plain, ![X14963, X14964]:(hAPP(X14964,esk448_2(X14963,X14964))!=hAPP(X14963,esk448_2(X14963,X14964))|X14963=X14964), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])). 4.05/4.31 fof(c_0_9177, plain, ![X5635]:(~class_Lattices_Oboolean__algebra(X5635)|c_Orderings_Otop__class_Otop(X5635)=hAPP(c_Groups_Ouminus__class_Ouminus(X5635),c_Orderings_Obot__class_Obot(X5635))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_compl__bot__eq])])])). 4.05/4.31 fof(c_0_9178, plain, ![X10232, X10233]:(~class_Int_Onumber__ring(X10233)|hAPP(c_Int_Oring__1__class_Oof__int(X10233),X10232)=hAPP(c_Int_Onumber__class_Onumber__of(X10233),X10232)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__eq])])). 4.05/4.31 fof(c_0_9179, plain, ![X17427, X17428]:(~c_Wellfounded_Owf(X17428,X17427)|c_Wellfounded_OwfP(X17428,c_FunDef_Oin__rel(X17428,X17428,X17427))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__in__rel])])])). 4.05/4.31 fof(c_0_9180, plain, ![X11063, X11064, X11066]:((~hBOOL(hAPP(X11063,esk336_2(X11063,X11064)))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X11064),X11063))|~class_Enum_Oenum(X11064))&(~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X11064),X11063))|hBOOL(hAPP(X11063,X11066))|~class_Enum_Oenum(X11064))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_enum__all])])])])])])). 4.05/4.31 fof(c_0_9181, plain, ![X1611, X1612, X1613]:((~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1612),X1611))|hBOOL(hAPP(X1611,X1613))|~class_Enum_Oenum(X1612))&(~hBOOL(hAPP(X1611,esk52_2(X1611,X1612)))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1612),X1611))|~class_Enum_Oenum(X1612))), 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])])])])])])). 4.05/4.31 fof(c_0_9182, plain, ![X16610, X16611, X16612]:(~c_Wellfounded_Owf(X16612,X16611)|c_Wellfounded_Owf(X16612,c_Wellfounded_Omlex__prod(X16612,X16610,X16611))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__mlex])])])). 4.05/4.31 fof(c_0_9183, plain, ![X2564, X2565]:(~c_Nat__Transfer_Ois__nat(X2565)|(~c_Nat__Transfer_Ois__nat(X2564)|c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X2565,X2564)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I2_J])])])). 4.05/4.31 fof(c_0_9184, plain, ![X9449]:(~class_Lattices_Oboolean__algebra(X9449)|c_Orderings_Obot__class_Obot(X9449)=hAPP(c_Groups_Ouminus__class_Ouminus(X9449),c_Orderings_Otop__class_Otop(X9449))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__top__eq])])). 4.05/4.31 cnf(c_0_9185, 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_5589])). 4.05/4.31 cnf(c_0_9186, 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),X1)))), inference(split_conjunct,[status(thm)],[c_0_5590])). 4.05/4.31 fof(c_0_9187, plain, ![X14293]:(~class_Groups_Omonoid__add(X14293)|c_Groups_Ozero__class_Ozero(X14293)=hAPP(c_List_Omonoid__add__class_Olistsum(X14293),c_List_Olist_ONil(X14293))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__simps_I1_J])])). 4.05/4.31 fof(c_0_9188, plain, ![X11768]:((hBOOL(hAPP(c_Nat__Numeral_Oneg,X11768))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11768)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11768))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X11768)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__neg__eq__ge__0])])])). 4.05/4.31 fof(c_0_9189, plain, ![X3577, X3578, X3579, X3580]:((hAPP(hAPP(c_Option_Omap(X3580,X3579),X3578),X3577)!=c_Option_Ooption_ONone(X3579)|c_Option_Ooption_ONone(X3580)=X3577)&(c_Option_Ooption_ONone(X3580)!=X3577|hAPP(hAPP(c_Option_Omap(X3580,X3579),X3578),X3577)=c_Option_Ooption_ONone(X3579))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option__map__is__None])])). 4.05/4.31 fof(c_0_9190, plain, ![X9301, X9302, X9303, X9304]:((c_List_Olist_ONil(X9304)!=X9303|hAPP(hAPP(c_List_Olist__update(X9304,X9303),X9302),X9301)=c_List_Olist_ONil(X9304))&(hAPP(hAPP(c_List_Olist__update(X9304,X9303),X9302),X9301)!=c_List_Olist_ONil(X9304)|c_List_Olist_ONil(X9304)=X9303)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__nonempty])])). 4.05/4.31 fof(c_0_9191, plain, ![X10833]:(~class_Groups_Oordered__ab__group__add__abs(X10833)|c_Groups_Ozero__class_Ozero(X10833)=hAPP(c_Groups_Oabs__class_Oabs(X10833),c_Groups_Ozero__class_Ozero(X10833))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zero])])). 4.05/4.31 fof(c_0_9192, plain, ![X9305, X9306, X9307, X9308]:((X9305!=c_List_Olist_ONil(X9307)|c_List_Olist_ONil(X9308)=hAPP(hAPP(c_List_Omap(X9307,X9308),X9306),X9305))&(c_List_Olist_ONil(X9308)!=hAPP(hAPP(c_List_Omap(X9307,X9308),X9306),X9305)|X9305=c_List_Olist_ONil(X9307))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__map__conv])])). 4.05/4.31 fof(c_0_9193, plain, ![X7475, X7476, X7477]:((X7475!=X7476|hAPP(c_SetInterval_Oord__class_OgreaterThan(X7477),X7475)=hAPP(c_SetInterval_Oord__class_OgreaterThan(X7477),X7476)|~class_Orderings_Olinorder(X7477))&(hAPP(c_SetInterval_Oord__class_OgreaterThan(X7477),X7475)!=hAPP(c_SetInterval_Oord__class_OgreaterThan(X7477),X7476)|X7475=X7476|~class_Orderings_Olinorder(X7477))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_greaterThan__eq__iff])])])])). 4.05/4.31 fof(c_0_9194, plain, ![X9834]:(~class_Rings_Olinordered__idom(X9834)|c_Groups_Oone__class_Oone(X9834)=hAPP(c_Groups_Oabs__class_Oabs(X9834),c_Groups_Oone__class_Oone(X9834))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__one])])])). 4.05/4.31 fof(c_0_9195, plain, ![X4501, X4502]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4502),X4501))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4502),X4501))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__imp__le__nat])])])). 4.05/4.31 fof(c_0_9196, plain, ![X15631, X15632, X15633]:((hAPP(c_SetInterval_Oord__class_OlessThan(X15633),X15632)!=hAPP(c_SetInterval_Oord__class_OlessThan(X15633),X15631)|X15631=X15632|~class_Orderings_Olinorder(X15633))&(X15631!=X15632|hAPP(c_SetInterval_Oord__class_OlessThan(X15633),X15632)=hAPP(c_SetInterval_Oord__class_OlessThan(X15633),X15631)|~class_Orderings_Olinorder(X15633))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lessThan__eq__iff])])])])). 4.05/4.31 fof(c_0_9197, plain, ![X12907, X12908, X12909]:((X12908!=X12907|hAPP(c_SetInterval_Oord__class_OatMost(X12909),X12908)=hAPP(c_SetInterval_Oord__class_OatMost(X12909),X12907)|~class_Orderings_Olinorder(X12909))&(hAPP(c_SetInterval_Oord__class_OatMost(X12909),X12908)!=hAPP(c_SetInterval_Oord__class_OatMost(X12909),X12907)|X12908=X12907|~class_Orderings_Olinorder(X12909))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_atMost__eq__iff])])])])). 4.05/4.31 fof(c_0_9198, plain, ![X5909, X5910, X5911]:((X5909!=X5910|hAPP(c_SetInterval_Oord__class_OatLeast(X5911),X5909)=hAPP(c_SetInterval_Oord__class_OatLeast(X5911),X5910)|~class_Orderings_Olinorder(X5911))&(hAPP(c_SetInterval_Oord__class_OatLeast(X5911),X5909)!=hAPP(c_SetInterval_Oord__class_OatLeast(X5911),X5910)|X5909=X5910|~class_Orderings_Olinorder(X5911))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__eq__iff])])])). 4.05/4.31 fof(c_0_9199, plain, ![X9862, X9863]:(~class_Orderings_Olinorder(X9863)|(~c_List_Olinorder__class_Osorted(X9863,X9862)|c_List_Olinorder__class_Osorted(X9863,c_List_Oremdups(X9863,X9862)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted__remdups])])])). 4.05/4.31 fof(c_0_9200, plain, ![X396]:(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X396),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,X396)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nat__le__0])])])). 4.05/4.31 fof(c_0_9201, plain, ![X5424, X5425]:(~class_Orderings_Olinorder(X5425)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X5425),X5424),X5424)=X5424), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oidem])])). 4.05/4.31 fof(c_0_9202, plain, ![X13396, X13397]:(~class_Orderings_Olinorder(X13397)|X13396=hAPP(hAPP(c_Orderings_Oord__class_Omin(X13397),X13396),X13396)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oidem])])). 4.05/4.31 fof(c_0_9203, plain, ![X17393, X17394, X17395]:((X17394!=X17393|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17395),X17394),X17393)=c_Groups_Ozero__class_Ozero(X17395)|~class_Groups_Ogroup__add(X17395))&(hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17395),X17394),X17393)!=c_Groups_Ozero__class_Ozero(X17395)|X17394=X17393|~class_Groups_Ogroup__add(X17395))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])])). 4.05/4.31 cnf(c_0_9204, 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_5591])). 4.05/4.31 fof(c_0_9205, plain, ![X2343, X2344, X2345]:(~hBOOL(hAPP(X2344,X2345))|hBOOL(hAPP(X2344,c_Hilbert__Choice_OEps(X2343,X2344)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_someI__ex])])])])). 4.05/4.31 fof(c_0_9206, plain, ![X16726, X16727]:(~class_Divides_Osemiring__div(X16727)|c_Groups_Ozero__class_Ozero(X16727)=c_Divides_Odiv__class_Omod(X16727,X16726,X16726)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_mod__self])])])). 4.05/4.31 fof(c_0_9207, plain, ![X3625, X3626, X3627, X3628, X3629, X3630]:((X3628!=X3626|X3625!=X3627|c_Nitpick_Opair__box_OPairBox(X3630,X3629,X3626,X3625)=c_Nitpick_Opair__box_OPairBox(X3630,X3629,X3628,X3627))&((X3628=X3626|c_Nitpick_Opair__box_OPairBox(X3630,X3629,X3626,X3625)!=c_Nitpick_Opair__box_OPairBox(X3630,X3629,X3628,X3627))&(X3625=X3627|c_Nitpick_Opair__box_OPairBox(X3630,X3629,X3626,X3625)!=c_Nitpick_Opair__box_OPairBox(X3630,X3629,X3628,X3627)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__box_Oinject])])])). 4.05/4.31 fof(c_0_9208, plain, ![X7518, X7519]:(~class_HOL_Oequal(X7519)|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X7519),X7518),X7518))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__refl])])). 4.05/4.31 fof(c_0_9209, plain, ![X16658, X16659]:(~class_Orderings_Opreorder(X16659)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16659),X16658),X16658))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])])). 4.05/4.31 fof(c_0_9210, plain, ![X15366, X15367, X15368]:(((X15367=c_List_Olist_ONil(X15368)|c_List_Olist_ONil(X15368)!=hAPP(hAPP(c_List_Oappend(X15368),X15367),X15366))&(X15366=c_List_Olist_ONil(X15368)|c_List_Olist_ONil(X15368)!=hAPP(hAPP(c_List_Oappend(X15368),X15367),X15366)))&(X15367!=c_List_Olist_ONil(X15368)|X15366!=c_List_Olist_ONil(X15368)|c_List_Olist_ONil(X15368)=hAPP(hAPP(c_List_Oappend(X15368),X15367),X15366))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__is__Nil__conv])])])). 4.05/4.31 fof(c_0_9211, plain, ![X11108, X11109]:((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X11108|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X11109|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11109),X11108)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&((c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X11108|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11109),X11108)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X11109|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11109),X11108)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__0])])])). 4.05/4.31 fof(c_0_9212, plain, ![X3385, X3386]:((c_Groups_Ozero__class_Ozero(X3386)!=X3385|c_Groups_Ozero__class_Ozero(X3386)=hAPP(c_Groups_Ouminus__class_Ouminus(X3386),X3385)|~class_Groups_Ogroup__add(X3386))&(c_Groups_Ozero__class_Ozero(X3386)!=hAPP(c_Groups_Ouminus__class_Ouminus(X3386),X3385)|c_Groups_Ozero__class_Ozero(X3386)=X3385|~class_Groups_Ogroup__add(X3386))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal])])])). 4.05/4.31 fof(c_0_9213, plain, ![X2828, X2829]:((X2828!=c_Groups_Ozero__class_Ozero(X2829)|c_Groups_Ozero__class_Ozero(X2829)=hAPP(c_Groups_Oabs__class_Oabs(X2829),X2828)|~class_Groups_Oordered__ab__group__add__abs(X2829))&(c_Groups_Ozero__class_Ozero(X2829)!=hAPP(c_Groups_Oabs__class_Oabs(X2829),X2828)|X2828=c_Groups_Ozero__class_Ozero(X2829)|~class_Groups_Oordered__ab__group__add__abs(X2829))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_abs__eq__0])])])])). 4.05/4.31 fof(c_0_9214, plain, ![X16274, X16275, X16276, X16277]:(~c_Map_Omap__le(X16277,X16276,X16275,X16274)|(~c_Map_Omap__le(X16277,X16276,X16274,X16275)|X16275=X16274)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_map__le__antisym])])])). 4.05/4.31 cnf(c_0_9215, plain, (X2=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5592])). 4.05/4.31 fof(c_0_9216, plain, ![X16480, X16481]:((X16481!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=X16480|c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16481),X16480))&((X16481=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),X16481),X16480))&(c_Groups_Oone__class_Oone(tc_Nat_Onat)=X16480|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16481),X16480)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff])])])). 4.05/4.31 fof(c_0_9217, plain, ![X5079, X5080]:((c_Groups_Oone__class_Oone(tc_Nat_Onat)!=X5080|X5079!=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),X5080),X5079))&((c_Groups_Oone__class_Oone(tc_Nat_Onat)=X5080|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5080),X5079))&(X5079=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),X5080),X5079)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])])). 4.05/4.31 fof(c_0_9218, plain, ![X13969, X13970]:(~c_Nat__Transfer_Ois__nat(X13970)|c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X13970,X13969))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__function__closures])])])). 4.05/4.31 fof(c_0_9219, plain, ![X6367, X6368, X6369]:((~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X6369),X6368),X6367))|X6367=X6368|~class_HOL_Oequal(X6369))&(X6367!=X6368|hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X6369),X6368),X6367))|~class_HOL_Oequal(X6369))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__eq])])])). 4.05/4.31 fof(c_0_9220, plain, ![X1725]:(~class_Rings_Olinordered__semidom(X1725)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1725),c_Groups_Oone__class_Oone(X1725)),c_Groups_Ozero__class_Ozero(X1725)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__one__less__zero])])])). 4.05/4.31 cnf(c_0_9221, plain, (c_Groups_Osgn__class_Osgn(X2,X1)=c_Groups_Ozero__class_Ozero(X2)|X1!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)), inference(split_conjunct,[status(thm)],[c_0_5593])). 4.05/4.31 fof(c_0_9222, plain, ![X13228, X13229, X13230]:(((hBOOL(hAPP(c_Com_OWT,X13228))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X13230,X13229,X13228))))&(hBOOL(hAPP(c_Com_OWT,X13229))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X13230,X13229,X13228)))))&(~hBOOL(hAPP(c_Com_OWT,X13228))|~hBOOL(hAPP(c_Com_OWT,X13229))|hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X13230,X13229,X13228))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I5_J])])])). 4.05/4.31 fof(c_0_9223, plain, ![X2450]:((~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2450),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|X2450=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(X2450!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2450),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__0__eq])])). 4.05/4.31 fof(c_0_9224, plain, ![X16907]:(~class_Rings_Olinordered__semidom(X16907)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X16907),c_Groups_Oone__class_Oone(X16907)),c_Groups_Ozero__class_Ozero(X16907)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__one__le__zero])])])). 4.05/4.31 fof(c_0_9225, plain, ![X6637, X6638, X6639, X6640]:(~c_Natural_Oevalc(X6640,X6639,X6638)|(~c_Natural_Oevalc(X6640,X6639,X6637)|X6637=X6638)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_com__det])])])). 4.05/4.31 fof(c_0_9226, plain, ![X11150, X11151, X11152]:((X11151!=X11150|hAPP(c_List_Orev(X11152),X11150)=hAPP(c_List_Orev(X11152),X11151))&(hAPP(c_List_Orev(X11152),X11150)!=hAPP(c_List_Orev(X11152),X11151)|X11151=X11150)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__is__rev__conv])])). 4.05/4.31 fof(c_0_9227, plain, ![X9837, X9838, X9839]:((X9837!=X9838|hAPP(c_Option_Ooption_OSome(X9839),X9837)=hAPP(c_Option_Ooption_OSome(X9839),X9838))&(hAPP(c_Option_Ooption_OSome(X9839),X9837)!=hAPP(c_Option_Ooption_OSome(X9839),X9838)|X9837=X9838)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_option_Oinject])])). 4.05/4.31 fof(c_0_9228, plain, ![X2456, X2457]:((X2456!=c_List_Olist_ONil(X2457)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2457)),X2456))&(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2457)),X2456)|X2456=c_List_Olist_ONil(X2457))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__0__conv])])). 4.05/4.31 fof(c_0_9229, plain, ![X1497, X1498]:((hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1497)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1498)|X1498=X1497)&(X1498!=X1497|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1497)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1498))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I1_J])])). 4.05/4.31 fof(c_0_9230, plain, ![X11139, X11140, X11141]:((~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X11140)))|hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X11141,X11140,X11139))))&(~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X11141,X11140,X11139)))|hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X11140))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I8_J])])). 4.05/4.31 fof(c_0_9231, plain, ![X1539, X1540, X1541]:(~c_Predicate_Oreflp(X1541,X1540)|hBOOL(hAPP(hAPP(X1540,X1539),X1539))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_reflpE])])])). 4.05/4.31 fof(c_0_9232, plain, ![X10570, X10571]:((X10570!=c_List_Olist_ONil(X10571)|hAPP(c_List_Oset(X10571),X10570)=c_Orderings_Obot__class_Obot(tc_fun(X10571,tc_HOL_Obool)))&(hAPP(c_List_Oset(X10571),X10570)!=c_Orderings_Obot__class_Obot(tc_fun(X10571,tc_HOL_Obool))|X10570=c_List_Olist_ONil(X10571))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty2])])). 4.05/4.31 fof(c_0_9233, plain, ![X6893, X6894, X6895]:(~c_Equiv__Relations_Oequivp(X6895,X6894)|hBOOL(hAPP(hAPP(X6894,X6893),X6893))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_equivp__reflp])])])). 4.05/4.31 fof(c_0_9234, plain, ![X2984, X2985, X2986]:((~hBOOL(hAPP(X2984,X2985))|hBOOL(hAPP(hAPP(c_member(X2986),X2985),X2984)))&(~hBOOL(hAPP(hAPP(c_member(X2986),X2985),X2984))|hBOOL(hAPP(X2984,X2985)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])])). 4.05/4.31 fof(c_0_9235, plain, ![X9617, X9618, X9619, X9620]:((~c_List_Olist__all2(X9620,X9619,X9618,c_List_Olist_ONil(X9620),X9617)|c_List_Olist_ONil(X9619)=X9617)&(c_List_Olist_ONil(X9619)!=X9617|c_List_Olist__all2(X9620,X9619,X9618,c_List_Olist_ONil(X9620),X9617))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Nil])])). 4.05/4.31 fof(c_0_9236, plain, ![X16852]:(~class_Groups_Oab__semigroup__mult(X16852)|c_Finite__Set_Ofun__left__comm(X16852,X16852,c_Groups_Otimes__class_Otimes(X16852))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm])])])). 4.05/4.31 fof(c_0_9237, plain, ![X861]:(~class_Orderings_Olinorder(X861)|c_Finite__Set_Ofun__left__comm__idem(X861,X861,c_Orderings_Oord__class_Omin(X861))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ofun__left__comm__idem__inf])])])). 4.05/4.31 fof(c_0_9238, plain, ![X8757]:(~class_Lattices_Osemilattice__inf(X8757)|c_Finite__Set_Ofun__left__comm__idem(X8757,X8757,c_Lattices_Osemilattice__inf__class_Oinf(X8757))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__inf])])). 4.05/4.31 fof(c_0_9239, plain, ![X4591]:(~class_Lattices_Oab__semigroup__idem__mult(X4591)|c_Finite__Set_Ofun__left__comm__idem(X4591,X4591,c_Groups_Otimes__class_Otimes(X4591))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem])])). 4.05/4.31 fof(c_0_9240, plain, ![X13014]:(~class_Orderings_Olinorder(X13014)|c_Finite__Set_Ofun__left__comm__idem(X13014,X13014,c_Orderings_Oord__class_Omax(X13014))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_min__max_Ofun__left__comm__idem__sup])])])). 4.05/4.31 fof(c_0_9241, plain, ![X3948]:(~class_Lattices_Osemilattice__sup(X3948)|c_Finite__Set_Ofun__left__comm__idem(X3948,X3948,c_Lattices_Osemilattice__sup__class_Osup(X3948))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_fun__left__comm__idem__sup])])])). 4.05/4.31 fof(c_0_9242, plain, ![X8422]:(~class_Groups_Osgn__if(X8422)|c_Groups_Osgn__class_Osgn(X8422,c_Groups_Ozero__class_Ozero(X8422))=c_Groups_Ozero__class_Ozero(X8422)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn0])])). 4.05/4.31 fof(c_0_9243, plain, ![X3275, X3276, X3277, X3278, X3279, X3280]:((((X3275=X3278|c_Com_Ocom_OLocal(X3280,X3279,X3278)!=c_Com_Ocom_OLocal(X3277,X3276,X3275))&(X3279=X3276|c_Com_Ocom_OLocal(X3280,X3279,X3278)!=c_Com_Ocom_OLocal(X3277,X3276,X3275)))&(X3277=X3280|c_Com_Ocom_OLocal(X3280,X3279,X3278)!=c_Com_Ocom_OLocal(X3277,X3276,X3275)))&(X3275!=X3278|X3279!=X3276|X3277!=X3280|c_Com_Ocom_OLocal(X3280,X3279,X3278)=c_Com_Ocom_OLocal(X3277,X3276,X3275))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I2_J])])])). 4.05/4.31 fof(c_0_9244, plain, ![X1087, X1088, X1089, X1090, X1091]:(((X1087=X1089|c_Lazy__Sequence_Olazy__sequence_OInsert(X1091,X1088,X1087)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X1091,X1090,X1089))&(X1090=X1088|c_Lazy__Sequence_Olazy__sequence_OInsert(X1091,X1088,X1087)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X1091,X1090,X1089)))&(X1087!=X1089|X1090!=X1088|c_Lazy__Sequence_Olazy__sequence_OInsert(X1091,X1088,X1087)=c_Lazy__Sequence_Olazy__sequence_OInsert(X1091,X1090,X1089))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Oinject])])])). 4.05/4.31 fof(c_0_9245, plain, ![X397]:(~class_Orderings_Oord(X397)|c_Orderings_Oord_Omax(X397,c_Orderings_Oord__class_Oless__eq(X397))=c_Orderings_Oord__class_Omax(X397)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_max__ord__max])])])). 4.05/4.31 fof(c_0_9246, plain, ![X10837, X10838, X10839]:((X10837!=c_List_Olist_ONil(X10838)|hAPP(hAPP(c_List_Oappend(X10838),X10839),X10837)=X10839)&(hAPP(hAPP(c_List_Oappend(X10838),X10839),X10837)!=X10839|X10837=c_List_Olist_ONil(X10838))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv])])). 4.05/4.31 fof(c_0_9247, plain, ![X11303, X11304, X11305]:((X11303!=c_List_Olist_ONil(X11304)|X11305=hAPP(hAPP(c_List_Oappend(X11304),X11303),X11305))&(X11305!=hAPP(hAPP(c_List_Oappend(X11304),X11303),X11305)|X11303=c_List_Olist_ONil(X11304))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv2])])). 4.05/4.31 fof(c_0_9248, plain, ![X16912, X16913]:(X16913!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16913),X16912)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X16912), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_add__eq__self__zero])])])). 4.05/4.31 fof(c_0_9249, plain, ![X5694]:(~class_Enum_Oenum(X5694)|hBOOL(hAPP(c_List_Odistinct(X5694),c_Enum_Oenum__class_Oenum(X5694)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__distinct])])). 4.05/4.31 fof(c_0_9250, plain, ![X7101, X7102, X7103, X7104, X7105, X7106]:((X7103!=X7106|X7101!=X7104|X7102!=X7105|c_Com_Ocom_OCall(X7106,X7105,X7104)=c_Com_Ocom_OCall(X7103,X7102,X7101))&(((X7103=X7106|c_Com_Ocom_OCall(X7106,X7105,X7104)!=c_Com_Ocom_OCall(X7103,X7102,X7101))&(X7101=X7104|c_Com_Ocom_OCall(X7106,X7105,X7104)!=c_Com_Ocom_OCall(X7103,X7102,X7101)))&(X7102=X7105|c_Com_Ocom_OCall(X7106,X7105,X7104)!=c_Com_Ocom_OCall(X7103,X7102,X7101)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I7_J])])])). 4.05/4.31 fof(c_0_9251, plain, ![X3889]:(~class_Orderings_Oord(X3889)|c_Orderings_Oord__class_Omin(X3889)=c_Orderings_Oord_Omin(X3889,c_Orderings_Oord__class_Oless__eq(X3889))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ord__min])])). 4.05/4.31 fof(c_0_9252, plain, ![X6443, X6444, X6445, X6446, X6447, X6448]:((((X6447=X6444|c_Com_Ocom_OCond(X6445,X6444,X6443)!=c_Com_Ocom_OCond(X6448,X6447,X6446))&(X6443=X6446|c_Com_Ocom_OCond(X6445,X6444,X6443)!=c_Com_Ocom_OCond(X6448,X6447,X6446)))&(X6445=X6448|c_Com_Ocom_OCond(X6445,X6444,X6443)!=c_Com_Ocom_OCond(X6448,X6447,X6446)))&(X6447!=X6444|X6443!=X6446|X6445!=X6448|c_Com_Ocom_OCond(X6445,X6444,X6443)=c_Com_Ocom_OCond(X6448,X6447,X6446))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I4_J])])])). 4.05/4.31 fof(c_0_9253, plain, ![X17232, X17233]:(~hBOOL(hAPP(c_List_Odistinct(X17233),X17232))|X17232=c_List_Oremdups(X17233,X17232)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remdups__id])])). 4.05/4.31 fof(c_0_9254, plain, ![X2867]:((~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2867))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2867),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2867),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X2867)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__def])])). 4.05/4.31 fof(c_0_9255, plain, ![X7634]:(~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X7634)))|hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk244_1(X7634))=hAPP(c_Com_Obody,X7634)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I7_J])])])). 4.05/4.31 fof(c_0_9256, plain, ![X2736, X2738, X2739]:((~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X2736)))|hAPP(c_Com_Obody,X2736)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk94_1(X2736)))&(hAPP(c_Com_Obody,X2738)!=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X2739)|hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X2738))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I7_J])])])])])). 4.05/4.31 fof(c_0_9257, plain, ![X16368]:(~class_Rings_Osemiring__1(X16368)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16368),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(X16368)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__0])])])). 4.05/4.31 fof(c_0_9258, plain, ![X11375]:(~class_Rings_Oring__1(X11375)|c_Groups_Ozero__class_Ozero(X11375)=hAPP(c_Int_Oring__1__class_Oof__int(X11375),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__int__0])])])). 4.05/4.31 fof(c_0_9259, plain, ![X5647]:(~class_Rings_Oring__1(X5647)|c_Groups_Oone__class_Oone(X5647)=hAPP(c_Int_Oring__1__class_Oof__int(X5647),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__1])])). 4.05/4.31 fof(c_0_9260, plain, ![X16962]:(~class_Rings_Osemiring__1(X16962)|c_Groups_Oone__class_Oone(X16962)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X16962),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_of__nat__1])])])). 4.05/4.31 cnf(c_0_9261, 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_5594])). 4.05/4.31 cnf(c_0_9262, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|X2!=X3|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5595])). 4.05/4.31 fof(c_0_9263, plain, ![X13745, X13746]:(~class_Smallcheck_Osmall(X13745)|~class_Smallcheck_Osmall(X13746)|class_Smallcheck_Osmall(tc_prod(X13746,X13745))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Smallcheck_Osmall])])). 4.05/4.31 fof(c_0_9264, plain, ![X5812, X5813, X5814]:(~hBOOL(hAPP(c_Com_OWT,X5814))|hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X5813,X5812,X5814)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_WT_OLocal])])])). 4.05/4.31 fof(c_0_9265, plain, ![X15413]:((~c_Nat__Transfer_Ois__nat(X15413)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15413)))&(~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X15413))|c_Nat__Transfer_Ois__nat(X15413))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_is__nat__def])])). 4.05/4.31 fof(c_0_9266, plain, ![X6189]:((c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6189)|X6189=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(X6189!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6189))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__0__conv])])). 4.05/4.31 fof(c_0_9267, plain, ![X7376, X7377]:(~class_HOL_Oequal(X7376)|~class_Enum_Oenum(X7377)|class_HOL_Oequal(tc_fun(X7377,X7376))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__HOL_Oequal])])). 4.05/4.31 fof(c_0_9268, plain, ![X10282, X10283]:(~class_Finite__Set_Ofinite(X10282)|~class_Finite__Set_Ofinite(X10283)|class_Finite__Set_Ofinite(tc_sum(X10283,X10282))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_sum__Finite__Set_Ofinite])])])). 4.05/4.31 fof(c_0_9269, plain, ![X6999, X7000]:(~class_Finite__Set_Ofinite(X6999)|~class_Finite__Set_Ofinite(X7000)|class_Finite__Set_Ofinite(tc_prod(X7000,X6999))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite])])). 4.05/4.31 fof(c_0_9270, plain, ![X15243, X15244]:(~class_Finite__Set_Ofinite(X15243)|~class_Finite__Set_Ofinite(X15244)|class_Finite__Set_Ofinite(tc_fun(X15244,X15243))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Finite__Set_Ofinite])])])). 4.05/4.31 fof(c_0_9271, plain, ![X6793, X6794]:(~c_Nat__Transfer_Ois__nat(X6794)|(~c_Nat__Transfer_Ois__nat(X6793)|c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X6794,X6793)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J])])). 4.05/4.31 fof(c_0_9272, plain, ![X6951, X6952]:(~class_Lazy__Sequence_Osmall__lazy(X6952)|~class_Lazy__Sequence_Osmall__lazy(X6951)|class_Lazy__Sequence_Osmall__lazy(tc_prod(X6952,X6951))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_prod__Lazy__Sequence_Osmall__lazy])])])). 4.05/4.31 fof(c_0_9273, plain, ![X13102, X13103]:(~class_Enum_Oenum(X13102)|~class_Enum_Oenum(X13103)|class_Enum_Oenum(tc_sum(X13103,X13102))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_sum__Enum_Oenum])])])). 4.05/4.31 fof(c_0_9274, plain, ![X10562, X10563]:(~class_Enum_Oenum(X10562)|~class_Enum_Oenum(X10563)|class_Enum_Oenum(tc_prod(X10563,X10562))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_prod__Enum_Oenum])])])). 4.05/4.31 fof(c_0_9275, plain, ![X3079, X3080]:(~class_Enum_Oenum(X3079)|~class_Enum_Oenum(X3080)|class_Enum_Oenum(tc_fun(X3080,X3079))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Enum_Oenum])])). 4.05/4.31 fof(c_0_9276, plain, ![X5837, X5838, X5839, X5840, X5841]:(~class_Orderings_Olinorder(X5841)|c_List_Olist_ONil(X5840)!=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5840,X5841,X5839),X5838),X5837)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__not__Nil])])). 4.05/4.31 fof(c_0_9277, plain, ![X5538, X5539]:(~class_Finite__Set_Ofinite(X5539)|hBOOL(hAPP(c_Finite__Set_Ofinite(X5539),X5538))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_finite])])])). 4.05/4.31 fof(c_0_9278, plain, ![X4084, X4085, X4086]:((c_List_Olist_ONil(X4086)!=c_List_Oreplicate(X4086,X4085,X4084)|X4085=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&(X4085!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Olist_ONil(X4086)=c_List_Oreplicate(X4086,X4085,X4084))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_replicate__empty])])). 4.05/4.31 fof(c_0_9279, plain, ![X6693, X6694]:((c_Option_Oset(X6694,X6693)!=c_Orderings_Obot__class_Obot(tc_fun(X6694,tc_HOL_Obool))|X6693=c_Option_Ooption_ONone(X6694))&(X6693!=c_Option_Ooption_ONone(X6694)|c_Option_Oset(X6694,X6693)=c_Orderings_Obot__class_Obot(tc_fun(X6694,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty__eq])])). 4.05/4.31 fof(c_0_9280, plain, ![X6315, X6316]:((~hBOOL(hAPP(c_List_Odistinct(X6316),X6315))|c_List_Oremdups(X6316,X6315)=X6315)&(c_List_Oremdups(X6316,X6315)!=X6315|hBOOL(hAPP(c_List_Odistinct(X6316),X6315)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__id__iff__distinct])])). 4.05/4.31 fof(c_0_9281, plain, ![X2280, X2281]:(((hBOOL(hAPP(c_Com_OWT,X2280))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X2281,X2280))))&(hBOOL(hAPP(c_Com_OWT,X2281))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X2281,X2280)))))&(~hBOOL(hAPP(c_Com_OWT,X2280))|~hBOOL(hAPP(c_Com_OWT,X2281))|hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X2281,X2280))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I4_J])])])). 4.05/4.31 fof(c_0_9282, plain, ![X1412, X1413]:((c_List_Olist_ONil(X1413)!=hAPP(c_List_Orotate1(X1413),X1412)|c_List_Olist_ONil(X1413)=X1412)&(c_List_Olist_ONil(X1413)!=X1412|c_List_Olist_ONil(X1413)=hAPP(c_List_Orotate1(X1413),X1412))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__is__Nil__conv])])). 4.05/4.31 fof(c_0_9283, plain, ![X8044, X8045]:((c_List_Olist_ONil(X8045)!=X8044|c_List_Olist_ONil(X8045)=hAPP(c_List_Orev(X8045),X8044))&(c_List_Olist_ONil(X8045)!=hAPP(c_List_Orev(X8045),X8044)|c_List_Olist_ONil(X8045)=X8044)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__is__Nil__conv])])). 4.05/4.31 fof(c_0_9284, plain, ![X6826, X6827, X6828]:(~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X6828,X6827,X6826)))|hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X6827)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_WTs__elim__cases_I8_J])])])). 4.05/4.31 fof(c_0_9285, plain, ![X16699, X16700]:(~class_Lattices_Obounded__lattice(X16700)|class_Lattices_Obounded__lattice__bot(tc_fun(X16699,X16700))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Lattices_Obounded__lattice__bot])])])). 4.05/4.31 fof(c_0_9286, plain, ![X17265, X17266]:(~hBOOL(X17266)|~hBOOL(X17265)|hBOOL(hAPP(hAPP(c_fconj,X17266),X17265))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fconj__1])])). 4.05/4.31 fof(c_0_9287, plain, ![X16905, X16906]:(~class_Orderings_Obot(X16906)|class_Orderings_Obot(tc_fun(X16905,X16906))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Obot])])). 4.05/4.31 fof(c_0_9288, plain, ![X12162, X12163]:(~class_Lattices_Odistrib__lattice(X12163)|class_Lattices_Odistrib__lattice(tc_fun(X12162,X12163))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Lattices_Odistrib__lattice])])])). 4.05/4.31 fof(c_0_9289, plain, ![X11430, X11431]:(~class_Groups_Ouminus(X11431)|class_Groups_Ouminus(tc_fun(X11430,X11431))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus])])). 4.05/4.31 fof(c_0_9290, plain, ![X6857, X6858]:(~class_Lattices_Obounded__lattice(X6858)|class_Lattices_Obounded__lattice__top(tc_fun(X6857,X6858))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__top])])). 4.05/4.31 fof(c_0_9291, plain, ![X10413, X10414]:(~class_Lattices_Obounded__lattice(X10414)|class_Lattices_Obounded__lattice(tc_fun(X10413,X10414))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Lattices_Obounded__lattice])])])). 4.05/4.31 fof(c_0_9292, plain, ![X4468, X4469]:(~class_Groups_Ominus(X4469)|class_Groups_Ominus(tc_fun(X4468,X4469))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Groups_Ominus])])])). 4.05/4.31 fof(c_0_9293, plain, ![X7939, X7940]:(~class_Lattices_Oboolean__algebra(X7940)|class_Lattices_Oboolean__algebra(tc_fun(X7939,X7940))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra])])). 4.05/4.31 fof(c_0_9294, plain, ![X6957, X6958]:(~class_Orderings_Otop(X6958)|class_Orderings_Otop(tc_fun(X6957,X6958))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Orderings_Otop])])])). 4.05/4.31 fof(c_0_9295, plain, ![X5300, X5301]:(~class_Orderings_Opreorder(X5301)|class_Orderings_Opreorder(tc_fun(X5300,X5301))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Orderings_Opreorder])])])). 4.05/4.31 fof(c_0_9296, plain, ![X7600, X7601]:(~class_Orderings_Oorder(X7601)|class_Orderings_Oorder(tc_fun(X7600,X7601))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Orderings_Oorder])])])). 4.05/4.31 fof(c_0_9297, plain, ![X16402, X16403]:(~class_Complete__Lattice_Ocomplete__lattice(X16403)|class_Complete__Lattice_Ocomplete__lattice(tc_fun(X16402,X16403))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Complete__Lattice_Ocomplete__lattice])])])). 4.05/4.31 fof(c_0_9298, plain, ![X12799, X12800]:(~class_Lattices_Olattice(X12800)|class_Lattices_Osemilattice__inf(tc_fun(X12799,X12800))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Lattices_Osemilattice__inf])])])). 4.05/4.31 cnf(c_0_9299, 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_5596])). 4.05/4.31 fof(c_0_9300, plain, ![X6007, X6008]:(~class_Orderings_Oord(X6008)|class_Orderings_Oord(tc_fun(X6007,X6008))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Orderings_Oord])])])). 4.05/4.31 fof(c_0_9301, plain, ![X7898, X7899]:(~class_Lattices_Olattice(X7899)|class_Lattices_Osemilattice__sup(tc_fun(X7898,X7899))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__sup])])). 4.05/4.31 fof(c_0_9302, plain, ![X13290, X13291]:(~class_Lattices_Olattice(X13291)|class_Lattices_Olattice(tc_fun(X13290,X13291))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_fun__Lattices_Olattice])])])). 4.05/4.31 fof(c_0_9303, plain, ![X6763]:(~class_Orderings_Olinorder(X6763)|c_List_Olinorder__class_Osorted(X6763,c_List_Olist_ONil(X6763))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_sorted_ONil])])])). 4.05/4.31 fof(c_0_9304, plain, ![X11675, X11676]:(~class_Orderings_Opreorder(X11676)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X11676),X11675),X11675))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_order__less__irrefl])])])). 4.05/4.31 cnf(c_0_9305, plain, (c_Int_Oiszero(X1,X2)|c_Groups_Ozero__class_Ozero(X1)!=X2|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_5597])). 4.05/4.31 fof(c_0_9306, plain, ![X3285]:((~c_List_Onat__list(X3285)|c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X3285)))&(~c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X3285))|c_List_Onat__list(X3285))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__list__def])])). 4.05/4.31 fof(c_0_9307, plain, ![X4399, X4400]:(hBOOL(X4400)|hBOOL(hAPP(hAPP(c_fimplies,X4400),X4399))), inference(variable_rename,[status(thm)],[help_c__fimplies__1])). 4.05/4.31 fof(c_0_9308, plain, ![X5238, X5239]:((hAPP(c_Int_ORep__Integ,X5239)!=hAPP(c_Int_ORep__Integ,X5238)|X5239=X5238)&(X5239!=X5238|hAPP(c_Int_ORep__Integ,X5239)=hAPP(c_Int_ORep__Integ,X5238))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__inject])])). 4.05/4.31 fof(c_0_9309, plain, ![X4592, X4593, X4594, X4595]:(((X4592=X4594|c_Com_Ocom_OSemi(X4595,X4594)!=c_Com_Ocom_OSemi(X4593,X4592))&(X4595=X4593|c_Com_Ocom_OSemi(X4595,X4594)!=c_Com_Ocom_OSemi(X4593,X4592)))&(X4592!=X4594|X4595!=X4593|c_Com_Ocom_OSemi(X4595,X4594)=c_Com_Ocom_OSemi(X4593,X4592))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I3_J])])])). 4.05/4.31 fof(c_0_9310, plain, ![X13205, X13206, X13207, X13208]:((X13207!=X13205|X13206!=X13208|c_Com_Ocom_OWhile(X13206,X13205)=c_Com_Ocom_OWhile(X13208,X13207))&((X13207=X13205|c_Com_Ocom_OWhile(X13206,X13205)!=c_Com_Ocom_OWhile(X13208,X13207))&(X13206=X13208|c_Com_Ocom_OWhile(X13206,X13205)!=c_Com_Ocom_OWhile(X13208,X13207)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I5_J])])])). 4.05/4.31 fof(c_0_9311, plain, ![X1115, X1116]:((hAPP(c_Code__Numeral_Onat__of,X1115)!=hAPP(c_Code__Numeral_Onat__of,X1116)|X1116=X1115)&(X1116!=X1115|hAPP(c_Code__Numeral_Onat__of,X1115)=hAPP(c_Code__Numeral_Onat__of,X1116))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Onat__of__inject])])). 4.05/4.31 cnf(c_0_9312, plain, (X2=X1|hAPP(c_Code__Numeral_Oof__nat,X1)!=hAPP(c_Code__Numeral_Oof__nat,X2)), inference(split_conjunct,[status(thm)],[c_0_5598])). 4.05/4.31 fof(c_0_9313, plain, ![X8146, X8147]:((c_List_Olist_ONil(X8147)!=c_List_Oremdups(X8147,X8146)|X8146=c_List_Olist_ONil(X8147))&(X8146!=c_List_Olist_ONil(X8147)|c_List_Olist_ONil(X8147)=c_List_Oremdups(X8147,X8146))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__iff])])). 4.05/4.31 fof(c_0_9314, plain, ![X14299, X14300]:((X14299!=X14300|hAPP(c_Nat_OSuc,X14300)=hAPP(c_Nat_OSuc,X14299))&(hAPP(c_Nat_OSuc,X14300)!=hAPP(c_Nat_OSuc,X14299)|X14299=X14300)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])])). 4.05/4.31 fof(c_0_9315, plain, ![X8860, X8861]:(~hBOOL(hAPP(c_Com_OWT,X8861))|hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X8860,X8861)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_While])])). 4.05/4.31 fof(c_0_9316, plain, ![X6733]:(c_Option_Ooption_ONone(tc_Com_Ocom)=hAPP(c_Com_Obody,X6733)|hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X6733)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT_OBody])])). 4.05/4.31 fof(c_0_9317, plain, ![X17444, X17445]:(hBOOL(hAPP(hAPP(c_fdisj,X17445),X17444))|~hBOOL(X17445)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fdisj__1])])). 4.05/4.31 fof(c_0_9318, plain, ![X15344, X15345]:(~hBOOL(X15345)|hBOOL(hAPP(hAPP(c_fdisj,X15344),X15345))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fdisj__2])])). 4.05/4.31 fof(c_0_9319, plain, ![X3407, X3408]:(hBOOL(hAPP(hAPP(c_fimplies,X3407),X3408))|~hBOOL(X3408)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fimplies__2])])). 4.05/4.31 fof(c_0_9320, plain, ![X11896, X11897, X11898]:((hBOOL(hAPP(c_Com_OWT,X11897))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X11898,X11897,X11896))))&(hBOOL(hAPP(c_Com_OWT,X11896))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X11898,X11897,X11896))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_WTs__elim__cases_I5_J])])])])). 4.05/4.31 fof(c_0_9321, plain, ![X14506]:(~class_Orderings_Olinorder(X14506)|~class_Lattices_Osemilattice__inf(X14506)|c_Orderings_Oord__class_Omin(X14506)=c_Lattices_Osemilattice__inf__class_Oinf(X14506)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__min])])). 4.05/4.31 fof(c_0_9322, plain, ![X10126]:(~class_Lattices_Osemilattice__sup(X10126)|~class_Orderings_Olinorder(X10126)|c_Lattices_Osemilattice__sup__class_Osup(X10126)=c_Orderings_Oord__class_Omax(X10126)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__max])])). 4.05/4.31 fof(c_0_9323, plain, ![X5360, X5361, X5362]:(~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X5362,X5361,X5360)))|hBOOL(hAPP(c_Com_OWT,X5360))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I3_J])])). 4.05/4.31 fof(c_0_9324, plain, ![X6836]:(~class_Int_Onumber__ring(X6836)|~c_Int_Oiszero(X6836,hAPP(c_Int_Onumber__class_Onumber__of(X6836),c_Int_OMin))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_nonzero__number__of__Min])])])). 4.05/4.31 fof(c_0_9325, plain, ![X7269, X7270]:(hBOOL(X7269)|hBOOL(X7270)|~hBOOL(hAPP(hAPP(c_fdisj,X7270),X7269))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fdisj__3])])). 4.05/4.31 fof(c_0_9326, plain, ![X17715, X17716]:(~c_Wellfounded_Owf(X17716,X17715)|c_Wellfounded_Oacyclic(X17716,X17715)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_wf__acyclic])])])). 4.05/4.31 fof(c_0_9327, plain, ![X9835, X9836]:((~c_Option_Ois__none(X9836,X9835)|c_Option_Ooption_ONone(X9836)=X9835)&(c_Option_Ooption_ONone(X9836)!=X9835|c_Option_Ois__none(X9836,X9835))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_is__none__def])])). 4.05/4.31 fof(c_0_9328, plain, ![X2786]:(~class_Finite__Set_Ofinite(X2786)|class_Finite__Set_Ofinite(tc_Option_Ooption(X2786))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])])])). 4.05/4.31 cnf(c_0_9329, plain, (hBOOL(hAPP(c_Com_OWT,X2))|~c_Com_OWT__bodies|hAPP(c_Com_Obody,X1)!=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X2)), inference(split_conjunct,[status(thm)],[c_0_5599])). 4.05/4.31 fof(c_0_9330, plain, ![X7789]:(~class_Lazy__Sequence_Osmall__lazy(X7789)|class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X7789))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_List__Olist__Lazy__Sequence_Osmall__lazy])])). 4.05/4.31 fof(c_0_9331, plain, ![X9669]:(~class_Enum_Oenum(X9669)|class_Enum_Oenum(tc_Option_Ooption(X9669))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[arity_Option__Ooption__Enum_Oenum])])])). 4.05/4.31 fof(c_0_9332, plain, ![X9697, X9698]:(X9698=X9697|~hBOOL(hAPP(hAPP(c_fequal,X9698),X9697))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fequal__1])])). 4.05/4.31 fof(c_0_9333, plain, ![X16143, X16144]:(hBOOL(X16143)|~hBOOL(X16144)|~hBOOL(hAPP(hAPP(c_fimplies,X16144),X16143))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fimplies__3])])). 4.05/4.31 fof(c_0_9334, plain, ![X2721, X2722]:((X2722!=X2721|c_Com_Ocom_OBODY(X2722)=c_Com_Ocom_OBODY(X2721))&(c_Com_Ocom_OBODY(X2722)!=c_Com_Ocom_OBODY(X2721)|X2722=X2721)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I6_J])])). 4.05/4.31 fof(c_0_9335, plain, ![X1464, X1465]:(~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X1465,X1464)))|hBOOL(hAPP(c_Com_OWT,X1464))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I6_J])])). 4.05/4.31 fof(c_0_9336, plain, ![X11273]:(~class_HOL_Oequal(X11273)|c_fequal=c_HOL_Oequal__class_Oequal(X11273)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equal])])). 4.05/4.31 fof(c_0_9337, plain, ![X15191]:(hBOOL(hAPP(c_fNot,X15191))|hBOOL(X15191)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fNot__2])])). 4.05/4.31 fof(c_0_9338, plain, ![X10429, X10430]:(hBOOL(X10430)|~hBOOL(hAPP(hAPP(c_fconj,X10430),X10429))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fconj__2])])). 4.05/4.31 fof(c_0_9339, plain, ![X8863, X8864]:(~hBOOL(hAPP(hAPP(c_fconj,X8864),X8863))|hBOOL(X8863)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fconj__3])])). 4.05/4.31 fof(c_0_9340, plain, ![X720]:(~class_Rings_Osemiring__1(X720)|~c_Int_Oiszero(X720,c_Groups_Oone__class_Oone(X720))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__iszero__1])])])). 4.05/4.31 fof(c_0_9341, plain, ![X1659]:(~class_Rings_Ozero__neq__one(X1659)|c_Groups_Oone__class_Oone(X1659)!=c_Groups_Ozero__class_Ozero(X1659)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_zero__neq__one])])])). 4.05/4.31 fof(c_0_9342, plain, ![X14904]:(~hBOOL(hAPP(c_fNot,X14904))|~hBOOL(X14904)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fNot__1])])). 4.05/4.31 cnf(c_0_9343, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5600, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9344, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5601, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9345, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5602, c_0_4505]), c_0_4795]), c_0_4795])). 4.05/4.31 cnf(c_0_9346, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5603, c_0_4505]), c_0_4795])). 4.05/4.31 cnf(c_0_9347, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5604, c_0_4505]), c_0_4795])). 4.05/4.31 cnf(c_0_9348, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))!=c_Int_OMin), inference(rw,[status(thm)],[c_0_5605, c_0_4795])). 4.05/4.31 cnf(c_0_9349, 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_5606])). 4.05/4.31 cnf(c_0_9350, 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))|X2!=X3), inference(split_conjunct,[status(thm)],[c_0_5607])). 4.05/4.31 fof(c_0_9351, plain, ![X17491, X17492, X17493]:~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X17493),tc_List_Olist(X17493))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X17493),tc_List_Olist(X17493)),c_List_Olist_ONil(X17493)),X17492)),c_List_Olistrel1(X17493,X17491))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__Nil__listrel1])])). 4.05/4.31 fof(c_0_9352, plain, ![X1859, X1860, X1861]:~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1861),tc_List_Olist(X1861))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1861),tc_List_Olist(X1861)),c_List_Olist_ONil(X1861)),X1860)),c_List_Olex(X1861,X1859))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nil__notin__lex])])). 4.05/4.31 fof(c_0_9353, plain, ![X4504, X4505, X4506]:~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4506),tc_List_Olist(X4506))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4506),tc_List_Olist(X4506)),X4505),c_List_Olist_ONil(X4506))),c_List_Olistrel1(X4506,X4504))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__listrel1__Nil])])). 4.05/4.31 fof(c_0_9354, plain, ![X9270, X9271, X9272]:~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X9272),tc_List_Olist(X9272))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X9272),tc_List_Olist(X9272)),X9271),c_List_Olist_ONil(X9272))),c_List_Olex(X9272,X9270))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Nil2__notin__lex])])). 4.05/4.31 fof(c_0_9355, plain, ![X5921, X5922, X5923]:~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5923),tc_List_Olist(X5923))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5923),tc_List_Olist(X5923)),X5922),c_List_Olist_ONil(X5923))),c_List_Olexord(X5923,X5921))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_lexord__Nil__right])])). 4.05/4.31 fof(c_0_9356, plain, ![X13932, X13933, X13934]:~hBOOL(hAPP(hAPP(c_member(tc_prod(X13934,X13934)),hAPP(hAPP(c_Product__Type_OPair(X13934,X13934),X13933),X13932)),c_List_Omeasures(X13934,c_List_Olist_ONil(tc_fun(X13934,tc_Nat_Onat))))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_in__measures_I1_J])])). 4.05/4.31 cnf(c_0_9357, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)))), inference(rw,[status(thm)],[c_0_5608, c_0_4427])). 4.05/4.31 cnf(c_0_9358, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_5609, c_0_4427])). 4.05/4.31 cnf(c_0_9359, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_5610, c_0_4427])). 4.05/4.31 fof(c_0_9360, plain, ![X7387, X7388, X7389, X7390, X7391]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X7391,tc_Option_Ooption(X7390)),X7389),X7388),hAPP(c_Option_Ooption_OSome(X7390),X7387))!=hAPP(c_COMBK(tc_Option_Ooption(X7390),X7391),c_Option_Ooption_ONone(X7390)), inference(variable_rename,[status(thm)],[fact_map__upd__nonempty])). 4.05/4.31 fof(c_0_9361, plain, ![X11055]:~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,X11055))))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__zle__0__negative])])). 4.05/4.31 fof(c_0_9362, plain, ![X9194, X9195]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X9195)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X9194)))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__int__zless__negative])])). 4.05/4.31 cnf(c_0_9363, plain, (X1!=c_List_Olist_ONil(X2)|X1!=hAPP(hAPP(c_List_Oappend(X2),X3),hAPP(hAPP(c_List_Olist_OCons(X2),X4),c_List_Olist_ONil(X2)))), inference(split_conjunct,[status(thm)],[c_0_5477])). 4.05/4.31 cnf(c_0_9364, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X1))|X1!=hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5547])). 4.05/4.31 fof(c_0_9365, plain, ![X2023, X2024]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2024,tc_HOL_Obool)),X2023),c_Orderings_Obot__class_Obot(tc_fun(X2024,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__psubset__empty])])). 4.05/4.31 fof(c_0_9366, plain, ![X2627, X2628, X2629]:hAPP(c_Set_OPow(X2628),X2627)!=hAPP(c_Set_Oimage(X2628,tc_fun(X2628,tc_HOL_Obool),X2629),X2627), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cantors__paradox])])). 4.05/4.31 fof(c_0_9367, plain, ![X2541, X2542, X2543, X2544]:~hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2544,tc_fun(X2543,tc_HOL_Obool))),X2542),X2541)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_bot2E])])). 4.05/4.31 fof(c_0_9368, plain, ![X11911]:~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X11911)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X11911),tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__listI])])). 4.05/4.31 cnf(c_0_9369, 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_5563])). 4.05/4.31 cnf(c_0_9370, 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_4648])). 4.05/4.31 fof(c_0_9371, plain, ![X9007, X9008]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9008),X9007)),X9008)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__add__less1])])). 4.05/4.31 fof(c_0_9372, plain, ![X2198, X2199]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2199),X2198)),X2198)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__add__less2])])). 4.05/4.31 fof(c_0_9373, plain, ![X13999]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X13999)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_int__less__0__conv])])). 4.05/4.31 fof(c_0_9374, plain, ![X3382, X3383, X3384]:~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3384,X3383,c_Orderings_Obot__class_Obot(tc_fun(X3384,tc_HOL_Obool))),X3382)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_empty__fold1SetE])])). 4.05/4.31 fof(c_0_9375, plain, ~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))), inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__int])). 4.05/4.31 fof(c_0_9376, plain, ~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__nat])). 4.05/4.31 fof(c_0_9377, plain, ![X9998, X9999, X10000]:c_Orderings_Obot__class_Obot(tc_fun(X10000,tc_HOL_Obool))!=hAPP(hAPP(c_Set_Oinsert(X10000),X9999),X9998), inference(variable_rename,[status(thm)],[fact_insert__not__empty])). 4.05/4.31 cnf(c_0_9378, 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_5611])). 4.05/4.31 cnf(c_0_9379, plain, (X1!=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5612])). 4.05/4.31 fof(c_0_9380, plain, ![X4714, X4715]:c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4715,tc_HOL_Obool),tc_HOL_Obool))!=hAPP(c_Set_OPow(X4715),X4714), inference(variable_rename,[status(thm)],[fact_Pow__not__empty])). 4.05/4.31 fof(c_0_9381, plain, ![X10737, X10738, X10739, X10740, X10741, X10742]:c_Com_Ocom_OCall(X10742,X10741,X10740)!=c_Com_Ocom_OLocal(X10739,X10738,X10737), inference(variable_rename,[status(thm)],[fact_com_Osimps_I43_J])). 4.05/4.31 fof(c_0_9382, plain, ![X2230, X2231, X2232, X2233, X2234, X2235]:c_Com_Ocom_OCond(X2232,X2231,X2230)!=c_Com_Ocom_OLocal(X2235,X2234,X2233), inference(variable_rename,[status(thm)],[fact_com_Osimps_I36_J])). 4.05/4.31 fof(c_0_9383, plain, ![X15687, X15688, X15689, X15690, X15691, X15692]:c_Com_Ocom_OCond(X15689,X15688,X15687)!=c_Com_Ocom_OCall(X15692,X15691,X15690), inference(variable_rename,[status(thm)],[fact_com_Osimps_I57_J])). 4.05/4.31 fof(c_0_9384, plain, ![X9716]:c_Orderings_Otop__class_Otop(tc_fun(X9716,tc_HOL_Obool))!=c_Orderings_Obot__class_Obot(tc_fun(X9716,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_UNIV__not__empty])). 4.05/4.31 cnf(c_0_9385, 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_5613, c_0_5583])). 4.05/4.31 fof(c_0_9386, plain, ![X6888, X6889, X6890]:c_List_Olist_ONil(X6890)!=hAPP(hAPP(c_List_Olist_OCons(X6890),X6889),X6888), inference(variable_rename,[status(thm)],[fact_list_Osimps_I2_J])). 4.05/4.31 fof(c_0_9387, plain, ![X8092]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8092),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__less0])])). 4.05/4.31 fof(c_0_9388, plain, ![X645, X646, X647, X648, X649]:c_Com_Ocom_OCond(X649,X648,X647)!=c_Com_Ocom_OWhile(X646,X645), inference(variable_rename,[status(thm)],[fact_com_Osimps_I52_J])). 4.05/4.31 fof(c_0_9389, plain, ![X14233, X14234, X14235, X14236, X14237]:c_Com_Ocom_OSemi(X14234,X14233)!=c_Com_Ocom_OLocal(X14237,X14236,X14235), inference(variable_rename,[status(thm)],[fact_com_Osimps_I34_J])). 4.05/4.31 fof(c_0_9390, plain, ![X13320, X13321, X13322, X13323, X13324]:c_Com_Ocom_OSemi(X13321,X13320)!=c_Com_Ocom_OCall(X13324,X13323,X13322), inference(variable_rename,[status(thm)],[fact_com_Osimps_I51_J])). 4.05/4.31 fof(c_0_9391, plain, ![X4769, X4770, X4771, X4772, X4773]:c_Com_Ocom_OSemi(X4770,X4769)!=c_Com_Ocom_OCond(X4773,X4772,X4771), inference(variable_rename,[status(thm)],[fact_com_Osimps_I45_J])). 4.05/4.31 fof(c_0_9392, plain, ![X17118, X17119, X17120, X17121, X17122]:c_Com_Ocom_OWhile(X17122,X17121)!=c_Com_Ocom_OLocal(X17120,X17119,X17118), inference(variable_rename,[status(thm)],[fact_com_Osimps_I39_J])). 4.05/4.31 fof(c_0_9393, plain, ![X12786, X12787, X12788, X12789, X12790]:c_Com_Ocom_OWhile(X12790,X12789)!=c_Com_Ocom_OCall(X12788,X12787,X12786), inference(variable_rename,[status(thm)],[fact_com_Osimps_I60_J])). 4.05/4.31 fof(c_0_9394, plain, ![X14995, X14996, X14997]:X14997!=hAPP(hAPP(c_List_Olist_OCons(X14996),X14995),X14997), inference(variable_rename,[status(thm)],[fact_not__Cons__self])). 4.05/4.31 fof(c_0_9395, plain, ![X5965, X5966]:c_Option_Ooption_ONone(X5966)!=hAPP(c_Option_Ooption_OSome(X5966),X5965), inference(variable_rename,[status(thm)],[fact_option_Osimps_I2_J])). 4.05/4.31 fof(c_0_9396, plain, ![X5585, X5586, X5587, X5588]:c_Com_Ocom_OBODY(X5588)!=c_Com_Ocom_OLocal(X5587,X5586,X5585), inference(variable_rename,[status(thm)],[fact_com_Osimps_I41_J])). 4.05/4.31 fof(c_0_9397, plain, ![X825, X826, X827, X828]:c_Com_Ocom_OBODY(X828)!=c_Com_Ocom_OCall(X827,X826,X825), inference(variable_rename,[status(thm)],[fact_com_Osimps_I62_J])). 4.05/4.31 fof(c_0_9398, plain, ![X4250]:~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4250),X4250)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat])])). 4.05/4.31 fof(c_0_9399, plain, ![X16988, X16989, X16990, X16991]:c_Com_Ocom_OBODY(X16991)!=c_Com_Ocom_OCond(X16990,X16989,X16988), inference(variable_rename,[status(thm)],[fact_com_Osimps_I55_J])). 4.05/4.31 fof(c_0_9400, plain, ![X9130, X9131, X9132, X9133]:c_Com_Ocom_OWhile(X9133,X9132)!=c_Com_Ocom_OSemi(X9131,X9130), inference(variable_rename,[status(thm)],[fact_com_Osimps_I47_J])). 4.05/4.31 fof(c_0_9401, plain, ![X7111, X7112]:~c_Option_Ois__none(X7112,hAPP(c_Option_Ooption_OSome(X7112),X7111)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_is__none__code_I2_J])])). 4.05/4.31 fof(c_0_9402, plain, ![X13679]:~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X13679))), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_not__neg__int])])). 4.05/4.31 cnf(c_0_9403, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls))), inference(split_conjunct,[status(thm)],[c_0_5614])). 4.05/4.31 cnf(c_0_9404, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_5615])). 4.05/4.31 fof(c_0_9405, plain, ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)), inference(fof_simplification,[status(thm)],[fact_rel__simps_I7_J])). 4.05/4.31 fof(c_0_9406, plain, ![X8122, X8123, X8124]:c_Com_Ocom_OSemi(X8124,X8123)!=c_Com_Ocom_OBODY(X8122), inference(variable_rename,[status(thm)],[fact_com_Osimps_I48_J])). 4.05/4.31 fof(c_0_9407, plain, ![X7054, X7055, X7056]:c_Com_Ocom_OBODY(X7056)!=c_Com_Ocom_OWhile(X7055,X7054), inference(variable_rename,[status(thm)],[fact_com_Osimps_I59_J])). 4.05/4.31 cnf(c_0_9408, 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_5616])). 4.05/4.31 cnf(c_0_9409, 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_5617])). 4.05/4.31 fof(c_0_9410, plain, ~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(fof_simplification,[status(thm)],[fact_not__neg__0])). 4.05/4.31 fof(c_0_9411, plain, ~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(fof_simplification,[status(thm)],[fact_not__neg__1])). 4.05/4.31 fof(c_0_9412, plain, ![X3340]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X3340), inference(variable_rename,[status(thm)],[fact_Zero__not__Suc])). 4.05/4.31 fof(c_0_9413, plain, ![X13072, X13073]:~c_List_Olist__ex(X13073,X13072,c_List_Olist_ONil(X13073)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__ex__simps_I2_J])])). 4.05/4.31 fof(c_0_9414, plain, ![X2939, X2940]:~c_List_Olist__ex1(X2940,X2939,c_List_Olist_ONil(X2940)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_list__ex1__simps_I1_J])])). 4.05/4.31 cnf(c_0_9415, plain, (c_Int_OPls!=c_Int_OMin), inference(split_conjunct,[status(thm)],[fact_rel__simps_I37_J])). 4.05/4.31 fof(c_0_9416, plain, ![X6395]:X6395!=hAPP(c_Nat_OSuc,X6395), inference(variable_rename,[status(thm)],[fact_Suc__n__not__n])). 4.05/4.31 cnf(c_0_9417, plain, (~c_Hoare__Mirabelle_Ostate__not__singleton|esk274_1(X1)!=X1), inference(split_conjunct,[status(thm)],[c_0_5618])). 4.05/4.31 cnf(c_0_9418, hypothesis, (c_Hoare__Mirabelle_Ostate__not__singleton), inference(split_conjunct,[status(thm)],[conj_0]), ['final']). 4.05/4.31 cnf(c_0_9419, plain, (~c_Hoare__Mirabelle_Ostate__not__singleton|esk137_0!=esk136_0), inference(split_conjunct,[status(thm)],[c_0_5619])). 4.05/4.31 fof(c_0_9420, plain, ~hBOOL(c_fFalse), inference(fof_simplification,[status(thm)],[help_c__fFalse__1])). 4.05/4.31 fof(c_0_9421, negated_conjecture, ~hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)))), inference(fof_simplification,[status(thm)],[c_0_5620])). 4.05/4.31 cnf(c_0_9422, 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),c_Transitive__Closure_Ortrancl(X1,X2)),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),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))),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_5621, c_0_5018]), c_0_5018])). 4.05/4.31 cnf(c_0_9423, 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_5622, c_0_4519]), c_0_4519])). 4.05/4.31 fof(c_0_9424, plain, ![X16730, X16731, X16732, X16733, X16734, X16735]:hAPP(c_Set_Oimage(X16735,tc_prod(X16734,X16733),hAPP(hAPP(c_COMBS(X16735,X16733,tc_prod(X16734,X16733)),hAPP(hAPP(c_COMBB(X16734,tc_fun(X16733,tc_prod(X16734,X16733)),X16735),c_Product__Type_OPair(X16734,X16733)),X16732)),X16731)),X16730)=hAPP(hAPP(c_Product__Type_OSigma(X16734,X16733),hAPP(c_Set_Oimage(X16735,X16734,X16732),X16730)),hAPP(hAPP(c_COMBB(tc_fun(X16735,tc_HOL_Obool),tc_fun(X16733,tc_HOL_Obool),X16734),c_Set_Oimage(X16735,X16733,X16731)),hAPP(hAPP(c_COMBC(X16734,tc_fun(X16735,tc_HOL_Obool),tc_fun(X16735,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16735,tc_HOL_Obool),tc_fun(tc_fun(X16735,tc_HOL_Obool),tc_fun(X16735,tc_HOL_Obool)),X16734),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16735,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X16734,tc_HOL_Obool),tc_fun(X16735,tc_HOL_Obool),X16734),c_Set_Ovimage(X16735,X16734,X16732)),hAPP(hAPP(c_COMBC(X16734,tc_fun(X16734,tc_HOL_Obool),tc_fun(X16734,tc_HOL_Obool)),c_Set_Oinsert(X16734)),c_Orderings_Obot__class_Obot(tc_fun(X16734,tc_HOL_Obool)))))),X16730))), inference(variable_rename,[status(thm)],[fact_image__split__eq__Sigma])). 4.05/4.31 cnf(c_0_9425, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X3)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5623, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9426, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_5624])). 4.05/4.31 cnf(c_0_9427, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5625, c_0_4474]), c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9428, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),hAPP(c_Set_OCollect(X1),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X5)),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X4))))=c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),X1),c_If(tc_Option_Ooption(X2))),X4)),X3)),X5))), inference(split_conjunct,[status(thm)],[c_0_5626])). 4.05/4.31 cnf(c_0_9429, 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_5627])). 4.05/4.31 fof(c_0_9430, plain, ![X9275, X9276, X9277, X9278]:hAPP(hAPP(c_List_Omap(tc_prod(X9278,tc_Nat_Onat),X9278),c_Product__Type_Ofst(X9278,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X9278,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X9278,tc_Nat_Onat)),X9277),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X9278,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X9278,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X9278,tc_Nat_Onat),X9276),X9275)))=hAPP(hAPP(c_List_Omap(tc_prod(X9278,tc_Nat_Onat),X9278),c_Product__Type_Ofst(X9278,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X9278,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X9278,tc_Nat_Onat)),X9277),c_Product__Type_Osnd(X9278,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X9278,tc_Nat_Onat),X9276),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X9275)))), inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma__Suc])). 4.05/4.31 fof(c_0_9431, plain, ![X4011, X4012, X4013, X4014, X4015]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4015,tc_fun(X4014,tc_HOL_Obool)),X4013),hAPP(hAPP(c_COMBS(X4015,tc_fun(X4014,tc_HOL_Obool),tc_fun(X4014,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4014,tc_HOL_Obool),tc_fun(tc_fun(X4014,tc_HOL_Obool),tc_fun(X4014,tc_HOL_Obool)),X4015),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4014,tc_HOL_Obool))),X4012)),X4011))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4014,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4015,tc_fun(X4014,tc_HOL_Obool)),X4013),X4012)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4015,tc_fun(X4014,tc_HOL_Obool)),X4013),X4011)), inference(variable_rename,[status(thm)],[fact_INT__Int__distrib])). 4.05/4.31 fof(c_0_9432, plain, ![X13209, X13210, X13211, X13212, X13213, X13214, X13215, X13216, X13217]:hAPP(hAPP(c_Product__Type_Oscomp(X13217,X13213,X13212,X13214),X13211),hAPP(hAPP(c_COMBC(X13213,tc_fun(X13216,tc_fun(X13215,X13214)),tc_fun(X13212,X13214)),hAPP(hAPP(c_COMBB(tc_fun(X13212,tc_prod(X13216,X13215)),tc_fun(tc_fun(X13216,tc_fun(X13215,X13214)),tc_fun(X13212,X13214)),X13213),c_Product__Type_Oscomp(X13212,X13216,X13215,X13214)),X13210)),X13209))=hAPP(hAPP(c_Product__Type_Oscomp(X13217,X13216,X13215,X13214),hAPP(hAPP(c_Product__Type_Oscomp(X13217,X13213,X13212,tc_prod(X13216,X13215)),X13211),X13210)),X13209), inference(variable_rename,[status(thm)],[fact_scomp__scomp])). 4.05/4.31 fof(c_0_9433, plain, ![X453, X454, X455, X456, X457]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X457,tc_fun(X456,tc_HOL_Obool)),X455),hAPP(hAPP(c_COMBS(X457,tc_fun(X456,tc_HOL_Obool),tc_fun(X456,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X456,tc_HOL_Obool),tc_fun(tc_fun(X456,tc_HOL_Obool),tc_fun(X456,tc_HOL_Obool)),X457),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X456,tc_HOL_Obool))),X454)),X453))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X456,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X457,tc_fun(X456,tc_HOL_Obool)),X455),X454)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X457,tc_fun(X456,tc_HOL_Obool)),X455),X453)), inference(variable_rename,[status(thm)],[fact_UN__Un__distrib])). 4.05/4.31 fof(c_0_9434, plain, ![X4208, X4209, X4210, X4211, X4212]:hAPP(hAPP(c_Product__Type_OSigma(X4212,X4211),X4210),hAPP(hAPP(c_COMBS(X4212,tc_fun(X4211,tc_HOL_Obool),tc_fun(X4211,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4211,tc_HOL_Obool),tc_fun(tc_fun(X4211,tc_HOL_Obool),tc_fun(X4211,tc_HOL_Obool)),X4212),c_Groups_Ominus__class_Ominus(tc_fun(X4211,tc_HOL_Obool))),X4209)),X4208))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4212,X4211),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4212,X4211),X4210),X4209)),hAPP(hAPP(c_Product__Type_OSigma(X4212,X4211),X4210),X4208)), inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib2])). 4.05/4.31 fof(c_0_9435, plain, ![X16553, X16554, X16555, X16556, X16557]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X16557,X16556),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X16557,X16556),X16555),X16554)),hAPP(hAPP(c_Product__Type_OSigma(X16557,X16556),X16555),X16553))=hAPP(hAPP(c_Product__Type_OSigma(X16557,X16556),X16555),hAPP(hAPP(c_COMBS(X16557,tc_fun(X16556,tc_HOL_Obool),tc_fun(X16556,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X16556,tc_HOL_Obool),tc_fun(tc_fun(X16556,tc_HOL_Obool),tc_fun(X16556,tc_HOL_Obool)),X16557),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16556,tc_HOL_Obool))),X16554)),X16553)), inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib2])). 4.05/4.31 fof(c_0_9436, plain, ![X6199, X6200, X6201, X6202, X6203]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X6203,X6202),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X6203,X6202),X6201),X6200)),hAPP(hAPP(c_Product__Type_OSigma(X6203,X6202),X6201),X6199))=hAPP(hAPP(c_Product__Type_OSigma(X6203,X6202),X6201),hAPP(hAPP(c_COMBS(X6203,tc_fun(X6202,tc_HOL_Obool),tc_fun(X6202,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6202,tc_HOL_Obool),tc_fun(tc_fun(X6202,tc_HOL_Obool),tc_fun(X6202,tc_HOL_Obool)),X6203),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6202,tc_HOL_Obool))),X6200)),X6199)), inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib2])). 4.05/4.31 cnf(c_0_9437, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X3))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1)))), inference(split_conjunct,[status(thm)],[c_0_5628])). 4.05/4.31 cnf(c_0_9438, 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_5629, c_0_4742])). 4.05/4.31 cnf(c_0_9439, 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_5630, c_0_5130]), ['final']). 4.05/4.31 cnf(c_0_9440, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Osublist(X1,X2,X3))=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))))), inference(split_conjunct,[status(thm)],[c_0_5631])). 4.05/4.31 fof(c_0_9441, plain, ![X13762, X13763, X13764, X13765, X13766, X13767, X13768]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13766,tc_Option_Ooption(X13767)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X13768),tc_Option_Ooption(X13767),X13766,hAPP(c_Option_Omap(X13768,X13767),X13765)),X13764)),X13763),hAPP(c_Option_Ooption_OSome(X13767),hAPP(X13765,X13762)))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X13768),tc_Option_Ooption(X13767),X13766,hAPP(c_Option_Omap(X13768,X13767),X13765)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X13766,tc_Option_Ooption(X13768)),X13764),X13763),hAPP(c_Option_Ooption_OSome(X13768),X13762))), inference(variable_rename,[status(thm)],[fact_option__map__o__map__upd])). 4.05/4.31 cnf(c_0_9442, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Int_OMin)))),c_Int_OMin)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5632, c_0_4474]), c_0_4422]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9443, plain, (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(hAPP(c_Product__Type_OSigma(X2,X8),X5),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X2),X6))|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_5633])). 4.05/4.31 cnf(c_0_9444, 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_5634])). 4.05/4.31 cnf(c_0_9445, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5635, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9446, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5636, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9447, 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_5637])). 4.05/4.31 cnf(c_0_9448, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(X2,X3)),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(X4,tc_List_Olist(X1)),X2),X5)))=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(X4,tc_List_Olist(X1)),X2),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X5)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5638, c_0_5639]), c_0_5639]), c_0_4767]), c_0_4767])). 4.05/4.31 cnf(c_0_9449, 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)), inference(rw,[status(thm)],[c_0_5640, c_0_4767]), ['final']). 4.05/4.31 cnf(c_0_9450, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5641, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.31 cnf(c_0_9451, 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_5642])). 4.05/4.31 cnf(c_0_9452, 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_5643])). 4.05/4.31 cnf(c_0_9453, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5644, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9454, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5645, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9455, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Oconcat(X1,X4))=c_List_Oconcat(X2,hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X2)),hAPP(c_List_Omap(X1,X2),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_5646])). 4.05/4.31 fof(c_0_9456, plain, ![X8442, X8443, X8444, X8445]:c_Map_Orestrict__map(X8445,X8444,hAPP(c_Fun_Ocomp(X8444,tc_Option_Ooption(X8444),X8445,c_Option_Ooption_OSome(X8444)),X8443),hAPP(c_List_Oset(X8445),X8442))=hAPP(c_Map_Omap__of(X8445,X8444),hAPP(hAPP(c_List_Omap(X8445,tc_prod(X8445,X8444)),hAPP(hAPP(c_COMBS(X8445,X8444,tc_prod(X8445,X8444)),c_Product__Type_OPair(X8445,X8444)),X8443)),X8442)), inference(variable_rename,[status(thm)],[fact_map__of__map__restrict])). 4.05/4.31 cnf(c_0_9457, 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_5647])). 4.05/4.31 cnf(c_0_9458, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),c_Int_OMin)),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5648, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9459, 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_5649]), ['final']). 4.05/4.31 cnf(c_0_9460, plain, (hAPP(c_Product__Type_Oapsnd(X1,X2,X3,X4),hAPP(c_Product__Type_Oapfst(X5,X3,X1,X6),X7))=hAPP(hAPP(c_Product__Type_OPair(X3,X2),hAPP(X6,hAPP(c_Product__Type_Ofst(X5,X1),X7))),hAPP(X4,hAPP(c_Product__Type_Osnd(X5,X1),X7)))), inference(split_conjunct,[status(thm)],[c_0_5650])). 4.05/4.31 cnf(c_0_9461, plain, (hAPP(c_Product__Type_Oapfst(X1,X2,X3,X4),hAPP(c_Product__Type_Oapsnd(X5,X3,X1,X6),X7))=hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X5),X7))),hAPP(X6,hAPP(c_Product__Type_Osnd(X1,X5),X7)))), inference(split_conjunct,[status(thm)],[c_0_5651])). 4.05/4.31 fof(c_0_9462, plain, ![X1092, X1093, X1094, X1095, X1096, X1097, X1098]:hAPP(hAPP(c_List_Olist__update(tc_prod(X1098,X1097),hAPP(hAPP(c_List_Ozip(X1098,X1097),X1096),X1093)),X1095),hAPP(hAPP(c_Product__Type_OPair(X1098,X1097),X1094),X1092))=hAPP(hAPP(c_List_Ozip(X1098,X1097),hAPP(hAPP(c_List_Olist__update(X1098,X1096),X1095),X1094)),hAPP(hAPP(c_List_Olist__update(X1097,X1093),X1095),X1092)), inference(variable_rename,[status(thm)],[fact_zip__update])). 4.05/4.31 cnf(c_0_9463, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))=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)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5652, c_0_4474]), c_0_4434]), c_0_4475])). 4.05/4.31 cnf(c_0_9464, plain, (hAPP(c_Product__Type_Oapfst(X1,X2,X3,X4),hAPP(c_Product__Type_Oapsnd(X5,X3,X1,X6),X7))=hAPP(c_Product__Type_Oapsnd(X5,X3,X2,X6),hAPP(c_Product__Type_Oapfst(X1,X2,X5,X4),X7))), inference(split_conjunct,[status(thm)],[c_0_5653])). 4.05/4.31 cnf(c_0_9465, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),c_Int_OMin)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5654, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 fof(c_0_9466, plain, ![X12537, X12538, X12539, X12540, X12541, X12542, X12543, X12544, X12545, X12546, X12547]:hAPP(c_Product__Type_Omap__pair(X12547,X12546,X12545,X12544,X12543,X12542),hAPP(c_Product__Type_Omap__pair(X12541,X12547,X12540,X12545,X12539,X12538),X12537))=hAPP(c_Product__Type_Omap__pair(X12541,X12546,X12540,X12544,hAPP(c_Fun_Ocomp(X12547,X12546,X12541,X12543),X12539),hAPP(c_Fun_Ocomp(X12545,X12544,X12540,X12542),X12538)),X12537), inference(variable_rename,[status(thm)],[fact_map__pair_Ocompositionality])). 4.05/4.31 cnf(c_0_9467, 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_5655])). 4.05/4.31 cnf(c_0_9468, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))),c_Int_OMin)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5656, c_0_4474]), c_0_4422]), c_0_4422]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9469, 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_5657])). 4.05/4.31 cnf(c_0_9470, plain, (hAPP(c_Product__Type_Oapfst(X1,X2,X3,X4),hAPP(c_Product__Type_Oapfst(X5,X1,X3,X6),X7))=hAPP(c_Product__Type_Oapfst(X5,X2,X3,hAPP(c_Fun_Ocomp(X1,X2,X5,X4),X6)),X7)), inference(split_conjunct,[status(thm)],[c_0_5658])). 4.05/4.31 cnf(c_0_9471, plain, (hAPP(c_List_Orotate(X1,X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5))=hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(c_List_Orotate(X3,X2),X5))), inference(split_conjunct,[status(thm)],[c_0_5659])). 4.05/4.31 fof(c_0_9472, plain, ![X12561, X12562, X12563, X12564, X12565, X12566]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12566,tc_fun(X12565,tc_HOL_Obool)),X12564),hAPP(hAPP(c_COMBB(X12563,tc_fun(X12565,tc_HOL_Obool),X12566),X12562),X12561))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12563,tc_fun(X12565,tc_HOL_Obool)),hAPP(c_Set_Oimage(X12566,X12563,X12561),X12564)),X12562), inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I10_J])). 4.05/4.31 fof(c_0_9473, plain, ![X2061, X2062, X2063, X2064, X2065, X2066]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2066,tc_fun(X2065,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2064,X2066,X2063),X2062)),X2061)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2064,tc_fun(X2065,tc_HOL_Obool)),X2062),hAPP(hAPP(c_COMBB(X2066,tc_fun(X2065,tc_HOL_Obool),X2064),X2061),X2063)), inference(variable_rename,[status(thm)],[fact_INT__simps_I10_J])). 4.05/4.31 fof(c_0_9474, plain, ![X7289, X7290, X7291]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7290),X7291)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7289),X7291))=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)),X7291)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X7290),X7289)), inference(variable_rename,[status(thm)],[fact_image__add__atLeastLessThan])). 4.05/4.31 cnf(c_0_9475, plain, (c_Map_Odom(X3,X1,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X1)),X4),X5),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),c_Map_Odom(X3,X1,X4)),hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))|c_Option_Ooption_ONone(X1)!=X2), inference(split_conjunct,[status(thm)],[c_0_5660])). 4.05/4.31 fof(c_0_9476, plain, ![X11702, X11703, X11704, X11705, X11706, X11707]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11704,tc_fun(X11706,tc_HOL_Obool)),hAPP(c_Set_Oimage(X11707,X11704,X11702),X11705)),X11703)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11707,tc_fun(X11706,tc_HOL_Obool)),X11705),hAPP(c_Fun_Ocomp(X11704,tc_fun(X11706,tc_HOL_Obool),X11707,X11703),X11702)), inference(variable_rename,[status(thm)],[fact_UN__o])). 4.05/4.31 fof(c_0_9477, plain, ![X16284, X16285, X16286, X16287, X16288, X16289]:hAPP(hAPP(c_List_Olist_OCons(tc_prod(X16289,X16288)),hAPP(hAPP(c_Product__Type_OPair(X16289,X16288),X16287),X16285)),hAPP(hAPP(c_List_Ozip(X16289,X16288),X16286),X16284))=hAPP(hAPP(c_List_Ozip(X16289,X16288),hAPP(hAPP(c_List_Olist_OCons(X16289),X16287),X16286)),hAPP(hAPP(c_List_Olist_OCons(X16288),X16285),X16284)), inference(variable_rename,[status(thm)],[fact_zip__Cons__Cons])). 4.05/4.31 fof(c_0_9478, plain, ![X4716, X4717, X4718, X4719, X4720, X4721, X4722]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4720,X4721),hAPP(c_Fun_Ocomp(X4722,X4721,X4720,X4719),X4718)),X4717),hAPP(X4719,X4716))=hAPP(c_Fun_Ocomp(X4722,X4721,X4720,X4719),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4720,X4722),X4718),X4717),X4716)), inference(variable_rename,[status(thm)],[fact_fun__upd__comp])). 4.05/4.31 fof(c_0_9479, plain, ![X11258, X11259, X11260]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11259),X11260),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11258),X11260))=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)),X11260)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X11259,X11258)), inference(variable_rename,[status(thm)],[fact_image__add__atLeastAtMost])). 4.05/4.31 fof(c_0_9480, plain, ![X10121, X10122, X10123, X10124, X10125]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10124,tc_HOL_Obool)),hAPP(X10121,X10123)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10125,tc_fun(X10124,tc_HOL_Obool)),X10122),X10121))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10125,tc_fun(X10124,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10125),X10123),X10122)),X10121), inference(variable_rename,[status(thm)],[fact_INT__insert])). 4.05/4.31 fof(c_0_9481, plain, ![X13095, X13096, X13097, X13098, X13099, X13100, X13101]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X13101,X13100,X13099),hAPP(c_Fun_Ocomp(X13098,tc_fun(X13100,X13099),X13101,X13097),X13096)),X13095)=hAPP(hAPP(X13097,hAPP(X13096,hAPP(c_Product__Type_Ofst(X13101,X13100),X13095))),hAPP(c_Product__Type_Osnd(X13101,X13100),X13095)), inference(variable_rename,[status(thm)],[fact_split__comp])). 4.05/4.31 fof(c_0_9482, plain, ![X16117, X16118, X16119, X16120, X16121]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16121,tc_fun(X16120,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X16121),X16119),X16118)),X16117)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16120,tc_HOL_Obool)),hAPP(X16117,X16119)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X16121,tc_fun(X16120,tc_HOL_Obool)),X16118),X16117)), inference(variable_rename,[status(thm)],[fact_UN__insert])). 4.05/4.31 fof(c_0_9483, plain, ![X9474, X9475, X9476, X9477]:c_List_Otranspose(X9477,hAPP(hAPP(c_List_Omap(tc_List_Olist(X9476),tc_List_Olist(X9477)),hAPP(c_List_Omap(X9476,X9477),X9475)),X9474))=hAPP(hAPP(c_List_Omap(tc_List_Olist(X9476),tc_List_Olist(X9477)),hAPP(c_List_Omap(X9476,X9477),X9475)),c_List_Otranspose(X9476,X9474)), inference(variable_rename,[status(thm)],[fact_transpose__map__map])). 4.05/4.31 fof(c_0_9484, plain, ![X7276, X7277, X7278, X7279, X7280]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7278)),hAPP(c_List_Ofilter(X7278,hAPP(c_Fun_Ocomp(X7280,tc_HOL_Obool,X7278,X7279),X7277)),X7276))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7280)),hAPP(c_List_Ofilter(X7280,X7279),hAPP(hAPP(c_List_Omap(X7278,X7280),X7277),X7276))), inference(variable_rename,[status(thm)],[fact_length__filter__map])). 4.05/4.31 fof(c_0_9485, plain, ![X2907, X2908, X2909, X2910, X2911, X2912]:hAPP(c_Fun_Ocomp(tc_prod(X2912,X2911),X2912,tc_prod(X2910,X2909),c_Product__Type_Ofst(X2912,X2911)),c_Product__Type_Omap__pair(X2910,X2912,X2909,X2911,X2908,X2907))=hAPP(c_Fun_Ocomp(X2910,X2912,tc_prod(X2910,X2909),X2908),c_Product__Type_Ofst(X2910,X2909)), inference(variable_rename,[status(thm)],[fact_fst__comp__map__pair])). 4.05/4.31 fof(c_0_9486, plain, ![X6613, X6614, X6615, X6616, X6617, X6618]:hAPP(c_Fun_Ocomp(tc_prod(X6618,X6617),X6617,tc_prod(X6616,X6615),c_Product__Type_Osnd(X6618,X6617)),c_Product__Type_Omap__pair(X6616,X6618,X6615,X6617,X6614,X6613))=hAPP(c_Fun_Ocomp(X6615,X6617,tc_prod(X6616,X6615),X6613),c_Product__Type_Osnd(X6616,X6615)), inference(variable_rename,[status(thm)],[fact_snd__comp__map__pair])). 4.05/4.31 fof(c_0_9487, plain, ![X656, X657, X658, X659]:c_Map_Orestrict__map(X659,X658,X657,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X659,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X659),X656),c_Orderings_Obot__class_Obot(tc_fun(X659,tc_HOL_Obool)))))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X659,tc_Option_Ooption(X658)),X657),X656),c_Option_Ooption_ONone(X658)), inference(variable_rename,[status(thm)],[fact_restrict__complement__singleton__eq])). 4.05/4.31 fof(c_0_9488, plain, ![X14068, X14069, X14070, X14071]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14071,tc_HOL_Obool)),X14070),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14071,tc_HOL_Obool)),X14069),X14068))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14071,tc_HOL_Obool)),X14069),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14071,tc_HOL_Obool)),X14070),X14068)), inference(variable_rename,[status(thm)],[fact_Int__left__commute])). 4.05/4.31 fof(c_0_9489, plain, ![X7167, X7168, X7169, X7170]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7170,tc_HOL_Obool)),X7169),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7170,tc_HOL_Obool)),X7168),X7167))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7170,tc_HOL_Obool)),X7168),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7170,tc_HOL_Obool)),X7169),X7167)), inference(variable_rename,[status(thm)],[fact_Un__left__commute])). 4.05/4.31 cnf(c_0_9490, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oconcat(X1,X2))=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2))), inference(split_conjunct,[status(thm)],[c_0_5661])). 4.05/4.31 fof(c_0_9491, plain, ![X7120, X7121]:hAPP(hAPP(c_List_Omap(X7121,tc_prod(X7121,X7121)),hAPP(hAPP(c_COMBS(X7121,X7121,tc_prod(X7121,X7121)),c_Product__Type_OPair(X7121,X7121)),c_COMBI(X7121))),X7120)=hAPP(hAPP(c_List_Ozip(X7121,X7121),X7120),X7120), inference(variable_rename,[status(thm)],[fact_zip__same__conv__map])). 4.05/4.31 fof(c_0_9492, plain, ![X3299, X3300, X3301]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X3301,X3300),tc_HOL_Obool),tc_fun(X3301,tc_HOL_Obool)),X3299),c_Relation_ODomain(X3301,X3300))=hAPP(c_Relation_ODomain(X3301,X3300),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X3301,X3300),tc_HOL_Obool),X3299)), inference(variable_rename,[status(thm)],[fact_Domain__Union])). 4.05/4.31 fof(c_0_9493, plain, ![X16737, X16738, X16739]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X16739,X16738),tc_HOL_Obool),tc_fun(X16738,tc_HOL_Obool)),X16737),c_Relation_ORange(X16739,X16738))=hAPP(c_Relation_ORange(X16739,X16738),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X16739,X16738),tc_HOL_Obool),X16737)), inference(variable_rename,[status(thm)],[fact_Range__Union])). 4.05/4.31 cnf(c_0_9494, 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_5662])). 4.05/4.31 cnf(c_0_9495, 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_5663])). 4.05/4.31 cnf(c_0_9496, 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_5664])). 4.05/4.31 fof(c_0_9497, plain, ![X9232, X9233, X9234, X9235, X9236, X9237]:hAPP(hAPP(c_List_Olist__update(X9236,hAPP(hAPP(c_List_Omap(X9237,X9236),X9235),X9234)),X9233),hAPP(X9235,X9232))=hAPP(hAPP(c_List_Omap(X9237,X9236),X9235),hAPP(hAPP(c_List_Olist__update(X9237,X9234),X9233),X9232)), inference(variable_rename,[status(thm)],[fact_map__update])). 4.05/4.31 fof(c_0_9498, plain, ![X7995, X7996, X7997, X7998, X7999, X8000, X8001]:hAPP(c_Fun_Ocomp(X7997,X8000,X7999,hAPP(c_Fun_Ocomp(X8001,X8000,X7997,X7998),X7996)),X7995)=hAPP(c_Fun_Ocomp(X8001,X8000,X7999,X7998),hAPP(c_Fun_Ocomp(X7997,X8001,X7999,X7996),X7995)), inference(variable_rename,[status(thm)],[fact_o__assoc])). 4.05/4.31 fof(c_0_9499, plain, ![X10957, X10958, X10959]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X10959,tc_HOL_Obool),tc_fun(X10959,tc_HOL_Obool)),X10957),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10959,tc_HOL_Obool)),X10958))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10959,tc_HOL_Obool)),X10958),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10959,tc_HOL_Obool),X10957)), inference(variable_rename,[status(thm)],[fact_Int__Union])). 4.05/4.31 fof(c_0_9500, plain, ![X10525, X10526, X10527]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10527,tc_HOL_Obool)),X10526),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10527,tc_HOL_Obool),X10525))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X10527,tc_HOL_Obool),tc_fun(X10527,tc_HOL_Obool)),X10525),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10527,tc_HOL_Obool)),X10526)), inference(variable_rename,[status(thm)],[fact_Un__Inter])). 4.05/4.31 fof(c_0_9501, plain, ![X1314, X1315, X1316, X1317, X1318, X1319]:hAPP(hAPP(c_Option_Omap(X1319,X1318),X1317),hAPP(hAPP(c_Option_Omap(X1316,X1319),X1315),X1314))=hAPP(hAPP(c_Option_Omap(X1316,X1318),hAPP(c_Fun_Ocomp(X1319,X1318,X1316,X1317),X1315)),X1314), inference(variable_rename,[status(thm)],[fact_Option_Omap_Ocompositionality])). 4.05/4.31 cnf(c_0_9502, 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_5665])). 4.05/4.31 fof(c_0_9503, plain, ![X1547, X1548, X1549, X1550]:hAPP(c_Set_Oimage(X1550,X1549,X1548),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1550,tc_HOL_Obool),X1547))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1550,tc_HOL_Obool),tc_fun(X1549,tc_HOL_Obool)),X1547),c_Set_Oimage(X1550,X1549,X1548)), inference(variable_rename,[status(thm)],[fact_image__Union])). 4.05/4.31 cnf(c_0_9504, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X3,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5666])). 4.05/4.31 cnf(c_0_9505, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)))=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X1,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5667, c_0_4867]), c_0_5668]), c_0_5669]), c_0_5670]), ['final']). 4.05/4.31 cnf(c_0_9506, 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_5671])). 4.05/4.31 fof(c_0_9507, plain, ![X4319, X4320, X4321, X4322, X4323]:hAPP(hAPP(c_List_Olist_OCons(X4322),hAPP(X4321,X4320)),hAPP(hAPP(c_List_Omap(X4323,X4322),X4321),X4319))=hAPP(hAPP(c_List_Omap(X4323,X4322),X4321),hAPP(hAPP(c_List_Olist_OCons(X4323),X4320),X4319)), inference(variable_rename,[status(thm)],[fact_map_Osimps_I2_J])). 4.05/4.31 cnf(c_0_9508, plain, (hAPP(c_Set_Ovimage(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6)=hAPP(c_Set_Ovimage(X1,X3,X5),hAPP(c_Set_Ovimage(X3,X2,X4),X6))), inference(split_conjunct,[status(thm)],[c_0_5672])). 4.05/4.31 fof(c_0_9509, plain, ![X15502, X15503, X15504, X15505, X15506, X15507]:hAPP(c_Set_Oimage(X15507,X15506,hAPP(c_Fun_Ocomp(X15505,X15506,X15507,X15504),X15503)),X15502)=hAPP(c_Set_Oimage(X15505,X15506,X15504),hAPP(c_Set_Oimage(X15507,X15505,X15503),X15502)), inference(variable_rename,[status(thm)],[fact_image__compose])). 4.05/4.31 fof(c_0_9510, plain, ![X3064, X3065, X3066, X3067, X3068]:hAPP(c_Set_Oimage(X3068,X3067,X3066),hAPP(hAPP(c_Set_Oinsert(X3068),X3065),X3064))=hAPP(hAPP(c_Set_Oinsert(X3067),hAPP(X3066,X3065)),hAPP(c_Set_Oimage(X3068,X3067,X3066),X3064)), inference(variable_rename,[status(thm)],[fact_image__insert])). 4.05/4.31 fof(c_0_9511, plain, ![X2174, X2175, X2176, X2177, X2178, X2179]:hAPP(c_List_Ofoldl(X2179,X2178,X2177,X2176),hAPP(hAPP(c_List_Olist_OCons(X2178),X2175),X2174))=hAPP(c_List_Ofoldl(X2179,X2178,X2177,hAPP(hAPP(X2177,X2176),X2175)),X2174), inference(variable_rename,[status(thm)],[fact_foldl__Cons])). 4.05/4.31 cnf(c_0_9512, plain, (hAPP(c_Set_Ovimage(X1,X2,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_Ovimage(X1,X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5673])). 4.05/4.31 fof(c_0_9513, plain, ![X5289, X5290, X5291, X5292, X5293]:hAPP(hAPP(c_List_Omap(X5291,X5293),X5290),hAPP(hAPP(c_List_Odrop(X5291),X5292),X5289))=hAPP(hAPP(c_List_Odrop(X5293),X5292),hAPP(hAPP(c_List_Omap(X5291,X5293),X5290),X5289)), inference(variable_rename,[status(thm)],[fact_drop__map])). 4.05/4.31 fof(c_0_9514, plain, ![X2045, X2046, X2047, X2048, X2049]:hAPP(hAPP(c_List_Omap(X2047,X2049),X2046),hAPP(hAPP(c_List_Otake(X2047),X2048),X2045))=hAPP(hAPP(c_List_Otake(X2049),X2048),hAPP(hAPP(c_List_Omap(X2047,X2049),X2046),X2045)), inference(variable_rename,[status(thm)],[fact_take__map])). 4.05/4.31 cnf(c_0_9515, 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_5674])). 4.05/4.31 fof(c_0_9516, plain, ![X13423, X13424, X13425, X13426]:hAPP(hAPP(c_Relation_Oinv__image(X13425,X13426),hAPP(c_Relation_Oconverse(X13425,X13425),X13424)),X13423)=hAPP(c_Relation_Oconverse(X13426,X13426),hAPP(hAPP(c_Relation_Oinv__image(X13425,X13426),X13424),X13423)), inference(variable_rename,[status(thm)],[fact_converse__inv__image])). 4.05/4.31 fof(c_0_9517, plain, ![X17260, X17261, X17262, X17263, X17264]:hAPP(hAPP(c_Power_Opower_Opower(X17264,X17263,X17262),X17261),hAPP(c_Nat_OSuc,X17260))=hAPP(hAPP(X17262,X17261),hAPP(hAPP(c_Power_Opower_Opower(X17264,X17263,X17262),X17261),X17260)), inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__Suc])). 4.05/4.31 cnf(c_0_9518, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X3,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5675])). 4.05/4.31 cnf(c_0_9519, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X2)))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5676, c_0_4867]), c_0_5668]), c_0_5669]), c_0_5670]), ['final']). 4.05/4.31 fof(c_0_9520, plain, ![X8576, X8577, X8578, X8579, X8580]:c_List_Olist_Olist__size(X8578,hAPP(c_Fun_Ocomp(X8580,tc_Nat_Onat,X8578,X8579),X8577),X8576)=c_List_Olist_Olist__size(X8580,X8579,hAPP(hAPP(c_List_Omap(X8578,X8580),X8577),X8576)), inference(variable_rename,[status(thm)],[fact_list__size__map])). 4.05/4.31 cnf(c_0_9521, 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_5677])). 4.05/4.31 fof(c_0_9522, plain, ![X7732, X7733, X7734, X7735, X7736]:hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X7735),X7735,hAPP(X7734,X7732),c_Option_Ooption_OSome(X7735)),hAPP(X7733,X7732))=hAPP(c_Map_Omap__add(X7736,X7735,X7734,X7733),X7732), inference(variable_rename,[status(thm)],[fact_map__add__def])). 4.05/4.31 fof(c_0_9523, plain, ![X509, X510, X511, X512, X513]:hAPP(hAPP(X510,hAPP(c_Product__Type_Ofst(X513,X512),X509)),hAPP(c_Product__Type_Osnd(X513,X512),X509))=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X513,X512,X511),X510),X509), inference(variable_rename,[status(thm)],[fact_prod__case__beta])). 4.05/4.31 fof(c_0_9524, plain, ![X785, X786, X787, X788]:hAPP(hAPP(c_Set_Oinsert(X788),X786),hAPP(hAPP(c_Set_Oinsert(X788),X787),X785))=hAPP(hAPP(c_Set_Oinsert(X788),X787),hAPP(hAPP(c_Set_Oinsert(X788),X786),X785)), inference(variable_rename,[status(thm)],[fact_insert__commute])). 4.05/4.31 cnf(c_0_9525, 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_5678])). 4.05/4.31 cnf(c_0_9526, plain, (hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=c_Relation_OId(X1)), inference(split_conjunct,[status(thm)],[c_0_5679])). 4.05/4.31 fof(c_0_9527, plain, ![X12193, X12194, X12195, X12196]:hAPP(hAPP(c_List_Omap(X12196,X12195),hAPP(c_COMBK(X12195,X12196),X12194)),X12193)=c_List_Oreplicate(X12195,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X12196)),X12193),X12194), inference(variable_rename,[status(thm)],[fact_map__replicate__const])). 4.05/4.31 fof(c_0_9528, plain, ![X4979, X4980, X4981, X4982]:hAPP(c_List_Otl(X4981),hAPP(hAPP(c_List_Omap(X4982,X4981),X4980),X4979))=hAPP(hAPP(c_List_Omap(X4982,X4981),X4980),hAPP(c_List_Otl(X4982),X4979)), inference(variable_rename,[status(thm)],[fact_map__tl])). 4.05/4.31 fof(c_0_9529, plain, ![X12733, X12734, X12735, X12736]:(hAPP(hAPP(c_List_Oappend(X12735),X12733),hAPP(hAPP(c_List_Olist_OCons(X12735),X12734),c_List_Olist_ONil(X12735)))=hAPP(c_List_Orotate1(X12735),hAPP(hAPP(c_List_Olist_OCons(X12735),X12734),X12733))&c_List_Olist_ONil(X12736)=hAPP(c_List_Orotate1(X12736),c_List_Olist_ONil(X12736))), inference(variable_rename,[status(thm)],[fact_rotate__simps])). 4.05/4.31 fof(c_0_9530, plain, ![X11949, X11950]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11950),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X11949),X11950))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X11949),c_Divides_Odiv__class_Omod(tc_Int_Oint,X11949,X11950)), inference(variable_rename,[status(thm)],[fact_zmult__div__cancel])). 4.05/4.31 fof(c_0_9531, plain, ![X4676, X4677]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4676),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4676,X4677))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4677),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X4676),X4677)), inference(variable_rename,[status(thm)],[fact_mult__div__cancel])). 4.05/4.31 fof(c_0_9532, plain, ![X8937, X8938, X8939, X8940]:hAPP(c_List_Oset(X8940),hAPP(hAPP(c_List_Omap(X8939,X8940),X8938),X8937))=hAPP(c_Set_Oimage(X8939,X8940,X8938),hAPP(c_List_Oset(X8939),X8937)), inference(variable_rename,[status(thm)],[fact_set__map])). 4.05/4.31 fof(c_0_9533, plain, ![X2566, X2567, X2568, X2569]:c_List_Obutlast(X2568,hAPP(hAPP(c_List_Omap(X2569,X2568),X2567),X2566))=hAPP(hAPP(c_List_Omap(X2569,X2568),X2567),c_List_Obutlast(X2569,X2566)), inference(variable_rename,[status(thm)],[fact_map__butlast])). 4.05/4.31 fof(c_0_9534, plain, ![X10769, X10770, X10771]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10771),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10770),X10769))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10770),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10771),X10769)), inference(variable_rename,[status(thm)],[fact_nat__add__left__commute])). 4.05/4.31 fof(c_0_9535, plain, ![X7046, X7047, X7048, X7049]:hAPP(hAPP(X7047,X7046),hAPP(c_Nat_Onat_Onat__rec(X7049,X7048,X7047),X7046))=hAPP(c_Nat_Onat_Onat__rec(X7049,X7048,X7047),hAPP(c_Nat_OSuc,X7046)), inference(variable_rename,[status(thm)],[fact_nat__rec__Suc])). 4.05/4.31 fof(c_0_9536, plain, ![X13090, X13091]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X13091),X13090))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X13091)),X13090), inference(variable_rename,[status(thm)],[fact_mult__Suc])). 4.05/4.31 fof(c_0_9537, plain, ![X13432, X13433]:hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X13433),tc_List_Olist(X13433)),c_List_Olist_ONil(X13433)),c_List_Olist_ONil(X13433))=c_List_Opartition(X13433,X13432,c_List_Olist_ONil(X13433)), inference(variable_rename,[status(thm)],[fact_partition_Osimps_I1_J])). 4.05/4.31 fof(c_0_9538, plain, ![X4087, X4088, X4089, X4090, X4091, X4092]:hAPP(hAPP(X4089,X4087),hAPP(X4088,X4087))=hAPP(hAPP(hAPP(c_COMBS(X4092,X4091,X4090),X4089),X4088),X4087), inference(variable_rename,[status(thm)],[help_c__COMBS__1])). 4.05/4.31 fof(c_0_9539, plain, ![X15420, X15421]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15421),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15421),X15420))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15421),hAPP(c_Nat_OSuc,X15420)), inference(variable_rename,[status(thm)],[fact_mult__Suc__right])). 4.05/4.31 fof(c_0_9540, plain, ![X4523, X4524, X4525]:hAPP(c_List_Ofilter(X4525,X4524),hAPP(c_List_Orev(X4525),X4523))=hAPP(c_List_Orev(X4525),hAPP(c_List_Ofilter(X4525,X4524),X4523)), inference(variable_rename,[status(thm)],[fact_rev__filter])). 4.05/4.31 fof(c_0_9541, plain, ![X1177, X1178]:c_Fun_Oid(tc_prod(X1178,X1177))=hAPP(c_Product__Type_Oprod_Oprod__case(X1178,X1177,tc_prod(X1178,X1177)),c_Product__Type_OPair(X1178,X1177)), inference(variable_rename,[status(thm)],[fact_split__Pair])). 4.05/4.31 fof(c_0_9542, plain, ![X1720, X1721]:c_Enum_On__lists(X1721,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1720)=hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1721)),c_List_Olist_ONil(X1721)),c_List_Olist_ONil(tc_List_Olist(X1721))), inference(variable_rename,[status(thm)],[fact_n__lists_Osimps_I1_J])). 4.05/4.31 fof(c_0_9543, plain, ![X10735, X10736]:c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X10736),tc_List_Olist(X10736)),tc_HOL_Obool))=hAPP(c_List_Olexn(X10736,X10735),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_lexn_Osimps_I1_J])). 4.05/4.31 fof(c_0_9544, plain, ![X9592, X9593, X9594, X9595]:c_List_Oremove1(X9595,X9594,c_List_Oremove1(X9595,X9593,X9592))=c_List_Oremove1(X9595,X9593,c_List_Oremove1(X9595,X9594,X9592)), inference(variable_rename,[status(thm)],[fact_remove1__commute])). 4.05/4.31 fof(c_0_9545, plain, ![X16618, X16619, X16620, X16621]:hAPP(c_New__DSequence_Opos__union(X16621,X16620,X16619),X16618)=c_Lazy__Sequence_Oappend(X16621,hAPP(X16620,X16618),hAPP(X16619,X16618)), inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__union__def])). 4.05/4.31 fof(c_0_9546, plain, ![X1065]:c_Enum_Osublists(X1065,c_List_Olist_ONil(X1065))=hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1065)),c_List_Olist_ONil(X1065)),c_List_Olist_ONil(tc_List_Olist(X1065))), inference(variable_rename,[status(thm)],[fact_sublists_Osimps_I1_J])). 4.05/4.31 cnf(c_0_9547, plain, (c_List_Olenlex(X1,X2)=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))))))), inference(split_conjunct,[status(thm)],[c_0_5680])). 4.05/4.31 cnf(c_0_9548, plain, (c_List_Oset__Cons(X1,X2,X3)=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))))))), inference(split_conjunct,[status(thm)],[c_0_5681])). 4.05/4.31 fof(c_0_9549, plain, ![X13921, X13922]:c_FunDef_Orp__inv__image(X13922,X13921)=hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X13922,X13922),tc_HOL_Obool),tc_fun(tc_prod(X13922,X13922),tc_HOL_Obool),tc_fun(tc_fun(X13921,X13922),tc_prod(tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X13922,X13922),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X13922,X13922),tc_HOL_Obool),tc_fun(tc_fun(X13921,X13922),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X13922,X13922),tc_HOL_Obool),tc_fun(tc_fun(X13921,X13922),tc_prod(tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X13921,X13922),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool)),tc_fun(tc_fun(X13921,X13922),tc_prod(tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X13922,X13922),tc_HOL_Obool),tc_fun(tc_fun(X13921,X13922),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X13922,X13922),tc_HOL_Obool),tc_fun(tc_fun(X13921,X13922),tc_prod(tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool))))),tc_fun(tc_prod(X13922,X13922),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X13921,X13922),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool)),tc_fun(tc_fun(X13921,X13922),tc_prod(tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool))),tc_fun(tc_prod(X13922,X13922),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X13921,X13922),tc_fun(tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X13921,X13922),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool)),tc_fun(tc_fun(X13921,X13922),tc_prod(tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool)))),tc_fun(tc_prod(X13922,X13922),tc_HOL_Obool)),c_COMBS(tc_fun(X13921,X13922),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X13921,X13922),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool)),tc_fun(tc_fun(X13921,X13922),tc_fun(tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool)))),tc_fun(tc_prod(X13922,X13922),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool))),tc_fun(X13921,X13922)),c_Product__Type_OPair(tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool),tc_fun(tc_prod(X13921,X13921),tc_HOL_Obool)))),c_Relation_Oinv__image(X13922,X13921))))),c_Relation_Oinv__image(X13922,X13921))), inference(variable_rename,[status(thm)],[fact_rp__inv__image__def])). 4.05/4.31 cnf(c_0_9550, plain, (hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X3))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBC(X3,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X1,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X3),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X1,X3)))),c_Product__Type_OPair(X1,X3)))),X4))))),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X3,X2)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X3,X2),tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X3,X2)))),hAPP(c_COMBC(X3,X2,tc_prod(X3,X2)),c_Product__Type_OPair(X3,X2))))),X5)))))=hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_5682])). 4.05/4.31 cnf(c_0_9551, plain, (c_Divides_Oadjust(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5683, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.31 fof(c_0_9552, plain, ![X3890]: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,X3890)),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),X3890), inference(variable_rename,[status(thm)],[fact_minus__int__def])). 4.05/4.31 fof(c_0_9553, plain, ![X5285, X5286, X5287, X5288]:c_List_Opartition(X5288,X5287,hAPP(hAPP(c_List_Olist_OCons(X5288),X5286),X5285))=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5288),tc_List_Olist(X5288),tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288))),hAPP(hAPP(c_COMBS(tc_List_Olist(X5288),tc_fun(tc_List_Olist(X5288),tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288))),tc_fun(tc_List_Olist(X5288),tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5288),tc_fun(tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288)),tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288)))),tc_fun(tc_fun(tc_List_Olist(X5288),tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288))),tc_fun(tc_List_Olist(X5288),tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288)))),tc_List_Olist(X5288)),c_COMBS(tc_List_Olist(X5288),tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288)),tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5288),tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288))),tc_fun(tc_List_Olist(X5288),tc_fun(tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288)),tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288)))),tc_List_Olist(X5288)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288)),tc_fun(tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288)),tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288))),tc_List_Olist(X5288)),hAPP(c_If(tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288))),hAPP(X5287,X5286)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X5288),tc_fun(tc_List_Olist(X5288),tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288))),tc_List_Olist(X5288)),c_Product__Type_OPair(tc_List_Olist(X5288),tc_List_Olist(X5288))),hAPP(c_List_Olist_OCons(X5288),X5286))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5288),tc_fun(tc_List_Olist(X5288),tc_List_Olist(X5288)),tc_fun(tc_List_Olist(X5288),tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5288),tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288))),tc_fun(tc_fun(tc_List_Olist(X5288),tc_List_Olist(X5288)),tc_fun(tc_List_Olist(X5288),tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288)))),tc_List_Olist(X5288)),c_COMBB(tc_List_Olist(X5288),tc_prod(tc_List_Olist(X5288),tc_List_Olist(X5288)),tc_List_Olist(X5288))),c_Product__Type_OPair(tc_List_Olist(X5288),tc_List_Olist(X5288)))),hAPP(c_List_Olist_OCons(X5288),X5286)))),c_List_Opartition(X5288,X5287,X5285)), inference(variable_rename,[status(thm)],[fact_partition_Osimps_I2_J])). 4.05/4.31 cnf(c_0_9554, plain, (hAPP(c_Set_OCollect(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2)),c_Set_OPow(X1)))))=hAPP(c_Set_OPow(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))), inference(split_conjunct,[status(thm)],[c_0_5684])). 4.05/4.31 cnf(c_0_9555, plain, (hAPP(c_List_Olexn(X1,X2),hAPP(c_Nat_OSuc,X3))=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))))))), inference(split_conjunct,[status(thm)],[c_0_5685])). 4.05/4.31 cnf(c_0_9556, plain, (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))))))=hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5686])). 4.05/4.31 fof(c_0_9557, plain, ![X15138, X15139, X15140, X15141, X15142]:c_Map_Omap__upds(X15142,X15141,X15140,X15139,X15138)=hAPP(c_List_Ofoldl(tc_fun(X15142,tc_Option_Ooption(X15141)),tc_prod(X15142,X15141),hAPP(hAPP(c_COMBB(tc_fun(X15142,tc_fun(X15141,tc_fun(X15142,tc_Option_Ooption(X15141)))),tc_fun(tc_prod(X15142,X15141),tc_fun(X15142,tc_Option_Ooption(X15141))),tc_fun(X15142,tc_Option_Ooption(X15141))),c_Product__Type_Oprod_Oprod__case(X15142,X15141,tc_fun(X15142,tc_Option_Ooption(X15141)))),hAPP(hAPP(c_COMBC(tc_fun(X15142,tc_Option_Ooption(X15141)),tc_fun(X15141,tc_Option_Ooption(X15141)),tc_fun(X15142,tc_fun(X15141,tc_fun(X15142,tc_Option_Ooption(X15141))))),hAPP(hAPP(c_COMBB(tc_fun(X15142,tc_fun(tc_fun(X15141,tc_Option_Ooption(X15141)),tc_fun(X15141,tc_fun(X15142,tc_Option_Ooption(X15141))))),tc_fun(tc_fun(X15141,tc_Option_Ooption(X15141)),tc_fun(X15142,tc_fun(X15141,tc_fun(X15142,tc_Option_Ooption(X15141))))),tc_fun(X15142,tc_Option_Ooption(X15141))),c_COMBC(X15142,tc_fun(X15141,tc_Option_Ooption(X15141)),tc_fun(X15141,tc_fun(X15142,tc_Option_Ooption(X15141))))),hAPP(hAPP(c_COMBB(tc_fun(X15142,tc_fun(tc_Option_Ooption(X15141),tc_fun(X15142,tc_Option_Ooption(X15141)))),tc_fun(X15142,tc_fun(tc_fun(X15141,tc_Option_Ooption(X15141)),tc_fun(X15141,tc_fun(X15142,tc_Option_Ooption(X15141))))),tc_fun(X15142,tc_Option_Ooption(X15141))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X15141),tc_fun(X15142,tc_Option_Ooption(X15141))),tc_fun(tc_fun(X15141,tc_Option_Ooption(X15141)),tc_fun(X15141,tc_fun(X15142,tc_Option_Ooption(X15141)))),X15142),c_COMBB(tc_Option_Ooption(X15141),tc_fun(X15142,tc_Option_Ooption(X15141)),X15141))),c_Fun_Ofun__upd(X15142,tc_Option_Ooption(X15141))))),c_Option_Ooption_OSome(X15141))),X15140),hAPP(hAPP(c_List_Ozip(X15142,X15141),X15139),X15138)), inference(variable_rename,[status(thm)],[fact_map__upds__fold__map__upd])). 4.05/4.31 fof(c_0_9558, plain, ![X12775, X12776, X12777, X12778]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12778,tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool)),X12776),hAPP(hAPP(c_COMBS(X12778,tc_fun(X12777,tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool)),tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12777,tc_HOL_Obool),tc_fun(tc_fun(X12777,tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool)),tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool)),X12778),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X12777,tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool))),X12775)),hAPP(hAPP(c_COMBC(X12778,tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool),tc_fun(X12777,tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X12777,tc_fun(tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool),tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool),tc_fun(X12777,tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool))),X12778),c_COMBC(X12777,tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool),tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X12777,tc_prod(X12778,X12777)),tc_fun(X12777,tc_fun(tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool),tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool))),X12778),hAPP(c_COMBB(tc_prod(X12778,X12777),tc_fun(tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool),tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool)),X12777),c_Set_Oinsert(tc_prod(X12778,X12777)))),c_Product__Type_OPair(X12778,X12777)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X12778,X12777),tc_HOL_Obool)))))=hAPP(hAPP(c_Product__Type_OSigma(X12778,X12777),X12776),X12775), inference(variable_rename,[status(thm)],[fact_Sigma__def])). 4.05/4.31 cnf(c_0_9559, plain, (c_List_Ofoldr(tc_prod(X1,X2),tc_fun(X1,tc_Option_Ooption(X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),X1),c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))),X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),X1),c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),X1,tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)))))),c_Option_Ooption_OSome(X2))),X3,X4)=c_Map_Omap__add(X1,X2,X4,hAPP(c_Map_Omap__of(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5687])). 4.05/4.31 cnf(c_0_9560, 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_5688])). 4.05/4.31 cnf(c_0_9561, plain, (hAPP(c_Divides_Oadjust(X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X1)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))),X2)),X3)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5689, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9562, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),c_Nitpick_Oint__lcm(hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X1),tc_Int_Oint),c_Nitpick_Ofrac(X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X1,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X1)),X3)))))),c_COMBI(tc_Int_Oint)))=c_Nitpick_Oplus__frac(X1,X2,X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5690, c_0_5049]), c_0_5049]), c_0_5050]), c_0_5050]), c_0_5050]), c_0_5050])). 4.05/4.31 cnf(c_0_9563, 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_5691])). 4.05/4.31 cnf(c_0_9564, plain, (hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X2)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X2,X2),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X2,X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X2),tc_fun(X1,tc_prod(X2,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X2,X2)),tc_fun(tc_fun(X1,X2),tc_fun(X1,tc_prod(X2,X2))),X1),c_COMBB(X2,tc_prod(X2,X2),X1)),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_prod(X2,X2)),X1),c_Product__Type_OPair(X2,X2)),X3))),X3)))),X4)))=hAPP(hAPP(c_Relation_Oinv__image(X2,X1),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_5692])). 4.05/4.31 cnf(c_0_9565, 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_5693, c_0_4767]), c_0_4767])). 4.05/4.31 cnf(c_0_9566, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X2))=hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),c_List_Ohd(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(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)],[c_0_5694, c_0_5695]), c_0_5696]), c_0_5201]), ['final']). 4.05/4.31 cnf(c_0_9567, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1)),c_List_Oappend(tc_List_Olist(X1)),c_List_Olist_ONil(tc_List_Olist(X1))),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),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)],[c_0_5697, c_0_5695]), c_0_5696]), c_0_5201]), ['final']). 4.05/4.31 cnf(c_0_9568, plain, (hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),X3)=hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X1,tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),hAPP(hAPP(c_COMBC(X1,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),X1),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X1),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),X1),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5698])). 4.05/4.31 cnf(c_0_9569, plain, (hAPP(c_Option_Ooption_Ooption__case(X1,tc_prod(X2,tc_Lazy__Sequence_Olazy__sequence(X2)),X3,hAPP(c_Product__Type_Oprod_Oprod__case(X2,tc_Lazy__Sequence_Olazy__sequence(X2),X1),X4)),hAPP(c_Lazy__Sequence_Oyield(X2),X5))=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_5699]), ['final']). 4.05/4.31 fof(c_0_9570, plain, ![X14998, X14999, X15000, X15001, X15002]:hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X15002,X15001)),X15002,c_List_Olist_ONil(tc_prod(X15002,X15001)),hAPP(hAPP(c_COMBC(X15002,tc_fun(tc_List_Olist(X15002),tc_List_Olist(tc_prod(X15002,X15001))),tc_fun(tc_List_Olist(X15002),tc_List_Olist(tc_prod(X15002,X15001)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X15002,X15001)),tc_List_Olist(tc_prod(X15002,X15001))),tc_fun(tc_fun(tc_List_Olist(X15002),tc_List_Olist(tc_prod(X15002,X15001))),tc_fun(tc_List_Olist(X15002),tc_List_Olist(tc_prod(X15002,X15001)))),X15002),c_COMBB(tc_List_Olist(tc_prod(X15002,X15001)),tc_List_Olist(tc_prod(X15002,X15001)),tc_List_Olist(X15002))),hAPP(hAPP(c_COMBB(tc_prod(X15002,X15001),tc_fun(tc_List_Olist(tc_prod(X15002,X15001)),tc_List_Olist(tc_prod(X15002,X15001))),X15002),c_List_Olist_OCons(tc_prod(X15002,X15001))),hAPP(hAPP(c_COMBC(X15002,X15001,tc_prod(X15002,X15001)),c_Product__Type_OPair(X15002,X15001)),X14999)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X15002),tc_List_Olist(X15001),tc_List_Olist(tc_prod(X15002,X15001))),c_List_Ozip(X15002,X15001)),X14998))),X15000)=hAPP(hAPP(c_List_Ozip(X15002,X15001),X15000),hAPP(hAPP(c_List_Olist_OCons(X15001),X14999),X14998)), inference(variable_rename,[status(thm)],[fact_zip__Cons])). 4.05/4.31 fof(c_0_9571, plain, ![X4509, X4510, X4511, X4512, X4513, X4514, X4515, X4516]:hAPP(hAPP(c_Product__Type_OSigma(X4514,X4513),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4516,tc_fun(X4514,tc_HOL_Obool)),X4512),X4510)),hAPP(c_COMBK(tc_fun(X4513,tc_HOL_Obool),X4514),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4515,tc_fun(X4513,tc_HOL_Obool)),X4511),X4509)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X4516,X4515),tc_fun(tc_prod(X4514,X4513),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4516,X4515),X4512),hAPP(c_COMBK(tc_fun(X4515,tc_HOL_Obool),X4516),X4511))),hAPP(c_Product__Type_Oprod_Oprod__case(X4516,X4515,tc_fun(tc_prod(X4514,X4513),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X4516,tc_fun(X4515,tc_fun(X4514,tc_fun(X4513,tc_HOL_Obool))),tc_fun(X4515,tc_fun(tc_prod(X4514,X4513),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X4514,tc_fun(X4513,tc_HOL_Obool)),tc_fun(tc_prod(X4514,X4513),tc_HOL_Obool)),tc_fun(tc_fun(X4515,tc_fun(X4514,tc_fun(X4513,tc_HOL_Obool))),tc_fun(X4515,tc_fun(tc_prod(X4514,X4513),tc_HOL_Obool))),X4516),c_COMBB(tc_fun(X4514,tc_fun(X4513,tc_HOL_Obool)),tc_fun(tc_prod(X4514,X4513),tc_HOL_Obool),X4515)),hAPP(hAPP(c_COMBB(tc_fun(X4514,tc_HOL_Obool),tc_fun(tc_fun(X4514,tc_fun(X4513,tc_HOL_Obool)),tc_fun(tc_prod(X4514,X4513),tc_HOL_Obool)),X4516),c_Product__Type_OSigma(X4514,X4513)),X4510))),hAPP(hAPP(c_COMBB(tc_fun(X4513,tc_HOL_Obool),tc_fun(X4514,tc_fun(X4513,tc_HOL_Obool)),X4515),c_COMBK(tc_fun(X4513,tc_HOL_Obool),X4514)),X4509)))), inference(variable_rename,[status(thm)],[fact_UN__Times__distrib])). 4.05/4.31 cnf(c_0_9572, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X3),hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X3)),X4)))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X3),hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X3)),hAPP(c_List_Ofilter(tc_List_Olist(X3),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X3)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_List_Olist(X3),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X3)))),X4)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5700, c_0_4742]), c_0_4742])). 4.05/4.31 cnf(c_0_9573, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X1),X2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))))=hAPP(c_List_Oset(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5701])). 4.05/4.31 fof(c_0_9574, plain, ![X12358, X12359, X12360, X12361, X12362]:hAPP(hAPP(c_List_Ozip(X12362,X12361),hAPP(hAPP(c_List_Olist_OCons(X12362),X12360),X12359)),X12358)=hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X12362,X12361)),X12361,c_List_Olist_ONil(tc_prod(X12362,X12361)),hAPP(hAPP(c_COMBC(X12361,tc_fun(tc_List_Olist(X12361),tc_List_Olist(tc_prod(X12362,X12361))),tc_fun(tc_List_Olist(X12361),tc_List_Olist(tc_prod(X12362,X12361)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X12362,X12361)),tc_List_Olist(tc_prod(X12362,X12361))),tc_fun(tc_fun(tc_List_Olist(X12361),tc_List_Olist(tc_prod(X12362,X12361))),tc_fun(tc_List_Olist(X12361),tc_List_Olist(tc_prod(X12362,X12361)))),X12361),c_COMBB(tc_List_Olist(tc_prod(X12362,X12361)),tc_List_Olist(tc_prod(X12362,X12361)),tc_List_Olist(X12361))),hAPP(hAPP(c_COMBB(tc_prod(X12362,X12361),tc_fun(tc_List_Olist(tc_prod(X12362,X12361)),tc_List_Olist(tc_prod(X12362,X12361))),X12361),c_List_Olist_OCons(tc_prod(X12362,X12361))),hAPP(c_Product__Type_OPair(X12362,X12361),X12360)))),hAPP(c_List_Ozip(X12362,X12361),X12359))),X12358), inference(variable_rename,[status(thm)],[fact_zip__Cons1])). 4.05/4.31 fof(c_0_9575, plain, ![X7829, X7830, X7831, X7832, X7833, X7834, X7835]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7835,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7834,tc_fun(X7835,tc_HOL_Obool)),X7833),X7832)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7831,tc_fun(X7835,tc_HOL_Obool)),X7830),X7829))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7834,tc_fun(X7835,tc_HOL_Obool)),X7833),hAPP(hAPP(c_COMBB(tc_fun(X7831,tc_fun(X7835,tc_HOL_Obool)),tc_fun(X7835,tc_HOL_Obool),X7834),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7831,tc_fun(X7835,tc_HOL_Obool)),X7830)),hAPP(hAPP(c_COMBC(X7834,tc_fun(X7831,tc_fun(X7835,tc_HOL_Obool)),tc_fun(X7831,tc_fun(X7835,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X7835,tc_HOL_Obool),tc_fun(X7835,tc_HOL_Obool)),tc_fun(tc_fun(X7831,tc_fun(X7835,tc_HOL_Obool)),tc_fun(X7831,tc_fun(X7835,tc_HOL_Obool))),X7834),c_COMBB(tc_fun(X7835,tc_HOL_Obool),tc_fun(X7835,tc_HOL_Obool),X7831)),hAPP(hAPP(c_COMBB(tc_fun(X7835,tc_HOL_Obool),tc_fun(tc_fun(X7835,tc_HOL_Obool),tc_fun(X7835,tc_HOL_Obool)),X7834),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7835,tc_HOL_Obool))),X7832))),X7829))), inference(variable_rename,[status(thm)],[fact_Int__UN__distrib2])). 4.05/4.31 fof(c_0_9576, plain, ![X550, X551, X552, X553, X554, X555, X556]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X556,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X555,tc_fun(X556,tc_HOL_Obool)),X554),X553)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X552,tc_fun(X556,tc_HOL_Obool)),X551),X550))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X555,tc_fun(X556,tc_HOL_Obool)),X554),hAPP(hAPP(c_COMBB(tc_fun(X552,tc_fun(X556,tc_HOL_Obool)),tc_fun(X556,tc_HOL_Obool),X555),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X552,tc_fun(X556,tc_HOL_Obool)),X551)),hAPP(hAPP(c_COMBC(X555,tc_fun(X552,tc_fun(X556,tc_HOL_Obool)),tc_fun(X552,tc_fun(X556,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X556,tc_HOL_Obool),tc_fun(X556,tc_HOL_Obool)),tc_fun(tc_fun(X552,tc_fun(X556,tc_HOL_Obool)),tc_fun(X552,tc_fun(X556,tc_HOL_Obool))),X555),c_COMBB(tc_fun(X556,tc_HOL_Obool),tc_fun(X556,tc_HOL_Obool),X552)),hAPP(hAPP(c_COMBB(tc_fun(X556,tc_HOL_Obool),tc_fun(tc_fun(X556,tc_HOL_Obool),tc_fun(X556,tc_HOL_Obool)),X555),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X556,tc_HOL_Obool))),X553))),X550))), inference(variable_rename,[status(thm)],[fact_Un__INT__distrib2])). 4.05/4.31 cnf(c_0_9577, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X1,X3,X4),X5))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X3,X4)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5)))))=hAPP(c_Nat_Onat_Onat__rec(X1,X3,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X5))), inference(rw,[status(thm)],[c_0_5702, c_0_4434])). 4.05/4.31 cnf(c_0_9578, 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_5703])). 4.05/4.31 cnf(c_0_9579, 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_5704])). 4.05/4.31 cnf(c_0_9580, plain, (hAPP(c_Int_Onat,X1)=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))))))), inference(split_conjunct,[status(thm)],[c_0_5705])). 4.05/4.31 cnf(c_0_9581, 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_5706])). 4.05/4.31 fof(c_0_9582, plain, ![X7912, X7913, X7914, X7915, X7916, X7917, X7918, X7919]:hAPP(hAPP(c_List_Omap(tc_prod(X7919,X7918),X7917),X7916),hAPP(hAPP(c_List_Ozip(X7919,X7918),X7915),hAPP(hAPP(c_List_Omap(X7914,X7918),X7913),X7912)))=hAPP(hAPP(c_List_Omap(tc_prod(X7919,X7914),X7917),hAPP(c_Product__Type_Oprod_Oprod__case(X7919,X7914,X7917),hAPP(hAPP(c_COMBB(tc_fun(X7914,tc_prod(X7919,X7918)),tc_fun(X7914,X7917),X7919),hAPP(c_COMBB(tc_prod(X7919,X7918),X7917,X7914),X7916)),hAPP(hAPP(c_COMBC(X7919,tc_fun(X7914,X7918),tc_fun(X7914,tc_prod(X7919,X7918))),hAPP(hAPP(c_COMBB(tc_fun(X7918,tc_prod(X7919,X7918)),tc_fun(tc_fun(X7914,X7918),tc_fun(X7914,tc_prod(X7919,X7918))),X7919),c_COMBB(X7918,tc_prod(X7919,X7918),X7914)),c_Product__Type_OPair(X7919,X7918))),X7913)))),hAPP(hAPP(c_List_Ozip(X7919,X7914),X7915),X7912)), inference(variable_rename,[status(thm)],[fact_map__zip__map2])). 4.05/4.31 cnf(c_0_9583, plain, (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))))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_5707])). 4.05/4.31 cnf(c_0_9584, 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_5708]), ['final']). 4.05/4.31 cnf(c_0_9585, 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_5709])). 4.05/4.31 cnf(c_0_9586, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),tc_prod(X3,X4)),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))),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(split_conjunct,[status(thm)],[c_0_5710])). 4.05/4.31 cnf(c_0_9587, 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_5711]), ['final']). 4.05/4.31 cnf(c_0_9588, plain, (c_Nat_Onat_Onat__case(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)),c_Nat_Onat_Onat__case(X1,X2,X3,X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,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))))), inference(rw,[status(thm)],[c_0_5712, c_0_4434])). 4.05/4.31 cnf(c_0_9589, 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_5713, c_0_4915]), c_0_4523])). 4.05/4.31 cnf(c_0_9590, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))=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),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_5714])). 4.05/4.31 cnf(c_0_9591, plain, (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)))))=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_5715, c_0_5716])). 4.05/4.31 cnf(c_0_9592, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool))))=c_FunDef_Omin__weak), inference(split_conjunct,[status(thm)],[fact_min__weak__def])). 4.05/4.31 cnf(c_0_9593, 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_5717, c_0_4434])). 4.05/4.31 cnf(c_0_9594, 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)),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_5718, c_0_4434])). 4.05/4.31 cnf(c_0_9595, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),X2))))=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))), inference(rw,[status(thm)],[c_0_5719, c_0_4434])). 4.05/4.31 cnf(c_0_9596, 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])). 4.05/4.31 cnf(c_0_9597, 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_5720])). 4.05/4.31 cnf(c_0_9598, 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_5721, c_0_5049]), c_0_5049]), c_0_5050]), c_0_5050])). 4.05/4.31 cnf(c_0_9599, plain, (c_Map_Odom(X1,X2,c_Fun_Ooverride__on(X1,tc_Option_Ooption(X2),X3,X4,X5))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),c_Map_Odom(X1,X2,X4)))))),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),c_Map_Odom(X1,X2,X4)))))), inference(split_conjunct,[status(thm)],[c_0_5722])). 4.05/4.31 fof(c_0_9600, plain, ![X4828, X4829, X4830, X4831, X4832]:hAPP(c_Map_Omap__of(X4832,X4831),hAPP(hAPP(c_List_Omap(tc_prod(X4832,X4830),tc_prod(X4832,X4831)),hAPP(c_Product__Type_Oprod_Oprod__case(X4832,X4830,tc_prod(X4832,X4831)),hAPP(hAPP(c_COMBC(X4832,tc_fun(X4830,X4831),tc_fun(X4830,tc_prod(X4832,X4831))),hAPP(hAPP(c_COMBB(tc_fun(X4831,tc_prod(X4832,X4831)),tc_fun(tc_fun(X4830,X4831),tc_fun(X4830,tc_prod(X4832,X4831))),X4832),c_COMBB(X4831,tc_prod(X4832,X4831),X4830)),c_Product__Type_OPair(X4832,X4831))),X4829))),X4828))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X4830),tc_Option_Ooption(X4831),X4832,hAPP(c_Option_Omap(X4830,X4831),X4829)),hAPP(c_Map_Omap__of(X4832,X4830),X4828)), inference(variable_rename,[status(thm)],[fact_map__of__map])). 4.05/4.31 fof(c_0_9601, plain, ![X3665, X3666, X3667, X3668, X3669, X3670]:hAPP(hAPP(c_List_Omap(tc_prod(X3670,X3667),tc_prod(X3670,X3669)),hAPP(c_Product__Type_Oprod_Oprod__case(X3670,X3667,tc_prod(X3670,X3669)),hAPP(hAPP(c_COMBC(X3670,tc_fun(X3667,X3669),tc_fun(X3667,tc_prod(X3670,X3669))),hAPP(hAPP(c_COMBB(tc_fun(X3669,tc_prod(X3670,X3669)),tc_fun(tc_fun(X3667,X3669),tc_fun(X3667,tc_prod(X3670,X3669))),X3670),c_COMBB(X3669,tc_prod(X3670,X3669),X3667)),c_Product__Type_OPair(X3670,X3669))),X3666))),hAPP(hAPP(c_List_Ozip(X3670,X3667),X3668),X3665))=hAPP(hAPP(c_List_Ozip(X3670,X3669),X3668),hAPP(hAPP(c_List_Omap(X3667,X3669),X3666),X3665)), inference(variable_rename,[status(thm)],[fact_zip__map2])). 4.05/4.31 cnf(c_0_9602, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X1),c_Set_Oinsert(tc_prod(X1,X1))),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))=c_Relation_OId__on(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5723])). 4.05/4.31 cnf(c_0_9603, 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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5724, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9604, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5725, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9605, 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_5726, c_0_4434])). 4.05/4.31 cnf(c_0_9606, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),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),X1)),c_Int_Onat))))), inference(rw,[status(thm)],[c_0_5727, c_0_4434])). 4.05/4.31 cnf(c_0_9607, 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_5728, c_0_4523])). 4.05/4.31 cnf(c_0_9608, 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_5729, c_0_4523]), c_0_4523]), ['final']). 4.05/4.31 cnf(c_0_9609, plain, (c_List_Osublist(X1,X2,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)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X3)),hAPP(hAPP(c_List_Ozip(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)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))))), inference(rw,[status(thm)],[c_0_5730, c_0_4519])). 4.05/4.31 fof(c_0_9610, plain, ![X2313, X2314]:c_Fun_Oinj__on(tc_fun(X2314,X2313),tc_fun(tc_prod(X2314,X2313),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2314,X2313),tc_HOL_Obool),tc_fun(tc_prod(X2314,X2313),tc_HOL_Obool),tc_fun(X2314,X2313)),c_Set_OCollect(tc_prod(X2314,X2313))),hAPP(hAPP(c_COMBB(tc_fun(X2314,tc_fun(X2313,tc_HOL_Obool)),tc_fun(tc_prod(X2314,X2313),tc_HOL_Obool),tc_fun(X2314,X2313)),c_Product__Type_Oprod_Oprod__case(X2314,X2313,tc_HOL_Obool)),hAPP(c_COMBB(X2313,tc_fun(X2313,tc_HOL_Obool),X2314),hAPP(c_COMBC(X2313,X2313,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2314,X2313),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_inj__graph])). 4.05/4.31 cnf(c_0_9611, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5731, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.31 fof(c_0_9612, plain, ![X9578, X9579, X9580, X9581, X9582, X9583, X9584]:hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X9584,X9583,X9582,X9581),X9580),X9579),X9578)=c_New__DSequence_Oneg__bind(X9584,X9583,hAPP(hAPP(hAPP(X9582,X9580),X9579),X9578),hAPP(hAPP(c_COMBC(X9584,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(X9583)))),hAPP(hAPP(c_COMBC(X9584,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(X9583))))),hAPP(hAPP(c_COMBC(X9584,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(X9583)))))),X9581),X9580)),X9579)),X9578)), inference(variable_rename,[status(thm)],[fact_neg__bind__def])). 4.05/4.31 fof(c_0_9613, plain, ![X15846, X15847, X15848]:hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X15848)),tc_List_Olist(tc_List_Olist(X15848))),c_Enum_Osublists(X15848,X15846)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(X15848)),tc_List_Olist(tc_List_Olist(X15848)),tc_List_Olist(tc_List_Olist(X15848))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(X15848)),tc_fun(tc_List_Olist(tc_List_Olist(X15848)),tc_List_Olist(tc_List_Olist(X15848))),tc_List_Olist(tc_List_Olist(X15848))),c_List_Oappend(tc_List_Olist(X15848))),hAPP(c_List_Omap(tc_List_Olist(X15848),tc_List_Olist(X15848)),hAPP(c_List_Olist_OCons(X15848),X15847)))),c_COMBI(tc_List_Olist(tc_List_Olist(X15848)))))=c_Enum_Osublists(X15848,hAPP(hAPP(c_List_Olist_OCons(X15848),X15847),X15846)), inference(variable_rename,[status(thm)],[fact_sublists_Osimps_I2_J])). 4.05/4.31 cnf(c_0_9614, 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_5732])). 4.05/4.31 cnf(c_0_9615, plain, (c_Enum_Oenum__the(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(c_fequal,X3)))),hAPP(c_fequal,X4))))=hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)), inference(rw,[status(thm)],[c_0_5733, c_0_4980])). 4.05/4.31 fof(c_0_9616, plain, ![X7867, X7868, X7869, X7870, X7871, X7872, X7873]:c_New__Random__Sequence_Oneg__decr__bind(X7873,X7872,X7871,X7870,X7869,X7868,X7867)=c_New__DSequence_Oneg__decr__bind(X7873,X7872,hAPP(hAPP(hAPP(X7871,X7869),X7868),X7867),hAPP(hAPP(c_COMBC(X7873,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(X7872)))),hAPP(hAPP(c_COMBC(X7873,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(X7872))))),hAPP(hAPP(c_COMBC(X7873,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(X7872)))))),X7870),X7869)),X7868)),X7867)), inference(variable_rename,[status(thm)],[fact_New__Random__Sequence_Oneg__decr__bind__def])). 4.05/4.31 fof(c_0_9617, plain, ![X3599, X3600, X3601, X3602, X3603, X3604, X3605, X3606]:hAPP(hAPP(c_List_Omap(tc_prod(X3602,X3605),X3604),hAPP(c_Product__Type_Oprod_Oprod__case(X3602,X3605,X3604),hAPP(hAPP(c_COMBB(tc_fun(X3605,tc_prod(X3606,X3605)),tc_fun(X3605,X3604),X3602),hAPP(c_COMBB(tc_prod(X3606,X3605),X3604,X3605),X3603)),hAPP(hAPP(c_COMBB(X3606,tc_fun(X3605,tc_prod(X3606,X3605)),X3602),c_Product__Type_OPair(X3606,X3605)),X3601)))),hAPP(hAPP(c_List_Ozip(X3602,X3605),X3600),X3599))=hAPP(hAPP(c_List_Omap(tc_prod(X3606,X3605),X3604),X3603),hAPP(hAPP(c_List_Ozip(X3606,X3605),hAPP(hAPP(c_List_Omap(X3602,X3606),X3601),X3600)),X3599)), inference(variable_rename,[status(thm)],[fact_map__zip__map])). 4.05/4.31 fof(c_0_9618, plain, ![X12177, X12178, X12179, X12180, X12181, X12182, X12183]:hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X12183,X12182,X12181,X12180),X12179),X12178),X12177)=c_New__DSequence_Opos__bind(X12183,X12182,hAPP(hAPP(hAPP(X12181,X12179),X12178),X12177),hAPP(hAPP(c_COMBC(X12183,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X12182))),hAPP(hAPP(c_COMBC(X12183,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(X12182)))),hAPP(hAPP(c_COMBC(X12183,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(X12182))))),X12180),X12179)),X12178)),X12177)), inference(variable_rename,[status(thm)],[fact_pos__bind__def])). 4.05/4.31 fof(c_0_9619, plain, ![X16593, X16594, X16595, X16596]:c_Lazy__Sequence_Oproduct(X16596,X16595,X16594,X16593)=hAPP(c_Lazy__Sequence_Obind(X16596,tc_prod(X16596,X16595),X16594),hAPP(hAPP(c_COMBB(tc_fun(X16595,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X16596,X16595))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X16596,X16595)),X16596),c_Lazy__Sequence_Obind(X16595,tc_prod(X16596,X16595),X16593)),hAPP(hAPP(c_COMBB(tc_fun(X16595,tc_prod(X16596,X16595)),tc_fun(X16595,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X16596,X16595))),X16596),hAPP(c_COMBB(tc_prod(X16596,X16595),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X16596,X16595)),X16595),c_Lazy__Sequence_Osingle(tc_prod(X16596,X16595)))),c_Product__Type_OPair(X16596,X16595)))), inference(variable_rename,[status(thm)],[fact__02])). 4.05/4.31 cnf(c_0_9620, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X2))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2)), inference(split_conjunct,[status(thm)],[c_0_5734])). 4.05/4.31 cnf(c_0_9621, 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_5735]), ['final']). 4.05/4.31 fof(c_0_9622, plain, ![X8022, X8023, X8024, X8025, X8026, X8027, X8028]:c_New__Random__Sequence_Opos__decr__bind(X8028,X8027,X8026,X8025,X8024,X8023,X8022)=c_New__DSequence_Opos__decr__bind(X8028,X8027,hAPP(hAPP(hAPP(X8026,X8024),X8023),X8022),hAPP(hAPP(c_COMBC(X8028,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X8027))),hAPP(hAPP(c_COMBC(X8028,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(X8027)))),hAPP(hAPP(c_COMBC(X8028,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(X8027))))),X8025),X8024)),X8023)),X8022)), inference(variable_rename,[status(thm)],[fact_New__Random__Sequence_Opos__decr__bind__def])). 4.05/4.31 fof(c_0_9623, plain, ![X8269, X8270, X8271, X8272, X8273, X8274, X8275]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8272,tc_fun(tc_prod(X8275,X8273),tc_HOL_Obool)),X8271),hAPP(hAPP(c_COMBC(X8272,tc_fun(tc_prod(X8274,X8273),tc_HOL_Obool),tc_fun(tc_prod(X8275,X8273),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X8275,X8274),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X8274,X8273),tc_HOL_Obool),tc_fun(tc_prod(X8275,X8273),tc_HOL_Obool)),X8272),c_Relation_Orel__comp(X8275,X8274,X8273)),X8270)),X8269))=hAPP(hAPP(c_Relation_Orel__comp(X8275,X8274,X8273),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8272,tc_fun(tc_prod(X8275,X8274),tc_HOL_Obool)),X8271),X8270)),X8269), inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib2])). 4.05/4.31 cnf(c_0_9624, 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_5736])). 4.05/4.31 fof(c_0_9625, plain, ![X6263, X6264, X6265, X6266, X6267]:hAPP(hAPP(c_List_Omap(X6267,X6266),X6265),hAPP(c_List_Ofilter(X6267,X6264),X6263))=c_List_Omap__filter(X6267,X6266,hAPP(hAPP(c_COMBC(X6267,tc_Option_Ooption(X6266),tc_Option_Ooption(X6266)),hAPP(hAPP(c_COMBS(X6267,tc_Option_Ooption(X6266),tc_fun(tc_Option_Ooption(X6266),tc_Option_Ooption(X6266))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X6266),tc_fun(tc_Option_Ooption(X6266),tc_Option_Ooption(X6266))),X6267),c_If(tc_Option_Ooption(X6266))),X6264)),hAPP(hAPP(c_COMBB(X6266,tc_Option_Ooption(X6266),X6267),c_Option_Ooption_OSome(X6266)),X6265))),c_Option_Ooption_ONone(X6266)),X6263), inference(variable_rename,[status(thm)],[fact_map__filter__map__filter])). 4.05/4.31 fof(c_0_9626, plain, ![X12171, X12172]:c_Relation_OId__on(X12172,X12171)=hAPP(c_Product__Type_Oprod_Oprod__case(X12172,X12172,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X12172,tc_HOL_Obool,tc_fun(X12172,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12172,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X12172,tc_HOL_Obool)),X12172),c_COMBC(X12172,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X12172,tc_HOL_Obool),tc_fun(X12172,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X12172),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X12172),c_fconj)),c_fequal))),X12171)), inference(variable_rename,[status(thm)],[fact_Id__on__def_H])). 4.05/4.31 cnf(c_0_9627, 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_5737])). 4.05/4.31 fof(c_0_9628, plain, ![X17217, X17218, X17219, X17220, X17221, X17222]:hAPP(hAPP(c_Set_Oinsert(tc_prod(X17222,X17221)),hAPP(hAPP(c_Product__Type_OPair(X17222,X17221),X17220),X17218)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X17222,X17221),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X17222,X17221),X17219),hAPP(c_COMBK(tc_fun(X17221,tc_HOL_Obool),X17222),hAPP(hAPP(c_Set_Oinsert(X17221),X17218),X17217)))),hAPP(hAPP(c_Product__Type_OSigma(X17222,X17221),hAPP(hAPP(c_Set_Oinsert(X17222),X17220),X17219)),hAPP(c_COMBK(tc_fun(X17221,tc_HOL_Obool),X17222),X17217))))=hAPP(hAPP(c_Product__Type_OSigma(X17222,X17221),hAPP(hAPP(c_Set_Oinsert(X17222),X17220),X17219)),hAPP(c_COMBK(tc_fun(X17221,tc_HOL_Obool),X17222),hAPP(hAPP(c_Set_Oinsert(X17221),X17218),X17217))), inference(variable_rename,[status(thm)],[fact_insert__times__insert])). 4.05/4.31 cnf(c_0_9629, 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)),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))=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))), inference(split_conjunct,[status(thm)],[c_0_5738])). 4.05/4.31 cnf(c_0_9630, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)), inference(split_conjunct,[status(thm)],[c_0_5739]), ['final']). 4.05/4.31 fof(c_0_9631, plain, ![X13241, X13242]:hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),X13242),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(X13242,tc_List_Olist(tc_fun(X13242,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X13242,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(X13242,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),X13242),c_List_Omap(tc_fun(X13242,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(X13242,tc_Nat_Onat),X13242,tc_Nat_Onat),c_COMBI(tc_fun(X13242,tc_Nat_Onat))))),X13241))=c_List_Omeasures(X13242,X13241), inference(variable_rename,[status(thm)],[fact_measures__def])). 4.05/4.31 fof(c_0_9632, plain, ![X15486, X15487]: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(X15487,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,X15487),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X15487)),X15486)))),hAPP(hAPP(c_COMBB(X15487,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X15487,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X15487,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X15487,X15486)))=c_Random_Oselect__weight(X15487,X15486), inference(variable_rename,[status(thm)],[fact_select__weight__def])). 4.05/4.31 cnf(c_0_9633, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5740, c_0_4475]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9634, plain, (c_List_Olenlex(X1,X2)=hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X1)),tc_List_Olist(X1)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X1),c_Wellfounded_Oless__than,c_List_Olex(X1,X2))),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_List_Olist(X1),tc_prod(tc_Nat_Onat,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X1),tc_prod(tc_Nat_Onat,tc_List_Olist(X1))),tc_List_Olist(X1)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X1))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_COMBI(tc_List_Olist(X1))))), inference(split_conjunct,[status(thm)],[c_0_5741])). 4.05/4.31 cnf(c_0_9635, 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_5742]), ['final']). 4.05/4.31 fof(c_0_9636, plain, ![X1742, X1743, X1744, X1745, X1746, X1747]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1744,tc_fun(X1746,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1747,tc_fun(X1744,tc_HOL_Obool)),X1745),X1743)),X1742)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1747,tc_fun(X1746,tc_HOL_Obool)),X1745),hAPP(hAPP(c_COMBC(X1747,tc_fun(X1744,tc_fun(X1746,tc_HOL_Obool)),tc_fun(X1746,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1744,tc_HOL_Obool),tc_fun(tc_fun(X1744,tc_fun(X1746,tc_HOL_Obool)),tc_fun(X1746,tc_HOL_Obool)),X1747),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1744,tc_fun(X1746,tc_HOL_Obool))),X1743)),X1742)), inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I9_J])). 4.05/4.31 cnf(c_0_9637, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Osublist(X1,X2,X3)),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)),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)))),X3))))=c_List_Osublist(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_5743])). 4.05/4.31 cnf(c_0_9638, 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)),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_5744, c_0_4434])). 4.05/4.31 cnf(c_0_9639, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X2)=hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X1,tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),X1),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(c_Lazy__Sequence_Oyield(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5745])). 4.05/4.31 fof(c_0_9640, plain, ![X13490]:c_Finite__Set_Ofun__left__comm__idem(X13490,tc_fun(X13490,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X13490,tc_HOL_Obool),tc_fun(tc_fun(X13490,tc_HOL_Obool),tc_fun(X13490,tc_HOL_Obool)),X13490),hAPP(c_COMBC(tc_fun(X13490,tc_HOL_Obool),tc_fun(X13490,tc_HOL_Obool),tc_fun(X13490,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X13490,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X13490,tc_fun(X13490,tc_HOL_Obool),tc_fun(X13490,tc_HOL_Obool)),c_Set_Oinsert(X13490)),c_Orderings_Obot__class_Obot(tc_fun(X13490,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_fun__left__comm__idem__remove])). 4.05/4.31 cnf(c_0_9641, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),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),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_5746])). 4.05/4.31 cnf(c_0_9642, 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_5747])). 4.05/4.31 cnf(c_0_9643, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3))=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)),X3)))),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat),X2),hAPP(c_List_Onth(X1),X3)))))), inference(split_conjunct,[status(thm)],[c_0_5748])). 4.05/4.31 cnf(c_0_9644, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))),c_Int_OMin)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5749, c_0_4474]), c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9645, plain, (hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),X5)=c_Enum_Oenum__the(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(rw,[status(thm)],[c_0_5750, c_0_4980])). 4.05/4.31 cnf(c_0_9646, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))),c_Int_OMin)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5751, c_0_4474]), c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9647, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5752, c_0_4795]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), c_0_4814]), ['final']). 4.05/4.31 fof(c_0_9648, plain, ![X8456, X8457, X8458, X8459, X8460]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8459,tc_fun(X8460,tc_HOL_Obool)),X8458),hAPP(hAPP(c_COMBC(X8459,tc_fun(X8460,tc_HOL_Obool),tc_fun(X8460,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8460,tc_HOL_Obool),tc_fun(tc_fun(X8460,tc_HOL_Obool),tc_fun(X8460,tc_HOL_Obool)),X8459),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8460,tc_HOL_Obool))),X8457)),X8456))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8460,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8459,tc_fun(X8460,tc_HOL_Obool)),X8458),X8457)),X8456), inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I6_J])). 4.05/4.31 fof(c_0_9649, plain, ![X10384, X10385, X10386, X10387, X10388]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10387,tc_fun(X10388,tc_HOL_Obool)),X10386),hAPP(hAPP(c_COMBC(X10387,tc_fun(X10388,tc_HOL_Obool),tc_fun(X10388,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10388,tc_HOL_Obool),tc_fun(tc_fun(X10388,tc_HOL_Obool),tc_fun(X10388,tc_HOL_Obool)),X10387),c_Groups_Ominus__class_Ominus(tc_fun(X10388,tc_HOL_Obool))),X10385)),X10384))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10388,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10387,tc_fun(X10388,tc_HOL_Obool)),X10386),X10385)),X10384), inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I6_J])). 4.05/4.31 fof(c_0_9650, plain, ![X6921, X6922, X6923, X6924, X6925]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6924,tc_fun(X6925,tc_HOL_Obool)),X6923),hAPP(hAPP(c_COMBC(X6924,tc_fun(X6925,tc_HOL_Obool),tc_fun(X6925,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6925,tc_HOL_Obool),tc_fun(tc_fun(X6925,tc_HOL_Obool),tc_fun(X6925,tc_HOL_Obool)),X6924),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6925,tc_HOL_Obool))),X6922)),X6921))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6925,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6924,tc_fun(X6925,tc_HOL_Obool)),X6923),X6922)),X6921), inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I4_J])). 4.05/4.31 cnf(c_0_9651, plain, (hAPP(c_Set_Ovimage(X1,tc_prod(X2,X3),X4),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X5),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X6)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,hAPP(c_Fun_Ocomp(tc_prod(X2,X3),X2,X1,c_Product__Type_Ofst(X2,X3)),X4)),X5)),hAPP(c_Set_Ovimage(X1,X3,hAPP(c_Fun_Ocomp(tc_prod(X2,X3),X3,X1,c_Product__Type_Osnd(X2,X3)),X4)),X6))), inference(split_conjunct,[status(thm)],[c_0_5754])). 4.05/4.31 cnf(c_0_9652, plain, (hAPP(hAPP(c_List_Omap(X1,X2),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2)),X3)),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3)),c_Option_Ooption_ONone(X2)))),X4))=c_List_Omap__filter(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_5755])). 4.05/4.31 cnf(c_0_9653, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3)),c_Option_Ooption_ONone(X2)))=c_Map_Odom(X1,X2,X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5756, c_0_5201]), c_0_4523]), ['final']). 4.05/4.31 cnf(c_0_9654, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5757, c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9655, 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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5758, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 fof(c_0_9656, plain, ![X8204, X8205, X8206, X8207]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X8207,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8206,tc_fun(tc_fun(X8207,tc_HOL_Obool),tc_HOL_Obool)),X8205),hAPP(hAPP(c_COMBB(tc_fun(X8207,tc_HOL_Obool),tc_fun(tc_fun(X8207,tc_HOL_Obool),tc_HOL_Obool),X8206),c_Set_OPow(X8207)),X8204))),hAPP(c_Set_OPow(X8207),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8206,tc_fun(X8207,tc_HOL_Obool)),X8205),X8204)))), inference(variable_rename,[status(thm)],[fact_UN__Pow__subset])). 4.05/4.31 fof(c_0_9657, plain, ![X8247, X8248, X8249, X8250]:hAPP(c_Set_Oimage(tc_prod(X8250,X8249),tc_prod(X8249,X8250),hAPP(c_Product__Type_Oprod_Oprod__case(X8250,X8249,tc_prod(X8249,X8250)),hAPP(c_COMBC(X8249,X8250,tc_prod(X8249,X8250)),c_Product__Type_OPair(X8249,X8250)))),hAPP(hAPP(c_Product__Type_OSigma(X8250,X8249),X8248),hAPP(c_COMBK(tc_fun(X8249,tc_HOL_Obool),X8250),X8247)))=hAPP(hAPP(c_Product__Type_OSigma(X8249,X8250),X8247),hAPP(c_COMBK(tc_fun(X8250,tc_HOL_Obool),X8249),X8248)), inference(variable_rename,[status(thm)],[fact_swap__product])). 4.05/4.31 cnf(c_0_9658, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2)),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5759, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9659, plain, (c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_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))|X1!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5760])). 4.05/4.31 cnf(c_0_9660, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),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)))))),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)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5761, c_0_5716]), c_0_5018])). 4.05/4.31 cnf(c_0_9661, 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_5762, c_0_5716]), ['final']). 4.05/4.31 cnf(c_0_9662, plain, (c_Map_Oran(X1,X2,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(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3))),c_Option_Ooption_OSome(X2))))), inference(split_conjunct,[status(thm)],[c_0_5763])). 4.05/4.31 fof(c_0_9663, plain, ![X7001, X7002, X7003, X7004, X7005, X7006]:hAPP(hAPP(c_List_Ozip(X7006,X7005),hAPP(hAPP(c_List_Omap(X7004,X7006),X7003),X7002)),X7001)=hAPP(hAPP(c_List_Omap(tc_prod(X7004,X7005),tc_prod(X7006,X7005)),hAPP(c_Product__Type_Oprod_Oprod__case(X7004,X7005,tc_prod(X7006,X7005)),hAPP(hAPP(c_COMBB(X7006,tc_fun(X7005,tc_prod(X7006,X7005)),X7004),c_Product__Type_OPair(X7006,X7005)),X7003))),hAPP(hAPP(c_List_Ozip(X7004,X7005),X7002),X7001)), inference(variable_rename,[status(thm)],[fact_zip__map1])). 4.05/4.31 cnf(c_0_9664, 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_5764])). 4.05/4.31 cnf(c_0_9665, plain, (hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))))=c_List_Oset__Cons(X1,hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_5765])). 4.05/4.31 cnf(c_0_9666, plain, (hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5766, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 fof(c_0_9667, plain, ![X12944, X12945]:hAPP(c_List_Olist_Olist__case(tc_List_Olist(X12945),X12945,c_List_Olist_ONil(X12945),hAPP(hAPP(c_COMBB(tc_List_Olist(X12945),tc_fun(tc_List_Olist(X12945),tc_List_Olist(X12945)),X12945),hAPP(c_COMBC(tc_List_Olist(X12945),tc_List_Olist(X12945),tc_List_Olist(X12945)),c_List_Oappend(X12945))),hAPP(hAPP(c_COMBC(X12945,tc_List_Olist(X12945),tc_List_Olist(X12945)),c_List_Olist_OCons(X12945)),c_List_Olist_ONil(X12945)))),X12944)=hAPP(c_List_Orotate1(X12945),X12944), inference(variable_rename,[status(thm)],[fact_rotate1__def])). 4.05/4.31 cnf(c_0_9668, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5767, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 fof(c_0_9669, plain, ![X4257, X4258, X4259, X4260, X4261, X4262]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4262,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4261,X4262,X4260),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4259,tc_fun(X4261,tc_HOL_Obool)),X4258),X4257))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4259,tc_fun(X4262,tc_HOL_Obool)),X4258),hAPP(hAPP(c_COMBB(tc_fun(X4261,tc_HOL_Obool),tc_fun(X4262,tc_HOL_Obool),X4259),c_Relation_OImage(X4261,X4262,X4260)),X4257)))), inference(variable_rename,[status(thm)],[fact_Image__INT__subset])). 4.05/4.31 fof(c_0_9670, plain, ![X10397, X10398, X10399, X10400, X10401]:hAPP(hAPP(c_List_Oappend(tc_prod(X10401,X10400)),hAPP(hAPP(c_List_Ozip(X10401,X10400),hAPP(hAPP(c_List_Otake(X10401),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10400)),X10398)),X10399)),X10398)),hAPP(hAPP(c_List_Ozip(X10401,X10400),hAPP(hAPP(c_List_Odrop(X10401),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10400)),X10398)),X10399)),X10397))=hAPP(hAPP(c_List_Ozip(X10401,X10400),X10399),hAPP(hAPP(c_List_Oappend(X10400),X10398),X10397)), inference(variable_rename,[status(thm)],[fact_zip__append2])). 4.05/4.31 cnf(c_0_9671, plain, (hAPP(c_New__DSequence_Opos__not__seq(X1),X2)=c_Lazy__Sequence_Ohb__not__seq(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5768, c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9672, plain, (hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5769, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 fof(c_0_9673, plain, ![X3335, X3336, X3337, X3338, X3339]:hAPP(hAPP(c_List_Oappend(tc_prod(X3339,X3338)),hAPP(hAPP(c_List_Ozip(X3339,X3338),X3337),hAPP(hAPP(c_List_Otake(X3338),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3339)),X3337)),X3335))),hAPP(hAPP(c_List_Ozip(X3339,X3338),X3336),hAPP(hAPP(c_List_Odrop(X3338),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3339)),X3337)),X3335)))=hAPP(hAPP(c_List_Ozip(X3339,X3338),hAPP(hAPP(c_List_Oappend(X3339),X3337),X3336)),X3335), inference(variable_rename,[status(thm)],[fact_zip__append1])). 4.05/4.31 fof(c_0_9674, plain, ![X11056, X11057, X11058, X11059, X11060, X11061, X11062]:hAPP(c_List_Ofoldl(X11062,X11058,hAPP(hAPP(c_COMBC(X11062,tc_fun(X11058,X11061),tc_fun(X11058,X11062)),hAPP(hAPP(c_COMBB(tc_fun(X11061,X11062),tc_fun(tc_fun(X11058,X11061),tc_fun(X11058,X11062)),X11062),c_COMBB(X11061,X11062,X11058)),X11060)),X11057),X11059),X11056)=hAPP(c_List_Ofoldl(X11062,X11061,X11060,X11059),hAPP(hAPP(c_List_Omap(X11058,X11061),X11057),X11056)), inference(variable_rename,[status(thm)],[fact_foldl__map])). 4.05/4.31 fof(c_0_9675, plain, ![X14624, X14625, X14626, X14627, X14628, X14629, X14630]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14626,tc_fun(tc_prod(X14630,X14628),tc_HOL_Obool)),X14625),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X14629,X14628),tc_HOL_Obool),tc_fun(tc_prod(X14630,X14628),tc_HOL_Obool),X14626),hAPP(c_Relation_Orel__comp(X14630,X14629,X14628),X14627)),X14624))=hAPP(hAPP(c_Relation_Orel__comp(X14630,X14629,X14628),X14627),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14626,tc_fun(tc_prod(X14629,X14628),tc_HOL_Obool)),X14625),X14624)), inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib])). 4.05/4.31 fof(c_0_9676, plain, ![X12856, X12857, X12858, X12859, X12860, X12861]:hAPP(hAPP(c_COMBS(tc_prod(X12861,X12860),X12860,X12859),hAPP(hAPP(c_COMBB(X12858,tc_fun(X12860,X12859),tc_prod(X12861,X12860)),X12857),hAPP(hAPP(c_COMBB(X12861,X12858,tc_prod(X12861,X12860)),X12856),c_Product__Type_Ofst(X12861,X12860)))),c_Product__Type_Osnd(X12861,X12860))=hAPP(c_Product__Type_Oprod_Oprod__case(X12861,X12860,X12859),hAPP(hAPP(c_COMBB(X12858,tc_fun(X12860,X12859),X12861),X12857),X12856)), inference(variable_rename,[status(thm)],[fact_split__comp__eq])). 4.05/4.31 fof(c_0_9677, plain, ![X5450, X5451, X5452, X5453, X5454, X5455, X5456, X5457]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5453,X5452,X5455),hAPP(hAPP(c_COMBB(tc_fun(X5452,tc_prod(X5457,X5456)),tc_fun(X5452,X5455),X5453),hAPP(c_COMBB(tc_prod(X5457,X5456),X5455,X5452),hAPP(c_Product__Type_Oprod_Oprod__case(X5457,X5456,X5455),X5454))),X5451)),X5450)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5457,X5456,X5455),X5454),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5453,X5452,tc_prod(X5457,X5456)),X5451),X5450)), inference(variable_rename,[status(thm)],[fact_split__twice])). 4.05/4.31 fof(c_0_9678, plain, ![X6310, X6311, X6312, X6313, X6314]:c_Map_Orestrict__map(X6314,X6313,X6312,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6314,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X6314),X6311),c_Orderings_Obot__class_Obot(tc_fun(X6314,tc_HOL_Obool)))))=c_Map_Orestrict__map(X6314,X6313,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6314,tc_Option_Ooption(X6313)),X6312),X6311),hAPP(c_Option_Ooption_OSome(X6313),X6310)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6314,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X6314),X6311),c_Orderings_Obot__class_Obot(tc_fun(X6314,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_restrict__upd__same])). 4.05/4.31 cnf(c_0_9679, plain, (c_Int_Oint__ge__less__than2(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_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))))), inference(split_conjunct,[status(thm)],[c_0_5770])). 4.05/4.31 cnf(c_0_9680, 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_5771, c_0_5049]), c_0_5050])). 4.05/4.31 fof(c_0_9681, plain, ![X13503, X13504, X13505, X13506]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X13506,tc_HOL_Obool),tc_fun(tc_prod(X13506,X13505),tc_HOL_Obool)),X13504),hAPP(hAPP(c_COMBC(tc_fun(X13506,tc_HOL_Obool),tc_fun(X13506,tc_fun(X13505,tc_HOL_Obool)),tc_fun(tc_prod(X13506,X13505),tc_HOL_Obool)),c_Product__Type_OSigma(X13506,X13505)),X13503))=hAPP(hAPP(c_Product__Type_OSigma(X13506,X13505),c_Complete__Lattice_OSup__class_OSup(tc_fun(X13506,tc_HOL_Obool),X13504)),X13503), inference(variable_rename,[status(thm)],[fact_Sigma__Union])). 4.05/4.31 fof(c_0_9682, plain, ![X10928, X10929, X10930, X10931, X10932]:c_Nat_Onat_Onat__case(tc_List_Olist(X10932),hAPP(hAPP(c_List_Olist_OCons(X10932),X10928),X10930),hAPP(hAPP(c_COMBB(tc_List_Olist(X10932),tc_List_Olist(X10932),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X10932),X10931)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X10932,tc_List_Olist(X10932)),c_List_Olist__update(X10932,X10930)),X10928)),X10929)=hAPP(hAPP(c_List_Olist__update(X10932,hAPP(hAPP(c_List_Olist_OCons(X10932),X10931),X10930)),X10929),X10928), inference(variable_rename,[status(thm)],[fact_list__update_Osimps_I2_J])). 4.05/4.31 fof(c_0_9683, plain, ![X11313, X11314, X11315, X11316]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11316,tc_fun(X11315,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X11316,tc_HOL_Obool),X11314)),X11313)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X11316,tc_HOL_Obool),tc_fun(X11315,tc_HOL_Obool)),X11314),hAPP(hAPP(c_COMBC(tc_fun(X11316,tc_HOL_Obool),tc_fun(X11316,tc_fun(X11315,tc_HOL_Obool)),tc_fun(X11315,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11316,tc_fun(X11315,tc_HOL_Obool))),X11313)), inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I8_J])). 4.05/4.31 cnf(c_0_9684, 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_5772])). 4.05/4.31 cnf(c_0_9685, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3))),X3))), inference(split_conjunct,[status(thm)],[c_0_5773])). 4.05/4.31 cnf(c_0_9686, 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_5774])). 4.05/4.31 fof(c_0_9687, plain, ![X1274, X1275, X1276, X1277]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1277,tc_fun(X1276,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1277,tc_HOL_Obool),X1275)),X1274)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1277,tc_HOL_Obool),tc_fun(X1276,tc_HOL_Obool)),X1275),hAPP(hAPP(c_COMBC(tc_fun(X1277,tc_HOL_Obool),tc_fun(X1277,tc_fun(X1276,tc_HOL_Obool)),tc_fun(X1276,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1277,tc_fun(X1276,tc_HOL_Obool))),X1274)), inference(variable_rename,[status(thm)],[fact_UN__simps_I8_J])). 4.05/4.31 cnf(c_0_9688, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))),c_Int_OMin)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5775, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9689, 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_5776])). 4.05/4.31 cnf(c_0_9690, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5777, c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9691, plain, (c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5778, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9692, plain, (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))))=hAPP(c_Set_OCollect(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_5779])). 4.05/4.31 fof(c_0_9693, plain, ![X7313]: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)),X7313),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)), inference(variable_rename,[status(thm)],[fact_wmin__emptyI])). 4.05/4.31 fof(c_0_9694, plain, ![X2701, X2702, X2703]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2703,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2703,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X2703,tc_HOL_Obool),tc_HOL_Obool)),X2702),X2701))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2703,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2703,tc_HOL_Obool),X2702)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2703,tc_HOL_Obool),X2701)))), inference(variable_rename,[status(thm)],[fact_Union__Int__subset])). 4.05/4.31 fof(c_0_9695, plain, ![X10389, X10390, X10391]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10391,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10391,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10391,tc_HOL_Obool),X10390)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10391,tc_HOL_Obool),X10389))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10391,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X10391,tc_HOL_Obool),tc_HOL_Obool)),X10390),X10389)))), inference(variable_rename,[status(thm)],[fact_Inter__Un__subset])). 4.05/4.31 cnf(c_0_9696, 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_5780])). 4.05/4.31 fof(c_0_9697, plain, ![X14474, X14475, X14476, X14477, X14478]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14476,tc_fun(tc_prod(X14477,X14478),tc_HOL_Obool)),X14475),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X14478,X14477),tc_HOL_Obool),tc_fun(tc_prod(X14477,X14478),tc_HOL_Obool),X14476),c_Relation_Oconverse(X14478,X14477)),X14474))=hAPP(c_Relation_Oconverse(X14478,X14477),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X14476,tc_fun(tc_prod(X14478,X14477),tc_HOL_Obool)),X14475),X14474)), inference(variable_rename,[status(thm)],[fact_converse__INTER])). 4.05/4.31 fof(c_0_9698, plain, ![X10174, X10175, X10176, X10177, X10178]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10176,tc_fun(tc_prod(X10177,X10178),tc_HOL_Obool)),X10175),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X10178,X10177),tc_HOL_Obool),tc_fun(tc_prod(X10177,X10178),tc_HOL_Obool),X10176),c_Relation_Oconverse(X10178,X10177)),X10174))=hAPP(c_Relation_Oconverse(X10178,X10177),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10176,tc_fun(tc_prod(X10178,X10177),tc_HOL_Obool)),X10175),X10174)), inference(variable_rename,[status(thm)],[fact_converse__UNION])). 4.05/4.31 fof(c_0_9699, plain, ![X9758, X9759, X9760, X9761, X9762]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9762,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9762,tc_HOL_Obool)),hAPP(c_Set_Oimage(X9761,X9762,X9760),X9759)),hAPP(c_Set_Oimage(X9761,X9762,X9760),X9758))),hAPP(c_Set_Oimage(X9761,X9762,X9760),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9761,tc_HOL_Obool)),X9759),X9758)))), inference(variable_rename,[status(thm)],[fact_image__diff__subset])). 4.05/4.31 fof(c_0_9700, plain, ![X7513, X7514, X7515, X7516, X7517]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7517,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7516,X7517,X7515),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7516,tc_HOL_Obool)),X7514),X7513))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7517,tc_HOL_Obool)),hAPP(c_Relation_OImage(X7516,X7517,X7515),X7514)),hAPP(c_Relation_OImage(X7516,X7517,X7515),X7513)))), inference(variable_rename,[status(thm)],[fact_Image__Int__subset])). 4.05/4.31 fof(c_0_9701, plain, ![X5826, X5827, X5828, X5829, X5830]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5830,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5829,X5830,X5828),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5829,tc_HOL_Obool)),X5827),X5826))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5830,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5829,X5830,X5828),X5827)),hAPP(c_Set_Oimage(X5829,X5830,X5828),X5826)))), inference(variable_rename,[status(thm)],[fact_image__Int__subset])). 4.05/4.31 cnf(c_0_9702, 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),c_Transitive__Closure_Ortrancl(X1,X2)),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_5781, c_0_5018])). 4.05/4.31 cnf(c_0_9703, plain, (hAPP(c_List_Orotate(X1,X2),X3)=hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3)),hAPP(hAPP(c_List_Otake(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3))), inference(split_conjunct,[status(thm)],[c_0_5782])). 4.05/4.31 fof(c_0_9704, plain, ![X10951, X10952]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X10952,X10952),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(X10952,X10952),tc_HOL_Obool),tc_fun(tc_prod(X10952,X10952),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X10952,X10952),tc_HOL_Obool)),X10951))=c_Transitive__Closure_Ortrancl(X10952,X10951), inference(variable_rename,[status(thm)],[fact_rtrancl__is__UN__rel__pow])). 4.05/4.31 fof(c_0_9705, plain, ![X15335, X15336, X15337, X15338]:c_Nat_Onat_Onat__case(tc_List_Olist(X15338),c_List_Olist_ONil(X15338),hAPP(hAPP(c_COMBB(tc_List_Olist(X15338),tc_List_Olist(X15338),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X15338),X15336)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X15338),tc_List_Olist(X15338)),c_List_Otake(X15338)),X15335)),X15337)=hAPP(hAPP(c_List_Otake(X15338),X15337),hAPP(hAPP(c_List_Olist_OCons(X15338),X15336),X15335)), inference(variable_rename,[status(thm)],[fact_take__Cons])). 4.05/4.31 fof(c_0_9706, plain, ![X1551, X1552, X1553]:hAPP(c_List_Otl(X1553),hAPP(hAPP(c_List_Oappend(X1553),X1552),X1551))=hAPP(c_List_Olist_Olist__case(tc_List_Olist(X1553),X1553,hAPP(c_List_Otl(X1553),X1551),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1553),tc_List_Olist(X1553)),X1553),hAPP(hAPP(c_COMBC(tc_List_Olist(X1553),tc_List_Olist(X1553),tc_List_Olist(X1553)),c_List_Oappend(X1553)),X1551))),X1552), inference(variable_rename,[status(thm)],[fact_tl__append])). 4.05/4.31 fof(c_0_9707, plain, ![X9604, X9605, X9606, X9607]:(c_Fun_Oinj__on(X9607,tc_prod(X9606,X9607),esk293_4(X9604,X9605,X9606,X9607),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9606,tc_fun(X9607,tc_HOL_Obool)),X9605),X9604))&hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X9606,X9607),tc_HOL_Obool)),hAPP(c_Set_Oimage(X9607,tc_prod(X9606,X9607),esk293_4(X9604,X9605,X9606,X9607)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9606,tc_fun(X9607,tc_HOL_Obool)),X9605),X9604))),hAPP(hAPP(c_Product__Type_OSigma(X9606,X9607),X9605),X9604)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_Ex__inj__on__UNION__Sigma])])). 4.05/4.31 fof(c_0_9708, plain, ![X12617, X12618, X12619, X12620]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12620,tc_HOL_Obool)),hAPP(c_Relation_ORange(X12619,X12620),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X12619,X12620),tc_HOL_Obool)),X12618),X12617))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12620,tc_HOL_Obool)),hAPP(c_Relation_ORange(X12619,X12620),X12618)),hAPP(c_Relation_ORange(X12619,X12620),X12617)))), inference(variable_rename,[status(thm)],[fact_Range__Int__subset])). 4.05/4.31 fof(c_0_9709, plain, ![X1238, X1239, X1240, X1241]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1241,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1241,X1240),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1241,X1240),tc_HOL_Obool)),X1239),X1238))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1241,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1241,X1240),X1239)),hAPP(c_Relation_ODomain(X1241,X1240),X1238)))), inference(variable_rename,[status(thm)],[fact_Domain__Int__subset])). 4.05/4.31 fof(c_0_9710, plain, ![X4643, X4644, X4645, X4646]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4646,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4646,tc_HOL_Obool)),hAPP(c_Relation_ORange(X4645,X4646),X4644)),hAPP(c_Relation_ORange(X4645,X4646),X4643))),hAPP(c_Relation_ORange(X4645,X4646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4645,X4646),tc_HOL_Obool)),X4644),X4643)))), inference(variable_rename,[status(thm)],[fact_Range__Diff__subset])). 4.05/4.31 fof(c_0_9711, plain, ![X9989, X9990, X9991]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X9991,tc_HOL_Obool),tc_fun(X9991,tc_HOL_Obool)),X9990),hAPP(hAPP(c_COMBC(tc_fun(X9991,tc_HOL_Obool),tc_fun(X9991,tc_HOL_Obool),tc_fun(X9991,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9991,tc_HOL_Obool))),X9989))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9991,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X9991,tc_HOL_Obool),X9990)),X9989), inference(variable_rename,[status(thm)],[fact_Int__Union2])). 4.05/4.31 fof(c_0_9712, plain, ![X11758, X11759, X11760, X11761]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11761,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X11761,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X11761,X11760),X11759)),hAPP(c_Relation_ODomain(X11761,X11760),X11758))),hAPP(c_Relation_ODomain(X11761,X11760),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X11761,X11760),tc_HOL_Obool)),X11759),X11758)))), inference(variable_rename,[status(thm)],[fact_Domain__Diff__subset])). 4.05/4.31 cnf(c_0_9713, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X1))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X1))),c_Int_OMin)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5783, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9714, 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_5784]), ['final']). 4.05/4.31 fof(c_0_9715, plain, ![X15858, X15859, X15860]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X15860,X15860),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15860,X15860),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X15860,X15859)),c_Transitive__Closure_Ortrancl(X15860,X15858))),c_Transitive__Closure_Ortrancl(X15860,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15860,X15860),tc_HOL_Obool)),X15859),X15858)))), inference(variable_rename,[status(thm)],[fact_rtrancl__Un__subset])). 4.05/4.31 fof(c_0_9716, plain, ![X782, X783, X784]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X784,X783),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X784,X783),X782),hAPP(c_COMBK(tc_fun(X783,tc_HOL_Obool),X784),c_Orderings_Otop__class_Otop(tc_fun(X783,tc_HOL_Obool)))))=hAPP(hAPP(c_Product__Type_OSigma(X784,X783),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X784,tc_HOL_Obool)),X782)),hAPP(c_COMBK(tc_fun(X783,tc_HOL_Obool),X784),c_Orderings_Otop__class_Otop(tc_fun(X783,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV2])). 4.05/4.31 cnf(c_0_9717, 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_5785])). 4.05/4.31 fof(c_0_9718, plain, ![X8076, X8077, X8078]:hAPP(hAPP(c_Product__Type_OSigma(X8078,X8077),c_Orderings_Otop__class_Otop(tc_fun(X8078,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X8077,tc_HOL_Obool),X8078),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8077,tc_HOL_Obool)),X8076)))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X8078,X8077),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X8078,X8077),c_Orderings_Otop__class_Otop(tc_fun(X8078,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X8077,tc_HOL_Obool),X8078),X8076))), inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV1])). 4.05/4.31 fof(c_0_9719, plain, ![X9111, X9112, X9113, X9114, X9115]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9115,tc_fun(X9114,tc_HOL_Obool)),X9113),hAPP(hAPP(c_COMBB(tc_fun(X9114,tc_HOL_Obool),tc_fun(X9114,tc_HOL_Obool),X9115),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9114,tc_HOL_Obool)),X9112)),X9111))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9114,tc_HOL_Obool)),X9112),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X9115,tc_fun(X9114,tc_HOL_Obool)),X9113),X9111)), inference(variable_rename,[status(thm)],[fact_INT__simps_I7_J])). 4.05/4.31 fof(c_0_9720, plain, ![X11484, X11485, X11486]:c_Hilbert__Choice_OEps(tc_prod(X11486,X11485),hAPP(hAPP(c_COMBS(tc_prod(X11486,X11485),X11485,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X11486,tc_fun(X11485,tc_HOL_Obool),tc_prod(X11486,X11485)),X11484),c_Product__Type_Ofst(X11486,X11485))),c_Product__Type_Osnd(X11486,X11485)))=c_Hilbert__Choice_OEps(tc_prod(X11486,X11485),hAPP(c_Product__Type_Oprod_Oprod__case(X11486,X11485,tc_HOL_Obool),X11484)), inference(variable_rename,[status(thm)],[fact_Eps__split])). 4.05/4.31 cnf(c_0_9721, 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_5786])). 4.05/4.31 fof(c_0_9722, plain, ![X1534, X1535, X1536, X1537, X1538]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1536,tc_fun(X1538,tc_HOL_Obool)),X1535),hAPP(hAPP(c_COMBB(tc_fun(X1538,tc_HOL_Obool),tc_fun(X1538,tc_HOL_Obool),X1536),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1538,tc_HOL_Obool)),X1537)),X1534))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1538,tc_HOL_Obool)),X1537),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1536,tc_fun(X1538,tc_HOL_Obool)),X1535),X1534)), inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I5_J])). 4.05/4.31 fof(c_0_9723, plain, ![X13024, X13025, X13026, X13027, X13028]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13027,tc_HOL_Obool)),X13025),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X13028,tc_fun(X13027,tc_HOL_Obool)),X13026),X13024))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X13028,tc_fun(X13027,tc_HOL_Obool)),X13026),hAPP(hAPP(c_COMBB(tc_fun(X13027,tc_HOL_Obool),tc_fun(X13027,tc_HOL_Obool),X13028),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X13027,tc_HOL_Obool)),X13025)),X13024)), inference(variable_rename,[status(thm)],[fact_UN__simps_I7_J])). 4.05/4.31 cnf(c_0_9724, 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_5787])). 4.05/4.31 fof(c_0_9725, plain, ![X9661, X9662, X9663, X9664, X9665, X9666]:hAPP(hAPP(c_List_Ozip(X9666,X9665),hAPP(hAPP(c_List_Olist__update(X9666,X9664),X9662),hAPP(c_Product__Type_Ofst(X9666,X9665),X9661))),hAPP(hAPP(c_List_Olist__update(X9665,X9663),X9662),hAPP(c_Product__Type_Osnd(X9666,X9665),X9661)))=hAPP(hAPP(c_List_Olist__update(tc_prod(X9666,X9665),hAPP(hAPP(c_List_Ozip(X9666,X9665),X9664),X9663)),X9662),X9661), inference(variable_rename,[status(thm)],[fact_update__zip])). 4.05/4.31 cnf(c_0_9726, plain, (hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)=hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5788])). 4.05/4.31 fof(c_0_9727, plain, ![X15659, X15660, X15661]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X15661,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X15661,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X15661),X15660)),hAPP(c_Set_OPow(X15661),X15659))),hAPP(c_Set_OPow(X15661),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15661,tc_HOL_Obool)),X15660),X15659)))), inference(variable_rename,[status(thm)],[fact_Un__Pow__subset])). 4.05/4.31 cnf(c_0_9728, plain, (c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5789, c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9729, 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_5790, c_0_5791])). 4.05/4.31 cnf(c_0_9730, 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_5792, c_0_5149]), c_0_5149]), c_0_5149]), ['final']). 4.05/4.31 fof(c_0_9731, plain, ![X934, X935, X936, X937, X938, X939]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X939,X937),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X939,X938,X937),X936),X934)),hAPP(hAPP(c_Relation_Orel__comp(X939,X938,X937),X935),X934))=hAPP(hAPP(c_Relation_Orel__comp(X939,X938,X937),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X939,X938),tc_HOL_Obool)),X936),X935)),X934), inference(variable_rename,[status(thm)],[fact_rel__comp__distrib2])). 4.05/4.31 cnf(c_0_9732, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),c_Int_OMin))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),c_Int_OMin))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5793, c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9733, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5794, c_0_4814]), c_0_5795]), c_0_4505]), c_0_4795]), c_0_5796]), ['final']). 4.05/4.31 fof(c_0_9734, plain, ![X1714, X1715, X1716, X1717, X1718, X1719]:hAPP(hAPP(c_Relation_Orel__comp(X1719,X1718,X1717),X1716),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1718,X1717),tc_HOL_Obool)),X1715),X1714))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1719,X1717),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1719,X1718,X1717),X1716),X1715)),hAPP(hAPP(c_Relation_Orel__comp(X1719,X1718,X1717),X1716),X1714)), inference(variable_rename,[status(thm)],[fact_rel__comp__distrib])). 4.05/4.31 cnf(c_0_9735, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))),c_Int_OMin)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5797, c_0_4474]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 cnf(c_0_9736, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)), inference(split_conjunct,[status(thm)],[c_0_5798])). 4.05/4.31 fof(c_0_9737, plain, ![X10055, X10056, X10057, X10058, X10059]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10058,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10059,tc_fun(X10058,tc_HOL_Obool)),X10057),X10055)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10059,tc_fun(X10058,tc_HOL_Obool)),X10056),X10055))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10059,tc_fun(X10058,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10059,tc_HOL_Obool)),X10057),X10056)),X10055), inference(variable_rename,[status(thm)],[fact_UN__Un])). 4.05/4.31 fof(c_0_9738, plain, ![X6370, X6371, X6372, X6373, X6374]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6374,tc_fun(X6373,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6374,tc_HOL_Obool)),X6372),X6371)),X6370)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6373,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6374,tc_fun(X6373,tc_HOL_Obool)),X6372),X6370)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6374,tc_fun(X6373,tc_HOL_Obool)),X6371),X6370)), inference(variable_rename,[status(thm)],[fact_INT__Un])). 4.05/4.31 cnf(c_0_9739, plain, (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))=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)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5799, c_0_4767]), c_0_4767])). 4.05/4.31 cnf(c_0_9740, 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_5800]), ['final']). 4.05/4.31 cnf(c_0_9741, 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_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))), inference(split_conjunct,[status(thm)],[c_0_5801])). 4.05/4.31 cnf(c_0_9742, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1)),c_Int_OMin))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))),c_Int_OMin)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5802, c_0_4474]), c_0_4474]), c_0_4434]), c_0_4434]), c_0_4475]), c_0_4475])). 4.05/4.31 fof(c_0_9743, plain, ![X9800, X9801, X9802]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9802),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X9801),X9800))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9802),c_Divides_Odiv__class_Omod(tc_Int_Oint,X9801,X9800))),X9800))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9802),X9801)),X9800), inference(variable_rename,[status(thm)],[fact_zdiv__zmult1__eq])). 4.05/4.31 fof(c_0_9744, plain, ![X6256, X6257, X6258]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6258),X6257)),X6256)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6258),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X6257),X6256))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6258),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X6257,X6256))),X6256)), inference(variable_rename,[status(thm)],[fact_div__mult1__eq])). 4.05/4.31 fof(c_0_9745, plain, ![X12962, X12963, X12964, X12965]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12964,tc_fun(tc_fun(X12965,tc_HOL_Obool),tc_HOL_Obool)),X12963),hAPP(hAPP(c_COMBB(tc_fun(X12965,tc_HOL_Obool),tc_fun(tc_fun(X12965,tc_HOL_Obool),tc_HOL_Obool),X12964),c_Set_OPow(X12965)),X12962))=hAPP(c_Set_OPow(X12965),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X12964,tc_fun(X12965,tc_HOL_Obool)),X12963),X12962)), inference(variable_rename,[status(thm)],[fact_Pow__INT__eq])). 4.05/4.31 cnf(c_0_9746, 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),esk114_1(X1)),esk115_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_5803])). 4.05/4.31 fof(c_0_9747, plain, ![X12439, X12440, X12441, X12442, X12443]:c_List_Omap__filter(X12443,X12442,X12441,hAPP(hAPP(c_List_Olist_OCons(X12443),X12440),X12439))=hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(X12442),X12442,c_List_Omap__filter(X12443,X12442,X12441,X12439),hAPP(hAPP(c_COMBC(X12442,tc_List_Olist(X12442),tc_List_Olist(X12442)),c_List_Olist_OCons(X12442)),c_List_Omap__filter(X12443,X12442,X12441,X12439))),hAPP(X12441,X12440)), inference(variable_rename,[status(thm)],[fact_map__filter__simps_I1_J])). 4.05/4.31 cnf(c_0_9748, 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_5804])). 4.05/4.31 fof(c_0_9749, plain, ![X11227, X11228, X11229, X11230]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11230,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11229,tc_fun(X11230,tc_HOL_Obool)),X11228),X11227))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X11229,tc_fun(X11230,tc_HOL_Obool)),X11228),hAPP(hAPP(c_COMBB(tc_fun(X11230,tc_HOL_Obool),tc_fun(X11230,tc_HOL_Obool),X11229),c_Groups_Ouminus__class_Ouminus(tc_fun(X11230,tc_HOL_Obool))),X11227)), inference(variable_rename,[status(thm)],[fact_Compl__INT])). 4.05/4.31 fof(c_0_9750, plain, ![X4109, X4110, X4111, X4112]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4112,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4111,tc_fun(X4112,tc_HOL_Obool)),X4110),X4109))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4111,tc_fun(X4112,tc_HOL_Obool)),X4110),hAPP(hAPP(c_COMBB(tc_fun(X4112,tc_HOL_Obool),tc_fun(X4112,tc_HOL_Obool),X4111),c_Groups_Ouminus__class_Ouminus(tc_fun(X4112,tc_HOL_Obool))),X4109)), inference(variable_rename,[status(thm)],[fact_Compl__UN])). 4.05/4.31 fof(c_0_9751, plain, ![X7315, X7316, X7317, X7318]:hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7318,X7318),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7317),X7316)),X7315)=hAPP(hAPP(c_Relation_Orel__comp(X7318,X7318,X7318),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7318,X7318),tc_HOL_Obool),X7317),X7315)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X7318,X7318),tc_HOL_Obool),X7316),X7315)), inference(variable_rename,[status(thm)],[fact_rel__pow__add])). 4.05/4.31 fof(c_0_9752, plain, ![X3497, X3498, X3499, X3500, X3501, X3502, X3503, X3504, X3505, X3506]:c_Product__Type_Omap__pair(X3502,X3504,X3501,X3503,hAPP(c_Fun_Ocomp(X3506,X3504,X3502,X3500),X3498),hAPP(c_Fun_Ocomp(X3505,X3503,X3501,X3499),X3497))=hAPP(c_Fun_Ocomp(tc_prod(X3506,X3505),tc_prod(X3504,X3503),tc_prod(X3502,X3501),c_Product__Type_Omap__pair(X3506,X3504,X3505,X3503,X3500,X3499)),c_Product__Type_Omap__pair(X3502,X3506,X3501,X3505,X3498,X3497)), inference(variable_rename,[status(thm)],[fact_map__pair_Ocomp])). 4.05/4.31 fof(c_0_9753, plain, ![X3209, X3210]:c_Random_Oselect__weight(X3210,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X3210),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X3210,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3210,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X3210)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X3209))=c_Random_Oselect__weight(X3210,X3209), inference(variable_rename,[status(thm)],[fact_select__weigth__drop__zero])). 4.05/4.31 fof(c_0_9754, plain, ![X3273, X3274]:c_Random_Opick(X3274,X3273)=c_Random_Opick(X3274,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X3274),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X3274,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3274,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X3274)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X3273)), inference(variable_rename,[status(thm)],[fact_pick__drop__zero])). 4.05/4.31 fof(c_0_9755, plain, ![X14741, X14742, X14743]:hAPP(c_Set_OPow(X14743),hAPP(hAPP(c_Set_Oinsert(X14743),X14742),X14741))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X14743,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X14743),X14741)),hAPP(c_Set_Oimage(tc_fun(X14743,tc_HOL_Obool),tc_fun(X14743,tc_HOL_Obool),hAPP(c_Set_Oinsert(X14743),X14742)),hAPP(c_Set_OPow(X14743),X14741))), inference(variable_rename,[status(thm)],[fact_Pow__insert])). 4.05/4.31 cnf(c_0_9756, 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_5805])). 4.05/4.31 fof(c_0_9757, plain, ![X5655, X5656, X5657, X5658, X5659]:hAPP(hAPP(c_Set_Oinsert(X5659),X5658),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5657,tc_fun(X5659,tc_HOL_Obool)),X5656),X5655))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5657,tc_fun(X5659,tc_HOL_Obool)),X5656),hAPP(hAPP(c_COMBB(tc_fun(X5659,tc_HOL_Obool),tc_fun(X5659,tc_HOL_Obool),X5657),hAPP(c_Set_Oinsert(X5659),X5658)),X5655)), inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I5_J])). 4.05/4.31 fof(c_0_9758, plain, ![X1012, X1013, X1014, X1015]:hAPP(c_Map_Omap__of(X1015,X1014),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1015,X1014)),X1013),X1012))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1015,tc_Option_Ooption(X1014)),hAPP(c_Map_Omap__of(X1015,X1014),X1012)),hAPP(c_Product__Type_Ofst(X1015,X1014),X1013)),hAPP(c_Option_Ooption_OSome(X1014),hAPP(c_Product__Type_Osnd(X1015,X1014),X1013))), inference(variable_rename,[status(thm)],[fact_map__of_Osimps_I2_J])). 4.05/4.31 cnf(c_0_9759, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5806, c_0_5018]), c_0_5018])). 4.05/4.31 cnf(c_0_9760, 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_5807]), ['final']). 4.05/4.31 cnf(c_0_9761, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)),X3)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)), inference(split_conjunct,[status(thm)],[c_0_5808])). 4.05/4.31 cnf(c_0_9762, 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_5809]), ['final']). 4.05/4.31 cnf(c_0_9763, 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_5810])). 4.05/4.31 cnf(c_0_9764, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_Ovimage(X2,X4,X5)),X6))=hAPP(c_Set_Ovimage(X2,X4,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6))), inference(split_conjunct,[status(thm)],[c_0_5811])). 4.05/4.31 cnf(c_0_9765, 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_5812])). 4.05/4.31 cnf(c_0_9766, 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_5813, c_0_4822]), c_0_5814]), c_0_4822]), ['final']). 4.05/4.31 fof(c_0_9767, plain, ![X14548, X14549, X14550, X14551, X14552, X14553]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14550,tc_fun(X14552,tc_HOL_Obool)),X14549),hAPP(hAPP(c_COMBB(tc_fun(X14553,tc_HOL_Obool),tc_fun(X14552,tc_HOL_Obool),X14550),c_Relation_OImage(X14553,X14552,X14551)),X14548))=hAPP(c_Relation_OImage(X14553,X14552,X14551),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X14550,tc_fun(X14553,tc_HOL_Obool)),X14549),X14548)), inference(variable_rename,[status(thm)],[fact_Image__UN])). 4.05/4.31 fof(c_0_9768, plain, ![X2500, X2501, X2502, X2503, X2504, X2505]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2502,tc_fun(X2504,tc_HOL_Obool)),X2501),hAPP(hAPP(c_COMBB(tc_fun(X2505,tc_HOL_Obool),tc_fun(X2504,tc_HOL_Obool),X2502),c_Set_Oimage(X2505,X2504,X2503)),X2500))=hAPP(c_Set_Oimage(X2505,X2504,X2503),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2502,tc_fun(X2505,tc_HOL_Obool)),X2501),X2500)), inference(variable_rename,[status(thm)],[fact_image__UN])). 4.05/4.31 cnf(c_0_9769, plain, (hAPP(c_Set_Ovimage(X1,X2,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_Set_Ovimage(X1,X2,X3)),X6))), inference(split_conjunct,[status(thm)],[c_0_5815])). 4.05/4.31 cnf(c_0_9770, 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_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),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_5816])). 4.05/4.31 fof(c_0_9771, plain, ![X17501, X17502, X17503, X17504]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17504,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17504,tc_HOL_Obool)),X17503),X17501)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17504,tc_HOL_Obool)),X17502),X17501))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17504,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17504,tc_HOL_Obool)),X17503),X17502)),X17501), inference(variable_rename,[status(thm)],[fact_Un__Diff])). 4.05/4.31 fof(c_0_9772, plain, ![X8005, X8006, X8007, X8008]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8008,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8008,tc_HOL_Obool)),X8007),X8006)),X8005)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8008,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8008,tc_HOL_Obool)),X8007),X8005)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8008,tc_HOL_Obool)),X8006),X8005)), inference(variable_rename,[status(thm)],[fact_Int__Un__distrib2])). 4.05/4.31 fof(c_0_9773, plain, ![X12744, X12745, X12746, X12747]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12747,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12747,tc_HOL_Obool)),X12746),X12745)),X12744)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12747,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12747,tc_HOL_Obool)),X12746),X12744)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12747,tc_HOL_Obool)),X12745),X12744)), inference(variable_rename,[status(thm)],[fact_Un__Int__distrib2])). 4.05/4.31 cnf(c_0_9774, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_5817])). 4.05/4.31 fof(c_0_9775, plain, ![X13282, X13283, X13284, X13285]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13285,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13285,tc_HOL_Obool)),X13284),X13283)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13285,tc_HOL_Obool)),X13284),X13282))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13285,tc_HOL_Obool)),X13284),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13285,tc_HOL_Obool)),X13283),X13282)), inference(variable_rename,[status(thm)],[fact_Int__Un__distrib])). 4.05/4.31 fof(c_0_9776, plain, ![X4283, X4284, X4285, X4286]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4286,tc_HOL_Obool)),X4285),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4286,tc_HOL_Obool)),X4284),X4283))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4286,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4286,tc_HOL_Obool)),X4285),X4284)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4286,tc_HOL_Obool)),X4285),X4283)), inference(variable_rename,[status(thm)],[fact_Diff__Int])). 4.05/4.31 cnf(c_0_9777, 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)),X5),hAPP(hAPP(c_List_Oappend(X2),X5),X1))),c_List_Olexord(X2,X6)))|X1!=hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_5818])). 4.05/4.31 fof(c_0_9778, plain, ![X5757, X5758, X5759, X5760]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5760,tc_HOL_Obool)),X5759),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5760,tc_HOL_Obool)),X5758),X5757))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5760,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5760,tc_HOL_Obool)),X5759),X5758)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5760,tc_HOL_Obool)),X5759),X5757)), inference(variable_rename,[status(thm)],[fact_Un__Int__distrib])). 4.05/4.31 fof(c_0_9779, plain, ![X2509, X2510, X2511, X2512, X2513]:c_Map_Odom(X2513,X2512,hAPP(hAPP(c_COMBS(X2513,tc_Option_Ooption(X2511),tc_Option_Ooption(X2512)),hAPP(hAPP(c_COMBB(tc_fun(X2511,X2512),tc_fun(tc_Option_Ooption(X2511),tc_Option_Ooption(X2512)),X2513),c_Option_Omap(X2511,X2512)),X2510)),X2509))=c_Map_Odom(X2513,X2511,X2509), inference(variable_rename,[status(thm)],[fact_dom__option__map])). 4.05/4.31 fof(c_0_9780, plain, ![X4788, X4789, X4790, X4791]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4791,tc_HOL_Obool)),X4790),hAPP(hAPP(c_Set_Oinsert(X4791),X4789),X4788))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4791,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4791,tc_HOL_Obool)),X4790),X4788)),hAPP(hAPP(c_Set_Oinsert(X4791),X4789),c_Orderings_Obot__class_Obot(tc_fun(X4791,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_Diff__insert])). 4.05/4.31 fof(c_0_9781, plain, ![X15973, X15974]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X15974),X15973)=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)),X15974)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X15973))), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J])). 4.05/4.31 cnf(c_0_9782, 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_5819])). 4.05/4.31 fof(c_0_9783, plain, ![X4069, X4070, X4071, X4072, X4073]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4073,X4072),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X4073,X4072),X4071),X4069)),hAPP(hAPP(c_Product__Type_OSigma(X4073,X4072),X4070),X4069))=hAPP(hAPP(c_Product__Type_OSigma(X4073,X4072),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4073,tc_HOL_Obool)),X4071),X4070)),X4069), inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib1])). 4.05/4.31 fof(c_0_9784, plain, ![X3248, X3249, X3250, X3251, X3252]:hAPP(hAPP(c_Product__Type_OSigma(X3252,X3251),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3252,tc_HOL_Obool)),X3250),X3249)),X3248)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X3252,X3251),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X3252,X3251),X3250),X3248)),hAPP(hAPP(c_Product__Type_OSigma(X3252,X3251),X3249),X3248)), inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib1])). 4.05/4.31 fof(c_0_9785, plain, ![X15169, X15170, X15171, X15172, X15173]:hAPP(hAPP(c_Product__Type_OSigma(X15173,X15172),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15173,tc_HOL_Obool)),X15171),X15170)),X15169)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X15173,X15172),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X15173,X15172),X15171),X15169)),hAPP(hAPP(c_Product__Type_OSigma(X15173,X15172),X15170),X15169)), inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib1])). 4.05/4.31 fof(c_0_9786, plain, ![X7038, X7039, X7040, X7041, X7042]:hAPP(hAPP(c_List_Oappend(tc_prod(X7042,X7041)),hAPP(hAPP(c_List_Omap(X7041,tc_prod(X7042,X7041)),hAPP(c_Product__Type_OPair(X7042,X7041),X7040)),X7038)),c_Enum_Oproduct(X7042,X7041,X7039,X7038))=c_Enum_Oproduct(X7042,X7041,hAPP(hAPP(c_List_Olist_OCons(X7042),X7040),X7039),X7038), inference(variable_rename,[status(thm)],[fact_product_Osimps_I2_J])). 4.05/4.31 cnf(c_0_9787, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))=c_FunDef_Opair__leq), inference(split_conjunct,[status(thm)],[fact_pair__leq__def])). 4.05/4.31 cnf(c_0_9788, 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_5820])). 4.05/4.31 cnf(c_0_9789, 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_5821])). 4.05/4.32 fof(c_0_9790, plain, ![X5903, X5904, X5905, X5906]:hAPP(hAPP(c_List_Odrop(X5906),X5905),hAPP(hAPP(c_List_Oappend(X5906),X5904),X5903))=hAPP(hAPP(c_List_Oappend(X5906),hAPP(hAPP(c_List_Odrop(X5906),X5905),X5904)),hAPP(hAPP(c_List_Odrop(X5906),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5905),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5906)),X5904))),X5903)), inference(variable_rename,[status(thm)],[fact_drop__append])). 4.05/4.32 fof(c_0_9791, plain, ![X3168, X3169, X3170, X3171]:hAPP(hAPP(c_List_Otake(X3171),X3170),hAPP(hAPP(c_List_Oappend(X3171),X3169),X3168))=hAPP(hAPP(c_List_Oappend(X3171),hAPP(hAPP(c_List_Otake(X3171),X3170),X3169)),hAPP(hAPP(c_List_Otake(X3171),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3170),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3171)),X3169))),X3168)), inference(variable_rename,[status(thm)],[fact_take__append])). 4.05/4.32 cnf(c_0_9792, 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_5822])). 4.05/4.32 fof(c_0_9793, plain, ![X12512, X12513, X12514, X12515]:c_New__Random__Sequence_Oneg__bind(X12515,X12514,X12512,hAPP(c_Fun_Ocomp(X12514,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(X12514)))))),X12515,c_New__Random__Sequence_Oneg__single(X12514)),X12513))=c_New__Random__Sequence_Oneg__map(X12515,X12514,X12513,X12512), inference(variable_rename,[status(thm)],[fact_neg__map__def])). 4.05/4.32 fof(c_0_9794, plain, ![X8238, X8239, X8240, X8241]:hAPP(c_Product__Type_Oprod_Oprod__case(X8241,X8240,X8239),hAPP(hAPP(c_COMBB(tc_fun(X8240,tc_prod(X8241,X8240)),tc_fun(X8240,X8239),X8241),hAPP(c_COMBB(tc_prod(X8241,X8240),X8239,X8240),X8238)),c_Product__Type_OPair(X8241,X8240)))=X8238, inference(variable_rename,[status(thm)],[fact_split__eta])). 4.05/4.32 fof(c_0_9795, plain, ![X2079, X2080, X2081, X2082, X2083]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2083,tc_HOL_Obool)),hAPP(c_List_Oset(X2083),hAPP(hAPP(c_List_Otake(X2083),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2082)),X2079)),X2080))),c_Map_Odom(X2083,X2082,X2081))=c_Map_Odom(X2083,X2082,c_Map_Omap__upds(X2083,X2082,X2081,X2080,X2079)), inference(variable_rename,[status(thm)],[fact_dom__map__upds])). 4.05/4.32 cnf(c_0_9796, 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_5823, c_0_5716])). 4.05/4.32 cnf(c_0_9797, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4))),hAPP(X5,hAPP(c_Product__Type_Osnd(X2,X3),X4)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Product__Type_Oprod_Oprod__size(X2,X3,X1,X5,X4)), inference(split_conjunct,[status(thm)],[c_0_5824])). 4.05/4.32 fof(c_0_9798, plain, ![X10991, X10992, X10993, X10994]:c_New__Random__Sequence_Opos__bind(X10994,X10993,X10991,hAPP(c_Fun_Ocomp(X10993,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(X10993))))),X10994,c_New__Random__Sequence_Opos__single(X10993)),X10992))=c_New__Random__Sequence_Opos__map(X10994,X10993,X10992,X10991), inference(variable_rename,[status(thm)],[fact_pos__map__def])). 4.05/4.32 cnf(c_0_9799, 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_5825, c_0_4523])). 4.05/4.32 fof(c_0_9800, plain, ![X12937, X12938, X12939]:c_Lazy__Sequence_Oappend(tc_Option_Ooption(X12939),hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X12939)),tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X12939)),c_Lazy__Sequence_Ohit__bound(X12939),c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X12939)))),X12938),c_Lazy__Sequence_Ohb__flat(X12939,X12937))=c_Lazy__Sequence_Ohb__flat(X12939,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X12939))),X12938,X12937)), inference(variable_rename,[status(thm)],[fact_hb__flat_Osimps_I2_J])). 4.05/4.32 cnf(c_0_9801, 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_5826, c_0_4655]), c_0_4655])). 4.05/4.32 fof(c_0_9802, plain, ![X11875, X11876, X11877, X11878, X11879]:c_List_OtakeWhile(tc_prod(X11879,X11878),hAPP(c_Fun_Ocomp(X11879,tc_HOL_Obool,tc_prod(X11879,X11878),X11877),c_Product__Type_Ofst(X11879,X11878)),hAPP(hAPP(c_List_Ozip(X11879,X11878),X11876),X11875))=hAPP(hAPP(c_List_Ozip(X11879,X11878),c_List_OtakeWhile(X11879,X11877,X11876)),X11875), inference(variable_rename,[status(thm)],[fact_zip__takeWhile__fst])). 4.05/4.32 fof(c_0_9803, plain, ![X687, X688, X689, X690, X691]:hAPP(hAPP(c_List_Ozip(X691,X690),X689),c_List_OtakeWhile(X690,X688,X687))=c_List_OtakeWhile(tc_prod(X691,X690),hAPP(c_Fun_Ocomp(X690,tc_HOL_Obool,tc_prod(X691,X690),X688),c_Product__Type_Osnd(X691,X690)),hAPP(hAPP(c_List_Ozip(X691,X690),X689),X687)), inference(variable_rename,[status(thm)],[fact_zip__takeWhile__snd])). 4.05/4.32 cnf(c_0_9804, 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_5827])). 4.05/4.32 cnf(c_0_9805, 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_5828, c_0_5829]), c_0_5830]), c_0_5830])). 4.05/4.32 cnf(c_0_9806, 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_5831]), ['final']). 4.05/4.32 fof(c_0_9807, plain, ![X14675, X14676, X14677, X14678]:hAPP(hAPP(c_List_Odrop(X14678),X14677),hAPP(hAPP(c_List_Olist_OCons(X14678),X14676),X14675))=c_Nat_Onat_Onat__case(tc_List_Olist(X14678),hAPP(hAPP(c_List_Olist_OCons(X14678),X14676),X14675),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X14678),tc_List_Olist(X14678)),c_List_Odrop(X14678)),X14675),X14677), inference(variable_rename,[status(thm)],[fact_drop__Cons])). 4.05/4.32 cnf(c_0_9808, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))=c_Divides_Opdivmod(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5832])). 4.05/4.32 cnf(c_0_9809, 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_5833]), ['final']). 4.05/4.32 cnf(c_0_9810, 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_5834])). 4.05/4.32 cnf(c_0_9811, 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_5835, c_0_4742])). 4.05/4.32 cnf(c_0_9812, plain, (X1=hAPP(c_List_Orev(X2),hAPP(c_List_Orev(X2),X1))), inference(split_conjunct,[status(thm)],[c_0_5836]), ['final']). 4.05/4.32 fof(c_0_9813, plain, ![X14424, X14425, X14426, X14427, X14428]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14427,tc_HOL_Obool)),hAPP(c_Relation_OImage(X14428,X14427,X14426),X14424)),hAPP(c_Relation_OImage(X14428,X14427,X14425),X14424))=hAPP(c_Relation_OImage(X14428,X14427,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X14428,X14427),tc_HOL_Obool)),X14426),X14425)),X14424), inference(variable_rename,[status(thm)],[fact_Un__Image])). 4.05/4.32 cnf(c_0_9814, 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_5837])). 4.05/4.32 fof(c_0_9815, plain, ![X2204, X2205, X2206, X2207]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2206,X2207),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X2207,X2206),X2205)),hAPP(c_Relation_Oconverse(X2207,X2206),X2204))=hAPP(c_Relation_Oconverse(X2207,X2206),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2207,X2206),tc_HOL_Obool)),X2205),X2204)), inference(variable_rename,[status(thm)],[fact_converse__Int])). 4.05/4.32 fof(c_0_9816, plain, ![X2715, X2716, X2717, X2718]:hAPP(c_Relation_Oconverse(X2718,X2717),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2718,X2717),tc_HOL_Obool)),X2716),X2715))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2717,X2718),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X2718,X2717),X2716)),hAPP(c_Relation_Oconverse(X2718,X2717),X2715)), inference(variable_rename,[status(thm)],[fact_converse__Un])). 4.05/4.32 fof(c_0_9817, plain, ![X17322]:c_Fun_Oinj__on(X17322,tc_fun(X17322,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X17322,tc_fun(X17322,tc_HOL_Obool),tc_fun(X17322,tc_HOL_Obool)),c_Set_Oinsert(X17322)),c_Orderings_Obot__class_Obot(tc_fun(X17322,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X17322,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_inj__singleton])). 4.05/4.32 cnf(c_0_9818, plain, (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)=hAPP(c_List_Orotate(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_5838])). 4.05/4.32 fof(c_0_9819, plain, ![X5240, X5241]:hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X5241),X5240)=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)),X5241)),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),X5240),X5241))), inference(variable_rename,[status(thm)],[fact_image__add__int__atLeastLessThan])). 4.05/4.32 fof(c_0_9820, plain, ![X4310, X4311, X4312, X4313, X4314, X4315]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4315,tc_Option_Ooption(X4314)),c_Map_Omap__add(X4315,X4314,X4313,X4312)),X4311),hAPP(c_Option_Ooption_OSome(X4314),X4310))=c_Map_Omap__add(X4315,X4314,X4313,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4315,tc_Option_Ooption(X4314)),X4312),X4311),hAPP(c_Option_Ooption_OSome(X4314),X4310))), inference(variable_rename,[status(thm)],[fact_map__add__upd])). 4.05/4.32 cnf(c_0_9821, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))=c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),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)),X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_5839])). 4.05/4.32 cnf(c_0_9822, plain, (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))=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(split_conjunct,[status(thm)],[c_0_5840])). 4.05/4.32 cnf(c_0_9823, 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_5841]), ['final']). 4.05/4.32 cnf(c_0_9824, plain, (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))=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))), inference(split_conjunct,[status(thm)],[c_0_5842])). 4.05/4.32 cnf(c_0_9825, 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),X3))=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))), inference(split_conjunct,[status(thm)],[c_0_5843]), ['final']). 4.05/4.32 cnf(c_0_9826, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))), inference(split_conjunct,[status(thm)],[c_0_5844])). 4.05/4.32 fof(c_0_9827, plain, ![X5567, X5568, X5569, X5570, X5571]:hAPP(hAPP(c_List_Olist__update(X5571,hAPP(hAPP(c_List_Oappend(X5571),X5570),hAPP(hAPP(c_List_Olist_OCons(X5571),X5569),X5568))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5571)),X5570)),X5567)=hAPP(hAPP(c_List_Oappend(X5571),X5570),hAPP(hAPP(c_List_Olist_OCons(X5571),X5567),X5568)), inference(variable_rename,[status(thm)],[fact_list__update__length])). 4.05/4.32 cnf(c_0_9828, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),hAPP(c_Set_Ovimage(X1,X2,X3),X5))=hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_5845])). 4.05/4.32 cnf(c_0_9829, 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_5846])). 4.05/4.32 fof(c_0_9830, plain, ![X11440, X11441, X11442, X11443, X11444]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11443,tc_HOL_Obool)),hAPP(c_Relation_OImage(X11444,X11443,X11442),X11441)),hAPP(c_Relation_OImage(X11444,X11443,X11442),X11440))=hAPP(c_Relation_OImage(X11444,X11443,X11442),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X11444,tc_HOL_Obool)),X11441),X11440)), inference(variable_rename,[status(thm)],[fact_Image__Un])). 4.05/4.32 cnf(c_0_9831, 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_5847])). 4.05/4.32 cnf(c_0_9832, 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_Orderings_Oord__class_Omin(tc_Nat_Onat)),X1)),X2)=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))), inference(split_conjunct,[status(thm)],[c_0_5848])). 4.05/4.32 cnf(c_0_9833, 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_5849])). 4.05/4.32 cnf(c_0_9834, 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_5850]), ['final']). 4.05/4.32 fof(c_0_9835, plain, ![X5302, X5303, X5304]:hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5304),tc_List_Olist(X5304)),hAPP(c_List_Ofilter(X5304,X5303),X5302)),hAPP(c_List_Ofilter(X5304,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X5304,c_fNot),X5303)),X5302))=c_List_Opartition(X5304,X5303,X5302), inference(variable_rename,[status(thm)],[fact_partition__filter__conv])). 4.05/4.32 cnf(c_0_9836, plain, (hAPP(c_Set_OPow(X3),X1)=hAPP(c_Set_Oimage(tc_fun(X2,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),c_Set_Oimage(X2,X3,X4)),hAPP(c_Set_OPow(X2),X5))|X1!=hAPP(c_Set_Oimage(X2,X3,X4),X5)), inference(split_conjunct,[status(thm)],[c_0_5851])). 4.05/4.32 cnf(c_0_9837, plain, (hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc)))=c_Wellfounded_Opred__nat), inference(split_conjunct,[status(thm)],[fact_pred__nat__def])). 4.05/4.32 cnf(c_0_9838, plain, (c_Map_Odom(X2,X3,X1)=hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))|X1!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X2,tc_Option_Ooption(X3)),hAPP(c_COMBK(tc_Option_Ooption(X3),X2),c_Option_Ooption_ONone(X3))),X4),hAPP(c_Option_Ooption_OSome(X3),X5))), inference(split_conjunct,[status(thm)],[c_0_5852])). 4.05/4.32 fof(c_0_9839, plain, ![X3985, X3986, X3987, X3988]:hAPP(c_Fun_Ocomp(X3988,X3988,X3988,hAPP(hAPP(c_Nat_Ocompow(X3988,X3988),X3987),X3985)),hAPP(hAPP(c_Nat_Ocompow(X3988,X3988),X3986),X3985))=hAPP(hAPP(c_Nat_Ocompow(X3988,X3988),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3987),X3986)),X3985), inference(variable_rename,[status(thm)],[fact_funpow__add])). 4.05/4.32 fof(c_0_9840, plain, ![X12069, X12070, X12071, X12072]:hAPP(c_List_Oset(tc_prod(X12072,X12071)),c_Enum_Oproduct(X12072,X12071,X12070,X12069))=hAPP(hAPP(c_Product__Type_OSigma(X12072,X12071),hAPP(c_List_Oset(X12072),X12070)),hAPP(c_COMBK(tc_fun(X12071,tc_HOL_Obool),X12072),hAPP(c_List_Oset(X12071),X12069))), inference(variable_rename,[status(thm)],[fact_product__list__set])). 4.05/4.32 fof(c_0_9841, plain, ![X4846, X4847]:X4846=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4847,tc_fun(X4847,tc_HOL_Obool)),X4846),hAPP(hAPP(c_COMBC(X4847,tc_fun(X4847,tc_HOL_Obool),tc_fun(X4847,tc_HOL_Obool)),c_Set_Oinsert(X4847)),c_Orderings_Obot__class_Obot(tc_fun(X4847,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_UN__singleton])). 4.05/4.32 cnf(c_0_9842, plain, (c_Lazy__Sequence_Ohb__bind(X1,X2,hAPP(X3,X4),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))),X5),X4))=hAPP(c_New__DSequence_Oneg__bind(X1,X2,X3,X5),X4)), inference(split_conjunct,[status(thm)],[c_0_5853])). 4.05/4.32 fof(c_0_9843, plain, ![X5961, X5962, X5963, X5964]:hAPP(c_Finite__Set_Ocard(tc_prod(X5964,X5963)),hAPP(hAPP(c_Product__Type_OSigma(X5964,X5963),X5962),hAPP(c_COMBK(tc_fun(X5963,tc_HOL_Obool),X5964),X5961)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5964),X5962)),hAPP(c_Finite__Set_Ocard(X5963),X5961)), inference(variable_rename,[status(thm)],[fact_card__cartesian__product])). 4.05/4.32 cnf(c_0_9844, 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(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)), inference(split_conjunct,[status(thm)],[c_0_5363])). 4.05/4.32 cnf(c_0_9845, 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_5854]), ['final']). 4.05/4.32 fof(c_0_9846, plain, ![X6149, X6150, X6151]:c_Fun_Oinj__on(tc_prod(X6151,X6150),tc_prod(X6150,X6151),hAPP(c_Product__Type_Oprod_Oprod__case(X6151,X6150,tc_prod(X6150,X6151)),hAPP(c_COMBC(X6150,X6151,tc_prod(X6150,X6151)),c_Product__Type_OPair(X6150,X6151))),X6149), inference(variable_rename,[status(thm)],[fact_swap__inj__on])). 4.05/4.32 fof(c_0_9847, plain, ![X3693, X3694, X3695, X3696, X3697]:hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3697),tc_Option_Ooption(X3696),tc_Option_Ooption(X3695),hAPP(c_Option_Omap(X3697,X3696),X3694)),hAPP(c_Option_Omap(X3695,X3697),X3693))=hAPP(c_Option_Omap(X3695,X3696),hAPP(c_Fun_Ocomp(X3697,X3696,X3695,X3694),X3693)), inference(variable_rename,[status(thm)],[fact_Option_Omap_Ocomp])). 4.05/4.32 fof(c_0_9848, plain, ![X7558, X7559, X7560, X7561, X7562]:hAPP(c_Fun_Ocomp(tc_List_Olist(X7562),tc_List_Olist(X7561),tc_List_Olist(X7560),hAPP(c_List_Omap(X7562,X7561),X7559)),hAPP(c_List_Omap(X7560,X7562),X7558))=hAPP(c_List_Omap(X7560,X7561),hAPP(c_Fun_Ocomp(X7562,X7561,X7560,X7559),X7558)), inference(variable_rename,[status(thm)],[fact_map__comp__map])). 4.05/4.32 fof(c_0_9849, plain, ![X7379, X7380]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X7380,X7380),tc_HOL_Obool)),c_Relation_OId__on(X7380,X7379)),hAPP(hAPP(c_Product__Type_OSigma(X7380,X7380),X7379),hAPP(c_COMBK(tc_fun(X7380,tc_HOL_Obool),X7380),X7379)))), inference(variable_rename,[status(thm)],[fact_Id__on__subset__Times])). 4.05/4.32 cnf(c_0_9850, 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_5855])). 4.05/4.32 fof(c_0_9851, plain, ![X1557, X1558, X1559, X1560]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1560,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1560,X1559),X1558)),hAPP(c_Relation_ODomain(X1560,X1559),X1557))=hAPP(c_Relation_ODomain(X1560,X1559),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1560,X1559),tc_HOL_Obool)),X1558),X1557)), inference(variable_rename,[status(thm)],[fact_Domain__Un__eq])). 4.05/4.32 fof(c_0_9852, plain, ![X8843, X8844, X8845, X8846]:hAPP(c_Relation_ORange(X8846,X8845),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X8846,X8845),tc_HOL_Obool)),X8844),X8843))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8845,tc_HOL_Obool)),hAPP(c_Relation_ORange(X8846,X8845),X8844)),hAPP(c_Relation_ORange(X8846,X8845),X8843)), inference(variable_rename,[status(thm)],[fact_Range__Un__eq])). 4.05/4.32 fof(c_0_9853, plain, ![X5690, X5691, X5692, X5693]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5693,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5693),X5692),X5691)),hAPP(hAPP(c_Set_Oinsert(X5693),X5692),X5690))=hAPP(hAPP(c_Set_Oinsert(X5693),X5692),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5693,tc_HOL_Obool)),X5691),X5690)), inference(variable_rename,[status(thm)],[fact_insert__inter__insert])). 4.05/4.32 cnf(c_0_9854, 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_5856])). 4.05/4.32 fof(c_0_9855, plain, ![X761, X762, X763, X764, X765]:hAPP(hAPP(c_List_Odrop(tc_prod(X765,X764)),X763),hAPP(hAPP(c_List_Ozip(X765,X764),X762),X761))=hAPP(hAPP(c_List_Ozip(X765,X764),hAPP(hAPP(c_List_Odrop(X765),X763),X762)),hAPP(hAPP(c_List_Odrop(X764),X763),X761)), inference(variable_rename,[status(thm)],[fact_drop__zip])). 4.05/4.32 cnf(c_0_9856, 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_5857])). 4.05/4.32 fof(c_0_9857, plain, ![X13751, X13752, X13753]:c_Transitive__Closure_Ortrancl(X13753,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X13753,X13753),tc_HOL_Obool)),X13752),X13751))=c_Transitive__Closure_Ortrancl(X13753,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X13753,X13753),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X13753,X13752)),c_Transitive__Closure_Ortrancl(X13753,X13751))), inference(variable_rename,[status(thm)],[fact_rtrancl__Un__rtrancl])). 4.05/4.32 fof(c_0_9858, plain, ![X4458, X4459, X4460, X4461]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4460,tc_fun(X4461,tc_HOL_Obool))),c_Predicate_Oconversep(X4461,X4460,X4459)),c_Predicate_Oconversep(X4461,X4460,X4458))=c_Predicate_Oconversep(X4461,X4460,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4461,tc_fun(X4460,tc_HOL_Obool))),X4459),X4458)), inference(variable_rename,[status(thm)],[fact_converse__meet])). 4.05/4.32 fof(c_0_9859, plain, ![X17421, X17422, X17423, X17424]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17423,tc_fun(X17424,tc_HOL_Obool))),c_Predicate_Oconversep(X17424,X17423,X17422)),c_Predicate_Oconversep(X17424,X17423,X17421))=c_Predicate_Oconversep(X17424,X17423,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X17424,tc_fun(X17423,tc_HOL_Obool))),X17422),X17421)), inference(variable_rename,[status(thm)],[fact_converse__join])). 4.05/4.32 fof(c_0_9860, plain, ![X16267, X16268, X16269, X16270]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16270,tc_HOL_Obool)),hAPP(c_List_Oset(X16270),hAPP(hAPP(c_List_Olist__update(X16270,X16269),X16268),X16267))),hAPP(hAPP(c_Set_Oinsert(X16270),X16267),hAPP(c_List_Oset(X16270),X16269)))), inference(variable_rename,[status(thm)],[fact_set__update__subset__insert])). 4.05/4.32 cnf(c_0_9861, plain, (hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),X3))=hAPP(c_Relation_ODomain(X1,X2),hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3)))), inference(split_conjunct,[status(thm)],[c_0_5858])). 4.05/4.32 cnf(c_0_9862, 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_5859])). 4.05/4.32 fof(c_0_9863, plain, ![X10988, X10989, X10990]: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),X10990),X10989))),X10988)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10990)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10989)),X10988)), inference(variable_rename,[status(thm)],[fact_zadd__int__left])). 4.05/4.32 cnf(c_0_9864, plain, (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))=X1), inference(split_conjunct,[status(thm)],[c_0_5860])). 4.05/4.32 fof(c_0_9865, plain, ![X14797, X14798, X14799, X14800, X14801]:c_Map_Omap__add(X14801,X14800,X14799,hAPP(c_Map_Omap__of(X14801,X14800),hAPP(c_List_Orev(tc_prod(X14801,X14800)),hAPP(hAPP(c_List_Ozip(X14801,X14800),X14798),X14797))))=c_Map_Omap__upds(X14801,X14800,X14799,X14798,X14797), inference(variable_rename,[status(thm)],[fact_map__upds__def])). 4.05/4.32 fof(c_0_9866, plain, ![X11127, X11128]:hAPP(hAPP(c_Product__Type_OSigma(X11128,X11127),c_Orderings_Otop__class_Otop(tc_fun(X11128,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X11127,tc_HOL_Obool),X11128),c_Orderings_Otop__class_Otop(tc_fun(X11127,tc_HOL_Obool))))=c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X11128,X11127),tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_UNIV__Times__UNIV])). 4.05/4.32 fof(c_0_9867, plain, ![X13343, X13344, X13345, X13346, X13347]:hAPP(hAPP(c_List_Omap(X13345,X13347),X13344),hAPP(c_List_Ofilter(X13345,hAPP(c_Fun_Ocomp(X13347,tc_HOL_Obool,X13345,X13346),X13344)),X13343))=hAPP(c_List_Ofilter(X13347,X13346),hAPP(hAPP(c_List_Omap(X13345,X13347),X13344),X13343)), inference(variable_rename,[status(thm)],[fact_filter__map])). 4.05/4.32 fof(c_0_9868, plain, ![X7332, X7333, X7334]:hAPP(hAPP(c_Set_Oinsert(X7334),X7333),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X7334,tc_HOL_Obool)),X7332),hAPP(hAPP(c_Set_Oinsert(X7334),X7333),c_Orderings_Obot__class_Obot(tc_fun(X7334,tc_HOL_Obool)))))=hAPP(hAPP(c_Set_Oinsert(X7334),X7333),X7332), inference(variable_rename,[status(thm)],[fact_insert__Diff__single])). 4.05/4.32 fof(c_0_9869, plain, ![X15050, X15051, X15052, X15053, X15054]:hAPP(c_Relation_ORange(X15054,X15053),hAPP(hAPP(c_Set_Oinsert(tc_prod(X15054,X15053)),hAPP(hAPP(c_Product__Type_OPair(X15054,X15053),X15052),X15051)),X15050))=hAPP(hAPP(c_Set_Oinsert(X15053),X15051),hAPP(c_Relation_ORange(X15054,X15053),X15050)), inference(variable_rename,[status(thm)],[fact_Range__insert])). 4.05/4.32 fof(c_0_9870, plain, ![X10392, X10393, X10394, X10395, X10396]:hAPP(c_Relation_ODomain(X10396,X10395),hAPP(hAPP(c_Set_Oinsert(tc_prod(X10396,X10395)),hAPP(hAPP(c_Product__Type_OPair(X10396,X10395),X10394),X10393)),X10392))=hAPP(hAPP(c_Set_Oinsert(X10396),X10394),hAPP(c_Relation_ODomain(X10396,X10395),X10392)), inference(variable_rename,[status(thm)],[fact_Domain__insert])). 4.05/4.32 cnf(c_0_9871, plain, (hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X1)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_5861])). 4.05/4.32 cnf(c_0_9872, plain, (hAPP(c_List_Orotate(X1,hAPP(c_Nat_OSuc,X2)),X3)=hAPP(c_List_Orotate1(X1),hAPP(c_List_Orotate(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_5862])). 4.05/4.32 cnf(c_0_9873, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Map_Odom(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3))))), inference(split_conjunct,[status(thm)],[c_0_5863])). 4.05/4.32 fof(c_0_9874, plain, ![X10195, X10196]:hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10196),tc_List_Olist(X10196))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10196),tc_List_Olist(X10196)),c_List_Olist_ONil(X10196)),c_List_Olist_ONil(X10196))),c_List_Olistrel(X10196,X10195))), inference(variable_rename,[status(thm)],[fact_listrel_ONil])). 4.05/4.32 fof(c_0_9875, plain, ![X17101, X17102, X17103]:hBOOL(hAPP(hAPP(c_member(tc_prod(X17103,X17103)),hAPP(hAPP(c_Product__Type_OPair(X17103,X17103),X17102),X17102)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X17103,X17103),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17101))), inference(variable_rename,[status(thm)],[fact_rel__pow__0__I])). 4.05/4.32 fof(c_0_9876, plain, ![X7372, X7373]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X7373),tc_List_Olist(X7373)),tc_HOL_Obool)),c_List_Olistrel1(X7373,c_Transitive__Closure_Ortrancl(X7373,X7372))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X7373),c_List_Olistrel1(X7373,X7372)))), inference(variable_rename,[status(thm)],[fact_listrel1__rtrancl__subset__rtrancl__listrel1])). 4.05/4.32 cnf(c_0_9877, plain, (hAPP(c_Option_Ooption_OSome(X3),X4)=hAPP(hAPP(c_Map_Omap__of(X5,X3),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X5,X3)),hAPP(hAPP(c_Product__Type_OPair(X5,X3),X1),X4)),X6)),X2)|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5864])). 4.05/4.32 cnf(c_0_9878, 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_5865])). 4.05/4.32 fof(c_0_9879, plain, ![X13480, X13481, X13482, X13483, X13484]:hAPP(c_Relation_Oconverse(X13484,X13483),hAPP(hAPP(c_Relation_Orel__comp(X13484,X13482,X13483),X13481),X13480))=hAPP(hAPP(c_Relation_Orel__comp(X13483,X13482,X13484),hAPP(c_Relation_Oconverse(X13482,X13483),X13480)),hAPP(c_Relation_Oconverse(X13484,X13482),X13481)), inference(variable_rename,[status(thm)],[fact_converse__rel__comp])). 4.05/4.32 fof(c_0_9880, plain, ![X11153, X11154, X11155]:hAPP(c_Set_OPow(X11155),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11155,tc_HOL_Obool)),X11154),X11153))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X11155,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X11155),X11154)),hAPP(c_Set_OPow(X11155),X11153)), inference(variable_rename,[status(thm)],[fact_Pow__Int__eq])). 4.05/4.32 cnf(c_0_9881, 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_5866])). 4.05/4.32 cnf(c_0_9882, plain, (c_List_Oreplicate(tc_prod(X1,X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X3),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6))=hAPP(hAPP(c_List_Ozip(X1,X2),c_List_Oreplicate(X1,X3,X5)),c_List_Oreplicate(X2,X4,X6))), inference(split_conjunct,[status(thm)],[c_0_5867])). 4.05/4.32 cnf(c_0_9883, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1)))), inference(split_conjunct,[status(thm)],[c_0_5868])). 4.05/4.32 fof(c_0_9884, plain, ![X2016, X2017, X2018, X2019]:hAPP(hAPP(c_List_Oappend(X2019),c_List_Oreplicate(X2019,X2018,X2017)),hAPP(hAPP(c_List_Olist_OCons(X2019),X2017),X2016))=hAPP(hAPP(c_List_Olist_OCons(X2019),X2017),hAPP(hAPP(c_List_Oappend(X2019),c_List_Oreplicate(X2019,X2018,X2017)),X2016)), inference(variable_rename,[status(thm)],[fact_replicate__app__Cons__same])). 4.05/4.32 fof(c_0_9885, plain, ![X15914, X15915, X15916]:hAPP(hAPP(c_List_Odrop(X15916),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15916)),X15914)),X15915)),hAPP(c_List_Orev(X15916),X15914))=hAPP(c_List_Orev(X15916),hAPP(hAPP(c_List_Otake(X15916),X15915),X15914)), inference(variable_rename,[status(thm)],[fact_rev__take])). 4.05/4.32 fof(c_0_9886, plain, ![X16200, X16201, X16202]:hAPP(c_List_Orev(X16202),hAPP(hAPP(c_List_Odrop(X16202),X16201),X16200))=hAPP(hAPP(c_List_Otake(X16202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16202)),X16200)),X16201)),hAPP(c_List_Orev(X16202),X16200)), inference(variable_rename,[status(thm)],[fact_rev__drop])). 4.05/4.32 cnf(c_0_9887, 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_5869])). 4.05/4.32 fof(c_0_9888, plain, ![X1542, X1543, X1544, X1545, X1546]:c_List_Osplice(X1546,hAPP(hAPP(c_List_Olist_OCons(X1546),X1545),X1544),hAPP(hAPP(c_List_Olist_OCons(X1546),X1543),X1542))=hAPP(hAPP(c_List_Olist_OCons(X1546),X1545),hAPP(hAPP(c_List_Olist_OCons(X1546),X1543),c_List_Osplice(X1546,X1544,X1542))), inference(variable_rename,[status(thm)],[fact_splice_Osimps_I3_J])). 4.05/4.32 fof(c_0_9889, plain, ![X6597, X6598, X6599, X6600]:hAPP(hAPP(c_List_Onth(X6600),X6598),X6597)=hAPP(hAPP(c_List_Onth(X6600),hAPP(hAPP(c_List_Oappend(X6600),X6599),X6598)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6600)),X6599)),X6597)), inference(variable_rename,[status(thm)],[fact_nth__append__length__plus])). 4.05/4.32 fof(c_0_9890, plain, ![X17198]:hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(X17198)),c_Option_Ooption_ONone(X17198)),hAPP(c_Set_Oimage(X17198,tc_Option_Ooption(X17198),c_Option_Ooption_OSome(X17198)),c_Orderings_Otop__class_Otop(tc_fun(X17198,tc_HOL_Obool))))=c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X17198),tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_UNIV__option__conv])). 4.05/4.32 cnf(c_0_9891, 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_5870])). 4.05/4.32 cnf(c_0_9892, plain, (hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X1)=hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))), inference(split_conjunct,[status(thm)],[c_0_5871]), ['final']). 4.05/4.32 fof(c_0_9893, plain, ![X9689, X9690, X9691]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X9691,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9691,tc_HOL_Obool)),X9690),X9689)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9691,tc_HOL_Obool)),X9690),X9689))=X9690, inference(variable_rename,[status(thm)],[fact_Un__Diff__Int])). 4.05/4.32 fof(c_0_9894, plain, ![X1397, X1398, X1399]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1399,tc_HOL_Obool)),hAPP(c_Relation_OField(X1399),X1398)),hAPP(c_Relation_OField(X1399),X1397))=hAPP(c_Relation_OField(X1399),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1399,X1399),tc_HOL_Obool)),X1398),X1397)), inference(variable_rename,[status(thm)],[fact_Field__Un])). 4.05/4.32 cnf(c_0_9895, plain, (hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_Set_Ovimage(X4,X5,X1),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))|hAPP(X1,X2)!=X3), inference(split_conjunct,[status(thm)],[c_0_5389])). 4.05/4.32 fof(c_0_9896, plain, ![X9904, X9905, X9906, X9907, X9908]:c_Map_Orestrict__map(X9908,X9907,X9906,hAPP(hAPP(c_Set_Oinsert(X9908),X9905),X9904))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X9908,tc_Option_Ooption(X9907)),c_Map_Orestrict__map(X9908,X9907,X9906,X9904)),X9905),hAPP(X9906,X9905)), inference(variable_rename,[status(thm)],[fact_restrict__map__insert])). 4.05/4.32 fof(c_0_9897, plain, ![X14148, X14149, X14150, X14151, X14152]:hAPP(hAPP(c_List_Omap(X14150,X14152),X14149),c_List_OtakeWhile(X14150,hAPP(c_Fun_Ocomp(X14152,tc_HOL_Obool,X14150,X14151),X14149),X14148))=c_List_OtakeWhile(X14152,X14151,hAPP(hAPP(c_List_Omap(X14150,X14152),X14149),X14148)), inference(variable_rename,[status(thm)],[fact_takeWhile__map])). 4.05/4.32 cnf(c_0_9898, 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_5872])). 4.05/4.32 cnf(c_0_9899, 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_5873])). 4.05/4.32 cnf(c_0_9900, plain, (X1=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X2),hAPP(c_List_Onth(X2),X1)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))), inference(split_conjunct,[status(thm)],[c_0_5874])). 4.05/4.32 fof(c_0_9901, plain, ![X3770, X3771, X3772]:c_Orderings_Obot__class_Obot(tc_fun(X3771,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3772,tc_fun(X3771,tc_HOL_Obool)),X3770),hAPP(c_COMBK(tc_fun(X3771,tc_HOL_Obool),X3772),c_Orderings_Obot__class_Obot(tc_fun(X3771,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_UN__empty2])). 4.05/4.32 fof(c_0_9902, plain, ![X10367, X10368, X10369, X10370, X10371, X10372]:hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10372,X10371),X10370),X10369),X10367)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10372,X10371),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X10372,X10371),X10370),X10369),X10368)),X10369),X10367), inference(variable_rename,[status(thm)],[fact_fun__upd__upd])). 4.05/4.32 fof(c_0_9903, plain, ![X2039, X2040]:c_List_Olex(X2040,X2039)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X2040),tc_List_Olist(X2040)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X2040,X2039)), inference(variable_rename,[status(thm)],[fact_lex__def])). 4.05/4.32 fof(c_0_9904, plain, ![X7988, X7989, X7990, X7991]:hAPP(hAPP(c_List_Otake(X7991),X7990),hAPP(hAPP(c_List_Odrop(X7991),X7989),X7988))=hAPP(hAPP(c_List_Odrop(X7991),X7989),hAPP(hAPP(c_List_Otake(X7991),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7990),X7989)),X7988)), inference(variable_rename,[status(thm)],[fact_take__drop])). 4.05/4.32 cnf(c_0_9905, 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_5875])). 4.05/4.32 fof(c_0_9906, plain, ![X5256, X5257, X5258]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5258),X5256)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5257),X5256))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X5258),X5257)),X5256), inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib])). 4.05/4.32 fof(c_0_9907, plain, ![X6047, X6048, X6049]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6049),X6048)),X6047)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6049),X6047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6048),X6047)), inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib])). 4.05/4.32 fof(c_0_9908, plain, ![X16419, X16420, X16421]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16421),X16420)),X16419)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16421),X16419)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16420),X16419)), inference(variable_rename,[status(thm)],[fact_diff__mult__distrib])). 4.05/4.32 fof(c_0_9909, plain, ![X2881, X2882, X2883]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2883),X2882)),X2881)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2883),X2881)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2882),X2881)), inference(variable_rename,[status(thm)],[fact_add__mult__distrib])). 4.05/4.32 cnf(c_0_9910, plain, (c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4))|X1!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5876])). 4.05/4.32 fof(c_0_9911, plain, ![X16848, X16849, X16850, X16851]:hAPP(hAPP(c_List_Otake(X16851),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16849),X16850)),hAPP(hAPP(c_List_Odrop(X16851),X16850),X16848))=hAPP(hAPP(c_List_Odrop(X16851),X16850),hAPP(hAPP(c_List_Otake(X16851),X16849),X16848)), inference(variable_rename,[status(thm)],[fact_drop__take])). 4.05/4.32 fof(c_0_9912, plain, ![X5751, X5752, X5753]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5753),X5752)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5753),X5751))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5753),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X5752),X5751)), inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib2])). 4.05/4.32 fof(c_0_9913, plain, ![X15422, X15423, X15424]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15424),X15423)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15424),X15422))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15424),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15423),X15422)), inference(variable_rename,[status(thm)],[fact_diff__mult__distrib2])). 4.05/4.32 fof(c_0_9914, plain, ![X14166, X14167, X14168]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14168),X14167)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14168),X14166))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X14168),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14167),X14166)), inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib])). 4.05/4.32 fof(c_0_9915, plain, ![X3427, X3428, X3429]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3429),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3428),X3427))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3429),X3428)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3429),X3427)), inference(variable_rename,[status(thm)],[fact_add__mult__distrib2])). 4.05/4.32 fof(c_0_9916, plain, ![X14334, X14335, X14336, X14337]:hAPP(hAPP(c_Nat_Ocompow(tc_fun(X14337,X14336),tc_fun(X14337,X14336)),X14335),c_Fun_Ocomp(X14336,X14336,X14337,X14334))=c_Fun_Ocomp(X14336,X14336,X14337,hAPP(hAPP(c_Nat_Ocompow(X14336,X14336),X14335),X14334)), inference(variable_rename,[status(thm)],[fact_comp__funpow])). 4.05/4.32 fof(c_0_9917, plain, ![X10863, X10864]:hAPP(c_Set_Oimage(tc_List_Olist(X10864),tc_fun(X10864,tc_HOL_Obool),c_List_Oset(X10864)),hAPP(c_List_Oset(tc_List_Olist(X10864)),c_Enum_Osublists(X10864,X10863)))=hAPP(c_Set_OPow(X10864),hAPP(c_List_Oset(X10864),X10863)), inference(variable_rename,[status(thm)],[fact_sublists__powset])). 4.05/4.32 fof(c_0_9918, plain, ![X15346, X15347]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X15347),tc_List_Olist(X15347)),tc_HOL_Obool)),c_List_Olistrel(X15347,X15346)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X15347),c_List_Olistrel1(X15347,X15346)))), inference(variable_rename,[status(thm)],[fact_listrel__subset__rtrancl__listrel1])). 4.05/4.32 cnf(c_0_9919, 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_5877])). 4.05/4.32 cnf(c_0_9920, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_5878])). 4.05/4.32 fof(c_0_9921, plain, ![X16721, X16722, X16723]:hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16723,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X16723),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X16722)),X16721)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X16723,tc_Nat_Onat),X16722),X16721)), inference(variable_rename,[status(thm)],[fact_int__setprod])). 4.05/4.32 fof(c_0_9922, plain, ![X8631, X8632, X8633]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8633,tc_Nat_Onat),X8632),X8631))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8633,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X8633),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X8632)),X8631), inference(variable_rename,[status(thm)],[fact_int__setsum])). 4.05/4.32 cnf(c_0_9923, 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_5879])). 4.05/4.32 fof(c_0_9924, plain, ![X14507, X14508, X14509, X14510, X14511, X14512, X14513, X14514]:hAPP(hAPP(c_Product__Type_OPair(X14513,X14511),hAPP(X14510,X14508)),hAPP(X14509,X14507))=hAPP(c_Product__Type_Omap__pair(X14514,X14513,X14512,X14511,X14510,X14509),hAPP(hAPP(c_Product__Type_OPair(X14514,X14512),X14508),X14507)), inference(variable_rename,[status(thm)],[fact_map__pair__simp])). 4.05/4.32 cnf(c_0_9925, 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_5880])). 4.05/4.32 cnf(c_0_9926, 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_5881])). 4.05/4.32 fof(c_0_9927, plain, ![X14282, X14283, X14284, X14285, X14286]:hAPP(c_New__DSequence_Opos__bind(X14286,X14285,X14284,X14283),X14282)=hAPP(c_Lazy__Sequence_Obind(X14286,X14285,hAPP(X14284,X14282)),hAPP(hAPP(c_COMBC(X14286,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X14285)),X14283),X14282)), inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__bind__def])). 4.05/4.32 fof(c_0_9928, plain, ![X730, X731]:hAPP(c_List_Orev(X731),X730)=hAPP(c_List_Ofoldl(tc_List_Olist(X731),X731,hAPP(c_COMBC(X731,tc_List_Olist(X731),tc_List_Olist(X731)),c_List_Olist_OCons(X731)),c_List_Olist_ONil(X731)),X730), inference(variable_rename,[status(thm)],[fact_rev__foldl__cons])). 4.05/4.32 fof(c_0_9929, plain, ![X7219, X7220, X7221, X7222, X7223]:hAPP(hAPP(c_List_Olist__update(X7223,hAPP(hAPP(c_List_Olist_OCons(X7223),X7222),X7221)),hAPP(c_Nat_OSuc,X7220)),X7219)=hAPP(hAPP(c_List_Olist_OCons(X7223),X7222),hAPP(hAPP(c_List_Olist__update(X7223,X7221),X7220),X7219)), inference(variable_rename,[status(thm)],[fact_list__update__code_I3_J])). 4.05/4.32 cnf(c_0_9930, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X3,X4))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Nitpick_Opair__box_Opair__box__size(X5,X6,X1,X3,c_Nitpick_Opair__box_OPairBox(X5,X6,X2,X4))), inference(split_conjunct,[status(thm)],[c_0_5882])). 4.05/4.32 cnf(c_0_9931, plain, (X3=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X4,tc_HOL_Obool)),X1),X5)),X3)|X1!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5883])). 4.05/4.32 fof(c_0_9932, plain, ![X1301, X1302, X1303]:c_List_Olistsp(X1303,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1303,tc_HOL_Obool)),X1302),X1301))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1303),tc_HOL_Obool)),c_List_Olistsp(X1303,X1302)),c_List_Olistsp(X1303,X1301)), inference(variable_rename,[status(thm)],[fact_listsp__inf__eq])). 4.05/4.32 cnf(c_0_9933, plain, (X3=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(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_5884])). 4.05/4.32 cnf(c_0_9934, 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(X2,tc_fun(X4,tc_HOL_Obool)),X1),X5))|X1!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5885])). 4.05/4.32 cnf(c_0_9935, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),hAPP(c_Nat_OSuc,X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_5886])). 4.05/4.32 fof(c_0_9936, plain, ![X15436, X15437, X15438, X15439, X15440]:c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X15439),hAPP(hAPP(c_Option_Omap(X15440,X15439),X15438),X15437),c_Lazy__Sequence_Ohb__map(X15440,X15439,X15438,X15436))=c_Lazy__Sequence_Ohb__map(X15440,X15439,X15438,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X15440),X15437,X15436)), inference(variable_rename,[status(thm)],[fact_hb__map_Osimps_I2_J])). 4.05/4.32 cnf(c_0_9937, 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_5887])). 4.05/4.32 fof(c_0_9938, plain, ![X2373, X2374, X2375, X2376]:hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X2376,tc_Option_Ooption(X2375)),hAPP(c_COMBK(tc_Option_Ooption(X2375),X2376),c_Option_Ooption_ONone(X2375))),X2374),c_Option_Ooption_ONone(X2375)),X2373)=c_Option_Ooption_ONone(X2375), inference(variable_rename,[status(thm)],[fact_empty__upd__none])). 4.05/4.32 cnf(c_0_9939, 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_5888, c_0_4519]), c_0_4519])). 4.05/4.32 fof(c_0_9940, plain, ![X1515, X1516, X1517]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1517,tc_HOL_Obool)),X1516),X1515)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1517,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1517,tc_HOL_Obool)),X1516),X1515)),X1515), inference(variable_rename,[status(thm)],[fact_Diff__idemp])). 4.05/4.32 fof(c_0_9941, plain, ![X14082, X14083, X14084]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14084,tc_HOL_Obool)),X14083),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14084,tc_HOL_Obool)),X14082),X14083))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X14084,tc_HOL_Obool)),X14083),X14082), inference(variable_rename,[status(thm)],[fact_Un__Diff__cancel])). 4.05/4.32 fof(c_0_9942, plain, ![X12093, X12094, X12095]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12095,tc_HOL_Obool)),X12094),X12093)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12095,tc_HOL_Obool)),X12094),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12095,tc_HOL_Obool)),X12094),X12093)), inference(variable_rename,[status(thm)],[fact_Int__left__absorb])). 4.05/4.32 fof(c_0_9943, plain, ![X12873, X12874, X12875]:c_Option_Ooption_Ooption__case(tc_Option_Ooption(X12874),X12875,c_Option_Ooption_ONone(X12874),hAPP(hAPP(c_COMBB(X12874,tc_Option_Ooption(X12874),X12875),c_Option_Ooption_OSome(X12874)),X12873))=hAPP(c_Option_Omap(X12875,X12874),X12873), inference(variable_rename,[status(thm)],[fact_Option_Omap__def])). 4.05/4.32 fof(c_0_9944, plain, ![X13814, X13815, X13816]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13816,tc_HOL_Obool)),X13815),X13814)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13816,tc_HOL_Obool)),X13815),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13816,tc_HOL_Obool)),X13815),X13814)), inference(variable_rename,[status(thm)],[fact_Un__left__absorb])). 4.05/4.32 fof(c_0_9945, plain, ![X17310, X17311, X17312, X17313]:hAPP(hAPP(c_Nat_Ocompow(X17313,X17313),X17312),hAPP(hAPP(c_Nat_Ocompow(X17313,X17313),X17311),X17310))=hAPP(hAPP(c_Nat_Ocompow(X17313,X17313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17311),X17312)),X17310), inference(variable_rename,[status(thm)],[fact_funpow__mult])). 4.05/4.32 fof(c_0_9946, plain, ![X2590, X2591, X2592, X2593]:hAPP(c_Map_Omap__of(X2593,X2592),hAPP(hAPP(c_List_Oappend(tc_prod(X2593,X2592)),X2591),X2590))=c_Map_Omap__add(X2593,X2592,hAPP(c_Map_Omap__of(X2593,X2592),X2590),hAPP(c_Map_Omap__of(X2593,X2592),X2591)), inference(variable_rename,[status(thm)],[fact_map__of__append])). 4.05/4.32 fof(c_0_9947, plain, ![X9544, X9545, X9546, X9547]:hAPP(hAPP(c_List_Oappend(X9547),hAPP(c_List_Ofilter(X9547,X9546),X9545)),hAPP(c_List_Ofilter(X9547,X9546),X9544))=hAPP(c_List_Ofilter(X9547,X9546),hAPP(hAPP(c_List_Oappend(X9547),X9545),X9544)), inference(variable_rename,[status(thm)],[fact_filter__append])). 4.05/4.32 cnf(c_0_9948, 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_5889])). 4.05/4.32 cnf(c_0_9949, 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)),c_List_Osplice(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_5890])). 4.05/4.32 cnf(c_0_9950, 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_5891])). 4.05/4.32 cnf(c_0_9951, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(c_Set_Ovimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5892])). 4.05/4.32 cnf(c_0_9952, plain, (hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_5893])). 4.05/4.32 cnf(c_0_9953, plain, (X1=hAPP(c_Set_Ovimage(X2,X2,c_COMBI(X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_5894])). 4.05/4.32 cnf(c_0_9954, plain, (c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3)=hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X2),c_List_Oupt(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_5895])). 4.05/4.32 fof(c_0_9955, plain, ![X9794, X9795, X9796]:hAPP(hAPP(c_List_Otake(X9796),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9795),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X9796),X9794))=hAPP(c_List_Otl(X9796),hAPP(hAPP(c_List_Otake(X9796),X9795),X9794)), inference(variable_rename,[status(thm)],[fact_tl__take])). 4.05/4.32 cnf(c_0_9956, plain, (hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|hAPP(c_Nat_OSuc,X3)=hAPP(c_Finite__Set_Ocard(X1),X5)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=X2|hAPP(c_Finite__Set_Ocard(X1),X2)!=X3|X5!=hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)), inference(split_conjunct,[status(thm)],[c_0_5466])). 4.05/4.32 cnf(c_0_9957, 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(split_conjunct,[status(thm)],[c_0_5896]), ['final']). 4.05/4.32 cnf(c_0_9958, 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_5897]), ['final']). 4.05/4.32 fof(c_0_9959, plain, ![X10168, X10169]:hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X10169,X10168),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X10169),X10168)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X10169,X10168)))), inference(variable_rename,[status(thm)],[fact_divmod__nat__rel])). 4.05/4.32 fof(c_0_9960, plain, ![X11884, X11885, X11886]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X11886)),hAPP(c_Set_Oimage(X11885,tc_Option_Ooption(X11886),hAPP(c_Map_Omap__of(X11885,X11886),X11884)),c_Orderings_Otop__class_Otop(tc_fun(X11885,tc_HOL_Obool))))), inference(variable_rename,[status(thm)],[fact_finite__range__map__of])). 4.05/4.32 fof(c_0_9961, plain, ![X2608, X2609, X2610, X2611, X2612, X2613]:hAPP(c_List_Ofoldl(X2613,X2612,X2611,X2610),hAPP(hAPP(c_List_Oappend(X2612),X2609),X2608))=hAPP(c_List_Ofoldl(X2613,X2612,X2611,hAPP(c_List_Ofoldl(X2613,X2612,X2611,X2610),X2609)),X2608), inference(variable_rename,[status(thm)],[fact_foldl__append])). 4.05/4.32 fof(c_0_9962, plain, ![X11099, X11100, X11101]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X11101,X11100)),X11099)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11101),X11099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11100),X11099)), inference(variable_rename,[status(thm)],[fact_mod__mult__distrib])). 4.05/4.32 fof(c_0_9963, plain, ![X14880, X14881, X14882]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14882),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X14881,X14880))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14882),X14881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X14882),X14880)), inference(variable_rename,[status(thm)],[fact_mod__mult__distrib2])). 4.05/4.32 fof(c_0_9964, plain, ![X15129, X15130, X15131]: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),X15131),X15130)),X15129)),X15130)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X15129),X15130), inference(variable_rename,[status(thm)],[fact_mod__mult__self4])). 4.05/4.32 fof(c_0_9965, plain, ![X16178, X16179, X16180, X16181]:hAPP(hAPP(c_List_Onth(X16181),hAPP(hAPP(c_List_Oappend(X16181),X16180),hAPP(hAPP(c_List_Olist_OCons(X16181),X16179),X16178))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X16181)),X16180))=X16179, inference(variable_rename,[status(thm)],[fact_nth__append__length])). 4.05/4.32 fof(c_0_9966, plain, ![X2901, X2902, X2903]:c_Random_Oselect__weight(X2903,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X2903)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X2903),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X2902)),X2901))=c_Random_Oselect__weight(X2903,X2901), inference(variable_rename,[status(thm)],[fact_select__weight__cons__zero])). 4.05/4.32 cnf(c_0_9967, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orotate(X1,X2),X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)), inference(split_conjunct,[status(thm)],[c_0_5898])). 4.05/4.32 fof(c_0_9968, plain, ![X3959, X3960, X3961, X3962]:c_Map_Odom(X3962,X3961,c_Map_Omap__add(X3962,X3961,X3960,X3959))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3962,tc_HOL_Obool)),c_Map_Odom(X3962,X3961,X3959)),c_Map_Odom(X3962,X3961,X3960)), inference(variable_rename,[status(thm)],[fact_dom__map__add])). 4.05/4.32 fof(c_0_9969, plain, ![X14527, X14528, X14529]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14529,tc_HOL_Obool)),hAPP(c_List_Oset(X14529),hAPP(hAPP(c_List_Odrop(X14529),X14528),X14527))),hAPP(c_List_Oset(X14529),X14527))), inference(variable_rename,[status(thm)],[fact_set__drop__subset])). 4.05/4.32 fof(c_0_9970, plain, ![X1139, X1140, X1141]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1141,tc_HOL_Obool)),hAPP(c_List_Oset(X1141),hAPP(hAPP(c_List_Otake(X1141),X1140),X1139))),hAPP(c_List_Oset(X1141),X1139))), inference(variable_rename,[status(thm)],[fact_set__take__subset])). 4.05/4.32 cnf(c_0_9971, plain, (c_Map_Omap__comp(X1,X2,X3,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),X4,X5)=c_Option_Ooption_ONone(X2)), inference(split_conjunct,[status(thm)],[c_0_5899])). 4.05/4.32 cnf(c_0_9972, 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_5900])). 4.05/4.32 fof(c_0_9973, plain, ![X13336, X13337, X13338]:hAPP(c_Option_Ooption_OSome(tc_prod(X13338,tc_Lazy__Sequence_Olazy__sequence(X13338))),hAPP(hAPP(c_Product__Type_OPair(X13338,tc_Lazy__Sequence_Olazy__sequence(X13338)),X13337),X13336))=hAPP(c_Lazy__Sequence_Oyield(X13338),c_Lazy__Sequence_Olazy__sequence_OInsert(X13338,X13337,X13336)), inference(variable_rename,[status(thm)],[fact__01])). 4.05/4.32 cnf(c_0_9974, 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_5901])). 4.05/4.32 cnf(c_0_9975, 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_5902])). 4.05/4.32 fof(c_0_9976, plain, ![X1748, X1749, X1750, X1751]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1751,tc_fun(X1750,tc_HOL_Obool)),X1749),X1748)=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1750,tc_HOL_Obool),hAPP(c_Set_Oimage(X1751,tc_fun(X1750,tc_HOL_Obool),X1748),X1749)), inference(variable_rename,[status(thm)],[fact_INTER__eq__Inter__image])). 4.05/4.32 fof(c_0_9977, plain, ![X17597, X17598, X17599]:hAPP(hAPP(c_Nat_Ocompow(X17599,X17599),hAPP(c_Nat_OSuc,X17598)),X17597)=hAPP(c_Fun_Ocomp(X17599,X17599,X17599,X17597),hAPP(hAPP(c_Nat_Ocompow(X17599,X17599),X17598),X17597)), inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I2_J])). 4.05/4.32 fof(c_0_9978, plain, ![X1829, X1830, X1831]:hAPP(c_Product__Type_Osnd(X1831,X1830),X1829)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1831,X1830,X1830),hAPP(c_COMBK(tc_fun(X1830,X1830),X1831),c_COMBI(X1830))),X1829), inference(variable_rename,[status(thm)],[fact_snd__def])). 4.05/4.32 fof(c_0_9979, plain, ![X4356, X4357, X4358]:hAPP(c_List_Ofilter(X4358,hAPP(c_fequal,X4357)),X4356)=c_List_Oreplicate(X4358,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4358)),hAPP(c_List_Ofilter(X4358,hAPP(c_fequal,X4357)),X4356)),X4357), inference(variable_rename,[status(thm)],[fact_replicate__length__filter])). 4.05/4.32 fof(c_0_9980, plain, ![X10127, X10128, X10129, X10130]:hAPP(hAPP(c_List_Olist_OCons(X10130),X10128),hAPP(hAPP(c_List_Otake(X10130),X10129),X10127))=hAPP(hAPP(c_List_Otake(X10130),hAPP(c_Nat_OSuc,X10129)),hAPP(hAPP(c_List_Olist_OCons(X10130),X10128),X10127)), inference(variable_rename,[status(thm)],[fact_take__Suc__Cons])). 4.05/4.32 fof(c_0_9981, plain, ![X2183, X2184, X2185]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2185)),hAPP(c_List_Ofilter(X2185,X2184),X2183))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2185)),X2183))), inference(variable_rename,[status(thm)],[fact_length__filter__le])). 4.05/4.32 fof(c_0_9982, plain, ![X15195, X15196]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X15196,tc_HOL_Obool),tc_HOL_Obool)),X15195),hAPP(c_Set_OPow(X15196),c_Complete__Lattice_OSup__class_OSup(tc_fun(X15196,tc_HOL_Obool),X15195)))), inference(variable_rename,[status(thm)],[fact_subset__Pow__Union])). 4.05/4.32 fof(c_0_9983, plain, ![X15825, X15826, X15827]: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,X15827,X15826)),X15825),X15826)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X15827),X15825),X15826), inference(variable_rename,[status(thm)],[fact_zpower__zmod])). 4.05/4.32 fof(c_0_9984, plain, ![X1281, X1282, X1283]: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,X1283,X1282)),X1281),X1282)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1283),X1281),X1282), inference(variable_rename,[status(thm)],[fact_zdiff__zmod__left])). 4.05/4.32 fof(c_0_9985, plain, ![X13957, X13958, X13959]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X13959),c_Divides_Odiv__class_Omod(tc_Int_Oint,X13958,X13957)),X13957)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X13959),X13958),X13957), inference(variable_rename,[status(thm)],[fact_zdiff__zmod__right])). 4.05/4.32 fof(c_0_9986, plain, ![X1416, X1417, X1418]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1418),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1417,X1416)),X1416)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1418),X1417),X1416), inference(variable_rename,[status(thm)],[fact_zmod__simps_I3_J])). 4.05/4.32 fof(c_0_9987, plain, ![X8574, X8575]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8575,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X8575,X8575),X8574)),hAPP(c_Relation_ORange(X8575,X8575),X8574))=hAPP(c_Relation_OField(X8575),X8574), inference(variable_rename,[status(thm)],[fact_Field__def])). 4.05/4.32 cnf(c_0_9988, plain, (hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))=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)))), inference(split_conjunct,[status(thm)],[c_0_5903])). 4.05/4.32 cnf(c_0_9989, 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_5904, c_0_5905]), ['final']). 4.05/4.32 fof(c_0_9990, plain, ![X9636, X9637]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X9637,tc_HOL_Obool),tc_fun(X9637,tc_HOL_Obool)),X9636),c_COMBI(tc_fun(X9637,tc_HOL_Obool)))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X9637,tc_HOL_Obool),X9636), inference(variable_rename,[status(thm)],[fact_Inter__def])). 4.05/4.32 fof(c_0_9991, plain, ![X15759, X15760]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X15760,tc_HOL_Obool),tc_fun(X15760,tc_HOL_Obool)),X15759),c_COMBI(tc_fun(X15760,tc_HOL_Obool)))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X15760,tc_HOL_Obool),X15759), inference(variable_rename,[status(thm)],[fact_Union__def])). 4.05/4.32 fof(c_0_9992, plain, ![X6843, X6844, X6845]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6845),X6844)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6843),X6844))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6845),X6843), inference(variable_rename,[status(thm)],[fact_diff__cancel2])). 4.05/4.32 fof(c_0_9993, plain, ![X1862, X1863, X1864]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1863),X1862)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1864),X1863)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1864),X1862)), inference(variable_rename,[status(thm)],[fact_diff__cancel])). 4.05/4.32 cnf(c_0_9994, 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_5906])). 4.05/4.32 cnf(c_0_9995, 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_5907]), ['final']). 4.05/4.32 cnf(c_0_9996, plain, (hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X2)=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))))), inference(split_conjunct,[status(thm)],[c_0_5908])). 4.05/4.32 fof(c_0_9997, plain, ![X355, X356, X357]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X357,tc_HOL_Obool)),X356),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X357,tc_HOL_Obool)),X355))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X357,tc_HOL_Obool)),X356),X355), inference(variable_rename,[status(thm)],[fact_Diff__Compl])). 4.05/4.32 cnf(c_0_9998, plain, (hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId(X1))=c_Relation_OId(X1)), inference(split_conjunct,[status(thm)],[c_0_5909])). 4.05/4.32 fof(c_0_9999, plain, ![X16359, X16360]: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),X16360),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16359)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X16360,X16359), inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I2_J])). 4.05/4.32 fof(c_0_10000, plain, ![X14973, X14974, X14975, X14976]:hAPP(hAPP(c_Relation_Orel__comp(X14976,X14975,X14974),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X14976,X14975),tc_HOL_Obool))),X14973)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X14976,X14974),tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_rel__comp__empty1])). 4.05/4.32 fof(c_0_10001, plain, ![X4996, X4997, X4998, X4999]:c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4999,X4997),tc_HOL_Obool))=hAPP(hAPP(c_Relation_Orel__comp(X4999,X4998,X4997),X4996),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4998,X4997),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_rel__comp__empty2])). 4.05/4.32 fof(c_0_10002, plain, ![X12972, X12973, X12974]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X12974,tc_HOL_Obool)),hAPP(c_List_Oset(X12974),c_List_Oremove1(X12974,X12973,X12972))),hAPP(c_List_Oset(X12974),X12972))), inference(variable_rename,[status(thm)],[fact_set__remove1__subset])). 4.05/4.32 fof(c_0_10003, plain, ![X3544, X3545, X3546]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3546,tc_HOL_Obool)),hAPP(c_List_Oset(X3546),c_List_Osublist(X3546,X3545,X3544))),hAPP(c_List_Oset(X3546),X3545))), inference(variable_rename,[status(thm)],[fact_set__sublist__subset])). 4.05/4.32 fof(c_0_10004, plain, ![X1892, X1893, X1894]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1894)),c_List_OtakeWhile(X1894,X1893,X1892))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1894)),X1892))), inference(variable_rename,[status(thm)],[fact_length__takeWhile__le])). 4.05/4.32 fof(c_0_10005, plain, ![X5886, X5887]:c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5887),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5887))),c_List_Otranspose(X5887,X5886)))), inference(variable_rename,[status(thm)],[fact_sorted__transpose])). 4.05/4.32 fof(c_0_10006, plain, ![X1270, X1271, X1272, X1273]:c_List_Oreplicate(X1273,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1272),X1271),X1270)=hAPP(hAPP(c_List_Oappend(X1273),c_List_Oreplicate(X1273,X1272,X1270)),c_List_Oreplicate(X1273,X1271,X1270)), inference(variable_rename,[status(thm)],[fact_replicate__add])). 4.05/4.32 cnf(c_0_10007, 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_5910])). 4.05/4.32 cnf(c_0_10008, 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_5911])). 4.05/4.32 cnf(c_0_10009, 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_5912]), ['final']). 4.05/4.32 cnf(c_0_10010, 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_5913])). 4.05/4.32 fof(c_0_10011, plain, ![X16570, X16571, X16572]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16572,tc_HOL_Obool)),X16571),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X16572,tc_HOL_Obool)),X16570),X16571))=c_Orderings_Obot__class_Obot(tc_fun(X16572,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Diff__disjoint])). 4.05/4.32 fof(c_0_10012, plain, ![X15525, X15526]:hAPP(hAPP(c_List_Otake(X15526),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X15526)),X15525)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X15525)=c_List_Obutlast(X15526,X15525), inference(variable_rename,[status(thm)],[fact_butlast__conv__take])). 4.05/4.32 cnf(c_0_10013, plain, (hAPP(c_Relation_ORange(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2))=hAPP(c_Relation_ORange(X1,X1),X2)), inference(rw,[status(thm)],[c_0_5914, c_0_5018])). 4.05/4.32 cnf(c_0_10014, plain, (hAPP(c_Relation_ODomain(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2))=hAPP(c_Relation_ODomain(X1,X1),X2)), inference(rw,[status(thm)],[c_0_5915, c_0_5018])). 4.05/4.32 cnf(c_0_10015, plain, (hAPP(c_List_Oset(X1),hAPP(c_List_Orotate(X1,X2),X3))=hAPP(c_List_Oset(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_5916])). 4.05/4.32 fof(c_0_10016, plain, ![X9466, X9467]: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),X9467),X9466))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X9467),hAPP(c_Nat_OSuc,X9466)), inference(variable_rename,[status(thm)],[fact_diff__Suc])). 4.05/4.32 fof(c_0_10017, plain, ![X15628, X15629, X15630]:hAPP(c_List_Ofilter(X15630,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X15630,c_fNot),X15629)),X15628)=hAPP(c_Product__Type_Osnd(tc_List_Olist(X15630),tc_List_Olist(X15630)),c_List_Opartition(X15630,X15629,X15628)), inference(variable_rename,[status(thm)],[fact_partition__filter2])). 4.05/4.32 fof(c_0_10018, plain, ![X13247, X13248, X13249, X13250, X13251]:hAPP(hAPP(c_List_Olist__update(X13251,X13250),X13249),X13247)=hAPP(hAPP(c_List_Olist__update(X13251,hAPP(hAPP(c_List_Olist__update(X13251,X13250),X13249),X13248)),X13249),X13247), inference(variable_rename,[status(thm)],[fact_list__update__overwrite])). 4.05/4.32 fof(c_0_10019, plain, ![X16042, X16043]:c_Code__Numeral_Odiv__mod__code__numeral(X16043,X16042)=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),X16043),X16042)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X16043,X16042)), inference(variable_rename,[status(thm)],[fact_div__mod__code__numeral__def])). 4.05/4.32 fof(c_0_10020, plain, ![X14359, X14360, X14361]:hAPP(c_List_Orev(X14361),hAPP(hAPP(c_List_Oappend(X14361),X14360),X14359))=hAPP(hAPP(c_List_Oappend(X14361),hAPP(c_List_Orev(X14361),X14359)),hAPP(c_List_Orev(X14361),X14360)), inference(variable_rename,[status(thm)],[fact_rev__append])). 4.05/4.32 fof(c_0_10021, plain, ![X13888, X13889, X13890, X13891]:hAPP(X13891,hAPP(hAPP(hAPP(c_Nat_Ocompow(X13890,X13890),X13889),X13891),X13888))=hAPP(hAPP(hAPP(c_Nat_Ocompow(X13890,X13890),X13889),X13891),hAPP(X13891,X13888)), inference(variable_rename,[status(thm)],[fact_funpow__swap1])). 4.05/4.32 fof(c_0_10022, plain, ![X11490, X11491, X11492, X11493]:hAPP(hAPP(c_List_Oappend(X11493),hAPP(hAPP(c_List_Oappend(X11493),X11492),X11491)),X11490)=hAPP(hAPP(c_List_Oappend(X11493),X11492),hAPP(hAPP(c_List_Oappend(X11493),X11491),X11490)), inference(variable_rename,[status(thm)],[fact_append__assoc])). 4.05/4.32 fof(c_0_10023, plain, ![X16344, X16345, X16346, X16347]:hAPP(hAPP(c_List_Olist_OCons(X16347),X16346),hAPP(hAPP(c_List_Oappend(X16347),X16345),X16344))=hAPP(hAPP(c_List_Oappend(X16347),hAPP(hAPP(c_List_Olist_OCons(X16347),X16346),X16345)),X16344), inference(variable_rename,[status(thm)],[fact_append__Cons])). 4.05/4.32 cnf(c_0_10024, 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_5917])). 4.05/4.32 fof(c_0_10025, plain, ![X6568, X6569, X6570, X6571]:hAPP(hAPP(c_List_Odrop(X6571),X6570),hAPP(hAPP(c_List_Odrop(X6571),X6569),X6568))=hAPP(hAPP(c_List_Odrop(X6571),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6570),X6569)),X6568), inference(variable_rename,[status(thm)],[fact_drop__drop])). 4.05/4.32 fof(c_0_10026, plain, ![X9931, X9932, X9933]:hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9933),X9932)),X9931)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X9933),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X9932),X9931)), inference(variable_rename,[status(thm)],[fact_zpower__zpower])). 4.05/4.32 fof(c_0_10027, plain, ![X2987, X2988, X2989]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2989),X2988)),X2987)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2988),X2987)), inference(variable_rename,[status(thm)],[fact_nat__mult__assoc])). 4.05/4.32 fof(c_0_10028, plain, ![X13924, X13925, X13926]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13925),X13924))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13926),X13925)),X13924), inference(variable_rename,[status(thm)],[fact_zmult__assoc])). 4.05/4.32 fof(c_0_10029, plain, ![X2398, X2399, X2400]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2399),X2398))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2400),X2399)),X2398), inference(variable_rename,[status(thm)],[fact_div__mult2__eq])). 4.05/4.32 fof(c_0_10030, plain, ![X3470, X3471]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3471),X3470))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3471)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3470)), inference(variable_rename,[status(thm)],[fact_zmult__int])). 4.05/4.32 fof(c_0_10031, plain, ![X10711, X10712, X10713, X10714, X10715, X10716, X10717]:hAPP(c_Product__Type_Osnd(X10717,X10716),hAPP(c_Product__Type_Omap__pair(X10715,X10717,X10714,X10716,X10713,X10712),X10711))=hAPP(X10712,hAPP(c_Product__Type_Osnd(X10715,X10714),X10711)), inference(variable_rename,[status(thm)],[fact_snd__prod__fun])). 4.05/4.32 fof(c_0_10032, plain, ![X4679, X4680, X4681, X4682, X4683, X4684, X4685]:hAPP(X4681,hAPP(c_Product__Type_Ofst(X4683,X4682),X4679))=hAPP(c_Product__Type_Ofst(X4685,X4684),hAPP(c_Product__Type_Omap__pair(X4683,X4685,X4682,X4684,X4681,X4680),X4679)), inference(variable_rename,[status(thm)],[fact_fst__map__pair])). 4.05/4.32 fof(c_0_10033, plain, ![X5379, X5380]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5380),X5379))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5380)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5379)), inference(variable_rename,[status(thm)],[fact_zadd__int])). 4.05/4.32 fof(c_0_10034, plain, ![X14587, X14588]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X14588),X14587))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14588)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14587)), inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I1_J])). 4.05/4.32 fof(c_0_10035, plain, ![X13356, X13357, X13358]:hBOOL(hAPP(hAPP(c_member(tc_prod(X13358,X13358)),hAPP(hAPP(c_Product__Type_OPair(X13358,X13358),X13357),X13357)),c_Transitive__Closure_Ortrancl(X13358,X13356))), inference(variable_rename,[status(thm)],[fact_rtrancl_Ortrancl__refl])). 4.05/4.32 cnf(c_0_10036, plain, (c_Enum_Oenum__the(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2))=X2), inference(rw,[status(thm)],[c_0_5918, c_0_4980])). 4.05/4.32 cnf(c_0_10037, 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_5919])). 4.05/4.32 fof(c_0_10038, plain, ![X5051, X5052, X5053, X5054, X5055, X5056, X5057]:hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X5057,X5056,X5055,X5054),X5053),X5052),X5051)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5056,X5055,X5054),X5052),hAPP(X5053,X5051)), inference(variable_rename,[status(thm)],[fact_scomp__apply])). 4.05/4.32 fof(c_0_10039, plain, ![X1255, X1256, X1257, X1258]:c_List_Oremdups(X1258,hAPP(hAPP(c_List_Omap(X1257,X1258),X1256),X1255))=c_List_Oremdups(X1258,hAPP(hAPP(c_List_Omap(X1257,X1258),X1256),c_List_Oremdups(X1257,X1255))), inference(variable_rename,[status(thm)],[fact_remdups__map__remdups])). 4.05/4.32 cnf(c_0_10040, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5920])). 4.05/4.32 cnf(c_0_10041, plain, (hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))=c_List_Olists(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5921])). 4.05/4.32 cnf(c_0_10042, plain, (hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X4,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X2))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5922])). 4.05/4.32 cnf(c_0_10043, 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_5923])). 4.05/4.32 cnf(c_0_10044, plain, (X1=hAPP(hAPP(c_Relation_Orel__comp(X2,X2,X3),c_Relation_OId(X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_5924])). 4.05/4.32 cnf(c_0_10045, plain, (X1=hAPP(hAPP(c_Relation_Orel__comp(X2,X3,X3),X1),c_Relation_OId(X3))), inference(split_conjunct,[status(thm)],[c_0_5925])). 4.05/4.32 fof(c_0_10046, plain, ![X3372, X3373, X3374]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3372,X3373)=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),X3374),X3373)),X3372),X3373), inference(variable_rename,[status(thm)],[fact_mod__mult__self3])). 4.05/4.32 fof(c_0_10047, plain, ![X9992, X9993, X9994]:c_Orderings_Otop__class_Otop(tc_fun(X9994,tc_HOL_Obool))=c_Map_Odom(X9994,X9993,hAPP(hAPP(c_COMBB(X9993,tc_Option_Ooption(X9993),X9994),c_Option_Ooption_OSome(X9993)),X9992)), inference(variable_rename,[status(thm)],[fact_dom__const])). 4.05/4.32 cnf(c_0_10048, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|hAPP(c_Set_Oimage(tc_Nat_Onat,X1,X2),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)),X3)))!=X4), inference(split_conjunct,[status(thm)],[c_0_5926])). 4.05/4.32 cnf(c_0_10049, 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_5927])). 4.05/4.32 fof(c_0_10050, plain, ![X9735, X9736, X9737, X9738, X9739, X9740]:hAPP(hAPP(X9737,X9736),X9735)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X9740,X9739,X9738),X9737),hAPP(hAPP(c_Product__Type_OPair(X9740,X9739),X9736),X9735)), inference(variable_rename,[status(thm)],[fact_split__conv])). 4.05/4.32 cnf(c_0_10051, 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)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=X1), inference(split_conjunct,[status(thm)],[c_0_5528])). 4.05/4.32 cnf(c_0_10052, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1))))), inference(rw,[status(thm)],[c_0_5928, c_0_5583])). 4.05/4.32 fof(c_0_10053, plain, ![X3088, X3089, X3090, X3091, X3092]:c_Predicate_Opred__comp(X3091,X3090,X3092,c_Predicate_Oconversep(X3090,X3091,X3088),c_Predicate_Oconversep(X3092,X3090,X3089))=c_Predicate_Oconversep(X3092,X3091,c_Predicate_Opred__comp(X3092,X3090,X3091,X3089,X3088)), inference(variable_rename,[status(thm)],[fact_converse__pred__comp])). 4.05/4.32 cnf(c_0_10054, plain, (c_List_Obutlast(X1,X2)=c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist__update(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), inference(split_conjunct,[status(thm)],[c_0_5929])). 4.05/4.32 fof(c_0_10055, plain, ![X12444, X12445]:c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X12445,X12444),tc_HOL_Obool))=c_Sum__Type_OPlus(X12445,X12444,c_Orderings_Otop__class_Otop(tc_fun(X12445,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12444,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV])). 4.05/4.32 fof(c_0_10056, plain, ![X7493, X7494, X7495, X7496]:hAPP(hAPP(c_List_Olist_OCons(X7496),X7493),X7494)=hAPP(hAPP(c_List_Olist__update(X7496,hAPP(hAPP(c_List_Olist_OCons(X7496),X7495),X7494)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7493), inference(variable_rename,[status(thm)],[fact_list__update__code_I2_J])). 4.05/4.32 cnf(c_0_10057, 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_5930])). 4.05/4.32 cnf(c_0_10058, plain, (c_Sum__Type_OPlus(X2,X3,X1,X4)=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X2,X3),tc_HOL_Obool))|X1!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))!=X4), inference(split_conjunct,[status(thm)],[c_0_5931])). 4.05/4.32 fof(c_0_10059, plain, ![X10624, X10625]: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,X10625)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X10624))), inference(variable_rename,[status(thm)],[fact_negative__zless])). 4.05/4.32 cnf(c_0_10060, 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_5453])). 4.05/4.32 cnf(c_0_10061, plain, (hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5932, c_0_5933]), c_0_5149])). 4.05/4.32 cnf(c_0_10062, plain, (hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5934, c_0_4795]), c_0_5149]), ['final']). 4.05/4.32 fof(c_0_10063, plain, ![X14725, X14726, X14727]:hAPP(hAPP(c_List_Otake(X14727),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X14727)),c_List_OtakeWhile(X14727,X14726,X14725))),X14725)=c_List_OtakeWhile(X14727,X14726,X14725), inference(variable_rename,[status(thm)],[fact_takeWhile__eq__take])). 4.05/4.32 fof(c_0_10064, plain, ![X6396, X6397]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X6397),hAPP(c_List_Oset(X6397),X6396))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X6397)),X6396))), inference(variable_rename,[status(thm)],[fact_card__length])). 4.05/4.32 cnf(c_0_10065, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2))), inference(rw,[status(thm)],[c_0_5935, c_0_5018])). 4.05/4.32 cnf(c_0_10066, plain, (hAPP(hAPP(c_Relation_Orel__comp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)),c_Wellfounded_Opred__nat)=c_Wellfounded_Oless__than), inference(rw,[status(thm)],[c_0_5936, c_0_5018])). 4.05/4.32 fof(c_0_10067, plain, ![X9444, X9445, X9446]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X9446))),c_Enum_On__lists(X9446,X9445,X9444))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9446)),X9444)),X9445), inference(variable_rename,[status(thm)],[fact_length__n__lists])). 4.05/4.32 fof(c_0_10068, plain, ![X3207, X3208]:c_Orderings_Otop__class_Otop(tc_fun(X3208,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3208,tc_HOL_Obool)),X3207),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3208,tc_HOL_Obool)),X3207)), inference(variable_rename,[status(thm)],[fact_Compl__partition])). 4.05/4.32 cnf(c_0_10069, 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)))|X1!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_5491])). 4.05/4.32 cnf(c_0_10070, 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_5937, c_0_4427]), c_0_4427]), ['final']). 4.05/4.32 fof(c_0_10071, plain, ![X14202, X14203, X14204]:hAPP(c_List_Otl(X14204),hAPP(hAPP(c_List_Otake(X14204),hAPP(c_Nat_OSuc,X14203)),X14202))=hAPP(hAPP(c_List_Otake(X14204),X14203),hAPP(c_List_Otl(X14204),X14202)), inference(variable_rename,[status(thm)],[fact_take__tl])). 4.05/4.32 fof(c_0_10072, plain, ![X1386, X1387, X1388]:hAPP(hAPP(c_List_Otake(X1388),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X1388),X1387),X1386))=hAPP(hAPP(c_List_Olist_OCons(X1388),X1387),c_List_Olist_ONil(X1388)), inference(variable_rename,[status(thm)],[fact_take__1__Cons])). 4.05/4.32 cnf(c_0_10073, 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_5938])). 4.05/4.32 cnf(c_0_10074, 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_5939])). 4.05/4.32 fof(c_0_10075, plain, ![X14180, X14181, X14182]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14182,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X14182,tc_HOL_Obool)),X14181),X14180)),X14181)), inference(variable_rename,[status(thm)],[fact_Diff__subset])). 4.05/4.32 fof(c_0_10076, plain, ![X7957, X7958, X7959]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7959,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7959,tc_HOL_Obool)),X7958),X7957)),X7958)), inference(variable_rename,[status(thm)],[fact_Int__lower1])). 4.05/4.32 fof(c_0_10077, plain, ![X4766, X4767, X4768]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4768,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4768,tc_HOL_Obool)),X4767),X4766)),X4766)), inference(variable_rename,[status(thm)],[fact_Int__lower2])). 4.05/4.32 fof(c_0_10078, plain, ![X727, X728, X729]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X729,tc_HOL_Obool)),X728),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X729,tc_HOL_Obool)),X728),X727))), inference(variable_rename,[status(thm)],[fact_Un__upper1])). 4.05/4.32 fof(c_0_10079, plain, ![X3936, X3937, X3938]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3938,tc_HOL_Obool)),X3937),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3938,tc_HOL_Obool)),X3936),X3937))), inference(variable_rename,[status(thm)],[fact_Un__upper2])). 4.05/4.32 fof(c_0_10080, plain, ![X8929, X8930, X8931, X8932, X8933]:c_Map_Orestrict__map(X8933,X8932,c_Map_Orestrict__map(X8933,X8932,X8931,X8930),X8929)=c_Map_Orestrict__map(X8933,X8932,X8931,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8933,tc_HOL_Obool)),X8930),X8929)), inference(variable_rename,[status(thm)],[fact_restrict__restrict])). 4.05/4.32 fof(c_0_10081, plain, ![X16996, X16997, X16998, X16999]:c_Map_Omap__le(X16999,X16998,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X16999,tc_Option_Ooption(X16998)),X16997),X16996),c_Option_Ooption_ONone(X16998)),X16997), inference(variable_rename,[status(thm)],[fact_upd__None__map__le])). 4.05/4.32 cnf(c_0_10082, 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_5453])). 4.05/4.32 cnf(c_0_10083, plain, (c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))), inference(rw,[status(thm)],[c_0_5940, c_0_4475])). 4.05/4.32 fof(c_0_10084, plain, ![X3941, X3942]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3942),X3941)=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,X3942,X3941)),X3941), inference(variable_rename,[status(thm)],[fact_zminus__zmod])). 4.05/4.32 cnf(c_0_10085, plain, (c_List_Olist_ONil(X2)=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X2),tc_List_Olist(X2)),X3),c_List_Orotate1(X2)),X1)|X1!=c_List_Olist_ONil(X2)), inference(rw,[status(thm)],[c_0_5941, c_0_5942])). 4.05/4.32 fof(c_0_10086, plain, ![X10467, X10468, X10469, X10470]:hAPP(hAPP(c_List_Onth(X10470),hAPP(hAPP(c_List_Olist_OCons(X10470),X10469),X10468)),hAPP(c_Nat_OSuc,X10467))=hAPP(hAPP(c_List_Onth(X10470),X10468),X10467), inference(variable_rename,[status(thm)],[fact_nth__Cons__Suc])). 4.05/4.32 fof(c_0_10087, plain, ![X7248, X7249, X7250, X7251]:hAPP(hAPP(c_List_Odrop(X7251),hAPP(c_Nat_OSuc,X7250)),hAPP(hAPP(c_List_Olist_OCons(X7251),X7249),X7248))=hAPP(hAPP(c_List_Odrop(X7251),X7250),X7248), inference(variable_rename,[status(thm)],[fact_drop__Suc__Cons])). 4.05/4.32 cnf(c_0_10088, plain, (hAPP(c_List_Orev(X2),X1)=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))), inference(split_conjunct,[status(thm)],[c_0_5943])). 4.05/4.32 cnf(c_0_10089, 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_5944])). 4.05/4.32 fof(c_0_10090, plain, ![X12168, X12169, X12170]:hAPP(hAPP(c_List_Oappend(X12170),hAPP(hAPP(c_List_Otake(X12170),X12169),X12168)),hAPP(hAPP(c_List_Odrop(X12170),X12169),X12168))=X12168, inference(variable_rename,[status(thm)],[fact_append__take__drop__id])). 4.05/4.32 fof(c_0_10091, plain, ![X2595, X2596, X2597]:X2595=hAPP(hAPP(c_Product__Type_OPair(X2597,X2596),hAPP(c_Product__Type_Ofst(X2597,X2596),X2595)),hAPP(c_Product__Type_Osnd(X2597,X2596),X2595)), inference(variable_rename,[status(thm)],[fact_pair__collapse])). 4.05/4.32 fof(c_0_10092, plain, ![X2474, X2475, X2476]:hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2476,tc_fun(X2475,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2476,tc_HOL_Obool))),X2474)=c_Orderings_Otop__class_Otop(tc_fun(X2475,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_INT__empty])). 4.05/4.32 fof(c_0_10093, plain, ![X3555, X3556]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3556,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3556,tc_HOL_Obool))),X3555)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3556,tc_HOL_Obool)),X3555), inference(variable_rename,[status(thm)],[fact_Compl__eq__Diff__UNIV])). 4.05/4.32 fof(c_0_10094, plain, ![X8758, X8759, X8760, X8761, X8762, X8763]:hAPP(hAPP(X8760,X8759),X8758)=c_Product__Type_Oprod_Oprod__rec(X8763,X8762,X8761,X8760,hAPP(hAPP(c_Product__Type_OPair(X8763,X8762),X8759),X8758)), inference(variable_rename,[status(thm)],[fact_prod_Orecs])). 4.05/4.32 cnf(c_0_10095, 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_5945])). 4.05/4.32 fof(c_0_10096, plain, ![X9763, X9764, X9765, X9766]:hAPP(c_Map_Orestrict__map(X9766,X9765,hAPP(c_COMBK(tc_Option_Ooption(X9765),X9766),c_Option_Ooption_ONone(X9765)),X9764),X9763)=c_Option_Ooption_ONone(X9765), inference(variable_rename,[status(thm)],[fact_restrict__map__empty])). 4.05/4.32 cnf(c_0_10097, plain, (c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat))))), inference(split_conjunct,[status(thm)],[fact_wf__less])). 4.05/4.32 fof(c_0_10098, plain, ![X13416, X13417]:hBOOL(hAPP(hAPP(c_member(tc_fun(X13417,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X13417,tc_HOL_Obool))),hAPP(c_Set_OPow(X13417),X13416))), inference(variable_rename,[status(thm)],[fact_Pow__bottom])). 4.05/4.32 fof(c_0_10099, plain, ![X10118, X10119, X10120]:hAPP(c_List_Oset(X10120),c_List_Oreplicate(X10120,hAPP(c_Nat_OSuc,X10119),X10118))=hAPP(hAPP(c_Set_Oinsert(X10120),X10118),c_Orderings_Obot__class_Obot(tc_fun(X10120,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_set__replicate__Suc])). 4.05/4.32 fof(c_0_10100, plain, ![X10756, X10757]:c_Divides_Odiv__class_Omod(tc_Int_Oint,X10757,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X10756))=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),X10757),X10756)), inference(variable_rename,[status(thm)],[fact_zmod__zminus2])). 4.05/4.32 fof(c_0_10101, plain, ![X5824, X5825]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5825)),X5824)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5825)),hAPP(c_List_Otl(X5825),X5824)), inference(variable_rename,[status(thm)],[fact_length__tl])). 4.05/4.32 cnf(c_0_10102, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X1,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_5946])). 4.05/4.32 fof(c_0_10103, plain, ![X13841, X13842]:c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X13842),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X13841))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X13842,X13841)), inference(variable_rename,[status(thm)],[fact_zmod__zminus__zminus])). 4.05/4.32 fof(c_0_10104, plain, ![X12189, X12190, X12191, X12192]:hAPP(hAPP(c_List_Odrop(X12192),X12191),c_List_Oreplicate(X12192,X12190,X12189))=c_List_Oreplicate(X12192,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12190),X12191),X12189), inference(variable_rename,[status(thm)],[fact_drop__replicate])). 4.05/4.32 cnf(c_0_10105, plain, (hAPP(hAPP(c_List_Otake(X1),X2),c_List_Oreplicate(X1,X3,X4))=c_List_Oreplicate(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X2),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_5947])). 4.05/4.32 fof(c_0_10106, plain, ![X1897, X1898]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1898,X1897))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1898),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1897)), inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I2_J])). 4.05/4.32 fof(c_0_10107, plain, ![X16974]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16974),X16974)))), inference(variable_rename,[status(thm)],[fact_le__cube])). 4.05/4.32 fof(c_0_10108, plain, ![X4630, X4631, X4632, X4633, X4634]:hAPP(hAPP(c_Product__Type_Oscomp(X4634,X4633,X4634,X4632),hAPP(c_Product__Type_OPair(X4633,X4634),X4631)),X4630)=hAPP(X4630,X4631), inference(variable_rename,[status(thm)],[fact_Pair__scomp])). 4.05/4.32 cnf(c_0_10109, plain, (hAPP(c_Relation_OImage(X1,X1,c_Relation_OId(X1)),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_5948])). 4.05/4.32 fof(c_0_10110, plain, ![X9346, X9347, X9348, X9349, X9350, X9351]:hAPP(c_List_Olist_Olist__case(X9351,X9350,X9349,X9348),hAPP(hAPP(c_List_Olist_OCons(X9350),X9347),X9346))=hAPP(hAPP(X9348,X9347),X9346), inference(variable_rename,[status(thm)],[fact_list_Osimps_I5_J])). 4.05/4.32 fof(c_0_10111, plain, ![X16383, X16384, X16385, X16386, X16387, X16388]:c_Map_Omap__upds(X16388,X16387,c_Map_Omap__add(X16388,X16387,X16386,X16385),X16384,X16383)=c_Map_Omap__add(X16388,X16387,X16386,c_Map_Omap__upds(X16388,X16387,X16385,X16384,X16383)), inference(variable_rename,[status(thm)],[fact_map__add__upds])). 4.05/4.32 cnf(c_0_10112, 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_5949, c_0_4519])). 4.05/4.32 fof(c_0_10113, plain, ![X4497, X4498, X4499, X4500]:hAPP(hAPP(c_List_Onth(X4500),hAPP(hAPP(c_List_Olist_OCons(X4500),X4499),X4498)),X4497)=c_Nat_Onat_Onat__case(X4500,X4499,hAPP(c_List_Onth(X4500),X4498),X4497), inference(variable_rename,[status(thm)],[fact_nth_Osimps])). 4.05/4.32 fof(c_0_10114, plain, ![X14731, X14732]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X14732),hAPP(c_Nat_OSuc,X14731))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X14732,X14731)), inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastAtMost])). 4.05/4.32 cnf(c_0_10115, 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_5950])). 4.05/4.32 fof(c_0_10116, plain, ![X6935]: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,X6935)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[fact_negative__zless__0])). 4.05/4.32 fof(c_0_10117, plain, ![X7923, X7924]: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),X7924))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7923))), inference(variable_rename,[status(thm)],[fact_negative__zle])). 4.05/4.32 fof(c_0_10118, plain, ![X11941, X11942]: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),X11942)),X11941))), inference(variable_rename,[status(thm)],[fact_zero__le__zpower__abs])). 4.05/4.32 fof(c_0_10119, plain, ![X3402, X3403]:c_Transitive__Closure_Ortrancl(X3403,X3402)=hAPP(hAPP(c_Relation_Orel__comp(X3403,X3403,X3403),c_Transitive__Closure_Ortrancl(X3403,X3402)),c_Transitive__Closure_Ortrancl(X3403,X3402)), inference(variable_rename,[status(thm)],[fact_rtrancl__idemp__self__comp])). 4.05/4.32 fof(c_0_10120, plain, ![X8674, X8675, X8676]:c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8676,X8675),tc_HOL_Obool))=hAPP(hAPP(c_Product__Type_OSigma(X8676,X8675),c_Orderings_Obot__class_Obot(tc_fun(X8676,tc_HOL_Obool))),X8674), inference(variable_rename,[status(thm)],[fact_Sigma__empty1])). 4.05/4.32 fof(c_0_10121, plain, ![X7726, X7727]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X7727),X7726))=c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7727),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X7726)), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J])). 4.05/4.32 fof(c_0_10122, plain, ![X16664, X16665]:hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X16665,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X16665),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X16664)=hAPP(c_Finite__Set_Ocard(X16665),X16664), inference(variable_rename,[status(thm)],[fact_card__eq__setsum])). 4.05/4.32 fof(c_0_10123, plain, ![X9472, X9473]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9473)),X9472)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9473)),c_List_Obutlast(X9473,X9472)), inference(variable_rename,[status(thm)],[fact_length__butlast])). 4.05/4.32 fof(c_0_10124, plain, ![X11106, X11107]:hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),X11107),X11106)=c_Smallcheck_Osmall_H(X11107,hAPP(c_Code__Numeral_Oint__of,X11106),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X11106))), inference(variable_rename,[status(thm)],[fact_small__int__def])). 4.05/4.32 fof(c_0_10125, plain, ![X930, X931, X932, X933]:X930=hAPP(hAPP(c_Product__Type_Oscomp(X933,X932,X931,tc_prod(X932,X931)),X930),c_Product__Type_OPair(X932,X931)), inference(variable_rename,[status(thm)],[fact_scomp__Pair])). 4.05/4.32 fof(c_0_10126, plain, ![X12110, X12111]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X12111,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X12111,tc_HOL_Obool))),X12110)=c_Orderings_Obot__class_Obot(tc_fun(X12111,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_empty__Diff])). 4.05/4.32 fof(c_0_10127, plain, ![X14589, X14590, X14591, X14592]:c_Map_Odom(X14592,X14591,c_Map_Orestrict__map(X14592,X14591,X14590,X14589))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14592,tc_HOL_Obool)),c_Map_Odom(X14592,X14591,X14590)),X14589), inference(variable_rename,[status(thm)],[fact_dom__restrict])). 4.05/4.32 fof(c_0_10128, plain, ![X2239, X2240]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2240,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2240,tc_HOL_Obool))),X2239)=c_Orderings_Obot__class_Obot(tc_fun(X2240,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Int__empty__left])). 4.05/4.32 fof(c_0_10129, plain, ![X12164, X12165]:c_Orderings_Otop__class_Otop(tc_fun(X12165,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12165,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X12165,tc_HOL_Obool))),X12164), inference(variable_rename,[status(thm)],[fact_Un__UNIV__left])). 4.05/4.32 fof(c_0_10130, plain, ![X9585, X9586]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9586,tc_HOL_Obool)),X9585),c_Orderings_Otop__class_Otop(tc_fun(X9586,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X9586,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Diff__UNIV])). 4.05/4.32 fof(c_0_10131, plain, ![X15959, X15960]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X15960,tc_HOL_Obool)),X15959),c_Orderings_Otop__class_Otop(tc_fun(X15960,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X15960,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Un__UNIV__right])). 4.05/4.32 fof(c_0_10132, plain, ![X9146, X9147]:c_Orderings_Obot__class_Obot(tc_fun(X9147,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X9147,tc_HOL_Obool)),X9146),c_Orderings_Obot__class_Obot(tc_fun(X9147,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Int__empty__right])). 4.05/4.32 fof(c_0_10133, plain, ![X8291]:c_Complete__Lattice_OInf__class_OInf(tc_fun(X8291,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X8291,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X8291,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Inter__UNIV])). 4.05/4.32 fof(c_0_10134, plain, ![X14183]:c_Orderings_Otop__class_Otop(tc_fun(X14183,tc_HOL_Obool))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X14183,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X14183,tc_HOL_Obool),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Union__UNIV])). 4.05/4.32 fof(c_0_10135, plain, ![X8320]:c_Orderings_Otop__class_Otop(tc_fun(X8320,tc_HOL_Obool))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X8320,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X8320,tc_HOL_Obool),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Inter__empty])). 4.05/4.32 fof(c_0_10136, plain, ![X16973]:c_Orderings_Obot__class_Obot(tc_fun(X16973,tc_HOL_Obool))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X16973,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X16973,tc_HOL_Obool),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Union__empty])). 4.05/4.32 cnf(c_0_10137, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Divides_Odivmod__nat(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_5951])). 4.05/4.32 fof(c_0_10138, plain, ![X9294, X9295, X9296, X9297]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9297)),hAPP(hAPP(c_List_Olist__update(X9297,X9296),X9295),X9294))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X9297)),X9296), inference(variable_rename,[status(thm)],[fact_length__list__update])). 4.05/4.32 cnf(c_0_10139, plain, (c_Option_Ooption_Ooption__size(X1,X2,hAPP(c_Option_Ooption_OSome(X1),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5952])). 4.05/4.32 fof(c_0_10140, plain, ![X5981, X5982]:c_List_Olistrel1(X5982,hAPP(c_Relation_Oconverse(X5982,X5982),X5981))=hAPP(c_Relation_Oconverse(tc_List_Olist(X5982),tc_List_Olist(X5982)),c_List_Olistrel1(X5982,X5981)), inference(variable_rename,[status(thm)],[fact_listrel1__converse])). 4.05/4.32 cnf(c_0_10141, 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_5953])). 4.05/4.32 cnf(c_0_10142, plain, (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)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5954])). 4.05/4.32 cnf(c_0_10143, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X1),X2)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))), inference(split_conjunct,[status(thm)],[c_0_5955])). 4.05/4.32 cnf(c_0_10144, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X1),X2)=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))), inference(split_conjunct,[status(thm)],[c_0_5956])). 4.05/4.32 fof(c_0_10145, plain, ![X15333, X15334]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X15334),X15333))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15334)),X15333), inference(variable_rename,[status(thm)],[fact_zpower__int])). 4.05/4.32 fof(c_0_10146, plain, ![X6158, X6159]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X6159),X6158))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6159)),X6158), inference(variable_rename,[status(thm)],[fact_zmult__zminus])). 4.05/4.32 fof(c_0_10147, plain, ![X14092, X14093]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14093),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X14092))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X14093)),X14092), inference(variable_rename,[status(thm)],[fact_zdiv__zminus2])). 4.05/4.32 fof(c_0_10148, plain, ![X14762, X14763]: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)),X14763),X14762), inference(variable_rename,[status(thm)],[fact_inj__on__add__nat])). 4.05/4.32 cnf(c_0_10149, 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_5957])). 4.05/4.32 cnf(c_0_10150, 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_5958, c_0_4523]), ['final']). 4.05/4.32 fof(c_0_10151, plain, ![X10718, X10719, X10720, X10721, X10722]:c_List_Oreplicate(X10721,X10719,hAPP(X10720,X10718))=hAPP(hAPP(c_List_Omap(X10722,X10721),X10720),c_List_Oreplicate(X10722,X10719,X10718)), inference(variable_rename,[status(thm)],[fact_map__replicate])). 4.05/4.32 fof(c_0_10152, plain, ![X8102, X8103, X8104]:hAPP(c_Product__Type_Ofst(tc_List_Olist(X8104),tc_List_Olist(X8104)),c_List_Opartition(X8104,X8103,X8102))=hAPP(c_List_Ofilter(X8104,X8103),X8102), inference(variable_rename,[status(thm)],[fact_partition__filter1])). 4.05/4.32 cnf(c_0_10153, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X1,X2,X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5959])). 4.05/4.32 cnf(c_0_10154, 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_5960, c_0_5905])). 4.05/4.32 fof(c_0_10155, plain, ![X3737, X3738, X3739]:hAPP(hAPP(c_Set_Oinsert(X3739),X3738),X3737)=hAPP(hAPP(c_Set_Oinsert(X3739),X3738),hAPP(hAPP(c_Set_Oinsert(X3739),X3738),X3737)), inference(variable_rename,[status(thm)],[fact_insert__absorb2])). 4.05/4.32 cnf(c_0_10156, 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_5961])). 4.05/4.32 cnf(c_0_10157, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X2)))!=X3), inference(split_conjunct,[status(thm)],[c_0_5962])). 4.05/4.32 fof(c_0_10158, plain, ![X17582]:c_Relation_Orefl__on(X17582,c_Orderings_Obot__class_Obot(tc_fun(X17582,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X17582,X17582),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_refl__on__empty])). 4.05/4.32 cnf(c_0_10159, 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_5963])). 4.05/4.32 fof(c_0_10160, plain, ![X10031, X10032, X10033, X10034, X10035]:X10031=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10035,X10034,X10033),X10032),X10031),c_Orderings_Obot__class_Obot(tc_fun(X10034,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_fold__image__empty])). 4.05/4.32 fof(c_0_10161, plain, ![X4018, X4019]:c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4019,X4018)),X4018)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X4019),X4018), inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__Suc__mod])). 4.05/4.32 cnf(c_0_10162, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X1)),hAPP(c_Code__Numeral_Oof__nat,X2))=hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5964])). 4.05/4.32 cnf(c_0_10163, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5965])). 4.05/4.32 cnf(c_0_10164, 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_5966])). 4.05/4.32 cnf(c_0_10165, 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_5967, c_0_5583])). 4.05/4.32 fof(c_0_10166, plain, ![X12412, X12413, X12414, X12415, X12416]:c_Map_Omap__add(X12416,X12415,X12414,c_Map_Omap__add(X12416,X12415,X12413,X12412))=c_Map_Omap__add(X12416,X12415,c_Map_Omap__add(X12416,X12415,X12414,X12413),X12412), inference(variable_rename,[status(thm)],[fact_map__add__assoc])). 4.05/4.32 fof(c_0_10167, plain, ![X4419, X4420, X4421]:X4419=hAPP(c_Finite__Set_Ofold1(X4421,X4420),hAPP(hAPP(c_Set_Oinsert(X4421),X4419),c_Orderings_Obot__class_Obot(tc_fun(X4421,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_fold1__singleton])). 4.05/4.32 fof(c_0_10168, plain, ![X3027, X3028]:c_Smallcheck_Ofull__small_H(X3028,hAPP(c_Code__Numeral_Oint__of,X3027),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X3027)))=c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,X3028,X3027), inference(variable_rename,[status(thm)],[fact_full__small__int__def])). 4.05/4.32 fof(c_0_10169, plain, ![X12957, X12958]:c_Orderings_Obot__class_Obot(tc_fun(X12957,tc_HOL_Obool))=c_Map_Oran(X12958,X12957,hAPP(c_COMBK(tc_Option_Ooption(X12957),X12958),c_Option_Ooption_ONone(X12957))), inference(variable_rename,[status(thm)],[fact_ran__empty])). 4.05/4.32 fof(c_0_10170, plain, ![X12073, X12074]:c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X12074,X12073)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X12074),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X12073),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(variable_rename,[status(thm)],[fact_atLeastLessThanPlusOne__atLeastAtMost__int])). 4.05/4.32 fof(c_0_10171, plain, ![X7255, X7256, X7257]:hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7257,X7256,X7257),c_COMBK(X7257,X7256)),X7255)=hAPP(c_Product__Type_Ofst(X7257,X7256),X7255), inference(variable_rename,[status(thm)],[fact_fst__def])). 4.05/4.32 fof(c_0_10172, plain, ![X11332, X11333, X11334]:hAPP(c_Relation_OImage(X11334,X11334,c_Relation_OId__on(X11334,X11333)),X11332)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X11334,tc_HOL_Obool)),X11333),X11332), inference(variable_rename,[status(thm)],[fact_Image__Id__on])). 4.05/4.32 fof(c_0_10173, plain, ![X16868, X16869, X16870]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16870,tc_HOL_Obool)),X16869),hAPP(hAPP(c_Set_Oinsert(X16870),X16868),X16869))), inference(variable_rename,[status(thm)],[fact_subset__insertI])). 4.05/4.32 fof(c_0_10174, plain, ![X1924]: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),X1924))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(variable_rename,[status(thm)],[fact_negative__zle__0])). 4.05/4.32 fof(c_0_10175, plain, ![X3908, X3909, X3910, X3911]:hAPP(c_Option_Ooption_OSome(X3910),hAPP(X3909,X3908))=hAPP(hAPP(c_Option_Omap(X3911,X3910),X3909),hAPP(c_Option_Ooption_OSome(X3911),X3908)), inference(variable_rename,[status(thm)],[fact_option__map__Some])). 4.05/4.32 fof(c_0_10176, plain, ![X564]: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),X564))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X564)), inference(variable_rename,[status(thm)],[fact_int__Suc])). 4.05/4.32 cnf(c_0_10177, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5968])). 4.05/4.32 cnf(c_0_10178, plain, (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))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=X2), inference(split_conjunct,[status(thm)],[c_0_5969])). 4.05/4.32 fof(c_0_10179, plain, ![X2305, X2306, X2307]:c_List_Oreplicate(X2307,hAPP(c_Nat_OSuc,X2306),X2305)=hAPP(hAPP(c_List_Olist_OCons(X2307),X2305),c_List_Oreplicate(X2307,X2306,X2305)), inference(variable_rename,[status(thm)],[fact_replicate__Suc])). 4.05/4.32 fof(c_0_10180, plain, ![X14782, X14783, X14784, X14785]:c_Lazy__Sequence_Oappend(tc_Option_Ooption(X14785),hAPP(X14784,X14782),hAPP(X14783,X14782))=hAPP(c_New__DSequence_Oneg__union(X14785,X14784,X14783),X14782), inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__union__def])). 4.05/4.32 fof(c_0_10181, plain, ![X927, X928, X929]:hAPP(hAPP(c_List_Odrop(X929),X928),c_List_Obutlast(X929,X927))=c_List_Obutlast(X929,hAPP(hAPP(c_List_Odrop(X929),X928),X927)), inference(variable_rename,[status(thm)],[fact_butlast__drop])). 4.05/4.32 fof(c_0_10182, plain, ![X3038, X3039, X3040]:hAPP(c_List_Oset(X3040),c_List_Oinsert(X3040,X3039,X3038))=hAPP(hAPP(c_Set_Oinsert(X3040),X3039),hAPP(c_List_Oset(X3040),X3038)), inference(variable_rename,[status(thm)],[fact_List_Oset__insert])). 4.05/4.32 fof(c_0_10183, plain, ![X1371, X1372, X1373, X1374]:hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1374,X1373,X1372,X1371,c_Orderings_Obot__class_Obot(tc_fun(X1374,tc_HOL_Obool))),X1371)), inference(variable_rename,[status(thm)],[fact_fold__graph_OemptyI])). 4.05/4.32 fof(c_0_10184, plain, ![X9055]:hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X9055)),c_Int_OInteg)), inference(variable_rename,[status(thm)],[fact_Rep__Integ])). 4.05/4.32 cnf(c_0_10185, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),c_Divides_Odivmod__nat(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_5970])). 4.05/4.32 fof(c_0_10186, plain, ![X3724]:hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X3724)=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)),X3724)), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J])). 4.05/4.32 fof(c_0_10187, plain, ![X5242, X5243, X5244, X5245, X5246, X5247]:hAPP(hAPP(X5244,X5243),X5242)=c_Nitpick_Opair__box_Opair__box__rec(X5247,X5246,X5245,X5244,c_Nitpick_Opair__box_OPairBox(X5247,X5246,X5243,X5242)), inference(variable_rename,[status(thm)],[fact_pair__box_Orecs])). 4.05/4.32 fof(c_0_10188, plain, ![X4691, X4692, X4693, X4694, X4695, X4696]:hAPP(hAPP(X4693,X4692),X4691)=c_Nitpick_Opair__box_Opair__box__case(X4696,X4695,X4694,X4693,c_Nitpick_Opair__box_OPairBox(X4696,X4695,X4692,X4691)), inference(variable_rename,[status(thm)],[fact_pair__box_Osimps_I2_J])). 4.05/4.32 cnf(c_0_10189, 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_5971])). 4.05/4.32 fof(c_0_10190, plain, ![X13963, X13964, X13965, X13966, X13967, X13968]:hAPP(hAPP(hAPP(c_COMBB(X13968,X13967,X13966),X13965),X13964),X13963)=hAPP(X13965,hAPP(X13964,X13963)), inference(variable_rename,[status(thm)],[help_c__COMBB__1])). 4.05/4.32 fof(c_0_10191, plain, ![X10626, X10627, X10628, X10629, X10630, X10631]:hAPP(hAPP(X10628,X10626),X10627)=hAPP(hAPP(hAPP(c_COMBC(X10631,X10630,X10629),X10628),X10627),X10626), inference(variable_rename,[status(thm)],[help_c__COMBC__1])). 4.05/4.32 cnf(c_0_10192, 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_5972, c_0_5583])). 4.05/4.32 cnf(c_0_10193, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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),X3))), inference(split_conjunct,[status(thm)],[c_0_5973])). 4.05/4.32 fof(c_0_10194, plain, ![X9002, X9003, X9004]:c_Map_Omap__add(X9004,X9003,hAPP(c_COMBK(tc_Option_Ooption(X9003),X9004),c_Option_Ooption_ONone(X9003)),X9002)=X9002, inference(variable_rename,[status(thm)],[fact_empty__map__add])). 4.05/4.32 cnf(c_0_10195, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)!=X1|hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)!=X2), inference(split_conjunct,[status(thm)],[c_0_5550])). 4.05/4.32 cnf(c_0_10196, 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_5974]), ['final']). 4.05/4.32 fof(c_0_10197, plain, ![X6634, X6635, X6636]:c_Map_Omap__add(X6636,X6635,X6634,hAPP(c_COMBK(tc_Option_Ooption(X6635),X6636),c_Option_Ooption_ONone(X6635)))=X6634, inference(variable_rename,[status(thm)],[fact_map__add__empty])). 4.05/4.32 cnf(c_0_10198, 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_5975])). 4.05/4.32 cnf(c_0_10199, 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_5976])). 4.05/4.32 cnf(c_0_10200, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X1,X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5977])). 4.05/4.32 cnf(c_0_10201, 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_5978, c_0_5583])). 4.05/4.32 fof(c_0_10202, plain, ![X3547]:hAPP(c_Relation_OField(X3547),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3547,X3547),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X3547,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Field__empty])). 4.05/4.32 fof(c_0_10203, plain, ![X14120, X14121, X14122]:hAPP(c_Relation_OImage(X14122,X14121,X14120),c_Orderings_Obot__class_Obot(tc_fun(X14122,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X14121,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Image__empty])). 4.05/4.32 fof(c_0_10204, plain, ![X17379]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17379,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X17379,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X17379,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq])). 4.05/4.32 fof(c_0_10205, plain, ![X17695]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X17695,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X17695,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X17695,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Compl__empty__eq])). 4.05/4.32 fof(c_0_10206, plain, ![X3487, X3488]:c_Predicate_Opred__comp(X3488,X3488,X3488,c_fequal,c_Predicate_Opred__comp(X3488,X3488,X3488,X3487,c_fequal))=X3487, inference(variable_rename,[status(thm)],[fact_eq__comp__r])). 4.05/4.32 fof(c_0_10207, plain, ![X2195, X2196, X2197]:c_List_Oset__Cons(X2197,X2196,c_List_Olistset(X2197,X2195))=c_List_Olistset(X2197,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X2197,tc_HOL_Obool)),X2196),X2195)), inference(variable_rename,[status(thm)],[fact_listset_Osimps_I2_J])). 4.05/4.32 cnf(c_0_10208, 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_5979])). 4.05/4.32 cnf(c_0_10209, plain, (c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral)=c_Code__Numeral_Osubtract__code__numeral), inference(split_conjunct,[status(thm)],[fact_subtract__code__numeral__def]), ['final']). 4.05/4.32 fof(c_0_10210, plain, ![X9408, X9409]:c_List_Otranspose(X9409,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X9409)),c_List_Olist_ONil(X9409)),X9408))=c_List_Otranspose(X9409,X9408), inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I2_J])). 4.05/4.32 fof(c_0_10211, plain, ![X1389, X1390, X1391]:hAPP(c_Relation_ODomain(X1390,X1391),hAPP(c_Relation_Oconverse(X1391,X1390),X1389))=hAPP(c_Relation_ORange(X1391,X1390),X1389), inference(variable_rename,[status(thm)],[fact_Range__def])). 4.05/4.32 fof(c_0_10212, plain, ![X4117, X4118, X4119]:hAPP(c_Relation_ODomain(X4118,X4119),X4117)=hAPP(c_Relation_ORange(X4119,X4118),hAPP(c_Relation_Oconverse(X4118,X4119),X4117)), inference(variable_rename,[status(thm)],[fact_Range__converse])). 4.05/4.32 fof(c_0_10213, plain, ![X15034]:(hAPP(c_Int_OAbs__Integ,esk449_1(X15034))=X15034&hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk449_1(X15034)),c_Int_OInteg))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Abs__Integ__cases])])])])). 4.05/4.32 fof(c_0_10214, plain, ![X7584, X7585, X7586, X7587]:hAPP(c_Map_Orestrict__map(X7587,X7586,X7585,c_Orderings_Obot__class_Obot(tc_fun(X7587,tc_HOL_Obool))),X7584)=c_Option_Ooption_ONone(X7586), inference(variable_rename,[status(thm)],[fact_restrict__map__to__empty])). 4.05/4.32 cnf(c_0_10215, 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_5980, c_0_5981])). 4.05/4.32 cnf(c_0_10216, 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_5982]), ['final']). 4.05/4.32 fof(c_0_10217, plain, ![X8344, X8345, X8346, X8347]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X8347,X8346)),c_Nitpick_Opair__box_OPairBox(X8347,X8346,X8345,X8344)), inference(variable_rename,[status(thm)],[fact_pair__box_Osize_I2_J])). 4.05/4.32 cnf(c_0_10218, plain, (c_Relation_Osingle__valued(X1,X1,c_Relation_OId(X1))), inference(split_conjunct,[status(thm)],[c_0_5983])). 4.05/4.32 fof(c_0_10219, plain, ![X880, X881]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X881,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X881,tc_HOL_Obool))),X880)), inference(variable_rename,[status(thm)],[fact_empty__subsetI])). 4.05/4.32 cnf(c_0_10220, plain, (c_List_Obutlast(X1,X2)=X3|X2!=hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),c_List_Olist_ONil(X1)))), inference(split_conjunct,[status(thm)],[c_0_5477])). 4.05/4.32 cnf(c_0_10221, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)))|X1!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_5984])). 4.05/4.32 fof(c_0_10222, plain, ![X13630, X13631]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13631,tc_HOL_Obool)),X13630),c_Orderings_Otop__class_Otop(tc_fun(X13631,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_subset__UNIV])). 4.05/4.32 cnf(c_0_10223, plain, (X1=c_List_Olast(X2,X3)|X3!=hAPP(hAPP(c_List_Oappend(X2),X4),hAPP(hAPP(c_List_Olist_OCons(X2),X1),c_List_Olist_ONil(X2)))), inference(split_conjunct,[status(thm)],[c_0_5477])). 4.05/4.32 fof(c_0_10224, plain, ![X15342, X15343]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X15343),X15342)),hAPP(c_Nat_OSuc,X15343))), inference(variable_rename,[status(thm)],[fact_diff__less__Suc])). 4.05/4.32 cnf(c_0_10225, 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_5985, c_0_4795])). 4.05/4.32 cnf(c_0_10226, 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))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X1), inference(split_conjunct,[status(thm)],[c_0_5986])). 4.05/4.32 fof(c_0_10227, plain, ![X7960, X7961]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7961),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7960),X7961)))), inference(variable_rename,[status(thm)],[fact_less__add__Suc2])). 4.05/4.32 cnf(c_0_10228, plain, (hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))=hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1))), inference(split_conjunct,[status(thm)],[c_0_5987])). 4.05/4.32 fof(c_0_10229, plain, ![X13082, X13083]:c_Product__Type_Omap__pair(X13083,X13083,X13082,X13082,c_COMBI(X13083),c_COMBI(X13082))=c_Fun_Oid(tc_prod(X13083,X13082)), inference(variable_rename,[status(thm)],[fact_map__pair_Oidentity])). 4.05/4.32 cnf(c_0_10230, plain, (c_Fun_Oid(tc_prod(X1,X2))=c_Product__Type_Oapfst(X1,X1,X2,c_Fun_Oid(X1))), inference(split_conjunct,[status(thm)],[c_0_5988])). 4.05/4.32 cnf(c_0_10231, 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_5989])). 4.05/4.32 fof(c_0_10232, plain, ![X6178, X6179, X6180, X6181, X6182, X6183]:c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X6183,X6182,X6181,X6180,c_Lazy__Sequence_Olazy__sequence_OInsert(X6182,X6179,X6178))=hAPP(hAPP(X6180,X6179),X6178), inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I5_J])). 4.05/4.32 fof(c_0_10233, plain, ![X4120, X4121, X4122, X4123, X4124]:hAPP(c_Option_Ooption_Ooption__case(X4124,X4123,X4122,X4121),hAPP(c_Option_Ooption_OSome(X4123),X4120))=hAPP(X4121,X4120), inference(variable_rename,[status(thm)],[fact_option_Osimps_I5_J])). 4.05/4.32 fof(c_0_10234, plain, ![X3793, X3794, X3795, X3796]:X3793=hAPP(hAPP(c_Finite__Set_Ofold(X3796,X3795,X3794),X3793),c_Orderings_Obot__class_Obot(tc_fun(X3796,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_fold__empty])). 4.05/4.32 fof(c_0_10235, plain, ![X11487, X11488, X11489]:X11488=hAPP(hAPP(c_List_Onth(X11489),hAPP(hAPP(c_List_Olist_OCons(X11489),X11488),X11487)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_nth__Cons__0])). 4.05/4.32 fof(c_0_10236, plain, ![X13859, X13860]:X13859=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X13860,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X13860,tc_HOL_Obool))),X13859), inference(variable_rename,[status(thm)],[fact_Int__UNIV__left])). 4.05/4.32 fof(c_0_10237, plain, ![X16040, X16041]:X16040=c_Set_Othe__elem(X16041,hAPP(hAPP(c_Set_Oinsert(X16041),X16040),c_Orderings_Obot__class_Obot(tc_fun(X16041,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_the__elem__eq])). 4.05/4.32 cnf(c_0_10238, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X3,X1))), inference(split_conjunct,[status(thm)],[c_0_5990])). 4.05/4.32 fof(c_0_10239, plain, ![X4786, X4787]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4787,tc_HOL_Obool)),X4786),c_Orderings_Obot__class_Obot(tc_fun(X4787,tc_HOL_Obool)))=X4786, inference(variable_rename,[status(thm)],[fact_Diff__empty])). 4.05/4.32 fof(c_0_10240, plain, ![X9512, X9513, X9514]:c_Map_Omap__le(X9514,X9513,hAPP(c_COMBK(tc_Option_Ooption(X9513),X9514),c_Option_Ooption_ONone(X9513)),X9512), inference(variable_rename,[status(thm)],[fact_map__le__empty])). 4.05/4.32 fof(c_0_10241, plain, ![X14631, X14632]:hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14632,tc_HOL_Obool)),X14631),c_Orderings_Otop__class_Otop(tc_fun(X14632,tc_HOL_Obool)))=X14631, inference(variable_rename,[status(thm)],[fact_Int__UNIV__right])). 4.05/4.32 cnf(c_0_10242, 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_5991])). 4.05/4.32 fof(c_0_10243, plain, ![X6463, X6464]:hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6464,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6464,tc_HOL_Obool)),X6463))=X6463, inference(variable_rename,[status(thm)],[fact_double__complement])). 4.05/4.32 fof(c_0_10244, plain, ![X4652, X4653]:hAPP(c_Relation_Oconverse(X4653,X4653),c_Transitive__Closure_Ortrancl(X4653,X4652))=c_Transitive__Closure_Ortrancl(X4653,hAPP(c_Relation_Oconverse(X4653,X4653),X4652)), inference(variable_rename,[status(thm)],[fact_rtrancl__converse])). 4.05/4.32 fof(c_0_10245, plain, ![X12307, X12308, X12309]:c_List_Oremdups(X12309,hAPP(c_List_Ofilter(X12309,X12308),X12307))=hAPP(c_List_Ofilter(X12309,X12308),c_List_Oremdups(X12309,X12307)), inference(variable_rename,[status(thm)],[fact_remdups__filter])). 4.05/4.32 cnf(c_0_10246, plain, (c_Map_Odom(X2,X1,X3)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(c_COMBK(tc_Option_Ooption(X1),X2),c_Option_Ooption_ONone(X1))!=X3), inference(split_conjunct,[status(thm)],[c_0_5992])). 4.05/4.32 fof(c_0_10247, plain, ![X3581, X3582, X3583]:X3582=hAPP(hAPP(c_List_Olist__update(X3583,X3582),X3581),hAPP(hAPP(c_List_Onth(X3583),X3582),X3581)), inference(variable_rename,[status(thm)],[fact_list__update__id])). 4.05/4.32 fof(c_0_10248, plain, ![X6457, X6458, X6459]:X6457=hAPP(hAPP(c_List_Odrop(X6459),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X6459),X6458),X6457)), inference(variable_rename,[status(thm)],[fact_drop__1__Cons])). 4.05/4.32 cnf(c_0_10249, plain, (hAPP(c_Product__Type_OPair(X2,X3),X4)=hAPP(c_Random_Oiterate(X2,X3,X1,X5),X4)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X1), inference(split_conjunct,[status(thm)],[c_0_5993])). 4.05/4.32 fof(c_0_10250, plain, ![X16836]:hAPP(c_Set_OPow(X16836),c_Orderings_Otop__class_Otop(tc_fun(X16836,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X16836,tc_HOL_Obool),tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Pow__UNIV])). 4.05/4.32 fof(c_0_10251, plain, ![X15043, X15044]:c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X15044,X15043)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15044),c_Groups_Oone__class_Oone(tc_Int_Oint))),X15043), inference(variable_rename,[status(thm)],[fact_atLeastPlusOneLessThan__greaterThanLessThan__int])). 4.05/4.32 fof(c_0_10252, plain, ![X16606, X16607, X16608]:c_Option_Ooption_ONone(X16607)=hAPP(hAPP(c_Map_Omap__of(X16608,X16607),c_List_Olist_ONil(tc_prod(X16608,X16607))),X16606), inference(variable_rename,[status(thm)],[fact_map__of_Osimps_I1_J])). 4.05/4.32 fof(c_0_10253, plain, ![X6566, X6567]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6567),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6567),X6566)), inference(variable_rename,[status(thm)],[fact_diff__add__0])). 4.05/4.32 fof(c_0_10254, plain, ![X13510, X13511]:hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X13511),X13510))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13510),X13511), inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan])). 4.05/4.32 cnf(c_0_10255, plain, (hAPP(c_Set_Oimage(X2,X3,X4),X1)=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_5994])). 4.05/4.32 fof(c_0_10256, plain, ![X16219, X16220]:hBOOL(hAPP(hAPP(c_member(tc_fun(X16220,tc_HOL_Obool)),X16219),hAPP(c_Set_OPow(X16220),X16219))), inference(variable_rename,[status(thm)],[fact_Pow__top])). 4.05/4.32 cnf(c_0_10257, plain, (c_List_Obutlast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1))=c_List_Olist_ONil(X2)|X1!=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_5995])). 4.05/4.32 fof(c_0_10258, plain, ![X4411, X4412, X4413, X4414, X4415]:c_Option_Ooption_Ooption__rec(X4415,X4414,X4413,X4412,hAPP(c_Option_Ooption_OSome(X4414),X4411))=hAPP(X4412,X4411), inference(variable_rename,[status(thm)],[fact_option_Orecs_I2_J])). 4.05/4.32 cnf(c_0_10259, plain, (hAPP(c_Relation_ODomain(X2,X3),X1)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|X1!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5996])). 4.05/4.32 cnf(c_0_10260, 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_5997])). 4.05/4.32 fof(c_0_10261, plain, ![X15180, X15181, X15182, X15183, X15184]:hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X15184),X15183),X15182),X15181),X15180)=c_New__DSequence_Oneg__single(X15184,X15183), inference(variable_rename,[status(thm)],[fact_neg__single__def])). 4.05/4.32 fof(c_0_10262, plain, ![X14406, X14407, X14408, X14409, X14410]:c_New__DSequence_Opos__single(X14410,X14409)=hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X14410),X14409),X14408),X14407),X14406), inference(variable_rename,[status(thm)],[fact_pos__single__def])). 4.05/4.32 fof(c_0_10263, plain, ![X7737, X7738, X7739, X7740]:c_Lazy__Sequence_Olazy__sequence_OInsert(X7740,X7739,c_Lazy__Sequence_Oappend(X7740,X7738,X7737))=c_Lazy__Sequence_Oappend(X7740,c_Lazy__Sequence_Olazy__sequence_OInsert(X7740,X7739,X7738),X7737), inference(variable_rename,[status(thm)],[fact__03])). 4.05/4.32 cnf(c_0_10264, plain, (X3=c_List_Oremove1(X4,X2,hAPP(hAPP(c_List_Olist_OCons(X4),X1),X3))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_5998])). 4.05/4.32 fof(c_0_10265, plain, ![X4213]:c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4213,X4213),tc_HOL_Obool))=c_Relation_OId__on(X4213,c_Orderings_Obot__class_Obot(tc_fun(X4213,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_Id__on__empty])). 4.05/4.32 fof(c_0_10266, plain, ![X1179, X1180]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1180)),hAPP(c_List_Orev(X1180),X1179))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1180)),X1179), inference(variable_rename,[status(thm)],[fact_length__rev])). 4.05/4.32 fof(c_0_10267, plain, ![X17648, X17649]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17649)),X17648)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X17649)),hAPP(c_List_Orotate1(X17649),X17648)), inference(variable_rename,[status(thm)],[fact_length__rotate1])). 4.05/4.32 cnf(c_0_10268, 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)|X1!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_4499])). 4.05/4.32 cnf(c_0_10269, plain, (hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_5999])). 4.05/4.32 cnf(c_0_10270, plain, (c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue))), inference(split_conjunct,[status(thm)],[fact_transfer__morphism__int__nat])). 4.05/4.32 cnf(c_0_10271, 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_6000, c_0_4523]), ['final']). 4.05/4.32 fof(c_0_10272, plain, ![X4922, X4923]:hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4923)),c_List_Olist_ONil(X4923)),c_List_Olists(X4923,X4922))), inference(variable_rename,[status(thm)],[fact_lists_ONil])). 4.05/4.32 cnf(c_0_10273, 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_6001])). 4.05/4.32 cnf(c_0_10274, plain, (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)), inference(split_conjunct,[status(thm)],[c_0_6002])). 4.05/4.32 fof(c_0_10275, plain, ![X8233, X8234]:hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X8234),X8233)=hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X8234,X8233)), inference(variable_rename,[status(thm)],[fact_div__int__def])). 4.05/4.32 cnf(c_0_10276, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))), inference(split_conjunct,[status(thm)],[c_0_6003])). 4.05/4.32 cnf(c_0_10277, 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])). 4.05/4.32 fof(c_0_10278, plain, ![X885, X886, X887, X888]:X886=c_Fun_Ooverride__on(X888,X887,X886,X885,c_Orderings_Obot__class_Obot(tc_fun(X888,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_override__on__emptyset])). 4.05/4.32 fof(c_0_10279, plain, ![X17587, X17588, X17589, X17590, X17591]:X17587=hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X17591,X17590),X17589),X17588),X17587),X17588), inference(variable_rename,[status(thm)],[fact_fun__upd__same])). 4.05/4.32 cnf(c_0_10280, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)!=X3), inference(split_conjunct,[status(thm)],[c_0_6004])). 4.05/4.32 cnf(c_0_10281, 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_6005])). 4.05/4.32 fof(c_0_10282, plain, ![X6926, X6927]:X6927=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6927),X6926)),X6926), inference(variable_rename,[status(thm)],[fact_diff__add__inverse2])). 4.05/4.32 fof(c_0_10283, plain, ![X10212, X10213]:X10212=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10213),X10212)),X10213), inference(variable_rename,[status(thm)],[fact_diff__add__inverse])). 4.05/4.32 fof(c_0_10284, plain, ![X16712, X16713, X16714, X16715]:X16713=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X16715,X16714),X16713),X16712),hAPP(X16713,X16712)), inference(variable_rename,[status(thm)],[fact_fun__upd__triv])). 4.05/4.32 fof(c_0_10285, plain, ![X5612, X5613, X5614, X5615]:c_Nitpick_Ofold__graph_H(X5615,X5614,X5613,X5612,c_Orderings_Obot__class_Obot(tc_fun(X5615,tc_HOL_Obool)),X5612), inference(variable_rename,[status(thm)],[fact_fold__graph_H_Oequations_I1_J])). 4.05/4.32 fof(c_0_10286, plain, ![X1513, X1514]:X1513=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1514,X1514),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1513), inference(variable_rename,[status(thm)],[fact_rel__pow__1])). 4.05/4.32 fof(c_0_10287, plain, ![X8328, X8329]:c_Orderings_Obot__class_Obot(tc_fun(X8329,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8329,tc_HOL_Obool)),X8328),X8328), inference(variable_rename,[status(thm)],[fact_Diff__cancel])). 4.05/4.32 fof(c_0_10288, plain, ![X13500, X13501, X13502]:c_List_Olist_ONil(tc_prod(X13502,X13501))=hAPP(hAPP(c_List_Ozip(X13502,X13501),c_List_Olist_ONil(X13502)),X13500), inference(variable_rename,[status(thm)],[fact_zip__Nil])). 4.05/4.32 fof(c_0_10289, plain, ![X13742, X13743, X13744]:c_List_Olist_ONil(tc_prod(X13744,X13743))=hAPP(hAPP(c_List_Ozip(X13744,X13743),X13742),c_List_Olist_ONil(X13743)), inference(variable_rename,[status(thm)],[fact_zip_Osimps_I1_J])). 4.05/4.32 cnf(c_0_10290, 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_5586])). 4.05/4.32 cnf(c_0_10291, plain, (X3=c_List_Olast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1))|X1!=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_6006])). 4.05/4.32 cnf(c_0_10292, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X1,X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_6007])). 4.05/4.32 cnf(c_0_10293, 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_6008])). 4.05/4.32 cnf(c_0_10294, plain, (hAPP(c_New__DSequence_Oneg__decr__bind(X2,X3,X4,X5),X1)=c_Lazy__Sequence_Ohit__bound(X3)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)!=X1), inference(split_conjunct,[status(thm)],[c_0_5120])). 4.05/4.32 fof(c_0_10295, plain, ![X11973, X11974]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11974),X11973)),X11974)), inference(variable_rename,[status(thm)],[fact_diff__le__self])). 4.05/4.32 fof(c_0_10296, plain, ![X4605, X4606]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X4606),X4605)),X4606)), inference(variable_rename,[status(thm)],[fact_div__le__dividend])). 4.05/4.32 cnf(c_0_10297, plain, (c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[fact_type__definition__code__numeral])). 4.05/4.32 fof(c_0_10298, plain, ![X12246]: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,X12246))))), inference(variable_rename,[status(thm)],[fact_neg__zminus__int])). 4.05/4.32 fof(c_0_10299, plain, ![X4054, X4055, X4056]:hBOOL(hAPP(hAPP(c_member(X4056),X4055),hAPP(hAPP(c_Set_Oinsert(X4056),X4055),X4054))), inference(variable_rename,[status(thm)],[fact_insertI1])). 4.05/4.32 fof(c_0_10300, plain, ![X2492]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2492),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2492),X2492))), inference(variable_rename,[status(thm)],[fact_le__square])). 4.05/4.32 fof(c_0_10301, plain, ![X6517, X6518]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6518),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6518),X6517))), inference(variable_rename,[status(thm)],[fact_le__add1])). 4.05/4.32 fof(c_0_10302, plain, ![X6351, X6352]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6352,X6351)),X6351), inference(variable_rename,[status(thm)],[fact_zmod__zdiv__trivial])). 4.05/4.32 fof(c_0_10303, plain, ![X3228, X3229]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3229),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3228),X3229))), inference(variable_rename,[status(thm)],[fact_le__add2])). 4.05/4.32 fof(c_0_10304, plain, ![X8042, X8043]:hAPP(c_Relation_OField(X8043),hAPP(c_Relation_Oconverse(X8043,X8043),X8042))=hAPP(c_Relation_OField(X8043),X8042), inference(variable_rename,[status(thm)],[fact_Field__converse])). 4.05/4.32 fof(c_0_10305, plain, ![X2925]:c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2925)=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])). 4.05/4.32 fof(c_0_10306, plain, ![X16433]:c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X16433),tc_HOL_Obool))=c_List_Olists(X16433,c_Orderings_Otop__class_Otop(tc_fun(X16433,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_lists__UNIV])). 4.05/4.32 fof(c_0_10307, plain, ![X3652, X3653]:c_Relation_Orefl__on(X3653,c_Orderings_Otop__class_Otop(tc_fun(X3653,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X3653,X3652)), inference(variable_rename,[status(thm)],[fact_refl__rtrancl])). 4.05/4.32 fof(c_0_10308, plain, ![X10359]: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),X10359))), inference(variable_rename,[status(thm)],[fact_zero__zle__int])). 4.05/4.32 fof(c_0_10309, plain, ![X3369, X3370, X3371]:hAPP(c_List_Orev(X3371),c_List_Oreplicate(X3371,X3370,X3369))=c_List_Oreplicate(X3371,X3370,X3369), inference(variable_rename,[status(thm)],[fact_rev__replicate])). 4.05/4.32 fof(c_0_10310, plain, ![X13861, X13862]:c_Divides_Odiv__class_Omod(tc_Int_Oint,X13862,X13861)=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X13862,X13861)), inference(variable_rename,[status(thm)],[fact_mod__int__def])). 4.05/4.32 fof(c_0_10311, plain, ![X3474, X3475, X3476]:c_List_Oremdups(X3476,c_List_Oinsert(X3476,X3475,X3474))=c_List_Oinsert(X3476,X3475,c_List_Oremdups(X3476,X3474)), inference(variable_rename,[status(thm)],[fact_insert__remdups])). 4.05/4.32 fof(c_0_10312, plain, ![X3083, X3084]:hAPP(c_Relation_ORange(X3084,X3084),c_Transitive__Closure_Ortrancl(X3084,X3083))=c_Orderings_Otop__class_Otop(tc_fun(X3084,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Range__rtrancl])). 4.05/4.32 cnf(c_0_10313, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X2)=X2|X1!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(rw,[status(thm)],[c_0_6009, c_0_5341])). 4.05/4.32 fof(c_0_10314, plain, ![X3530, X3531]:c_Orderings_Otop__class_Otop(tc_fun(X3531,tc_HOL_Obool))=hAPP(c_Relation_ODomain(X3531,X3531),c_Transitive__Closure_Ortrancl(X3531,X3530)), inference(variable_rename,[status(thm)],[fact_Domain__rtrancl])). 4.05/4.32 fof(c_0_10315, plain, ![X14429, X14430]:hAPP(hAPP(c_List_Olist_OCons(X14430),X14429),c_List_Olist_ONil(X14430))=c_List_Oinsert(X14430,X14429,c_List_Olist_ONil(X14430)), inference(variable_rename,[status(thm)],[fact_insert__Nil])). 4.05/4.32 fof(c_0_10316, plain, ![X17520, X17521]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17521,X17520)),X17521)), inference(variable_rename,[status(thm)],[fact_mod__less__eq__dividend])). 4.05/4.32 fof(c_0_10317, plain, ![X7981, X7982]:hBOOL(hAPP(hAPP(c_member(X7982),X7981),c_Orderings_Otop__class_Otop(tc_fun(X7982,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_UNIV__I])). 4.05/4.32 cnf(c_0_10318, plain, (c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_6010])). 4.05/4.32 cnf(c_0_10319, 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_6011])). 4.05/4.32 fof(c_0_10320, plain, ![X3174, X3175, X3176, X3177]:hAPP(hAPP(c_Power_Opower_Opower(X3177,X3176,X3175),X3174),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X3176, inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__0])). 4.05/4.32 cnf(c_0_10321, plain, (c_HOL_OThe(X1,c_Finite__Set_Ofold1Set(X1,X2,X3))=hAPP(c_Finite__Set_Ofold1(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_6012])). 4.05/4.32 fof(c_0_10322, plain, ![X692, X693, X694]:hAPP(c_Relation_Oconverse(X694,X693),hAPP(c_Relation_Oconverse(X693,X694),X692))=X692, inference(variable_rename,[status(thm)],[fact_converse__converse])). 4.05/4.32 fof(c_0_10323, plain, ![X10330, X10331]:c_Relation_OId__on(X10331,X10330)=hAPP(c_Relation_Oconverse(X10331,X10331),c_Relation_OId__on(X10331,X10330)), inference(variable_rename,[status(thm)],[fact_converse__Id__on])). 4.05/4.32 cnf(c_0_10324, plain, (c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6013])). 4.05/4.32 fof(c_0_10325, plain, ![X8752, X8753, X8754]:c_List_Olist_ONil(X8754)=hAPP(hAPP(c_List_Olist__update(X8754,c_List_Olist_ONil(X8754)),X8753),X8752), inference(variable_rename,[status(thm)],[fact_list__update__code_I1_J])). 4.05/4.32 fof(c_0_10326, plain, ![X15519, X15520]:c_List_Osublist(X15520,X15519,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_List_Olist_ONil(X15520), inference(variable_rename,[status(thm)],[fact_sublist__empty])). 4.05/4.32 fof(c_0_10327, plain, ![X17192, X17193]:hAPP(hAPP(c_Nat_Ocompow(X17193,X17193),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17192)=c_Fun_Oid(X17193), inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I1_J])). 4.05/4.32 fof(c_0_10328, plain, ![X15516, X15517, X15518]:c_Option_Ooption_ONone(X15517)=hAPP(hAPP(c_Option_Omap(X15518,X15517),X15516),c_Option_Ooption_ONone(X15518)), inference(variable_rename,[status(thm)],[fact_option__map__None])). 4.05/4.32 fof(c_0_10329, plain, ![X12737]:c_Wellfounded_Owf(X12737,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X12737,X12737),tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_wf__empty])). 4.05/4.32 fof(c_0_10330, plain, ![X2833, X2834]:c_List_Olistrel(X2834,c_Transitive__Closure_Ortrancl(X2834,X2833))=c_Transitive__Closure_Ortrancl(tc_List_Olist(X2834),c_List_Olistrel1(X2834,X2833)), inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__eq__rtrancl__listrel1])). 4.05/4.32 fof(c_0_10331, plain, ![X17505, X17506, X17507]:c_Nitpick_OAbs__Frac(X17507,c_Nitpick_Onorm__frac(X17506,X17505))=hAPP(hAPP(c_Nitpick_Ofrac(X17507),X17506),X17505), inference(variable_rename,[status(thm)],[fact_Nitpick_Ofrac__def])). 4.05/4.32 fof(c_0_10332, plain, ![X8956, X8957]:hAPP(c_List_Oset(X8957),hAPP(c_List_Orev(X8957),X8956))=hAPP(c_List_Oset(X8957),X8956), inference(variable_rename,[status(thm)],[fact_set__rev])). 4.05/4.32 fof(c_0_10333, plain, ![X2763, X2764]:hAPP(c_List_Oset(X2764),X2763)=hAPP(c_List_Oset(X2764),hAPP(c_List_Orotate1(X2764),X2763)), inference(variable_rename,[status(thm)],[fact_set__rotate1])). 4.05/4.32 fof(c_0_10334, plain, ![X4093, X4094]:hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X4094)),hAPP(c_Option_Ooption_OSome(X4094),X4093))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_option_Osize_I4_J])). 4.05/4.32 fof(c_0_10335, plain, ![X1666]:hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1666)=hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1666)), inference(variable_rename,[status(thm)],[fact_abs__int__eq])). 4.05/4.32 fof(c_0_10336, plain, ![X10972, X10973, X10974]:c_Enum_Oproduct(X10974,X10973,c_List_Olist_ONil(X10974),X10972)=c_List_Olist_ONil(tc_prod(X10974,X10973)), inference(variable_rename,[status(thm)],[fact_product_Osimps_I1_J])). 4.05/4.32 fof(c_0_10337, plain, ![X3409, X3410, X3411]:hAPP(c_Fun_Ocomp(X3411,X3411,X3410,c_Fun_Oid(X3411)),X3409)=X3409, inference(variable_rename,[status(thm)],[fact_id__o])). 4.05/4.32 fof(c_0_10338, plain, ![X1326, X1327, X1328, X1329]:hAPP(c_List_Olist_Olist__case(X1329,X1328,X1327,X1326),c_List_Olist_ONil(X1328))=X1327, inference(variable_rename,[status(thm)],[fact_list_Osimps_I4_J])). 4.05/4.32 fof(c_0_10339, plain, ![X768, X769, X770, X771]:hAPP(c_List_Ofoldl(X771,X770,X769,X768),c_List_Olist_ONil(X770))=X768, inference(variable_rename,[status(thm)],[fact_foldl__Nil])). 4.05/4.32 fof(c_0_10340, plain, ![X9079, X9080, X9081]:hAPP(c_Fun_Ocomp(X9081,X9080,X9081,X9079),c_Fun_Oid(X9081))=X9079, inference(variable_rename,[status(thm)],[fact_o__id])). 4.05/4.32 fof(c_0_10341, plain, ![X15549, X15550, X15551, X15552]:X15550=hAPP(c_Option_Ooption_Ooption__case(X15552,X15551,X15550,X15549),c_Option_Ooption_ONone(X15551)), inference(variable_rename,[status(thm)],[fact_option_Osimps_I4_J])). 4.05/4.32 cnf(c_0_10342, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_6014])). 4.05/4.32 fof(c_0_10343, plain, ![X14176, X14177, X14178, X14179]:hAPP(X14177,X14176)=c_Nat_Onat_Onat__case(X14179,X14178,X14177,hAPP(c_Nat_OSuc,X14176)), inference(variable_rename,[status(thm)],[fact_nat__case__Suc])). 4.05/4.32 fof(c_0_10344, plain, ![X5736, X5737, X5738]:X5737=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5738)),c_List_Oreplicate(X5738,X5737,X5736)), inference(variable_rename,[status(thm)],[fact_length__replicate])). 4.05/4.32 fof(c_0_10345, plain, ![X4740, X4741, X4742, X4743]:c_Map_Omap__le(X4743,X4742,X4741,c_Map_Omap__add(X4743,X4742,X4740,X4741)), inference(variable_rename,[status(thm)],[fact_map__le__map__add])). 4.05/4.32 fof(c_0_10346, plain, ![X4959, X4960, X4961]:X4960=hAPP(c_List_Ohd(X4961),hAPP(hAPP(c_List_Olist_OCons(X4961),X4960),X4959)), inference(variable_rename,[status(thm)],[fact_hd_Osimps])). 4.05/4.32 fof(c_0_10347, plain, ![X13198, X13199, X13200]:X13198=hAPP(c_List_Otl(X13200),hAPP(hAPP(c_List_Olist_OCons(X13200),X13199),X13198)), inference(variable_rename,[status(thm)],[fact_tl_Osimps_I2_J])). 4.05/4.32 fof(c_0_10348, plain, ![X9864]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X9864)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X9864, inference(variable_rename,[status(thm)],[fact_diff__Suc__1])). 4.05/4.32 fof(c_0_10349, plain, ![X10945, X10946, X10947]:c_Fun_Oinj__on(X10947,X10946,X10945,c_Orderings_Obot__class_Obot(tc_fun(X10947,tc_HOL_Obool))), inference(variable_rename,[status(thm)],[fact_inj__on__empty])). 4.05/4.32 fof(c_0_10350, plain, ![X15450, X15451]:c_Fun_Oinj__on(tc_List_Olist(X15451),tc_List_Olist(X15451),c_List_Orev(X15451),X15450), inference(variable_rename,[status(thm)],[fact_inj__on__rev])). 4.05/4.32 cnf(c_0_10351, 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_6015])). 4.05/4.32 fof(c_0_10352, plain, ![X14846, X14847]:c_Complete__Lattice_OSup__class_OSup(tc_fun(X14847,tc_HOL_Obool),hAPP(c_Set_OPow(X14847),X14846))=X14846, inference(variable_rename,[status(thm)],[fact_Union__Pow__eq])). 4.05/4.32 fof(c_0_10353, plain, ![X16325, X16326]:c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X16326,X16325)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X16326)),X16325), inference(variable_rename,[status(thm)],[fact_atLeastSucLessThan__greaterThanLessThan])). 4.05/4.32 cnf(c_0_10354, plain, (c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral)=hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat)), inference(split_conjunct,[status(thm)],[fact_number__of__code__numeral__def])). 4.05/4.32 fof(c_0_10355, plain, ![X11264]: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)),X11264)), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J])). 4.05/4.32 cnf(c_0_10356, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[c_0_6016])). 4.05/4.32 cnf(c_0_10357, 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_6017])). 4.05/4.32 fof(c_0_10358, plain, ![X2451, X2452]:hAPP(c_List_Oset(X2452),c_List_Oremdups(X2452,X2451))=hAPP(c_List_Oset(X2452),X2451), inference(variable_rename,[status(thm)],[fact_set__remdups])). 4.05/4.32 fof(c_0_10359, plain, ![X2963, X2964]:hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2964,tc_HOL_Obool)),X2963),X2963)=X2963, inference(variable_rename,[status(thm)],[fact_Un__absorb])). 4.05/4.32 fof(c_0_10360, plain, ![X12010, X12011]:X12010=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12011,tc_HOL_Obool)),X12010),X12010), inference(variable_rename,[status(thm)],[fact_Int__absorb])). 4.05/4.32 cnf(c_0_10361, 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_6018])). 4.05/4.32 fof(c_0_10362, plain, ![X5681]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X5681))), inference(variable_rename,[status(thm)],[fact_zero__less__Suc])). 4.05/4.32 fof(c_0_10363, plain, ![X7505, X7506]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7506,tc_HOL_Obool)),X7505),X7505)), inference(variable_rename,[status(thm)],[fact_subset__refl])). 4.05/4.32 fof(c_0_10364, plain, ![X16395, X16396]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X16396),X16395))), inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan__int])). 4.05/4.32 fof(c_0_10365, plain, ![X8668, X8669]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X8669),X8668))), inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan])). 4.05/4.32 fof(c_0_10366, plain, ![X16941, X16942, X16943, X16944]:c_Map_Omap__upds(X16944,X16943,X16942,c_List_Olist_ONil(X16944),X16941)=X16942, inference(variable_rename,[status(thm)],[fact_map__upds__Nil1])). 4.05/4.32 fof(c_0_10367, plain, ![X1117, X1118, X1119, X1120]:c_Map_Omap__upds(X1120,X1119,X1118,X1117,c_List_Olist_ONil(X1119))=X1118, inference(variable_rename,[status(thm)],[fact_map__upds__Nil2])). 4.05/4.32 fof(c_0_10368, plain, ![X10373, X10374, X10375, X10376]:X10374=c_Option_Ooption_Ooption__rec(X10376,X10375,X10374,X10373,c_Option_Ooption_ONone(X10375)), inference(variable_rename,[status(thm)],[fact_option_Orecs_I1_J])). 4.05/4.32 fof(c_0_10369, plain, ![X9416]:c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X9416)=c_Lazy__Sequence_Osmall__lazy_H(X9416,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X9416)), inference(variable_rename,[status(thm)],[fact_small__lazy__int__def])). 4.05/4.32 fof(c_0_10370, plain, ![X10811]:hAPP(c_List_Omap(X10811,X10811),c_Fun_Oid(X10811))=c_Fun_Oid(tc_List_Olist(X10811)), inference(variable_rename,[status(thm)],[fact_List_Omap_Oid])). 4.05/4.32 fof(c_0_10371, plain, ![X8642, X8643, X8644]:c_Predicate_Oconversep(X8644,X8643,c_Predicate_Oconversep(X8643,X8644,X8642))=X8642, inference(variable_rename,[status(thm)],[fact_conversep__conversep])). 4.05/4.32 fof(c_0_10372, plain, ![X8862]:hAPP(c_Option_Omap(X8862,X8862),c_Fun_Oid(X8862))=c_Fun_Oid(tc_Option_Ooption(X8862)), inference(variable_rename,[status(thm)],[fact_Option_Omap_Oid])). 4.05/4.32 fof(c_0_10373, plain, ![X7263]:c_Fun_Oid(tc_Option_Ooption(X7263))=hAPP(c_Option_Omap(X7263,X7263),c_COMBI(X7263)), inference(variable_rename,[status(thm)],[fact_Option_Omap_Oidentity])). 4.05/4.32 fof(c_0_10374, plain, ![X16482]:c_Fun_Oid(tc_List_Olist(X16482))=hAPP(c_List_Omap(X16482,X16482),c_COMBI(X16482)), inference(variable_rename,[status(thm)],[fact_List_Omap_Oidentity])). 4.05/4.32 cnf(c_0_10375, plain, (hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X4),X1))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_6019])). 4.05/4.32 cnf(c_0_10376, plain, (hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_6020])). 4.05/4.32 fof(c_0_10377, plain, ![X8831, X8832, X8833]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(X8833,X8832,X8831)), inference(variable_rename,[status(thm)],[fact_com_Osize_I16_J])). 4.05/4.32 fof(c_0_10378, plain, ![X3035, X3036, X3037]:c_List_Omap__filter(X3037,X3036,X3035,c_List_Olist_ONil(X3037))=c_List_Olist_ONil(X3036), inference(variable_rename,[status(thm)],[fact_map__filter__simps_I2_J])). 4.05/4.32 fof(c_0_10379, plain, ![X5672, X5673]:hAPP(hAPP(c_List_Otake(X5673),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5672)=c_List_Olist_ONil(X5673), inference(variable_rename,[status(thm)],[fact_take__0])). 4.05/4.32 fof(c_0_10380, plain, ![X8423, X8424]:c_List_Olist_ONil(X8424)=hAPP(hAPP(c_List_Odrop(X8424),X8423),c_List_Olist_ONil(X8424)), inference(variable_rename,[status(thm)],[fact_drop__Nil])). 4.05/4.32 fof(c_0_10381, plain, ![X10452, X10453]:c_Relation_Ototal__on(X10453,c_Orderings_Obot__class_Obot(tc_fun(X10453,tc_HOL_Obool)),X10452), inference(variable_rename,[status(thm)],[fact_total__on__empty])). 4.05/4.32 fof(c_0_10382, plain, ![X7499]:c_Finite__Set_Ofun__left__comm__idem(X7499,tc_fun(X7499,tc_HOL_Obool),c_Set_Oinsert(X7499)), inference(variable_rename,[status(thm)],[fact_fun__left__comm__idem__insert])). 4.05/4.32 fof(c_0_10383, plain, ![X16639, X16640]:c_List_Olist_ONil(X16640)=hAPP(hAPP(c_List_Otake(X16640),X16639),c_List_Olist_ONil(X16640)), inference(variable_rename,[status(thm)],[fact_take__Nil])). 4.05/4.32 fof(c_0_10384, plain, ![X8501]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8501)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_diff__0__eq__0])). 4.05/4.32 fof(c_0_10385, plain, ![X13104, X13105]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X13105,X13104))), inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost__int])). 4.05/4.32 fof(c_0_10386, plain, ![X12502]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X12502), inference(variable_rename,[status(thm)],[fact_zdiv__zero])). 4.05/4.32 cnf(c_0_10387, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_6021])). 4.05/4.32 fof(c_0_10388, plain, ![X1673, X1674]:hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1674,X1673))), inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost])). 4.05/4.32 fof(c_0_10389, plain, ![X1078]:hBOOL(hAPP(c_Finite__Set_Ofinite(X1078),c_Orderings_Obot__class_Obot(tc_fun(X1078,tc_HOL_Obool)))), inference(variable_rename,[status(thm)],[fact_finite_Oequations_I1_J])). 4.05/4.32 cnf(c_0_10390, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_6022])). 4.05/4.32 cnf(c_0_10391, 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_6023])). 4.05/4.32 fof(c_0_10392, plain, ![X1858]:(c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1858),c_Groups_Ozero__class_Ozero(tc_Int_Oint))&c_Divides_Odiv__class_Omod(tc_Int_Oint,X1858,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X1858), inference(variable_rename,[status(thm)],[fact_DIVISION__BY__ZERO])). 4.05/4.32 fof(c_0_10393, plain, ![X10696]:hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X10696)=hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X10696)), inference(variable_rename,[status(thm)],[fact_nat__of__number])). 4.05/4.32 fof(c_0_10394, plain, ![X10981, X10982]:hAPP(c_Set_Oimage(X10982,X10982,c_COMBI(X10982)),X10981)=X10981, inference(variable_rename,[status(thm)],[fact_image__ident])). 4.05/4.32 fof(c_0_10395, plain, ![X17314, X17315]:c_Fun_Oinj__on(X17315,tc_Option_Ooption(X17315),c_Option_Ooption_OSome(X17315),X17314), inference(variable_rename,[status(thm)],[fact_inj__Some])). 4.05/4.32 fof(c_0_10396, plain, ![X2077, X2078]:c_List_Olistrelp(X2078,X2077,c_List_Olist_ONil(X2078),c_List_Olist_ONil(X2078)), inference(variable_rename,[status(thm)],[fact_listrelp_Oequations_I1_J])). 4.05/4.32 fof(c_0_10397, plain, ![X13184, X13185]:X13184=hAPP(c_Set_Oimage(X13185,X13185,c_Fun_Oid(X13185)),X13184), inference(variable_rename,[status(thm)],[fact_image__id])). 4.05/4.32 fof(c_0_10398, plain, ![X2275, X2276, X2277]:hAPP(c_Nat_Onat_Onat__rec(X2277,X2276,X2275),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2276, inference(variable_rename,[status(thm)],[fact_nat__rec__0])). 4.05/4.32 fof(c_0_10399, plain, ![X3525, X3526]:hAPP(c_Relation_ODomain(X3526,X3526),c_Relation_OId__on(X3526,X3525))=X3525, inference(variable_rename,[status(thm)],[fact_Domain__Id__on])). 4.05/4.32 fof(c_0_10400, plain, ![X2300, X2301]:X2300=hAPP(c_Relation_ORange(X2301,X2301),c_Relation_OId__on(X2301,X2300)), inference(variable_rename,[status(thm)],[fact_Range__Id__on])). 4.05/4.32 fof(c_0_10401, plain, ![X4097]:hAPP(c_List_Oset(X4097),c_List_Olist_ONil(X4097))=c_Orderings_Obot__class_Obot(tc_fun(X4097,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I1_J])). 4.05/4.32 fof(c_0_10402, plain, ![X14775, X14776]:c_Transitive__Closure_Ortrancl(X14776,c_Transitive__Closure_Ortrancl(X14776,X14775))=c_Transitive__Closure_Ortrancl(X14776,X14775), inference(variable_rename,[status(thm)],[fact_rtrancl__idemp])). 4.05/4.32 fof(c_0_10403, plain, ![X805, X806]:c_List_Oremdups(X806,X805)=c_List_Oremdups(X806,c_List_Oremdups(X806,X805)), inference(variable_rename,[status(thm)],[fact_remdups__remdups])). 4.05/4.32 fof(c_0_10404, plain, ![X17663]:c_List_Otranspose(X17663,c_List_Olist_ONil(tc_List_Olist(X17663)))=c_List_Olist_ONil(tc_List_Olist(X17663)), inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I1_J])). 4.05/4.32 fof(c_0_10405, plain, ![X15567, X15568, X15569]:hAPP(c_Lazy__Sequence_Osingle(X15569),X15568)=hAPP(c_New__DSequence_Opos__single(X15569,X15568),X15567), inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__single__def])). 4.05/4.32 fof(c_0_10406, plain, ![X4650, X4651]:c_List_Olist_ONil(X4651)=hAPP(c_List_Ofilter(X4651,X4650),c_List_Olist_ONil(X4651)), inference(variable_rename,[status(thm)],[fact_filter_Osimps_I1_J])). 4.05/4.32 fof(c_0_10407, plain, ![X2802]:hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2802)),c_List_Olist_ONil(X2802))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_list_Osize_I3_J])). 4.05/4.32 fof(c_0_10408, plain, ![X7574]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X7574)),c_Option_Ooption_ONone(X7574)), inference(variable_rename,[status(thm)],[fact_option_Osize_I3_J])). 4.05/4.32 fof(c_0_10409, plain, ![X17329, X17330, X17331]:c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X17331,X17330,X17329,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=X17330, inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I4_J])). 4.05/4.32 fof(c_0_10410, plain, ![X13809, X13810, X13811]:X13810=c_Nat_Onat_Onat__case(X13811,X13810,X13809,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_nat__case__0])). 4.05/4.32 fof(c_0_10411, plain, ![X9240, X9241, X9242, X9243]:X9241=hAPP(hAPP(c_COMBK(X9243,X9242),X9241),X9240), inference(variable_rename,[status(thm)],[help_c__COMBK__1])). 4.05/4.32 fof(c_0_10412, plain, ![X12402, X12403]:hAPP(hAPP(c_List_Oappend(X12403),c_List_Olist_ONil(X12403)),X12402)=X12402, inference(variable_rename,[status(thm)],[fact_append__Nil])). 4.05/4.32 cnf(c_0_10413, plain, (c_List_Olist__all2(X3,X3,c_fequal,X2,X1)|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_6024])). 4.05/4.32 fof(c_0_10414, plain, ![X12710, X12711]:X12710=hAPP(hAPP(c_List_Odrop(X12711),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12710), inference(variable_rename,[status(thm)],[fact_drop__0])). 4.05/4.32 fof(c_0_10415, plain, ![X6837, X6838]:hAPP(hAPP(c_List_Oappend(X6838),X6837),c_List_Olist_ONil(X6838))=X6837, inference(variable_rename,[status(thm)],[fact_append__Nil2])). 4.05/4.32 fof(c_0_10416, plain, ![X6734]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X6734)=X6734, inference(variable_rename,[status(thm)],[fact_zmult__1])). 4.05/4.32 fof(c_0_10417, plain, ![X3571]:hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3571)=X3571, inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0])). 4.05/4.32 fof(c_0_10418, plain, ![X17687]:X17687=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X17687), inference(variable_rename,[status(thm)],[fact_nat__mult__1])). 4.05/4.32 cnf(c_0_10419, plain, (X1=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_6025])). 4.05/4.32 fof(c_0_10420, plain, ![X6281]:hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6281),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X6281, inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0])). 4.05/4.32 fof(c_0_10421, plain, ![X9084]:hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X9084),c_Groups_Oone__class_Oone(tc_Int_Oint))=X9084, inference(variable_rename,[status(thm)],[fact_zmult__1__right])). 4.05/4.32 fof(c_0_10422, plain, ![X2095]:X2095=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2095),c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(variable_rename,[status(thm)],[fact_nat__mult__1__right])). 4.05/4.32 cnf(c_0_10423, 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_6026])). 4.05/4.32 fof(c_0_10424, plain, ![X5196]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5196),hAPP(c_Nat_OSuc,X5196))), inference(variable_rename,[status(thm)],[fact_lessI])). 4.05/4.32 fof(c_0_10425, plain, ![X750]:X750=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X750)), inference(variable_rename,[status(thm)],[fact_zminus__zminus])). 4.05/4.32 fof(c_0_10426, plain, ![X2084]:c_Option_Oset(X2084,c_Option_Ooption_ONone(X2084))=c_Orderings_Obot__class_Obot(tc_fun(X2084,tc_HOL_Obool)), inference(variable_rename,[status(thm)],[fact_Option_Oset_Osimps_I1_J])). 4.05/4.32 fof(c_0_10427, plain, ![X4440, X4441, X4442]:c_Lazy__Sequence_Ohb__single(X4442,X4441)=hAPP(c_New__DSequence_Oneg__single(X4442,X4441),X4440), inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__single__def])). 4.05/4.32 fof(c_0_10428, plain, ![X17610, X17611]:c_Fun_Oinj__on(X17611,X17611,c_COMBI(X17611),X17610), inference(variable_rename,[status(thm)],[fact_inj__on__id2])). 4.05/4.32 fof(c_0_10429, plain, ![X3454, X3455]:c_Fun_Oinj__on(X3455,X3455,c_Fun_Oid(X3455),X3454), inference(variable_rename,[status(thm)],[fact_inj__on__id])). 4.05/4.32 fof(c_0_10430, plain, ![X12263, X12264, X12265]:c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(X12265,X12264,X12263))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_com_Osize_I8_J])). 4.05/4.32 fof(c_0_10431, plain, ![X17374, X17375]:c_Relation_Orefl__on(X17375,X17374,c_Relation_OId__on(X17375,X17374)), inference(variable_rename,[status(thm)],[fact_refl__on__Id__on])). 4.05/4.32 fof(c_0_10432, plain, ![X2659, X2660]:hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2660,tc_HOL_Obool)),X2659)), inference(variable_rename,[status(thm)],[fact_top1I])). 4.05/4.32 fof(c_0_10433, plain, ![X16837, X16838]:c_Relation_Osingle__valued(X16838,X16838,c_Relation_OId__on(X16838,X16837)), inference(variable_rename,[status(thm)],[fact_single__valued__Id__on])). 4.05/4.32 fof(c_0_10434, plain, ![X11928, X11929]:c_List_OtakeWhile(X11929,X11928,c_List_Olist_ONil(X11929))=c_List_Olist_ONil(X11929), inference(variable_rename,[status(thm)],[fact_takeWhile_Osimps_I1_J])). 4.05/4.32 fof(c_0_10435, plain, ![X3352, X3353]:hBOOL(hAPP(c_List_Olistsp(X3353,X3352),c_List_Olist_ONil(X3353))), inference(variable_rename,[status(thm)],[fact_listsp_ONil])). 4.05/4.32 fof(c_0_10436, plain, ![X7154, X7155]:hBOOL(hAPP(c_List_Odistinct(X7155),c_List_Oremdups(X7155,X7154))), inference(variable_rename,[status(thm)],[fact_distinct__remdups])). 4.05/4.32 fof(c_0_10437, plain, ![X6187, X6188]:hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X6188,X6187))), inference(variable_rename,[status(thm)],[fact_distinct__upto])). 4.05/4.32 fof(c_0_10438, plain, ![X14022, X14023]:c_List_Olist_ONil(X14023)=c_List_Osublist(X14023,c_List_Olist_ONil(X14023),X14022), inference(variable_rename,[status(thm)],[fact_sublist__nil])). 4.05/4.32 fof(c_0_10439, plain, ![X4848, X4849]:c_List_Olist_ONil(X4849)=c_List_Oremove1(X4849,X4848,c_List_Olist_ONil(X4849)), inference(variable_rename,[status(thm)],[fact_remove1_Osimps_I1_J])). 4.05/4.32 fof(c_0_10440, plain, ![X14764, X14765]:c_List_Olist_Olist__size(X14765,X14764,c_List_Olist_ONil(X14765))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_list_Osize_I1_J])). 4.05/4.32 fof(c_0_10441, plain, ![X9447, X9448]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Option_Ooption_Ooption__size(X9448,X9447,c_Option_Ooption_ONone(X9448)), inference(variable_rename,[status(thm)],[fact_option_Osize_I1_J])). 4.05/4.32 fof(c_0_10442, plain, ![X5803, X5804]:c_List_Oreplicate(X5804,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5803)=c_List_Olist_ONil(X5804), inference(variable_rename,[status(thm)],[fact_replicate__0])). 4.05/4.32 fof(c_0_10443, plain, ![X5512]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5512), inference(variable_rename,[status(thm)],[fact_zmod__zero])). 4.05/4.32 fof(c_0_10444, plain, ![X12474]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X12474),X12474), inference(variable_rename,[status(thm)],[fact_diff__self__eq__0])). 4.05/4.32 fof(c_0_10445, plain, ![X9034]:c_Wellfounded_Owf(tc_fun(X9034,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X9034)), inference(variable_rename,[status(thm)],[fact_wf__finite__psubset])). 4.05/4.32 fof(c_0_10446, plain, ![X3453]:hAPP(c_List_Orev(X3453),c_List_Olist_ONil(X3453))=c_List_Olist_ONil(X3453), inference(variable_rename,[status(thm)],[fact_rev_Osimps_I1_J])). 4.05/4.32 fof(c_0_10447, plain, ![X14660]:c_List_Olist_ONil(X14660)=hAPP(c_List_Otl(X14660),c_List_Olist_ONil(X14660)), inference(variable_rename,[status(thm)],[fact_tl_Osimps_I1_J])). 4.05/4.32 fof(c_0_10448, plain, ![X6695, X6696]:c_List_Osplice(X6696,c_List_Olist_ONil(X6696),X6695)=X6695, inference(variable_rename,[status(thm)],[fact_splice_Osimps_I1_J])). 4.05/4.32 fof(c_0_10449, plain, ![X10840, X10841]:hAPP(c_Option_Othe(X10841),hAPP(c_Option_Ooption_OSome(X10841),X10840))=X10840, inference(variable_rename,[status(thm)],[fact_the_Osimps])). 4.05/4.32 fof(c_0_10450, plain, ![X7955, X7956]:X7955=c_List_Osplice(X7956,X7955,c_List_Olist_ONil(X7956)), inference(variable_rename,[status(thm)],[fact_splice__Nil2])). 4.05/4.32 cnf(c_0_10451, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OPls)), inference(split_conjunct,[status(thm)],[c_0_6027])). 4.05/4.32 cnf(c_0_10452, plain, (c_Int_OPls=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X1)), inference(split_conjunct,[status(thm)],[c_0_6028])). 4.05/4.32 fof(c_0_10453, plain, ![X14848]:c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X14848), inference(variable_rename,[status(thm)],[fact_inj__Suc])). 4.05/4.32 fof(c_0_10454, plain, ![X7920]:c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X7920,X7920), inference(variable_rename,[status(thm)],[fact_zmod__self])). 4.05/4.32 cnf(c_0_10455, plain, (c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=X1), inference(split_conjunct,[status(thm)],[c_0_5534])). 4.05/4.32 fof(c_0_10456, plain, ![X4844, X4845]:c_List_Olist__all(X4845,X4844,c_List_Olist_ONil(X4845)), inference(variable_rename,[status(thm)],[fact_list__all__simps_I2_J])). 4.05/4.32 fof(c_0_10457, plain, ![X17132, X17133]:c_Wellfounded_Owf(X17133,c_List_Omeasures(X17133,X17132)), inference(variable_rename,[status(thm)],[fact_wf__measures])). 4.05/4.32 fof(c_0_10458, plain, ![X17006, X17007]:c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X17007,X17006)), inference(variable_rename,[status(thm)],[fact_sorted__upto])). 4.05/4.32 fof(c_0_10459, plain, ![X3029]:hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X3029),X3029)), inference(variable_rename,[status(thm)],[fact_eq__int__refl])). 4.05/4.32 fof(c_0_10460, plain, ![X6156]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6156),X6156)), inference(variable_rename,[status(thm)],[fact_zle__refl])). 4.05/4.32 fof(c_0_10461, plain, ![X15763]:hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15763),X15763)), inference(variable_rename,[status(thm)],[fact_le__refl])). 4.05/4.32 cnf(c_0_10462, 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_4509])). 4.05/4.32 cnf(c_0_10463, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls))), inference(split_conjunct,[status(thm)],[fact_rel__simps_I6_J])). 4.05/4.32 fof(c_0_10464, plain, ![X13289]:c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OBODY(X13289)), inference(variable_rename,[status(thm)],[fact_com_Osize_I15_J])). 4.05/4.32 cnf(c_0_10465, plain, (c_Nitpick_Onat__gcd(X2,X1)=X2|X1!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_6029])). 4.05/4.32 cnf(c_0_10466, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls))), inference(split_conjunct,[status(thm)],[fact_rel__simps_I23_J])). 4.05/4.32 cnf(c_0_10467, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)))), inference(split_conjunct,[status(thm)],[fact_neg__number__of__Min])). 4.05/4.32 fof(c_0_10468, plain, ![X7557]:c_List_Obutlast(X7557,c_List_Olist_ONil(X7557))=c_List_Olist_ONil(X7557), inference(variable_rename,[status(thm)],[fact_butlast_Osimps_I1_J])). 4.05/4.32 cnf(c_0_10469, 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_6030])). 4.05/4.32 fof(c_0_10470, plain, ![X12822]:hBOOL(hAPP(c_List_Odistinct(X12822),c_List_Olist_ONil(X12822))), inference(variable_rename,[status(thm)],[fact_distinct_Osimps_I1_J])). 4.05/4.32 cnf(c_0_10471, plain, (hBOOL(hAPP(hAPP(c_fequal,X1),X2))|X2!=X1), inference(split_conjunct,[status(thm)],[c_0_6031])). 4.05/4.32 fof(c_0_10472, plain, ![X7575]:c_List_Olist_ONil(X7575)=c_List_Oremdups(X7575,c_List_Olist_ONil(X7575)), inference(variable_rename,[status(thm)],[fact_remdups_Osimps_I1_J])). 4.05/4.32 fof(c_0_10473, plain, ![X3253, X3254]:c_Hilbert__Choice_OEps(X3254,hAPP(c_fequal,X3253))=X3253, inference(variable_rename,[status(thm)],[fact_some__sym__eq__trivial])). 4.05/4.32 cnf(c_0_10474, plain, (c_HOL_OThe(X1,hAPP(c_fequal,X2))=X2), inference(split_conjunct,[status(thm)],[c_0_6032])). 4.05/4.32 fof(c_0_10475, plain, ![X3107]:c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3107)), inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J])). 4.05/4.32 fof(c_0_10476, plain, ![X11543, X11544]:hAPP(c_New__DSequence_Opos__empty(X11544),X11543)=c_Lazy__Sequence_Oempty(X11544), inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__empty__def])). 4.05/4.32 fof(c_0_10477, plain, ![X14115, X14116, X14117]:c_Map_Omap__le(X14117,X14116,X14115,X14115), inference(variable_rename,[status(thm)],[fact_map__le__refl])). 4.05/4.32 cnf(c_0_10478, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls)=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[fact_zero__code__numeral__code])). 4.05/4.32 fof(c_0_10479, plain, ![X3102]:c_fequal=c_Predicate_Oconversep(X3102,X3102,c_fequal), inference(variable_rename,[status(thm)],[fact_conversep__eq])). 4.05/4.32 fof(c_0_10480, plain, ![X2972]:X2972=hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X2972)), inference(variable_rename,[status(thm)],[fact_Rep__Integ__inverse])). 4.05/4.32 cnf(c_0_10481, plain, (X1=hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X1))), inference(split_conjunct,[status(thm)],[c_0_6033])). 4.05/4.32 cnf(c_0_10482, 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])). 4.05/4.32 cnf(c_0_10483, plain, (X1=hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X1))), inference(split_conjunct,[status(thm)],[c_0_6034])). 4.05/4.32 fof(c_0_10484, plain, ![X16823, X16824]:class_HOL_Oequal(tc_Nitpick_Opair__box(X16824,X16823)), inference(variable_rename,[status(thm)],[arity_Nitpick__Opair____box__HOL_Oequal])). 4.05/4.32 fof(c_0_10485, plain, ![X7497, X7498]:class_HOL_Oequal(tc_sum(X7498,X7497)), inference(variable_rename,[status(thm)],[arity_sum__HOL_Oequal])). 4.05/4.32 fof(c_0_10486, plain, ![X16336, X16337]:class_HOL_Oequal(tc_prod(X16337,X16336)), inference(variable_rename,[status(thm)],[arity_prod__HOL_Oequal])). 4.05/4.32 fof(c_0_10487, plain, ![X8737, X8738]:class_Nat_Osize(tc_Nitpick_Opair__box(X8738,X8737)), inference(variable_rename,[status(thm)],[arity_Nitpick__Opair____box__Nat_Osize])). 4.05/4.32 fof(c_0_10488, plain, ![X12500, X12501]:class_Nat_Osize(tc_sum(X12501,X12500)), inference(variable_rename,[status(thm)],[arity_sum__Nat_Osize])). 4.05/4.32 fof(c_0_10489, plain, ![X10096, X10097]:class_Nat_Osize(tc_prod(X10097,X10096)), inference(variable_rename,[status(thm)],[arity_prod__Nat_Osize])). 4.05/4.32 fof(c_0_10490, plain, ![X2954]:c_Option_Ois__none(X2954,c_Option_Ooption_ONone(X2954)), inference(variable_rename,[status(thm)],[fact_is__none__code_I1_J])). 4.05/4.32 fof(c_0_10491, plain, ![X15656]:c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X15656)), inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than2])). 4.05/4.32 fof(c_0_10492, plain, ![X3755]:c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X3755)), inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than])). 4.05/4.32 fof(c_0_10493, plain, ![X11438, X11439]:X11438=hAPP(c_COMBI(X11439),X11438), inference(variable_rename,[status(thm)],[help_c__COMBI__1])). 4.05/4.32 fof(c_0_10494, plain, ![X518, X519]:X518=hAPP(c_Fun_Oid(X519),X518), inference(variable_rename,[status(thm)],[fact_id__def])). 4.05/4.32 fof(c_0_10495, plain, ![X2951]:X2951=hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X2951), inference(variable_rename,[status(thm)],[fact_nat__size])). 4.05/4.32 fof(c_0_10496, plain, ![X14766]:c_Com_Ocom_Ocom__size(c_Com_Ocom_OBODY(X14766))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat), inference(variable_rename,[status(thm)],[fact_com_Osize_I7_J])). 4.05/4.32 fof(c_0_10497, plain, ![X5713]:c_Equiv__Relations_Oequivp(X5713,c_fequal), inference(variable_rename,[status(thm)],[fact_identity__equivp])). 4.05/4.32 fof(c_0_10498, plain, ![X11210]:class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X11210)), inference(variable_rename,[status(thm)],[arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal])). 4.05/4.32 fof(c_0_10499, plain, ![X5951]:class_HOL_Oequal(tc_Option_Ooption(X5951)), inference(variable_rename,[status(thm)],[arity_Option__Ooption__HOL_Oequal])). 4.05/4.32 fof(c_0_10500, plain, ![X13325]:class_HOL_Oequal(tc_List_Olist(X13325)), inference(variable_rename,[status(thm)],[arity_List__Olist__HOL_Oequal])). 4.05/4.32 fof(c_0_10501, plain, ![X2473]:class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X2473)), inference(variable_rename,[status(thm)],[arity_Lazy____Sequence__Olazy____sequence__Nat_Osize])). 4.05/4.32 fof(c_0_10502, plain, ![X16564]:class_Nat_Osize(tc_Option_Ooption(X16564)), inference(variable_rename,[status(thm)],[arity_Option__Ooption__Nat_Osize])). 4.05/4.32 fof(c_0_10503, plain, ![X17199]:class_Nat_Osize(tc_List_Olist(X17199)), inference(variable_rename,[status(thm)],[arity_List__Olist__Nat_Osize])). 4.05/4.32 cnf(c_0_10504, 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_6035, c_0_4915]), c_0_4915]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10505, 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))=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))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6036, c_0_4915]), c_0_4915]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10506, 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))|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_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_6037, c_0_4915]), c_0_4915]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10507, 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_6038, c_0_4915]), c_0_4915]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10508, 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_6039, c_0_4915]), c_0_4915]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10509, plain, (hAPP(c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1))))=c_Divides_Odivmod__int(X2,X1)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_6040, c_0_5695]), ['final']). 4.05/4.32 cnf(c_0_10510, plain, (hAPP(c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,X2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1))))=c_Divides_Odivmod__int(X2,X1)|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_6041, c_0_5695]), ['final']). 4.05/4.32 cnf(c_0_10511, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X1,X1)),tc_fun(tc_Int_Oint,X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),X1),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X1,X1)),tc_fun(tc_Int_Oint,X1)),tc_Int_Oint),c_COMBB(tc_fun(X1,X1),X1,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_fun(X1,X1),X1),tc_Int_Oint),c_HOL_OLet(X1,X1)),c_Int_Oring__1__class_Oof__int(X1)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X1,X1),tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,X1)),tc_fun(tc_fun(X1,X1),tc_fun(X1,X1)),tc_Int_Oint),c_COMBS(X1,X1,X1)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X1,X1),tc_fun(X1,tc_fun(X1,X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,X1)),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_fun(X1,X1))),tc_Int_Oint),c_COMBB(X1,tc_fun(X1,X1),X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_COMBI(X1))))),hAPP(hAPP(c_COMBC(X1,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X1),c_Groups_Oplus__class_Oplus(X1)),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_COMBI(X1)))),c_Groups_Oone__class_Oone(X1))))),c_Divides_Odivmod__int(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))=hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)|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)))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6042, c_0_5695]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_10512, 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_6043]), ['final']). 4.05/4.32 cnf(c_0_10513, 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_6044]), ['final']). 4.05/4.32 cnf(c_0_10514, 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_6045]), ['final']). 4.05/4.32 cnf(c_0_10515, 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_6046]), ['final']). 4.05/4.32 cnf(c_0_10516, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBS(X1,tc_fun(X3,tc_HOL_Obool),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,X2),tc_fun(tc_fun(X3,tc_HOL_Obool),X2),X1),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2)),hAPP(c_COMBC(X3,X1,X2),X4))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),c_Set_OCollect(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),X5))),hAPP(c_COMBC(X3,X1,tc_HOL_Obool),X6))))),X7)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),hAPP(hAPP(c_COMBS(X3,tc_fun(X1,tc_HOL_Obool),X2),hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_fun(tc_fun(X1,tc_HOL_Obool),X2),X3),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2)),X4)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),c_Set_OCollect(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X7))),X6)))),X5)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X7))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6047, c_0_4915]), c_0_4915]), ['final']). 4.05/4.32 cnf(c_0_10517, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X2,X3,X4),X1),X5)=hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X3),X2),tc_prod(X3,X2),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),X2),c_List_Olist_ONil(X3)),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X2,tc_prod(tc_List_Olist(X3),X2)),hAPP(hAPP(c_COMBC(X3,tc_fun(X2,tc_prod(tc_List_Olist(X3),X2)),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X3),X2),tc_prod(tc_List_Olist(X3),X2)),tc_fun(tc_fun(X2,tc_prod(tc_List_Olist(X3),X2)),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2))),X3),c_COMBB(tc_prod(tc_List_Olist(X3),X2),tc_prod(tc_List_Olist(X3),X2),X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2))),tc_fun(tc_prod(tc_List_Olist(X3),X2),tc_prod(tc_List_Olist(X3),X2)),X3),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X3),X2,tc_prod(tc_List_Olist(X3),X2))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3),tc_List_Olist(X3)),tc_fun(tc_List_Olist(X3),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2))),X3),hAPP(c_COMBB(tc_List_Olist(X3),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2)),tc_List_Olist(X3)),c_Product__Type_OPair(tc_List_Olist(X3),X2))),c_List_Olist_OCons(X3))))),hAPP(c_Lazy__Sequence_Oanamorph(X2,X3,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(X4,X5))), inference(split_conjunct,[status(thm)],[c_0_5678]), ['final']). 4.05/4.32 cnf(c_0_10518, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X2)),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6048, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10519, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X2)),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6050, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10520, 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_6051, c_0_4915]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10521, 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_6052, c_0_4915]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10522, 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))|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_6053, c_0_4915]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10523, 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))|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_6054, c_0_4915]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10524, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6055, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), c_0_5165]), c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_10525, 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_6056, c_0_4915]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10526, 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_6057]), ['final']). 4.05/4.32 cnf(c_0_10527, 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_6058]), ['final']). 4.05/4.32 cnf(c_0_10528, 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_6059]), ['final']). 4.05/4.32 cnf(c_0_10529, 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))|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_6060, c_0_4915]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10530, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6061, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_10531, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))=hAPP(c_Code__Numeral_Oint__of,X1)|c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6062, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_10532, 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_6063, c_0_5716]), ['final']). 4.05/4.32 cnf(c_0_10533, 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_6043]), ['final']). 4.05/4.32 cnf(c_0_10534, 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_6044]), ['final']). 4.05/4.32 cnf(c_0_10535, plain, (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(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat,X4),c_Finite__Set_Ocard(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),c_Set_OCollect(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),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))),X5)))),X6)|hAPP(X2,esk148_6(X2,X5,X3,X1,X6,X4))!=hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X6),hAPP(hAPP(c_COMBC(X4,X1,tc_HOL_Obool),X5),esk148_6(X2,X5,X3,X1,X6,X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6064, c_0_4915]), c_0_4915]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10536, 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_6065, c_0_4523]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10537, 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),esk379_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_6066, c_0_4915]), c_0_4915]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10538, 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_6045]), ['final']). 4.05/4.32 cnf(c_0_10539, 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_6067]), ['final']). 4.05/4.32 cnf(c_0_10540, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))=hAPP(c_Code__Numeral_Oint__of,X1)|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),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6068, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), ['final']). 4.05/4.32 cnf(c_0_10541, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6069, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), c_0_4635]), c_0_4635]), c_0_5165]), c_0_4795]), c_0_4795]), c_0_4635]), c_0_4505]), c_0_4795]), c_0_5796]), c_0_4635]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_10542, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6070, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_10543, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6071, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_10544, 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_6072, c_0_5165]), c_0_5165]), ['final']). 4.05/4.32 cnf(c_0_10545, 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_6046]), ['final']). 4.05/4.32 cnf(c_0_10546, 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_6073, c_0_5696]), ['final']). 4.05/4.32 cnf(c_0_10547, 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_6074, c_0_5696]), ['final']). 4.05/4.32 cnf(c_0_10548, 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_6075]), ['final']). 4.05/4.32 cnf(c_0_10549, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)), inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6076, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049])])]), ['final']). 4.05/4.32 cnf(c_0_10550, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))|~class_Rings_Olinordered__idom(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6077, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10551, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),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))))))|~class_Rings_Olinordered__idom(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6078, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10552, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6079, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), c_0_4635]), c_0_4635]), c_0_4795]), c_0_4795]), c_0_4635]), c_0_4505]), c_0_4795]), c_0_5796]), c_0_4635]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_10553, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X2,X1),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),X4)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),c_Set_OCollect(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),X5))),hAPP(c_COMBC(X3,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,tc_HOL_Obool),X3),c_fequal),X6)))))),hAPP(c_Set_Oimage(X3,X1,X6),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),X4),X5)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5))), inference(rw,[status(thm)],[c_0_6080, c_0_4915]), ['final']). 4.05/4.32 cnf(c_0_10554, 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_6081]), ['final']). 4.05/4.32 cnf(c_0_10555, 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_6082]), ['final']). 4.05/4.32 cnf(c_0_10556, 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_6083]), ['final']). 4.05/4.32 cnf(c_0_10557, 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),esk379_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_6084, c_0_4915]), ['final']). 4.05/4.32 cnf(c_0_10558, plain, (c_List_Olist_ONil(tc_List_Olist(X2))=X3|hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))=c_List_Otranspose(X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk391_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_6085, c_0_4519]), c_0_4519]), ['final']). 4.05/4.32 cnf(c_0_10559, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6086, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10560, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1)), inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6087, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049])])]), ['final']). 4.05/4.32 cnf(c_0_10561, 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),esk391_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_6088]), c_0_4898]), c_0_6089]), c_0_6090]), ['final']). 4.05/4.32 cnf(c_0_10562, 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_6091]), ['final']). 4.05/4.32 cnf(c_0_10563, plain, (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(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat,X4),c_Finite__Set_Ocard(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),c_Set_OCollect(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),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))),X5)))),X6)|hBOOL(hAPP(hAPP(c_member(X1),esk148_6(X2,X5,X3,X1,X6,X4)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(rw,[status(thm)],[c_0_6092, c_0_4915]), ['final']). 4.05/4.32 cnf(c_0_10564, 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_6093]), ['final']). 4.05/4.32 cnf(c_0_10565, plain, (c_List_Olist_ONil(tc_List_Olist(X2))=X3|hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X2),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X2)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X2)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBB(tc_List_Olist(X2),tc_fun(tc_Nat_Onat,X2),tc_Nat_Onat),c_List_Onth(X2)),hAPP(c_List_Onth(tc_List_Olist(X2)),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),X3))))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))=c_List_Otranspose(X2,X3)|X1!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X2)),X3),esk391_3(X1,X2,X3)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6094, c_0_4519]), c_0_4519]), ['final']). 4.05/4.32 cnf(c_0_10566, 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_6095, c_0_6096]), c_0_5205]), c_0_4523]), c_0_4915]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10567, 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),esk391_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_6097]), c_0_4898]), c_0_6089]), c_0_6090]), ['final']). 4.05/4.32 cnf(c_0_10568, 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_6098, c_0_6096]), c_0_5205]), c_0_4523]), c_0_4915]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10569, 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_6099, c_0_6100]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10570, 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_6101]), ['final']). 4.05/4.32 cnf(c_0_10571, 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_6102]), ['final']). 4.05/4.32 cnf(c_0_10572, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))|~class_Groups_Omonoid__mult(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6103, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10573, plain, (hBOOL(hAPP(hAPP(X1,esk214_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk215_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),esk215_3(X1,X2,X3)),esk214_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk215_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6104, c_0_4795]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_10574, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBS(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),X3)),X4)),X5)),X6)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X6),X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X6),X3)))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6105, c_0_4523]), c_0_4523]), c_0_6106]), ['final']). 4.05/4.32 cnf(c_0_10575, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6107, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10576, 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_6108, c_0_6100]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10577, 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,esk190_4(X1,X3,X4,X2)))),hAPP(X4,esk190_4(X1,X3,X4,X2))))), inference(rw,[status(thm)],[c_0_6109, c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10578, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk394_6(X2,X3,X4,X5,X1,X6)),X5))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBS(X1,tc_fun(X4,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBC(X1,X6,tc_fun(tc_fun(X4,tc_HOL_Obool),X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,X6),tc_fun(X6,tc_fun(tc_fun(X4,tc_HOL_Obool),X6)),X1),c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6))),X2)),c_Groups_Oone__class_Oone(X6))),X3)),c_Groups_Oone__class_Oone(X6)),X5)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,tc_prod(X1,X4),c_Groups_Otimes__class_Otimes(X6)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X4,X6),X2)),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X5),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~class_Groups_Ocomm__monoid__mult(X6)), inference(split_conjunct,[status(thm)],[c_0_6110]), ['final']). 4.05/4.32 cnf(c_0_10579, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,X1),tc_fun(tc_fun(X3,tc_HOL_Obool),X1),X2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,X1),tc_fun(X3,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,X1),tc_fun(tc_fun(X3,X1),tc_fun(X3,X1)),X2),c_COMBB(X1,X1,X3)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4))),X5))),X6)),X7)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X7)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),X5),X6))|~class_Rings_Osemiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_6111]), ['final']). 4.05/4.32 cnf(c_0_10580, 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_6112, c_0_6113]), ['final']). 4.05/4.32 cnf(c_0_10581, 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_6114, c_0_6113]), ['final']). 4.05/4.32 cnf(c_0_10582, 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_6115, c_0_4915]), c_0_4915]), c_0_4926]), ['final']). 4.05/4.32 cnf(c_0_10583, 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,esk190_4(X1,X3,X4,X2)))), inference(rw,[status(thm)],[c_0_6116, c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10584, 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_6057]), ['final']). 4.05/4.32 cnf(c_0_10585, 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_6058]), ['final']). 4.05/4.32 cnf(c_0_10586, 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_6117, c_0_4635]), c_0_5201]), c_0_5201]), c_0_6118]), c_0_5205]), c_0_6106]), ['final']). 4.05/4.32 cnf(c_0_10587, 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),hAPP(hAPP(c_COMBB(X1,X1,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X1),X2)),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))),X3))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),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),X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X3))))|~class_Rings_Ocomm__semiring__1(X1)), inference(rw,[status(thm)],[c_0_6119, c_0_6120]), ['final']). 4.05/4.32 cnf(c_0_10588, plain, (hBOOL(hAPP(hAPP(X1,esk499_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk500_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk499_3(X1,X2,X3)),esk500_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6121, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_10589, 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_6122, c_0_6123]), ['final']). 4.05/4.32 cnf(c_0_10590, 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_6124]), ['final']). 4.05/4.32 cnf(c_0_10591, 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_6125]), ['final']). 4.05/4.32 cnf(c_0_10592, 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_6126]), ['final']). 4.05/4.32 cnf(c_0_10593, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))|~class_Groups_Omonoid__mult(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6127, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10594, 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_6128, c_0_4635]), c_0_5201]), c_0_5201]), c_0_6118]), c_0_5205]), c_0_6106]), ['final']). 4.05/4.32 cnf(c_0_10595, 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_6129]), ['final']). 4.05/4.32 cnf(c_0_10596, 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_6130]), ['final']). 4.05/4.32 cnf(c_0_10597, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBS(X5,tc_fun(X1,tc_HOL_Obool),X6),hAPP(hAPP(c_COMBC(X5,X6,tc_fun(tc_fun(X1,tc_HOL_Obool),X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,X6),tc_fun(X6,tc_fun(tc_fun(X1,tc_HOL_Obool),X6)),X5),c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6))),X3)),c_Groups_Oone__class_Oone(X6))),X2)),c_Groups_Oone__class_Oone(X6)),X4)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,tc_prod(X5,X1),c_Groups_Otimes__class_Otimes(X6)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X1,X6),X3)),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk394_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_6110]), ['final']). 4.05/4.32 cnf(c_0_10598, plain, (hAPP(hAPP(X8,X9),X10)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X9),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X7,tc_HOL_Obool)),tc_fun(X7,tc_HOL_Obool),X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X7,tc_HOL_Obool)),hAPP(c_Relation_OImage(X4,X4,X6),hAPP(hAPP(c_Set_Oinsert(X4),X10),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))),X8))|~c_Equiv__Relations_Oequiv(X1,X2,X3)|~c_Equiv__Relations_Oequiv(X4,X5,X6)|~c_Equiv__Relations_Ocongruent2(X1,X4,tc_fun(X7,tc_HOL_Obool),X3,X6,X8)|~hBOOL(hAPP(hAPP(c_member(X1),X9),X2))|~hBOOL(hAPP(hAPP(c_member(X4),X10),X5))), inference(split_conjunct,[status(thm)],[c_0_6131]), ['final']). 4.05/4.32 cnf(c_0_10599, 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_6132, c_0_4635]), c_0_5201]), c_0_5201]), c_0_6118]), c_0_5205]), c_0_6106]), c_0_6133]), ['final']). 4.05/4.32 cnf(c_0_10600, 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_6134, c_0_5696]), c_0_5696]), ['final']). 4.05/4.32 cnf(c_0_10601, 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_6135, c_0_5696]), c_0_5696]), ['final']). 4.05/4.32 cnf(c_0_10602, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk434_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_6136]), ['final']). 4.05/4.32 cnf(c_0_10603, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk433_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_6136]), ['final']). 4.05/4.32 cnf(c_0_10604, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_Option_Ooption(X2),tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),hAPP(c_Map_Omap__of(X1,X2),X3)))),c_Option_Ooption_OSome(X2)))=hAPP(c_List_Oset(tc_prod(X1,X2)),X3)|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))), inference(rw,[status(thm)],[c_0_6137, c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10605, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6138, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10606, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6139, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10607, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6140, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10608, 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_6141, c_0_5716]), ['final']). 4.05/4.32 cnf(c_0_10609, 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,esk433_11(X3,X4,X5,X2,X1,X6,X7,X8,X9,X10,X11)),esk434_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_6136]), ['final']). 4.05/4.32 cnf(c_0_10610, plain, (hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(X2,X1)),X3),X4)=hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(X2),hAPP(hAPP(c_COMBC(X2,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X2),c_Smallcheck_Osmall__class_Osmall(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X1)),tc_fun(X1,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X2),hAPP(c_COMBB(tc_prod(X2,X1),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),X1),X3)),c_Product__Type_OPair(X2,X1)))),X4)),X4)|~class_Smallcheck_Osmall(X1)|~class_Smallcheck_Osmall(X2)), inference(split_conjunct,[status(thm)],[c_0_6142]), ['final']). 4.05/4.32 cnf(c_0_10611, 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)),esk457_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_6059]), ['final']). 4.05/4.32 cnf(c_0_10612, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk121_6(X2,X3,X4,X5,X1,X6)),X5))|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)=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))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~class_Groups_Ocomm__monoid__add(X6)), inference(split_conjunct,[status(thm)],[c_0_6143]), ['final']). 4.05/4.32 cnf(c_0_10613, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),c_Hilbert__Choice_OEps(tc_List_Olist(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X2),tc_HOL_Obool)),c_List_Odistinct(X2)),hAPP(hAPP(c_COMBC(tc_List_Olist(X2),tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X2)),c_fequal),c_List_Oset(X2))),X4)))))=c_Nitpick_Osetsum_H(X2,X1,X3,X4)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6144, c_0_5205]), c_0_6145]), ['final']). 4.05/4.32 cnf(c_0_10614, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))|~class_Rings_Ocomm__semiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6146, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10615, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))!=c_Groups_Oone__class_Oone(tc_Nat_Onat)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6147, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10616, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),esk160_4(X1,X2,X3,X4)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk161_4(X1,X2,X3,X4)),esk162_4(X1,X2,X3,X4)))))|hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))), inference(split_conjunct,[status(thm)],[c_0_4947]), ['final']). 4.05/4.32 cnf(c_0_10617, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6148, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10618, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))), inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6149, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049])])]), ['final']). 4.05/4.32 cnf(c_0_10619, 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_6150, c_0_6151]), ['final']). 4.05/4.32 cnf(c_0_10620, plain, (hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_fun(X2,X1)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(X1)),tc_fun(X2,X1),tc_List_Olist(X1)),c_Fun_Ocomp(tc_Option_Ooption(X1),X1,X2,c_Option_Othe(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X2,X1)),tc_fun(X2,tc_Option_Ooption(X1)),tc_List_Olist(X1)),c_Map_Omap__of(X2,X1)),hAPP(c_List_Ozip(X2,X1),c_Enum_Oenum__class_Oenum(X2))))),c_Enum_On__lists(X1,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_Enum_Oenum__class_Oenum(X2)),c_Enum_Oenum__class_Oenum(X1)))=c_Enum_Oenum__class_Oenum(tc_fun(X2,X1))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_6152]), ['final']). 4.05/4.32 cnf(c_0_10621, plain, (c_Enum_Oex__n__lists(X2,hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_HOL_Obool,tc_List_Olist(X2)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,X2),tc_List_Olist(X2)),c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_fun(X1,tc_Option_Ooption(X2)),tc_List_Olist(X2)),c_Map_Omap__of(X1,X2)),hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1)))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X1,X2)),X3))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_6153]), ['final']). 4.05/4.32 cnf(c_0_10622, 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),esk515_3(X3,X2,X1)),esk515_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)),esk514_3(X3,X2,X1)))), inference(rw,[status(thm)],[c_0_6154, c_0_4926]), ['final']). 4.05/4.32 cnf(c_0_10623, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk515_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)),esk514_3(X3,X2,X1)))), inference(rw,[status(thm)],[c_0_6155, c_0_4926]), ['final']). 4.05/4.32 cnf(c_0_10624, plain, (c_Enum_Oall__n__lists(X2,hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_HOL_Obool,tc_List_Olist(X2)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,X2),tc_List_Olist(X2)),c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_fun(X1,tc_Option_Ooption(X2)),tc_List_Olist(X2)),c_Map_Omap__of(X1,X2)),hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1)))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X1,X2)),X3))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_6156]), ['final']). 4.05/4.32 cnf(c_0_10625, plain, (hBOOL(hAPP(hAPP(hAPP(X1,esk160_4(X1,X2,X3,X4)),esk161_4(X1,X2,X3,X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),esk162_4(X1,X2,X3,X4))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk161_4(X1,X2,X3,X4)),esk162_4(X1,X2,X3,X4)))|hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))|hAPP(esk160_4(X1,X2,X3,X4),esk162_4(X1,X2,X3,X4))!=c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))), inference(rw,[status(thm)],[c_0_6157, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_10626, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6158, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10627, 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_6159, c_0_5695]), c_0_5201]), c_0_5695]), c_0_5201]), ['final']). 4.05/4.32 cnf(c_0_10628, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)))|~class_Rings_Osemiring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6160, c_0_5149]), c_0_5149]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), c_0_5149]), ['final']). 4.05/4.32 cnf(c_0_10629, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk258_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_6161]), ['final']). 4.05/4.32 cnf(c_0_10630, 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_6075]), ['final']). 4.05/4.32 cnf(c_0_10631, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6162, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10632, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))!=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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6163, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10633, plain, (X1=c_Groups_Ozero__class_Ozero(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)|~class_Rings_Olinordered__idom(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6164, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10634, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Hilbert__Choice_OEps(tc_List_Olist(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Odistinct(X1)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_List_Oset(X1))),X2))))=c_Nitpick_Ocard_H(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6165, c_0_5205]), c_0_6145]), ['final']). 4.05/4.32 cnf(c_0_10635, plain, (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)=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))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk121_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_6143]), ['final']). 4.05/4.32 cnf(c_0_10636, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OnegDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))=c_Divides_OnegDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6166, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_10637, 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),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_Ocomm__semiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6167, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10638, 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_6168]), ['final']). 4.05/4.32 cnf(c_0_10639, 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_6169, c_0_5695]), ['final']). 4.05/4.32 cnf(c_0_10640, 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_6067]), ['final']). 4.05/4.32 cnf(c_0_10641, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))), inference(split_conjunct,[status(thm)],[c_0_6170]), ['final']). 4.05/4.32 cnf(c_0_10642, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OnegDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))=c_Divides_OnegDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6171, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_10643, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X4),c_Groups_Oone__class_Oone(X1)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X3))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4)),X5)),c_Groups_Oone__class_Oone(X1)),X3)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6172]), ['final']). 4.05/4.32 cnf(c_0_10644, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6173, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10645, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk6_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_6174]), ['final']). 4.05/4.32 cnf(c_0_10646, 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),esk333_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_6175, c_0_4523]), c_0_4523]), c_0_4523]), ['final']). 4.05/4.32 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)),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_6081]), ['final']). 4.05/4.32 cnf(c_0_10648, 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_6176]), ['final']). 4.05/4.32 cnf(c_0_10649, 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_6177, c_0_4635]), c_0_5201]), c_0_6118]), ['final']). 4.05/4.32 cnf(c_0_10650, 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_6178, c_0_4635]), c_0_5201]), c_0_6118]), ['final']). 4.05/4.32 cnf(c_0_10651, 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)),X4)),X5)),X6)=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),X6),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X5)))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6179]), ['final']). 4.05/4.32 cnf(c_0_10652, 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_6180]), ['final']). 4.05/4.32 cnf(c_0_10653, 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_6181, c_0_4915]), ['final']). 4.05/4.32 cnf(c_0_10654, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk519_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_6182]), ['final']). 4.05/4.32 cnf(c_0_10655, 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,esk321_2(X2,X1)))|hBOOL(hAPP(X2,esk321_2(X2,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6183, c_0_4523]), c_0_5205]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10656, 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_6184, c_0_4977]), c_0_4635]), c_0_4427]), ['final']). 4.05/4.32 cnf(c_0_10657, 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)),esk321_2(X1,X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6185, c_0_4523]), c_0_5205]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10658, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OposDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))=c_Divides_OposDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6186, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_10659, 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_6187]), ['final']). 4.05/4.32 cnf(c_0_10660, 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_6188, c_0_4915]), c_0_4902]), ['final']). 4.05/4.32 cnf(c_0_10661, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk83_5(X5,X4,X3,X2,X1)),esk83_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_6189]), ['final']). 4.05/4.32 cnf(c_0_10662, 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_6190]), ['final']). 4.05/4.32 cnf(c_0_10663, 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_6191, c_0_4915]), c_0_4902]), ['final']). 4.05/4.32 cnf(c_0_10664, 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_6192, c_0_5669]), ['final']). 4.05/4.32 cnf(c_0_10665, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6193, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10666, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OposDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))=c_Divides_OposDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6194, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_10667, 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,esk321_2(X2,X1)))|~hBOOL(hAPP(X1,esk321_2(X2,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6195, c_0_4523]), c_0_5205]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10668, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6196, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10669, 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_6197]), ['final']). 4.05/4.32 cnf(c_0_10670, 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_6198, c_0_5696]), c_0_5696]), ['final']). 4.05/4.32 cnf(c_0_10671, 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,esk333_4(X4,X1,X3,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6199, c_0_4523]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10672, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6200, c_0_5669]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10673, 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_6201, c_0_5695]), ['final']). 4.05/4.32 cnf(c_0_10674, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X3)))), inference(rw,[status(thm)],[c_0_6202, c_0_6203]), ['final']). 4.05/4.32 cnf(c_0_10675, 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_6083]), ['final']). 4.05/4.32 cnf(c_0_10676, 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_6082]), ['final']). 4.05/4.32 cnf(c_0_10677, 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_6204]), ['final']). 4.05/4.32 cnf(c_0_10678, plain, (hBOOL(hAPP(hAPP(c_member(X3),X6),hAPP(c_List_Oset(X3),X4)))|hAPP(c_Map_Omap__of(X3,X1),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2))=hAPP(c_Map_Omap__of(X3,X1),hAPP(hAPP(c_List_Ozip(X3,X1),X4),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)),X4)|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X1)),hAPP(c_Map_Omap__of(X3,X1),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2))),X6),hAPP(c_Option_Ooption_OSome(X1),X7))!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X1)),hAPP(c_Map_Omap__of(X3,X1),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X5))),X6),hAPP(c_Option_Ooption_OSome(X1),X8))), inference(split_conjunct,[status(thm)],[c_0_6205]), ['final']). 4.05/4.32 cnf(c_0_10679, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X3,tc_HOL_Obool)),X2),X4)),X5)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(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__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool))),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_6206]), ['final']). 4.05/4.32 cnf(c_0_10680, 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)),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)))=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_6207]), ['final']). 4.05/4.32 cnf(c_0_10681, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(X2,esk6_5(X2,X3,X4,X5,X1))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X1),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X1),X2),X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_6174]), ['final']). 4.05/4.32 cnf(c_0_10682, 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_6208, c_0_4915]), c_0_4902]), ['final']). 4.05/4.32 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(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)))=hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6209, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10684, 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_Enum_Oenum__the(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_6210, c_0_4902]), ['final']). 4.05/4.32 cnf(c_0_10685, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|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)=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))), inference(split_conjunct,[status(thm)],[c_0_5883]), ['final']). 4.05/4.32 cnf(c_0_10686, 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_6211, c_0_5695]), c_0_6212]), ['final']). 4.05/4.32 cnf(c_0_10687, 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_6213, c_0_5695]), c_0_6214]), ['final']). 4.05/4.32 cnf(c_0_10688, 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_6215, c_0_4915]), c_0_4902]), ['final']). 4.05/4.32 cnf(c_0_10689, 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_6216]), ['final']). 4.05/4.32 cnf(c_0_10690, 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_6217, c_0_5668]), ['final']). 4.05/4.32 cnf(c_0_10691, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))|~class_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6218, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), ['final']). 4.05/4.32 cnf(c_0_10692, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6219, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10693, 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_6220]), ['final']). 4.05/4.32 cnf(c_0_10694, 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_6221, c_0_4635]), c_0_5201]), c_0_5201]), c_0_6118]), c_0_5205]), c_0_6106]), ['final']). 4.05/4.32 cnf(c_0_10695, 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_6222, c_0_4635]), c_0_5201]), c_0_5201]), c_0_6118]), c_0_5205]), c_0_6106]), ['final']). 4.05/4.32 cnf(c_0_10696, 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_6223, c_0_6133]), c_0_4635]), c_0_5201]), c_0_5201]), c_0_6118]), c_0_5205]), c_0_6106]), ['final']). 4.05/4.32 cnf(c_0_10697, plain, (hAPP(c_Option_Ooption_OSome(X4),X7)=hAPP(hAPP(c_Map_Omap__of(X2,X4),hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),tc_prod(X2,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X4,tc_prod(X2,X4)),hAPP(hAPP(c_COMBB(X2,tc_fun(X4,tc_prod(X2,X4)),X1),c_Product__Type_OPair(X2,X4)),X3))),X5)),hAPP(X3,X6))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|hAPP(hAPP(c_Map_Omap__of(X1,X4),X5),X6)!=hAPP(c_Option_Ooption_OSome(X4),X7)), inference(split_conjunct,[status(thm)],[c_0_6224]), ['final']). 4.05/4.32 cnf(c_0_10698, 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_6225, c_0_5695]), c_0_5201]), c_0_6226]), c_0_5695]), c_0_5201]), ['final']). 4.05/4.32 cnf(c_0_10699, 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_6227, c_0_4814]), ['final']). 4.05/4.32 cnf(c_0_10700, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6228, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10701, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),c_List_Otranspose(X1,X2)),X3)),X4)=hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),X4)),X3)|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X2))))), inference(split_conjunct,[status(thm)],[c_0_6229]), ['final']). 4.05/4.32 cnf(c_0_10702, 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_6091]), ['final']). 4.05/4.32 cnf(c_0_10703, 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_6230, c_0_5696]), c_0_5696]), ['final']). 4.05/4.32 cnf(c_0_10704, 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_6231, c_0_5696]), c_0_5696]), ['final']). 4.05/4.32 cnf(c_0_10705, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|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)))=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_5491]), ['final']). 4.05/4.32 cnf(c_0_10706, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6232, c_0_4795]), c_0_4635]), c_0_4505]), c_0_4795]), c_0_5796]), c_0_4635]), c_0_4635]), c_0_4635]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_10707, 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_6233, c_0_5695]), ['final']). 4.05/4.32 cnf(c_0_10708, 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_6234, c_0_5695]), ['final']). 4.05/4.32 cnf(c_0_10709, 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_6235]), ['final']). 4.05/4.32 cnf(c_0_10710, plain, (hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X1),c_Groups_Otimes__class_Otimes(X1)),hAPP(c_Groups_Otimes__class_Otimes(X1),X2))),c_COMBI(X1)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X3))))|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6236, c_0_4795]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_10711, 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),esk508_4(X4,X3,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X3),esk508_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_5029]), ['final']). 4.05/4.32 cnf(c_0_10712, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6237, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10713, 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_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|~class_Rings_Olinordered__idom(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6238, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10714, 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,esk262_3(X2,X1,X3))),hAPP(X1,esk262_3(X2,X1,X3))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6239, c_0_6120]), c_0_6120]), c_0_6120]), ['final']). 4.05/4.32 cnf(c_0_10715, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|c_Groups_Ozero__class_Ozero(X3)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X3,X3),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,X3),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X3)),X4)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X3,tc_Nat_Onat),X4),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))|~class_Groups_Oab__group__add(X3)), inference(split_conjunct,[status(thm)],[c_0_4969]), ['final']). 4.05/4.32 cnf(c_0_10716, 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,esk519_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_6182]), ['final']). 4.05/4.32 cnf(c_0_10717, plain, (c_Map_Omap__upds(X1,X3,X5,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X6),c_List_Olist_ONil(X1))),X4)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),c_Map_Omap__upds(X1,X3,X5,X2,X4)),X6),hAPP(c_Option_Ooption_OSome(X3),hAPP(hAPP(c_List_Onth(X3),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)))), inference(split_conjunct,[status(thm)],[c_0_6240]), ['final']). 4.05/4.32 cnf(c_0_10718, 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_6241]), ['final']). 4.05/4.32 cnf(c_0_10719, 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)),esk158_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),esk158_4(X3,X4,X2,X1)))),X3)))), inference(rw,[status(thm)],[c_0_6242, c_0_5131]), ['final']). 4.05/4.32 cnf(c_0_10720, 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,X2))!=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))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6243, c_0_5696]), c_0_5696]), ['final']). 4.05/4.32 cnf(c_0_10721, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6244, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10722, 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_6245]), ['final']). 4.05/4.32 cnf(c_0_10723, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Oplus__class_Oplus(X1)),X3)),X4)),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X4),X5)))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6246]), ['final']). 4.05/4.32 cnf(c_0_10724, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk392_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_6247]), ['final']). 4.05/4.32 cnf(c_0_10725, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk326_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_6248]), ['final']). 4.05/4.32 cnf(c_0_10726, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk366_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_6249]), ['final']). 4.05/4.32 cnf(c_0_10727, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk150_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_6250]), ['final']). 4.05/4.32 cnf(c_0_10728, 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_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6251, c_0_4795]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_10729, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6252, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049])]), ['final']). 4.05/4.32 cnf(c_0_10730, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk275_8(X2,X3,X4,X1,X5,X6,X7,X8)),X4))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X7,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool),X1),c_Set_Oimage(X8,X7,X6)),X3))=hAPP(c_Set_Oimage(X8,X7,X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X8,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~c_Fun_Oinj__on(X8,X7,X6,X5)), inference(split_conjunct,[status(thm)],[c_0_6253]), ['final']). 4.05/4.32 cnf(c_0_10731, 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)))),esk257_3(X3,X2,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6254, c_0_4767]), c_0_4767]), ['final']). 4.05/4.32 cnf(c_0_10732, 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)))),esk75_3(X2,X3,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6255, c_0_4767]), c_0_4767]), ['final']). 4.05/4.32 cnf(c_0_10733, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk469_5(X2,X3,X4,X5,X1)),esk470_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_6256]), ['final']). 4.05/4.32 cnf(c_0_10734, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|~class_Rings_Olinordered__idom(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6257, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10735, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X2)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6258, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), ['final']). 4.05/4.32 cnf(c_0_10736, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk237_5(X2,X3,X4,X5,X1)),esk236_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_6259]), ['final']). 4.05/4.32 cnf(c_0_10737, 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_6093]), ['final']). 4.05/4.32 cnf(c_0_10738, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(X5,hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6260, c_0_5011]), c_0_6261]), c_0_5011]), c_0_6261]), ['final']). 4.05/4.32 cnf(c_0_10739, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6262, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), ['final']). 4.05/4.32 cnf(c_0_10740, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6263, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10741, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6264, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10742, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),X2)|~class_Groups_Omonoid__mult(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6265, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_6266]), ['final']). 4.05/4.32 cnf(c_0_10743, 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))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6267, c_0_6268]), c_0_6268]), c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_10744, 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_6269]), ['final']). 4.05/4.32 cnf(c_0_10745, 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)))|X1=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)),X1),X2)),c_List_Olexord(X4,X3)))|esk204_4(X1,X2,X3,X4)!=esk205_4(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_6270]), ['final']). 4.05/4.32 cnf(c_0_10746, 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_6271]), ['final']). 4.05/4.32 cnf(c_0_10747, 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_6272, c_0_6273]), ['final']). 4.05/4.32 cnf(c_0_10748, 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_6274, c_0_5149]), c_0_5149]), ['final']). 4.05/4.32 cnf(c_0_10749, 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),esk508_4(X4,X3,X1,X2))),hAPP(hAPP(c_List_Onth(X2),X3),esk508_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_5029]), ['final']). 4.05/4.32 cnf(c_0_10750, 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_6275]), ['final']). 4.05/4.32 cnf(c_0_10751, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk461_7(X2,X3,X4,X5,X6,X7,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)))|hAPP(hAPP(X7,hAPP(X4,X3)),hAPP(X4,X2))=hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~c_Finite__Set_Ofolding__image__simple(X8,X1,X7,X6,X5,X4)), inference(split_conjunct,[status(thm)],[c_0_6276]), ['final']). 4.05/4.32 cnf(c_0_10752, 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_6277]), ['final']). 4.05/4.32 cnf(c_0_10753, 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_6278, c_0_6214]), ['final']). 4.05/4.32 cnf(c_0_10754, 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_6279, c_0_6212]), ['final']). 4.05/4.32 cnf(c_0_10755, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4)),X2))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X4),X2))))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_6280]), ['final']). 4.05/4.32 cnf(c_0_10756, plain, (hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)|~c_Equiv__Relations_Oequiv(X1,X5,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X3))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_6281, c_0_6282]), c_0_6283]), ['final']). 4.05/4.32 cnf(c_0_10757, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X4))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_6284]), ['final']). 4.05/4.32 cnf(c_0_10758, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk236_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_6259]), ['final']). 4.05/4.32 cnf(c_0_10759, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk469_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_6256]), ['final']). 4.05/4.32 cnf(c_0_10760, 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_6285]), ['final']). 4.05/4.32 cnf(c_0_10761, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6286]), ['final']). 4.05/4.32 cnf(c_0_10762, 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_6287]), ['final']). 4.05/4.32 cnf(c_0_10763, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__upds(X1,X2,X3,X4,X5)),X6),hAPP(c_Option_Ooption_OSome(X2),X7))=c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4),hAPP(hAPP(c_List_Olist_OCons(X2),X7),X5))|hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)),X4))))), inference(rw,[status(thm)],[c_0_6288, c_0_6289]), ['final']). 4.05/4.32 cnf(c_0_10764, 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),X3)!=hAPP(hAPP(c_List_Otake(X1),X5),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),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_6290, c_0_5011]), ['final']). 4.05/4.32 cnf(c_0_10765, 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),esk140_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_6291]), ['final']). 4.05/4.32 cnf(c_0_10766, 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),esk351_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_5606]), ['final']). 4.05/4.32 cnf(c_0_10767, 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_6292]), ['final']). 4.05/4.32 cnf(c_0_10768, 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_6293, c_0_5669]), c_0_5669]), ['final']). 4.05/4.32 cnf(c_0_10769, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk508_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_6294, c_0_5011]), ['final']). 4.05/4.32 cnf(c_0_10770, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6295, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), ['final']). 4.05/4.32 cnf(c_0_10771, plain, (hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Otimes__class_Otimes(X1)),c_COMBI(X1)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),c_Int_OMin)))))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6296, c_0_4814]), c_0_4814]), c_0_4814]), ['final']). 4.05/4.32 cnf(c_0_10772, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X5,c_Groups_Otimes__class_Otimes(X1)),X2),c_Groups_Oone__class_Oone(X1)),X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X5,c_Groups_Otimes__class_Otimes(X1)),X2),c_Groups_Oone__class_Oone(X1)),X3))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X5,c_Groups_Otimes__class_Otimes(X1)),X2),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X4),X3))|c_Groups_Oone__class_Oone(X1)!=hAPP(X2,esk258_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_6161]), ['final']). 4.05/4.32 cnf(c_0_10773, 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_6297]), ['final']). 4.05/4.32 cnf(c_0_10774, 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_6298]), ['final']). 4.05/4.32 cnf(c_0_10775, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Enum_Oenum__the(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_Enum_Oenum__the(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_6299, c_0_6300]), c_0_6300]), ['final']). 4.05/4.32 cnf(c_0_10776, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6301, c_0_4795]), c_0_4635]), c_0_4505]), c_0_4795]), c_0_5796]), c_0_4635]), c_0_4635]), c_0_4635]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_10777, 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_6302]), ['final']). 4.05/4.32 cnf(c_0_10778, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6303, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049])]), ['final']). 4.05/4.32 cnf(c_0_10779, 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_6101]), ['final']). 4.05/4.32 cnf(c_0_10780, 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_5024]), ['final']). 4.05/4.32 cnf(c_0_10781, plain, (hAPP(X4,X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),hAPP(hAPP(c_COMBC(X1,X5,X5),hAPP(hAPP(c_COMBS(X1,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X1),c_If(X5)),hAPP(c_fequal,X2))),X4)),c_Groups_Ozero__class_Ozero(X5))),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Ocomm__monoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_5023]), ['final']). 4.05/4.32 cnf(c_0_10782, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X3)))))|~class_Rings_Oring__1(X1)), inference(rw,[status(thm)],[c_0_6304, c_0_5696]), ['final']). 4.05/4.32 cnf(c_0_10783, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6305, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049])]), ['final']). 4.05/4.32 cnf(c_0_10784, 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_6306]), ['final']). 4.05/4.32 cnf(c_0_10785, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))), inference(split_conjunct,[status(thm)],[c_0_6307]), ['final']). 4.05/4.32 cnf(c_0_10786, 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_6308]), ['final']). 4.05/4.32 cnf(c_0_10787, 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_6309]), ['final']). 4.05/4.32 cnf(c_0_10788, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk140_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_6291]), ['final']). 4.05/4.32 cnf(c_0_10789, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk351_4(X2,X3,X4,X1)),X4))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_5606]), ['final']). 4.05/4.32 cnf(c_0_10790, 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_6310]), ['final']). 4.05/4.32 cnf(c_0_10791, 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)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6311, c_0_6268]), c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_10792, 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)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6312, c_0_6268]), c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_10793, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X8,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X5),c_Set_Oimage(X1,X8,X7)),X2))=hAPP(c_Set_Oimage(X1,X8,X7),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk275_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_6253]), ['final']). 4.05/4.32 cnf(c_0_10794, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk523_8(X2,X3,X4,X5,X6,X7,X8,X1)),hAPP(c_List_Oset(X1),X8)))|hAPP(X4,hAPP(c_List_Ofoldl(X6,X1,hAPP(c_COMBC(X1,X6,X6),X3),X2),X8))=hAPP(c_List_Ofoldl(X7,X1,hAPP(c_COMBC(X1,X7,X7),X5),hAPP(X4,X2)),X8)), inference(split_conjunct,[status(thm)],[c_0_6313]), ['final']). 4.05/4.32 cnf(c_0_10795, 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_6314]), ['final']). 4.05/4.32 cnf(c_0_10796, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Osemiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6315, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10797, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Osemiring__1(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6316, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10798, 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_6317, c_0_5201]), c_0_5201]), ['final']). 4.05/4.32 cnf(c_0_10799, plain, (X2=X3|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk257_3(X3,X2,X1)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3)|hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)!=hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6318, c_0_4767]), c_0_4767]), ['final']). 4.05/4.32 cnf(c_0_10800, plain, (X2=X3|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk75_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_6319, c_0_4767]), c_0_4767]), ['final']). 4.05/4.32 cnf(c_0_10801, 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_5039]), ['final']). 4.05/4.32 cnf(c_0_10802, 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_6320, c_0_4523]), c_0_4523]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10803, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),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_6321]), ['final']). 4.05/4.32 cnf(c_0_10804, 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_6322]), ['final']). 4.05/4.32 cnf(c_0_10805, 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),esk508_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_6323, c_0_5011]), ['final']). 4.05/4.32 cnf(c_0_10806, 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_6324]), ['final']). 4.05/4.32 cnf(c_0_10807, 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))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6325, c_0_6268]), c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_10808, 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))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6326, c_0_6268]), c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_10809, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk175_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk176_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_6327]), ['final']). 4.05/4.32 cnf(c_0_10810, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),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_6328]), ['final']). 4.05/4.32 cnf(c_0_10811, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,hAPP(X2,X3)))),hAPP(hAPP(c_List_Omap(X4,X1),X2),X5))=hAPP(hAPP(c_List_Omap(X4,X1),X2),hAPP(c_List_Ofilter(X4,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_fequal,X3))),X5))|~c_Fun_Oinj__on(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6329, c_0_5201]), c_0_5201]), ['final']). 4.05/4.32 cnf(c_0_10812, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk388_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk389_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_6330]), ['final']). 4.05/4.32 cnf(c_0_10813, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3))|~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_6331]), ['final']). 4.05/4.32 cnf(c_0_10814, 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_6332]), ['final']). 4.05/4.32 cnf(c_0_10815, plain, (hAPP(X6,hAPP(c_List_Ofoldl(X2,X8,hAPP(c_COMBC(X8,X2,X2),X5),X4),X7))=hAPP(c_List_Ofoldl(X1,X8,hAPP(c_COMBC(X8,X1,X1),X3),hAPP(X6,X4)),X7)|hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,esk523_8(X4,X5,X6,X3,X2,X1,X7,X8))),X6)!=hAPP(c_Fun_Ocomp(X2,X1,X2,X6),hAPP(X5,esk523_8(X4,X5,X6,X3,X2,X1,X7,X8)))), inference(split_conjunct,[status(thm)],[c_0_6313]), ['final']). 4.05/4.32 cnf(c_0_10816, 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_6333]), ['final']). 4.05/4.32 cnf(c_0_10817, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Rings_Oinverse__class_Odivide(X1)),X4)),X5)),X3)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3))|~class_Fields_Ofield__inverse__zero(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6334]), ['final']). 4.05/4.32 cnf(c_0_10818, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6335]), ['final']). 4.05/4.32 cnf(c_0_10819, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),c_Big__Operators_Olinorder__class_OMin(X1,X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6336]), ['final']). 4.05/4.32 cnf(c_0_10820, 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_6337]), ['final']). 4.05/4.32 cnf(c_0_10821, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~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_6338]), ['final']). 4.05/4.32 cnf(c_0_10822, 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_6339, c_0_6340]), c_0_6340]), ['final']). 4.05/4.32 cnf(c_0_10823, 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_6341])]), ['final']). 4.05/4.32 cnf(c_0_10824, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk34_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_6342]), ['final']). 4.05/4.32 cnf(c_0_10825, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk457_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_6059]), ['final']). 4.05/4.32 cnf(c_0_10826, 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),esk279_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_6343, c_0_4523]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10827, 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_6344, c_0_4635]), c_0_5201]), c_0_6118]), ['final']). 4.05/4.32 cnf(c_0_10828, 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_6345, c_0_4635]), c_0_5201]), c_0_6118]), ['final']). 4.05/4.32 cnf(c_0_10829, 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_6346]), ['final']). 4.05/4.32 cnf(c_0_10830, 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_6347]), ['final']). 4.05/4.32 cnf(c_0_10831, 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_6348]), ['final']). 4.05/4.32 cnf(c_0_10832, 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_6349]), ['final']). 4.05/4.32 cnf(c_0_10833, 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_6350]), ['final']). 4.05/4.32 cnf(c_0_10834, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2)),c_List_Olexord(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_Olexord(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk205_4(X2,X3,X4,X1)),esk204_4(X2,X3,X4,X1))),X4))), inference(split_conjunct,[status(thm)],[c_0_6270]), ['final']). 4.05/4.32 cnf(c_0_10835, 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)))|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_Olexord(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk204_4(X2,X3,X4,X1)),esk205_4(X2,X3,X4,X1))),X4))), inference(split_conjunct,[status(thm)],[c_0_6270]), ['final']). 4.05/4.32 cnf(c_0_10836, plain, (hAPP(hAPP(X1,X2),X3)=X4|c_Nitpick_Ofold__graph_H(X5,X6,X1,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X7),hAPP(hAPP(c_Set_Oinsert(X5),esk307_7(X3,X2,X7,X4,X1,X6,X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),esk308_7(X3,X2,X7,X4,X1,X6,X5))|~c_Nitpick_Ofold__graph_H(X5,X6,X1,X4,X7,hAPP(hAPP(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6351]), ['final']). 4.05/4.32 cnf(c_0_10837, 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),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_6352]), ['final']). 4.05/4.32 cnf(c_0_10838, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk324_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_6353]), ['final']). 4.05/4.32 cnf(c_0_10839, 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_6354, c_0_4915]), c_0_4915]), ['final']). 4.05/4.32 cnf(c_0_10840, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk175_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk176_5(X2,X3,X4,X5,X1)),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_6327]), ['final']). 4.05/4.32 cnf(c_0_10841, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk388_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk389_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_6330]), ['final']). 4.05/4.32 cnf(c_0_10842, 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),esk508_4(X4,X3,X2,X1)),X3)=hAPP(hAPP(c_List_Otake(X1),esk508_4(X4,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)),X2),X3)),c_List_Olexord(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_5029]), ['final']). 4.05/4.32 cnf(c_0_10843, 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),esk307_7(X6,X7,X1,X5,X4,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),esk308_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_6351]), ['final']). 4.05/4.32 cnf(c_0_10844, 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_6355]), ['final']). 4.05/4.32 cnf(c_0_10845, plain, (hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6356, c_0_4795]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_10846, 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_6357]), ['final']). 4.05/4.32 cnf(c_0_10847, 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_6358]), ['final']). 4.05/4.32 cnf(c_0_10848, 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_6359, c_0_4950]), c_0_4950]), ['final']). 4.05/4.32 cnf(c_0_10849, 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_6360]), ['final']). 4.05/4.32 cnf(c_0_10850, 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_5079]), ['final']). 4.05/4.32 cnf(c_0_10851, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6361]), ['final']). 4.05/4.32 cnf(c_0_10852, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk317_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk319_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_6362, c_0_4767]), ['final']). 4.05/4.32 cnf(c_0_10853, 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)))), inference(split_conjunct,[status(thm)],[c_0_6363]), ['final']). 4.05/4.32 cnf(c_0_10854, 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_5080]), ['final']). 4.05/4.32 cnf(c_0_10855, 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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),esk375_4(X2,X4,X3,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)),esk375_4(X2,X4,X3,X1))),X3)), inference(rw,[status(thm)],[c_0_6364, c_0_5131]), ['final']). 4.05/4.32 cnf(c_0_10856, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X4),X5))|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_6365]), ['final']). 4.05/4.32 cnf(c_0_10857, 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),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_6366]), ['final']). 4.05/4.32 cnf(c_0_10858, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk317_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk318_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_6367, c_0_4767]), ['final']). 4.05/4.32 cnf(c_0_10859, 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(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5)),X6)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~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)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1))), inference(split_conjunct,[status(thm)],[c_0_6368]), ['final']). 4.05/4.32 cnf(c_0_10860, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X5))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5)),X6)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X5)),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1))), inference(split_conjunct,[status(thm)],[c_0_6369]), ['final']). 4.05/4.32 cnf(c_0_10861, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk510_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_6370]), ['final']). 4.05/4.32 cnf(c_0_10862, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Ominus__class_Ominus(X1)),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X5))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6371]), ['final']). 4.05/4.32 cnf(c_0_10863, 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_6372, c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_10864, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk511_8(X3,X4,X5,X2,X1,X6,X7,X8)),esk512_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_6373]), ['final']). 4.05/4.32 cnf(c_0_10865, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk438_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),X1),c_Product__Type_Ofst(X1,X4)),X3))))|hAPP(c_Map_Omap__of(X1,X4),X3)=hAPP(c_Map_Omap__of(X1,X4),X2)|hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),X1),c_Product__Type_Ofst(X1,X4)),X2))!=hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),X1),c_Product__Type_Ofst(X1,X4)),X3))), inference(split_conjunct,[status(thm)],[c_0_6374]), ['final']). 4.05/4.32 cnf(c_0_10866, 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_6375]), ['final']). 4.05/4.32 cnf(c_0_10867, 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,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_6376]), ['final']). 4.05/4.32 cnf(c_0_10868, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X2,tc_HOL_Obool)),X3))=hAPP(c_Finite__Set_Ocard(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk106_3(X1,X3,X2)),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk104_3(X1,X3,X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3)))), inference(csr,[status(thm)],[c_0_6377, c_0_6378]), ['final']). 4.05/4.32 cnf(c_0_10869, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X2,tc_HOL_Obool)),X3))=hAPP(c_Finite__Set_Ocard(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk105_3(X1,X3,X2)),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk104_3(X1,X3,X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3)))), inference(csr,[status(thm)],[c_0_6379, c_0_6378]), ['final']). 4.05/4.32 cnf(c_0_10870, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6380, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10871, 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_6381]), ['final']). 4.05/4.32 cnf(c_0_10872, plain, (c_Enum_Oenum__the(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_6382, c_0_4915]), ['final']). 4.05/4.32 cnf(c_0_10873, 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))), inference(rw,[status(thm)],[c_0_6383, c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_10874, 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_6384]), ['final']). 4.05/4.32 cnf(c_0_10875, 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,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_6385]), ['final']). 4.05/4.32 cnf(c_0_10876, 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_6370]), ['final']). 4.05/4.32 cnf(c_0_10877, 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),X4),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2))),c_List_Olex(X1,X6)))|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),X4),X5)),X6))), inference(split_conjunct,[status(thm)],[c_0_5079]), ['final']). 4.05/4.32 cnf(c_0_10878, 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_6386]), ['final']). 4.05/4.32 cnf(c_0_10879, plain, (hAPP(X1,esk210_7(X2,X3,X1,X4,X5,X6,X7))=hAPP(X1,esk209_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_6387]), ['final']). 4.05/4.32 cnf(c_0_10880, plain, (c_Map_Orestrict__map(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),X5),X6)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X6)),X4),X5)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X6))), inference(rw,[status(thm)],[c_0_6388, c_0_6389]), ['final']). 4.05/4.32 cnf(c_0_10881, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))=X2|c_Groups_Oone__class_Oone(X1)=X2|hAPP(hAPP(c_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_6390, c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10882, 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_6391, c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10883, 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_6392, c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10884, 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_6393, c_0_6049]), ['final']). 4.05/4.32 cnf(c_0_10885, 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_6394, c_0_6395]), c_0_6396]), ['final']). 4.05/4.32 cnf(c_0_10886, 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_5039]), ['final']). 4.05/4.32 cnf(c_0_10887, 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_6397]), ['final']). 4.05/4.32 cnf(c_0_10888, 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_6398]), ['final']). 4.05/4.32 cnf(c_0_10889, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk111_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_6399]), ['final']). 4.05/4.32 cnf(c_0_10890, plain, (hAPP(X1,esk498_6(X2,X3,X1,X4,X5,X6))=hAPP(X1,esk497_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_6400]), ['final']). 4.05/4.32 cnf(c_0_10891, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~c_Equiv__Relations_Oequiv(X1,X5,X4)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X6),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X5),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X6))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X6))), inference(er,[status(thm)],[c_0_6401]), ['final']). 4.05/4.32 cnf(c_0_10892, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMin(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6402]), ['final']). 4.05/4.32 cnf(c_0_10893, 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_6403]), ['final']). 4.05/4.32 cnf(c_0_10894, 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_6404]), ['final']). 4.05/4.32 cnf(c_0_10895, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk498_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_6400]), ['final']). 4.05/4.32 cnf(c_0_10896, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk497_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_6400]), ['final']). 4.05/4.32 cnf(c_0_10897, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|c_Big__Operators_Olattice__class_OInf__fin(X1,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(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_6405]), ['final']). 4.05/4.32 cnf(c_0_10898, 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_6406]), ['final']). 4.05/4.32 cnf(c_0_10899, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),X3))|hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)!=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X5))|~c_Equiv__Relations_Oequiv(X1,X5,X3)), inference(split_conjunct,[status(thm)],[c_0_5025]), ['final']). 4.05/4.32 cnf(c_0_10900, 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))), inference(rw,[status(thm)],[c_0_6407, c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_10901, 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,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_6408]), ['final']). 4.05/4.32 cnf(c_0_10902, 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,esk279_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_6409, c_0_4523]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10903, plain, (X4=X5|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X3))|~c_Relation_Ototal__on(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X2))), inference(split_conjunct,[status(thm)],[c_0_6410]), ['final']). 4.05/4.32 cnf(c_0_10904, 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,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)))=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))), inference(split_conjunct,[status(thm)],[c_0_6411]), ['final']). 4.05/4.32 cnf(c_0_10905, 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_6412]), ['final']). 4.05/4.32 cnf(c_0_10906, 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_6413]), ['final']). 4.05/4.32 cnf(c_0_10907, plain, (c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))=X5|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))|~c_Relation_Osingle__valued(X1,X2,hAPP(c_Relation_Oconverse(X2,X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6414]), ['final']). 4.05/4.32 cnf(c_0_10908, 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,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6415]), ['final']). 4.05/4.32 cnf(c_0_10909, 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_6416]), ['final']). 4.05/4.32 cnf(c_0_10910, 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_6417]), ['final']). 4.05/4.32 cnf(c_0_10911, 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_6418]), ['final']). 4.05/4.32 cnf(c_0_10912, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X3,tc_HOL_Obool)),X2),X5))=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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_6419]), ['final']). 4.05/4.32 cnf(c_0_10913, 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,esk259_6(X3,X2,X1,X4,X5,X6))),hAPP(X3,esk259_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_6420]), ['final']). 4.05/4.32 cnf(c_0_10914, plain, (hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~c_Equiv__Relations_Oequiv(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X3))), inference(split_conjunct,[status(thm)],[c_0_6421]), ['final']). 4.05/4.32 cnf(c_0_10915, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))|X3=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X6),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_6275]), ['final']). 4.05/4.32 cnf(c_0_10916, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6422]), ['final']). 4.05/4.32 cnf(c_0_10917, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X3,X2))),X2)=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))|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_6423, c_0_4950]), c_0_4950]), ['final']). 4.05/4.32 cnf(c_0_10918, 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_6424]), ['final']). 4.05/4.32 cnf(c_0_10919, 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_6425]), ['final']). 4.05/4.32 cnf(c_0_10920, 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_6426]), ['final']). 4.05/4.32 cnf(c_0_10921, 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)),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_OINFI(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_5885]), ['final']). 4.05/4.32 cnf(c_0_10922, 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_6427]), ['final']). 4.05/4.32 cnf(c_0_10923, plain, (c_Map_Orestrict__map(X1,X4,X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Orestrict__map(X1,X4,X5,X3)),X2),c_Option_Ooption_ONone(X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6428]), ['final']). 4.05/4.32 cnf(c_0_10924, 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),esk508_4(X4,X3,X1,X2)),X3)=hAPP(hAPP(c_List_Otake(X2),esk508_4(X4,X3,X1,X2)),X1)|~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_5029]), ['final']). 4.05/4.32 cnf(c_0_10925, 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_5884]), ['final']). 4.05/4.32 cnf(c_0_10926, 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_6429]), ['final']). 4.05/4.32 cnf(c_0_10927, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk134_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_6430]), ['final']). 4.05/4.32 cnf(c_0_10928, plain, (c_Enum_Oenum__the(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_6431, c_0_6300]), ['final']). 4.05/4.32 cnf(c_0_10929, 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_6432, c_0_5131]), c_0_6433])])]), ['final']). 4.05/4.32 cnf(c_0_10930, 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_6434]), ['final']). 4.05/4.32 cnf(c_0_10931, 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_6435, c_0_6436]), ['final']). 4.05/4.32 cnf(c_0_10932, 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)),X3)),X2)!=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_6437]), ['final']). 4.05/4.32 cnf(c_0_10933, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk259_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_6420]), ['final']). 4.05/4.32 cnf(c_0_10934, 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_6438]), ['final']). 4.05/4.32 cnf(c_0_10935, plain, (hAPP(c_Fun_Ocomp(X2,X2,X6,hAPP(X3,X7)),hAPP(c_Fun_Ocomp(X2,X2,X6,hAPP(X4,X5)),X8))=hAPP(c_Fun_Ocomp(X2,X2,X6,hAPP(X4,X5)),hAPP(c_Fun_Ocomp(X2,X2,X6,hAPP(X3,X7)),X8))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_6439]), ['final']). 4.05/4.32 cnf(c_0_10936, 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))))),esk390_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_6440]), ['final']). 4.05/4.32 cnf(c_0_10937, 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_6441]), ['final']). 4.05/4.32 cnf(c_0_10938, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6442]), ['final']). 4.05/4.32 cnf(c_0_10939, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Int_Onumber__ring(X1)|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6443, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), ['final']). 4.05/4.32 cnf(c_0_10940, plain, (hBOOL(hAPP(hAPP(c_member(X2),X4),X3))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X5,X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),X6),X3))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),X6),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6444]), ['final']). 4.05/4.32 cnf(c_0_10941, 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_6445, c_0_6340]), ['final']). 4.05/4.32 cnf(c_0_10942, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk1_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_6446]), ['final']). 4.05/4.32 cnf(c_0_10943, plain, (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)))=hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6))), inference(split_conjunct,[status(thm)],[c_0_6447]), ['final']). 4.05/4.32 cnf(c_0_10944, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Ozero__class_Ozero(X1)=X3|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X5),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_6448]), ['final']). 4.05/4.32 cnf(c_0_10945, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk313_6(X2,X3,X4,X5,X1,X6)),X5))|hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X3),X2),X5)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X4),X2),X5)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~class_Groups_Oab__semigroup__mult(X6)), inference(split_conjunct,[status(thm)],[c_0_6449]), ['final']). 4.05/4.32 cnf(c_0_10946, 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_6450]), ['final']). 4.05/4.32 cnf(c_0_10947, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),X4)=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))))))|~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_6451]), ['final']). 4.05/4.32 cnf(c_0_10948, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|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_6452]), ['final']). 4.05/4.32 cnf(c_0_10949, 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_6453]), ['final']). 4.05/4.32 cnf(c_0_10950, 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_6454]), ['final']). 4.05/4.32 cnf(c_0_10951, 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_6455]), ['final']). 4.05/4.32 cnf(c_0_10952, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),X6))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),hAPP(c_Set_Oimage(X1,X2,X3),X6))|~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X4))), inference(split_conjunct,[status(thm)],[c_0_6456]), ['final']). 4.05/4.32 cnf(c_0_10953, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),X6))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),hAPP(c_Set_Oimage(X1,X2,X3),X6))|~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X4))), inference(split_conjunct,[status(thm)],[c_0_6457]), ['final']). 4.05/4.32 cnf(c_0_10954, 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_6458]), ['final']). 4.05/4.32 cnf(c_0_10955, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk95_5(X2,X3,X4,X1,X5)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X2),X4)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X4|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Ocomm__monoid__add(X5)|~class_Groups_Oordered__cancel__ab__semigroup__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6459]), ['final']). 4.05/4.32 cnf(c_0_10956, 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_6460]), ['final']). 4.05/4.32 cnf(c_0_10957, plain, (hAPP(hAPP(X5,hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),X3),X7)),X8)),X6)=hAPP(hAPP(X3,hAPP(hAPP(X5,X7),X6)),hAPP(hAPP(X5,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_6461]), ['final']). 4.05/4.32 cnf(c_0_10958, 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,esk134_5(X3,X2,X4,X5,X1))),hAPP(X3,esk134_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_6430]), ['final']). 4.05/4.32 cnf(c_0_10959, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk348_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_6462]), ['final']). 4.05/4.32 cnf(c_0_10960, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk207_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_6463]), ['final']). 4.05/4.32 cnf(c_0_10961, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk492_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_6464]), ['final']). 4.05/4.32 cnf(c_0_10962, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),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),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__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_6465]), ['final']). 4.05/4.32 cnf(c_0_10963, 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_6466]), ['final']). 4.05/4.32 cnf(c_0_10964, 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,esk279_5(X5,X3,X4,X2,X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6467, c_0_4523]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10965, 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,esk172_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_6468, c_0_4915]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_10966, 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_6469, c_0_6470]), ['final']). 4.05/4.32 cnf(c_0_10967, plain, (X4=hAPP(c_Map_Omap__of(X1,X3),hAPP(hAPP(c_List_Omap(X1,tc_prod(X1,X3)),hAPP(hAPP(c_COMBS(X1,X3,tc_prod(X1,X3)),c_Product__Type_OPair(X1,X3)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X3),X3,X1),c_Option_Othe(X3)),X4))),X2))|hAPP(c_List_Oset(X1),X2)!=c_Map_Odom(X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_6471]), ['final']). 4.05/4.32 cnf(c_0_10968, 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_6472]), ['final']). 4.05/4.32 cnf(c_0_10969, plain, (hAPP(c_Set_Oimage(X1,X4,hAPP(hAPP(hAPP(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_6473]), ['final']). 4.05/4.32 cnf(c_0_10970, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_3(X1,X2,X3)))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_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_6474, c_0_4795]), c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_10971, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X2,tc_HOL_Obool)),X3))=hAPP(c_Finite__Set_Ocard(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk104_3(X1,X3,X2)),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),esk105_3(X1,X3,X2)),esk106_3(X1,X3,X2))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3)))), inference(csr,[status(thm)],[c_0_6475, c_0_6378]), ['final']). 4.05/4.32 cnf(c_0_10972, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X2,X1)),X3))|~c_Enum_Oall__n__lists(X1,hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_HOL_Obool,tc_List_Olist(X1)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(X1)),tc_fun(X2,X1),tc_List_Olist(X1)),c_Fun_Ocomp(tc_Option_Ooption(X1),X1,X2,c_Option_Othe(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X2,X1)),tc_fun(X2,tc_Option_Ooption(X1)),tc_List_Olist(X1)),c_Map_Omap__of(X2,X1)),hAPP(c_List_Ozip(X2,X1),c_Enum_Oenum__class_Oenum(X2))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_Enum_Oenum__class_Oenum(X2)))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_6156]), ['final']). 4.05/4.32 cnf(c_0_10973, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X2,X1)),X3))|~c_Enum_Oex__n__lists(X1,hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_HOL_Obool,tc_List_Olist(X1)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(X1)),tc_fun(X2,X1),tc_List_Olist(X1)),c_Fun_Ocomp(tc_Option_Ooption(X1),X1,X2,c_Option_Othe(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X2,X1)),tc_fun(X2,tc_Option_Ooption(X1)),tc_List_Olist(X1)),c_Map_Omap__of(X2,X1)),hAPP(c_List_Ozip(X2,X1),c_Enum_Oenum__class_Oenum(X2))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_Enum_Oenum__class_Oenum(X2)))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_6153]), ['final']). 4.05/4.32 cnf(c_0_10974, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_3(X1,X2,X3)))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_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_6476, c_0_4795]), c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_10975, 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_6477, c_0_5201]), c_0_5201]), ['final']). 4.05/4.32 cnf(c_0_10976, 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X3)),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),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))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6478]), ['final']). 4.05/4.32 cnf(c_0_10977, 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),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))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),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_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X3)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6479]), ['final']). 4.05/4.32 cnf(c_0_10978, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X2,tc_HOL_Obool)),X3))=hAPP(c_Finite__Set_Ocard(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk106_3(X1,X3,X2)),X3))|hAPP(c_Finite__Set_Ocard(X2),esk104_3(X1,X3,X2))!=X1|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3)))), inference(csr,[status(thm)],[c_0_6480, c_0_6378]), ['final']). 4.05/4.32 cnf(c_0_10979, 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))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6481, c_0_6268]), c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_10980, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X2,tc_HOL_Obool)),X3))=hAPP(c_Finite__Set_Ocard(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk105_3(X1,X3,X2)),X3))|hAPP(c_Finite__Set_Ocard(X2),esk104_3(X1,X3,X2))!=X1|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3)))), inference(csr,[status(thm)],[c_0_6482, c_0_6378]), ['final']). 4.05/4.32 cnf(c_0_10981, 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_6483]), ['final']). 4.05/4.32 cnf(c_0_10982, 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)),esk415_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_6484]), ['final']). 4.05/4.32 cnf(c_0_10983, plain, (c_FunDef_Oreduction__pair(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)))), inference(split_conjunct,[status(thm)],[c_0_6180]), ['final']). 4.05/4.32 cnf(c_0_10984, 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_6485]), ['final']). 4.05/4.32 cnf(c_0_10985, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3)))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_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_6486, c_0_4795]), c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_10986, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3)))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_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_6487, c_0_4795]), c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_10987, 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),esk64_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_6488]), ['final']). 4.05/4.32 cnf(c_0_10988, 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_6489]), ['final']). 4.05/4.32 cnf(c_0_10989, 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_6490]), ['final']). 4.05/4.32 cnf(c_0_10990, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk350_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_5606]), ['final']). 4.05/4.32 cnf(c_0_10991, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk71_2(X1,X2)))))|hBOOL(hAPP(X1,esk72_2(X1,X2)))|hBOOL(hAPP(X1,esk70_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_6491, c_0_6492]), ['final']). 4.05/4.32 cnf(c_0_10992, 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_6493]), ['final']). 4.05/4.32 cnf(c_0_10993, 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_6494]), ['final']). 4.05/4.32 cnf(c_0_10994, 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_5080]), ['final']). 4.05/4.32 cnf(c_0_10995, 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_6495]), ['final']). 4.05/4.32 cnf(c_0_10996, 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_6496]), ['final']). 4.05/4.32 cnf(c_0_10997, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6497, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), ['final']). 4.05/4.32 cnf(c_0_10998, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6498, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), ['final']). 4.05/4.32 cnf(c_0_10999, 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_6499]), ['final']). 4.05/4.32 cnf(c_0_11000, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk250_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),X4))=hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X1,X5),X2),hAPP(c_List_Ofilter(X1,X3),X4)))|~class_Groups_Omonoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6500]), ['final']). 4.05/4.32 cnf(c_0_11001, 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),esk184_4(X3,X4,X2,X1))),esk183_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_5065]), ['final']). 4.05/4.32 cnf(c_0_11002, 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_6501]), ['final']). 4.05/4.32 cnf(c_0_11003, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6502, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), ['final']). 4.05/4.32 cnf(c_0_11004, 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_6503]), ['final']). 4.05/4.32 cnf(c_0_11005, plain, (hBOOL(hAPP(hAPP(X1,esk38_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),esk39_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk38_3(X1,X2,X3)),esk39_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_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_6504, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11006, 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,esk419_8(X6,X3,X5,X5,X4,X4,X1,X2))!=hAPP(X6,esk419_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_6505])]), ['final']). 4.05/4.32 cnf(c_0_11007, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk232_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,esk231_4(X1,X2,X3,X4)))),hAPP(X2,esk231_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_6506, c_0_5669]), ['final']). 4.05/4.32 cnf(c_0_11008, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk232_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,esk231_4(X2,X3,X4,X1)))),hAPP(X3,esk231_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_6507, c_0_5669]), ['final']). 4.05/4.32 cnf(c_0_11009, 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_6508]), ['final']). 4.05/4.32 cnf(c_0_11010, 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_6509]), ['final']). 4.05/4.32 cnf(c_0_11011, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6510, c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), ['final']). 4.05/4.32 cnf(c_0_11012, 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_6511]), ['final']). 4.05/4.32 cnf(c_0_11013, plain, (X2=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk209_7(X2,X3,X4,X5,X6,X7,X1)),esk210_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_6387]), ['final']). 4.05/4.32 cnf(c_0_11014, 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_6512, c_0_5131])]), ['final']). 4.05/4.32 cnf(c_0_11015, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk319_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),esk317_2(X2,X1)))), inference(rw,[status(thm)],[c_0_6513, c_0_4767]), ['final']). 4.05/4.32 cnf(c_0_11016, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk318_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),esk317_2(X2,X1)))), inference(rw,[status(thm)],[c_0_6514, c_0_4767]), ['final']). 4.05/4.32 cnf(c_0_11017, plain, (hAPP(hAPP(X3,hAPP(X6,X7)),hAPP(X6,X8))=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)))|~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_6515]), ['final']). 4.05/4.32 cnf(c_0_11018, 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),esk510_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk510_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_6370]), ['final']). 4.05/4.32 cnf(c_0_11019, plain, (hAPP(hAPP(c_List_Odrop(X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_List_OtakeWhile(X4,X1,X2))),X2)=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))|~hBOOL(hAPP(X1,esk230_4(X2,X1,X3,X4)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6516, c_0_4950]), c_0_4950]), ['final']). 4.05/4.32 cnf(c_0_11020, 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_6517]), ['final']). 4.05/4.32 cnf(c_0_11021, plain, (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))=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(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_6518]), ['final']). 4.05/4.32 cnf(c_0_11022, 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_6519, c_0_5201]), c_0_6520]), c_0_4920]), ['final']). 4.05/4.32 cnf(c_0_11023, 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_6521]), ['final']). 4.05/4.32 cnf(c_0_11024, 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_4647]), ['final']). 4.05/4.32 cnf(c_0_11025, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5122]), ['final']). 4.05/4.32 cnf(c_0_11026, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Set_Oinsert(X3),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X2),X5))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X3),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_5866]), ['final']). 4.05/4.32 cnf(c_0_11027, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),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))))|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_6522]), ['final']). 4.05/4.32 cnf(c_0_11028, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk210_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_6387]), ['final']). 4.05/4.32 cnf(c_0_11029, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk209_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_6387]), ['final']). 4.05/4.32 cnf(c_0_11030, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X2))|hAPP(X1,esk392_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_6247]), ['final']). 4.05/4.32 cnf(c_0_11031, plain, (c_Groups_Oone__class_Oone(X1)=X2|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Groups_Oone__class_Oone(X1)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(c_Power_Opower__class_Opower(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_6523]), ['final']). 4.05/4.32 cnf(c_0_11032, 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_6524]), ['final']). 4.05/4.32 cnf(c_0_11033, 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))|c_Groups_Oone__class_Oone(X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),X6)), inference(split_conjunct,[status(thm)],[c_0_6525]), ['final']). 4.05/4.32 cnf(c_0_11034, 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))|c_Groups_Oone__class_Oone(X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),X6)), inference(split_conjunct,[status(thm)],[c_0_6526]), ['final']). 4.05/4.32 cnf(c_0_11035, 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_6527]), ['final']). 4.05/4.32 cnf(c_0_11036, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X2))|hAPP(X1,esk326_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_6248]), ['final']). 4.05/4.32 cnf(c_0_11037, 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,esk366_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_6249]), ['final']). 4.05/4.32 cnf(c_0_11038, 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,esk150_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_6250]), ['final']). 4.05/4.32 cnf(c_0_11039, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X5),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3)))),hAPP(hAPP(c_List_Oappend(X3),X6),hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_Olist_ONil(X3))))),c_List_Olistrel1(X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_6275]), ['final']). 4.05/4.32 cnf(c_0_11040, 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_6528]), ['final']). 4.05/4.32 cnf(c_0_11041, 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_6529]), ['final']). 4.05/4.32 cnf(c_0_11042, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk493_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_6530]), ['final']). 4.05/4.32 cnf(c_0_11043, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk238_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_6531]), ['final']). 4.05/4.32 cnf(c_0_11044, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk518_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_6532]), ['final']). 4.05/4.32 cnf(c_0_11045, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk178_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_6533]), ['final']). 4.05/4.32 cnf(c_0_11046, 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_6534]), ['final']). 4.05/4.32 cnf(c_0_11047, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),esk317_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)))|esk319_2(X1,X2)!=esk318_2(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1))), inference(rw,[status(thm)],[c_0_6535, c_0_4767]), ['final']). 4.05/4.32 cnf(c_0_11048, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X2,tc_HOL_Obool)),X3))=hAPP(c_Finite__Set_Ocard(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk104_3(X1,X3,X2)),X3))|esk106_3(X1,X3,X2)!=esk105_3(X1,X3,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3)))), inference(csr,[status(thm)],[c_0_6536, c_0_6378]), ['final']). 4.05/4.32 cnf(c_0_11049, 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,esk182_5(X3,X4,X5,X2,X1)))),hAPP(X2,esk182_5(X3,X4,X5,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X5)))), inference(split_conjunct,[status(thm)],[c_0_6537]), ['final']). 4.05/4.32 cnf(c_0_11050, 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),esk165_6(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)),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6538])]), ['final']). 4.05/4.32 cnf(c_0_11051, 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_6539]), ['final']). 4.05/4.32 cnf(c_0_11052, 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_6540]), ['final']). 4.05/4.32 cnf(c_0_11053, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk408_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_6541]), ['final']). 4.05/4.32 cnf(c_0_11054, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk388_5(X2,X3,X4,X5,X1)),X4)),X2))|X3=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_6330]), ['final']). 4.05/4.32 cnf(c_0_11055, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk175_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_6327]), ['final']). 4.05/4.32 cnf(c_0_11056, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__upds(X1,X2,X3,X4,X5)),X6),hAPP(c_Option_Ooption_OSome(X2),X7))=c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4),hAPP(hAPP(c_List_Olist_OCons(X2),X7),X5))|hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),X4)))), inference(rw,[status(thm)],[c_0_6542, c_0_6289]), ['final']). 4.05/4.32 cnf(c_0_11057, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk407_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_6541]), ['final']). 4.05/4.32 cnf(c_0_11058, 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_6543]), ['final']). 4.05/4.32 cnf(c_0_11059, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk71_2(X1,X2)))))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk73_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|hBOOL(hAPP(X1,esk70_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_6544, c_0_6492]), ['final']). 4.05/4.32 cnf(c_0_11060, plain, (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))))))=hAPP(X6,X7)|~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_6545]), ['final']). 4.05/4.32 cnf(c_0_11061, 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_6546, c_0_5695]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_11062, 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_6547]), ['final']). 4.05/4.32 cnf(c_0_11063, 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_6548, c_0_5695]), c_0_5696]), c_0_5201]), ['final']). 4.05/4.32 cnf(c_0_11064, 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_6549]), ['final']). 4.05/4.32 cnf(c_0_11065, 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_6550]), ['final']). 4.05/4.32 cnf(c_0_11066, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X5),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4)))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_6551]), ['final']). 4.05/4.32 cnf(c_0_11067, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X2,tc_Option_Ooption(X1)),X3),X4),hAPP(c_Option_Ooption_OSome(X1),X5))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_6552]), ['final']). 4.05/4.32 cnf(c_0_11068, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6553, c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), ['final']). 4.05/4.32 cnf(c_0_11069, plain, (hAPP(X2,X3)=hAPP(X2,X4)|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))=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))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6554]), ['final']). 4.05/4.32 cnf(c_0_11070, plain, (hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))|~hBOOL(hAPP(hAPP(hAPP(X1,esk160_4(X1,X2,X3,X4)),esk161_4(X1,X2,X3,X4)),esk162_4(X1,X2,X3,X4)))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))), inference(split_conjunct,[status(thm)],[c_0_4947]), ['final']). 4.05/4.32 cnf(c_0_11071, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk414_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_6484]), ['final']). 4.05/4.32 cnf(c_0_11072, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk63_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_6488]), ['final']). 4.05/4.32 cnf(c_0_11073, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk45_4(X1,X2,X3,X4)),esk44_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_6555]), ['final']). 4.05/4.32 cnf(c_0_11074, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk240_4(X1,X2,X3,X4)),esk239_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_6556, c_0_5165]), ['final']). 4.05/4.32 cnf(c_0_11075, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk317_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),esk318_2(X2,X1))),hAPP(c_List_Oset(X1),esk319_2(X2,X1)))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))), inference(rw,[status(thm)],[c_0_6557, c_0_4767]), ['final']). 4.05/4.32 cnf(c_0_11076, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(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(c_Set_Oimage(X1,X1,X2),X3))|~class_Lattices_Oab__semigroup__idem__mult(X1)|hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk450_3(X3,X2,X1)),esk451_3(X3,X2,X1)))!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,esk450_3(X3,X2,X1))),hAPP(X2,esk451_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6558]), ['final']). 4.05/4.32 cnf(c_0_11077, plain, (X1=hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,esk511_8(X5,X6,X4,X7,X8,X1,X3,X2))),hAPP(X6,esk512_8(X5,X6,X4,X7,X8,X1,X3,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),X1),hAPP(c_Set_Oimage(tc_prod(X8,X7),tc_prod(X2,X3),c_Product__Type_Omap__pair(X8,X2,X7,X3,X4,X6)),X5)))), inference(split_conjunct,[status(thm)],[c_0_6373]), ['final']). 4.05/4.32 cnf(c_0_11078, 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_6559]), ['final']). 4.05/4.32 cnf(c_0_11079, 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_6560, c_0_6561]), c_0_5669]), ['final']). 4.05/4.32 cnf(c_0_11080, 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_6562]), ['final']). 4.05/4.32 cnf(c_0_11081, 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(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(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_5086]), ['final']). 4.05/4.32 cnf(c_0_11082, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X4))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_6563]), ['final']). 4.05/4.32 cnf(c_0_11083, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk44_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_6555]), ['final']). 4.05/4.32 cnf(c_0_11084, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk239_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_6564, c_0_5165]), ['final']). 4.05/4.32 cnf(c_0_11085, 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_6565, c_0_5201]), ['final']). 4.05/4.32 cnf(c_0_11086, plain, (X5=X6|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X6))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X6),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X7),X4)))|~c_Equiv__Relations_Oequiv(X1,X7,X4)), inference(split_conjunct,[status(thm)],[c_0_5078]), ['final']). 4.05/4.32 cnf(c_0_11087, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X3))|~c_Equiv__Relations_Oequiv(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))))), inference(split_conjunct,[status(thm)],[c_0_6566]), ['final']). 4.05/4.32 cnf(c_0_11088, 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_6567]), ['final']). 4.05/4.32 cnf(c_0_11089, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk404_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk403_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_6568]), ['final']). 4.05/4.32 cnf(c_0_11090, 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_6569]), ['final']). 4.05/4.32 cnf(c_0_11091, 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_6570]), ['final']). 4.05/4.32 cnf(c_0_11092, 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_6571]), ['final']). 4.05/4.32 cnf(c_0_11093, 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_6572]), ['final']). 4.05/4.32 cnf(c_0_11094, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),X1),X2),X4)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),X3),X2),X4)|hAPP(X1,esk313_6(X2,X1,X3,X4,X5,X6))!=hAPP(X3,esk313_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_6449]), ['final']). 4.05/4.32 cnf(c_0_11095, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk388_5(X2,X3,X4,X5,X1)),X4)),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_6330]), ['final']). 4.05/4.32 cnf(c_0_11096, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk175_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_6327]), ['final']). 4.05/4.32 cnf(c_0_11097, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6573, c_0_4519]), c_0_4519]), c_0_4519]), ['final']). 4.05/4.32 cnf(c_0_11098, 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_6574]), ['final']). 4.05/4.32 cnf(c_0_11099, 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_6575]), ['final']). 4.05/4.32 cnf(c_0_11100, 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,esk147_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_6576]), ['final']). 4.05/4.32 cnf(c_0_11101, 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,esk34_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_6342]), ['final']). 4.05/4.32 cnf(c_0_11102, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X6),hAPP(c_Fun_Ocomp(X3,X6,X5,X1),X2)),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X6),X1),hAPP(c_Set_Oimage(X5,X3,X2),X4))|hAPP(X1,hAPP(X2,esk497_6(X3,X1,X2,X4,X5,X6)))!=c_Groups_Ozero__class_Ozero(X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Ocomm__monoid__add(X6)), inference(split_conjunct,[status(thm)],[c_0_6400]), ['final']). 4.05/4.32 cnf(c_0_11103, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk187_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_6577, c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_11104, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk185_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_6578, c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_11105, plain, (hAPP(hAPP(c_List_Ozip(X1,X3),hAPP(hAPP(c_List_Oappend(X1),X2),X5)),hAPP(hAPP(c_List_Oappend(X3),X4),X6))=hAPP(hAPP(c_List_Oappend(tc_prod(X1,X3)),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4)),hAPP(hAPP(c_List_Ozip(X1,X3),X5),X6))|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_6579]), ['final']). 4.05/4.32 cnf(c_0_11106, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk102_3(X2,X3,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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))=hAPP(c_Finite__Set_Ocard(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_6580]), ['final']). 4.05/4.32 cnf(c_0_11107, 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_6581]), ['final']). 4.05/4.32 cnf(c_0_11108, 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_6582]), ['final']). 4.05/4.32 cnf(c_0_11109, 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_6583]), ['final']). 4.05/4.32 cnf(c_0_11110, 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))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6584, c_0_6268]), c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_11111, plain, (X4=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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,esk76_4(X4,X3,X2,X1)),esk77_4(X4,X3,X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk76_4(X4,X3,X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk77_4(X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_6585]), ['final']). 4.05/4.32 cnf(c_0_11112, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk492_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_6464]), ['final']). 4.05/4.32 cnf(c_0_11113, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk348_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_6462]), ['final']). 4.05/4.32 cnf(c_0_11114, 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__flat(X3,c_Lazy__Sequence_Ohb__map(X2,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X3)),hAPP(hAPP(c_COMBC(X2,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X3))),X5),X1),hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))), inference(rw,[status(thm)],[c_0_6586, c_0_6587]), ['final']). 4.05/4.32 cnf(c_0_11115, 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_6588]), ['final']). 4.05/4.32 cnf(c_0_11116, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_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_6589, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11117, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_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)),esk364_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_6590, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11118, 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_6591, c_0_5696]), ['final']). 4.05/4.32 cnf(c_0_11119, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk207_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_6463]), ['final']). 4.05/4.32 cnf(c_0_11120, 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)),X5),X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,X4)))|hAPP(X5,X2)!=hAPP(X5,X3)), inference(split_conjunct,[status(thm)],[c_0_6524]), ['final']). 4.05/4.32 cnf(c_0_11121, plain, (c_Map_Omap__upds(X3,X1,c_Map_Orestrict__map(X3,X1,X6,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X5),hAPP(c_List_Oset(X3),X4))),X4,X2)=c_Map_Orestrict__map(X3,X1,c_Map_Omap__upds(X3,X1,X6,X4,X2),X5)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_List_Oset(X3),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_6592]), ['final']). 4.05/4.32 cnf(c_0_11122, plain, (X1=X2|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X1),X6)),X2),X7)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X4),X5),X2),X7)),X1),X6)), inference(split_conjunct,[status(thm)],[c_0_6593]), ['final']). 4.05/4.32 cnf(c_0_11123, 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_6594]), ['final']). 4.05/4.32 cnf(c_0_11124, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),esk516_3(X1,X2,X3))),esk517_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),esk516_3(X1,X2,X3)),esk517_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_6595, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11125, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))|c_Map_Omap__add(X1,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),X5),X2),hAPP(c_Option_Ooption_OSome(X3),X6)),X4)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),c_Map_Omap__add(X1,X3,X5,X4)),X2),hAPP(c_Option_Ooption_OSome(X3),X6))), inference(split_conjunct,[status(thm)],[c_0_6596]), ['final']). 4.05/4.32 cnf(c_0_11126, 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_6597]), ['final']). 4.05/4.32 cnf(c_0_11127, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk255_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_6598]), ['final']). 4.05/4.32 cnf(c_0_11128, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk9_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_6599]), ['final']). 4.05/4.32 cnf(c_0_11129, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk309_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_6600]), ['final']). 4.05/4.32 cnf(c_0_11130, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk112_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_6601]), ['final']). 4.05/4.32 cnf(c_0_11131, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2)=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))|~c_Nat__Transfer_Onat__set(X1)|~c_Nat__Transfer_Onat__set(X2)), inference(split_conjunct,[status(thm)],[c_0_6602]), ['final']). 4.05/4.32 cnf(c_0_11132, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))|X3=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olistrel1(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_6363]), ['final']). 4.05/4.32 cnf(c_0_11133, plain, (hAPP(X1,esk232_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,esk231_4(X2,X1,X3,X4)))),hAPP(X1,esk231_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_6603, c_0_5669]), ['final']). 4.05/4.32 cnf(c_0_11134, 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_6604, c_0_6605]), c_0_6606]), ['final']). 4.05/4.32 cnf(c_0_11135, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X2,X4)))|hAPP(hAPP(c_List_Olist_OCons(X5),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_Olist_OCons(X5),X4),X6))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6607]), ['final']). 4.05/4.32 cnf(c_0_11136, 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_6608]), c_0_6609]), c_0_6610]), ['final']). 4.05/4.32 cnf(c_0_11137, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_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),esk362_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_6611, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11138, plain, (c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X2,X5),tc_HOL_Obool))=hAPP(c_Set_Oimage(tc_prod(X1,X4),tc_prod(X2,X5),c_Product__Type_Omap__pair(X1,X2,X4,X5,X3,X6)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X4),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(X4,X5,X6),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_6612]), ['final']). 4.05/4.32 cnf(c_0_11139, 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,esk324_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_6353]), ['final']). 4.05/4.32 cnf(c_0_11140, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk411_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_6613]), ['final']). 4.05/4.32 cnf(c_0_11141, 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_6614, c_0_4950]), c_0_4950]), ['final']). 4.05/4.32 cnf(c_0_11142, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_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)),esk364_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_6615, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11143, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))|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)))=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)))|~class_Groups_Ocomm__monoid__add(X3)), inference(split_conjunct,[status(thm)],[c_0_6616]), ['final']). 4.05/4.32 cnf(c_0_11144, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6617, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11145, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk249_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_6618]), ['final']). 4.05/4.32 cnf(c_0_11146, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk420_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_6619]), ['final']). 4.05/4.32 cnf(c_0_11147, 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_6620]), ['final']). 4.05/4.32 cnf(c_0_11148, 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_6621, c_0_5131]), c_0_6433])])]), ['final']). 4.05/4.32 cnf(c_0_11149, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6622, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11150, 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_6623, c_0_5131]), c_0_6433])]), c_0_6624])]), ['final']). 4.05/4.32 cnf(c_0_11151, 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))|esk498_6(X1,X2,X3,X4,X5,X6)!=esk497_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_6400]), ['final']). 4.05/4.32 cnf(c_0_11152, plain, (hAPP(c_Map_Omap__of(X1,X2),X4)=hAPP(c_Map_Omap__of(X1,X2),X3)|hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),esk438_4(X3,X4,X2,X1))!=hAPP(hAPP(c_Map_Omap__of(X1,X2),X4),esk438_4(X3,X4,X2,X1))|hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))!=hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4))), inference(split_conjunct,[status(thm)],[c_0_6374]), ['final']). 4.05/4.32 cnf(c_0_11153, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6625, c_0_4795]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), ['final']). 4.05/4.32 cnf(c_0_11154, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6626, c_0_4795]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), ['final']). 4.05/4.32 cnf(c_0_11155, plain, (hBOOL(hAPP(hAPP(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk29_3(X1,X2,X3))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk30_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk30_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_6627]), ['final']). 4.05/4.32 cnf(c_0_11156, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2)),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X3))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|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_6628]), ['final']). 4.05/4.32 cnf(c_0_11157, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_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_6629, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11158, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_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)),esk355_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_6630, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11159, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4)=X5|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hAPP(hAPP(c_List_Oappend(X1),X2),X5)!=hAPP(hAPP(c_List_Oappend(X1),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_5087]), ['final']). 4.05/4.32 cnf(c_0_11160, 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,esk1_4(X2,X1,X3,X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_6446]), ['final']). 4.05/4.32 cnf(c_0_11161, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2)),X2))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk314_2(X2,X1)),esk315_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk314_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk315_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_6631]), ['final']). 4.05/4.32 cnf(c_0_11162, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X5),X4))|~class_Groups_Oab__group__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_6632]), ['final']). 4.05/4.32 cnf(c_0_11163, plain, (hAPP(c_Map_Omap__of(X1,X2),X3)=hAPP(c_Map_Omap__of(X1,X2),X4)|hAPP(c_List_Oset(tc_prod(X1,X2)),X3)!=hAPP(c_List_Oset(tc_prod(X1,X2)),X4)|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4)))), inference(split_conjunct,[status(thm)],[c_0_6633]), ['final']). 4.05/4.32 cnf(c_0_11164, 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_6634]), ['final']). 4.05/4.32 cnf(c_0_11165, 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,esk111_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_6399]), ['final']). 4.05/4.32 cnf(c_0_11166, 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),esk419_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_6635])]), ['final']). 4.05/4.32 cnf(c_0_11167, 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),esk419_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_6636])]), ['final']). 4.05/4.32 cnf(c_0_11168, 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),esk421_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_6637])]), ['final']). 4.05/4.32 cnf(c_0_11169, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_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_6638, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11170, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk362_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_6639, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11171, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk147_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_6576]), ['final']). 4.05/4.32 cnf(c_0_11172, 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_6640, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_6641]), ['final']). 4.05/4.32 cnf(c_0_11173, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_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),esk353_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_6642, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11174, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Groups_Oone__class_Oone(X1)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),c_Nat_Osemiring__1__class_Oof__nat(X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_6643]), ['final']). 4.05/4.32 cnf(c_0_11175, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6644, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4977]), ['final']). 4.05/4.32 cnf(c_0_11176, 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_6645]), ['final']). 4.05/4.32 cnf(c_0_11177, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_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),esk364_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_6646, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11178, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk343_4(X2,X3,X4,X1)),esk342_4(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),X1),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),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_6647]), ['final']). 4.05/4.32 cnf(c_0_11179, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk323_4(X1,X2,X3,X4)),esk322_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),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_6648]), ['final']). 4.05/4.32 cnf(c_0_11180, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk296_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,esk295_3(X1,X2,X3)))),hAPP(X2,esk295_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_6649, c_0_5669]), ['final']). 4.05/4.32 cnf(c_0_11181, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk97_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,esk96_3(X1,X2,X3)))),hAPP(X2,esk96_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_6650, c_0_5669]), ['final']). 4.05/4.32 cnf(c_0_11182, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_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)),esk355_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(rw,[status(thm)],[c_0_6651, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11183, 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_6652]), ['final']). 4.05/4.32 cnf(c_0_11184, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_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),esk362_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_6653, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11185, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(c_Set_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,esk412_3(X3,X2,X1))),hAPP(X2,esk413_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk412_3(X3,X2,X1)),esk413_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6654]), ['final']). 4.05/4.32 cnf(c_0_11186, 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(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk340_3(X3,X2,X1))),hAPP(X2,esk341_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk340_3(X3,X2,X1)),esk341_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6655]), ['final']). 4.05/4.32 cnf(c_0_11187, 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_6656, c_0_5695]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_11188, 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_6657]), ['final']). 4.05/4.32 cnf(c_0_11189, 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_6658, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11190, plain, (hAPP(c_Option_Ooption_OSome(X1),X2)=hAPP(hAPP(c_Map_Omap__of(X3,X1),hAPP(c_List_Ofilter(tc_prod(X3,X1),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X1,tc_HOL_Obool),X6)),X4)),X5)|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(hAPP(c_Map_Omap__of(X3,X1),X4),X5)|~hBOOL(hAPP(hAPP(X6,X5),X2))), inference(split_conjunct,[status(thm)],[c_0_6659]), ['final']). 4.05/4.32 cnf(c_0_11191, 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_6660, c_0_5011]), c_0_5011]), c_0_6661]), ['final']). 4.05/4.32 cnf(c_0_11192, 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_5029]), ['final']). 4.05/4.32 cnf(c_0_11193, plain, (X3=X4|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)|hAPP(c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2)),hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1)),X3)))!=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2)),hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1)),X4)))), inference(split_conjunct,[status(thm)],[c_0_6662]), ['final']). 4.05/4.32 cnf(c_0_11194, plain, (hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Otake(X2),X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Odrop(X2),X1),X3))),c_List_Olist_ONil(X2)))=hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_OSuc,X1)),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6663]), ['final']). 4.05/4.32 cnf(c_0_11195, 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_6664]), ['final']). 4.05/4.32 cnf(c_0_11196, 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_6665]), ['final']). 4.05/4.32 cnf(c_0_11197, 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),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_6647]), ['final']). 4.05/4.32 cnf(c_0_11198, 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_6666]), ['final']). 4.05/4.32 cnf(c_0_11199, 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)))), inference(rw,[status(thm)],[c_0_6667, c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_11200, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_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),esk355_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(rw,[status(thm)],[c_0_6668, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11201, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk322_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_6648]), ['final']). 4.05/4.32 cnf(c_0_11202, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk232_4(X2,X3,X4,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk231_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_5104]), ['final']). 4.05/4.32 cnf(c_0_11203, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk232_4(X1,X2,X3,X4)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk231_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_5104]), ['final']). 4.05/4.32 cnf(c_0_11204, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_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_6669, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11205, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_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),esk353_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(rw,[status(thm)],[c_0_6670, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11206, plain, (hAPP(hAPP(X6,hAPP(X5,X4)),hAPP(X5,X3))=hAPP(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X4),X3))|X1!=hAPP(X2,esk461_7(X3,X4,X5,X2,X1,X6,X7))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X4))|~c_Finite__Set_Ofolding__image__simple(X8,X7,X6,X1,X2,X5)), inference(split_conjunct,[status(thm)],[c_0_6276]), ['final']). 4.05/4.32 cnf(c_0_11207, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk353_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_6671, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11208, plain, (hAPP(hAPP(c_List_Otake(X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X4)=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)))|~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_6672]), ['final']). 4.05/4.32 cnf(c_0_11209, 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_6332]), ['final']). 4.05/4.32 cnf(c_0_11210, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X5),X3)|hAPP(X5,X2)=c_Groups_Ozero__class_Ozero(X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Fields_Ofield(X4)), inference(split_conjunct,[status(thm)],[c_0_6501]), ['final']). 4.05/4.32 cnf(c_0_11211, 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_6333]), ['final']). 4.05/4.32 cnf(c_0_11212, 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_5039]), ['final']). 4.05/4.32 cnf(c_0_11213, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk505_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk504_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))), inference(split_conjunct,[status(thm)],[c_0_6673]), ['final']). 4.05/4.32 cnf(c_0_11214, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk484_6(X3,X4,X1,X5,X2,X6)),esk485_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_6674]), ['final']). 4.05/4.32 cnf(c_0_11215, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),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)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4),X5),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Groups_Oab__group__add(X4)), inference(split_conjunct,[status(thm)],[c_0_6518]), ['final']). 4.05/4.32 cnf(c_0_11216, 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_5127]), ['final']). 4.05/4.32 cnf(c_0_11217, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk483_6(X3,X4,X2,X5,X6,X1)),esk484_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_6674]), ['final']). 4.05/4.32 cnf(c_0_11218, 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),esk525_2(X2,X1)),esk526_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk525_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk526_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_6675]), ['final']). 4.05/4.32 cnf(c_0_11219, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk234_2(X2,X1)),esk235_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk234_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk235_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_6676]), ['final']). 4.05/4.32 cnf(c_0_11220, 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_6677]), ['final']). 4.05/4.32 cnf(c_0_11221, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4))|~class_Rings_Oring(X1)|~class_Int_Onumber(X1)), inference(split_conjunct,[status(thm)],[c_0_6678]), ['final']). 4.05/4.32 cnf(c_0_11222, 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_6679]), ['final']). 4.05/4.32 cnf(c_0_11223, 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_6680, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_6681]), c_0_4427]), c_0_6682]), ['final']). 4.05/4.32 cnf(c_0_11224, 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),esk516_3(X1,X2,X3)),esk517_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_5123]), ['final']). 4.05/4.32 cnf(c_0_11225, 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),esk499_3(X1,X2,X3)),esk500_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_4535]), ['final']). 4.05/4.32 cnf(c_0_11226, 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),esk214_3(X1,X2,X3)),esk215_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_4526]), ['final']). 4.05/4.32 cnf(c_0_11227, 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),esk38_3(X1,X2,X3)),esk39_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_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_5102]), ['final']). 4.05/4.32 cnf(c_0_11228, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))|~class_Int_Onumber(X1)|~class_Rings_Osemiring(X1)), inference(split_conjunct,[status(thm)],[c_0_6683]), ['final']). 4.05/4.32 cnf(c_0_11229, 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),esk29_3(X1,X2,X3)),esk30_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_6627]), ['final']). 4.05/4.32 cnf(c_0_11230, 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),esk81_3(X1,X2,X3)),esk82_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_6684]), ['final']). 4.05/4.32 cnf(c_0_11231, 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_6685]), ['final']). 4.05/4.32 cnf(c_0_11232, 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_6686, c_0_4977]), ['final']). 4.05/4.32 cnf(c_0_11233, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk185_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_6687, c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_11234, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk187_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_6688, c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_11235, plain, (c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X6),X7))=c_Map_Omap__upds(X1,X2,X3,X5,X7)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X7)),X5))))), inference(rw,[status(thm)],[c_0_6689, c_0_6289]), ['final']). 4.05/4.32 cnf(c_0_11236, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|c_Smallcheck_Osmall_H(X3,X1,X2)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X3,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_6690]), ['final']). 4.05/4.32 cnf(c_0_11237, 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_6691]), ['final']). 4.05/4.32 cnf(c_0_11238, 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_6692]), ['final']). 4.05/4.32 cnf(c_0_11239, 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_6693]), ['final']). 4.05/4.32 cnf(c_0_11240, plain, (hAPP(X4,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X6))=hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),X6)), inference(split_conjunct,[status(thm)],[c_0_6694]), ['final']). 4.05/4.32 cnf(c_0_11241, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X2,tc_HOL_Obool)),X3))=hAPP(c_Finite__Set_Ocard(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),esk105_3(X1,X3,X2)),esk106_3(X1,X3,X2))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X2),esk104_3(X1,X3,X2))!=X1|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3)))), inference(csr,[status(thm)],[c_0_6695, c_0_6378]), ['final']). 4.05/4.32 cnf(c_0_11242, 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_6696, c_0_5905]), ['final']). 4.05/4.32 cnf(c_0_11243, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk198_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk197_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_6697, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11244, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk377_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk376_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_6698, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11245, plain, (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(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(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6699]), ['final']). 4.05/4.32 cnf(c_0_11246, 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,esk90_5(X3,X2,X1,X4,X5)),hAPP(X3,esk90_5(X3,X2,X1,X4,X5)))), inference(split_conjunct,[status(thm)],[c_0_6700]), ['final']). 4.05/4.32 cnf(c_0_11247, plain, (c_Map_Oran(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3))=hAPP(c_Relation_ORange(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))), inference(rw,[status(thm)],[c_0_6701, c_0_6702]), ['final']). 4.05/4.32 cnf(c_0_11248, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=esk82_3(X1,X2,X3)|hBOOL(hAPP(hAPP(X1,esk82_3(X1,X2,X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk81_3(X1,X2,X3),esk82_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_6684]), ['final']). 4.05/4.32 cnf(c_0_11249, 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_6703]), ['final']). 4.05/4.32 cnf(c_0_11250, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_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_6704, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11251, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_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_6705, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11252, 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_6569]), ['final']). 4.05/4.32 cnf(c_0_11253, 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_6570]), ['final']). 4.05/4.32 cnf(c_0_11254, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk226_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_6706]), ['final']). 4.05/4.32 cnf(c_0_11255, 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_6707, c_0_5716]), ['final']). 4.05/4.32 cnf(c_0_11256, plain, (X1=X2|hAPP(c_List_Oset(X3),X1)!=hAPP(c_List_Oset(X3),X2)|~c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X5),X2))|~c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X5),X1))|~c_Fun_Oinj__on(X3,X4,X5,hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Oappend(X3),X1),X2)))|~class_Orderings_Olinorder(X4)|~hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(X3,X4),X5),X2)))|~hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(X3,X4),X5),X1)))), inference(rw,[status(thm)],[c_0_6708, c_0_6709]), ['final']). 4.05/4.32 cnf(c_0_11257, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk384_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_6710]), ['final']). 4.05/4.32 cnf(c_0_11258, 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_6711, c_0_4635]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_11259, 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_6571]), ['final']). 4.05/4.32 cnf(c_0_11260, 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_6574]), ['final']). 4.05/4.32 cnf(c_0_11261, plain, (hAPP(hAPP(c_List_Oappend(X1),esk329_4(X2,X3,X4,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),esk327_4(X2,X3,X4,X1)),esk330_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_6712]), ['final']). 4.05/4.32 cnf(c_0_11262, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),esk329_4(X3,X1,X4,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk328_4(X3,X1,X4,X2)),esk330_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_6712]), ['final']). 4.05/4.32 cnf(c_0_11263, plain, (X6=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)|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_5143]), ['final']). 4.05/4.32 cnf(c_0_11264, plain, (X4=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X5|hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))=hAPP(hAPP(X2,hAPP(X3,X4)),hAPP(X3,X5))|~c_Finite__Set_Ofolding__one(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|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_6713]), ['final']). 4.05/4.32 cnf(c_0_11265, 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_6714]), ['final']). 4.05/4.32 cnf(c_0_11266, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X6),hAPP(c_List_Ofilter(X2,X5),X4))=hAPP(c_List_Ofilter(X2,X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X6),X4))|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))|~hBOOL(hAPP(X5,X6))), inference(split_conjunct,[status(thm)],[c_0_6715]), ['final']). 4.05/4.32 cnf(c_0_11267, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk90_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_6700]), ['final']). 4.05/4.32 cnf(c_0_11268, 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_4647]), ['final']). 4.05/4.32 cnf(c_0_11269, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(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_6716]), ['final']). 4.05/4.32 cnf(c_0_11270, 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_6717, c_0_6641]), c_0_4635]), c_0_6718]), c_0_4795]), c_0_4977]), c_0_6719]), c_0_6720]), c_0_4635]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_11271, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)))),X3))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(rw,[status(thm)],[c_0_6721, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11272, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_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_6722, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11273, 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_6723]), ['final']). 4.05/4.32 cnf(c_0_11274, plain, (hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X1))),X1)=hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)|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_6724, c_0_4950]), ['final']). 4.05/4.32 cnf(c_0_11275, 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))), inference(rw,[status(thm)],[c_0_6725, c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_11276, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk410_5(X2,X3,X4,X5,X1)),hAPP(X3,esk409_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_6613]), ['final']). 4.05/4.32 cnf(c_0_11277, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_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_6726, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11278, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6727]), ['final']). 4.05/4.32 cnf(c_0_11279, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)))),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(rw,[status(thm)],[c_0_6728, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11280, 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_6729]), ['final']). 4.05/4.32 cnf(c_0_11281, 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_6693]), ['final']). 4.05/4.32 cnf(c_0_11282, plain, (c_Wellfounded_Oacyclic(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk125_2(X2,X1)),esk125_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_6730, c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_11283, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X3),X4)))|c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X4|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk95_5(X3,X2,X4,X5,X1))),hAPP(X3,esk95_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_6459]), ['final']). 4.05/4.32 cnf(c_0_11284, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk327_4(X2,X3,X4,X1)),esk328_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_6712]), ['final']). 4.05/4.32 cnf(c_0_11285, 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_6731]), ['final']). 4.05/4.32 cnf(c_0_11286, plain, (c_Wellfounded_Oacyclic(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk124_2(X2,X1)),esk124_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_6732, c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_11287, 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_6733, c_0_6641]), c_0_4635]), c_0_6718]), c_0_4795]), c_0_4977]), c_0_6719]), c_0_6734]), c_0_4635]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_11288, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|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),esk289_2(X2,X1)),esk290_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk289_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk290_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_6735]), ['final']). 4.05/4.32 cnf(c_0_11289, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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),esk431_2(X2,X1)),esk432_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk431_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk432_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))), inference(split_conjunct,[status(thm)],[c_0_6736]), ['final']). 4.05/4.32 cnf(c_0_11290, plain, (X1=hAPP(hAPP(c_List_Olist_OCons(X2),esk63_5(X3,X1,X4,X5,X2)),esk64_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_6488]), ['final']). 4.05/4.32 cnf(c_0_11291, plain, (X1=hAPP(hAPP(c_List_Olist_OCons(X2),esk414_5(X3,X4,X5,X1,X2)),esk415_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_6484]), ['final']). 4.05/4.32 cnf(c_0_11292, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk23_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_6737, c_0_6268]), ['final']). 4.05/4.32 cnf(c_0_11293, 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_6738, c_0_4915]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_11294, 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_6739]), ['final']). 4.05/4.32 cnf(c_0_11295, 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_6740]), ['final']). 4.05/4.32 cnf(c_0_11296, 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)),esk427_4(X3,X4,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_6187]), ['final']). 4.05/4.32 cnf(c_0_11297, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk297_6(X3,X4,X5,X2,X1,X6)),esk298_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_6741]), ['final']). 4.05/4.32 cnf(c_0_11298, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),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)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_6567]), ['final']). 4.05/4.32 cnf(c_0_11299, 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)), inference(split_conjunct,[status(thm)],[c_0_6742]), ['final']). 4.05/4.32 cnf(c_0_11300, 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_6743]), ['final']). 4.05/4.32 cnf(c_0_11301, 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_6744]), ['final']). 4.05/4.32 cnf(c_0_11302, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk71_2(X1,X2)))))|hBOOL(hAPP(X1,esk73_2(X1,X2)))|hBOOL(hAPP(X1,esk70_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_6745, c_0_6492]), ['final']). 4.05/4.32 cnf(c_0_11303, plain, (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),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),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),X3),X4)),X5))|~class_Rings_Osemiring(X1)), inference(split_conjunct,[status(thm)],[c_0_6746]), ['final']). 4.05/4.32 cnf(c_0_11304, 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_5993]), ['final']). 4.05/4.32 cnf(c_0_11305, 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_6418]), ['final']). 4.05/4.32 cnf(c_0_11306, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk85_6(X2,X3,X4,X5,X1,X6)),X6))|c_Fun_Oinj__on(X5,X4,X3,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X5,tc_HOL_Obool)),X6),X2))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X6), inference(split_conjunct,[status(thm)],[c_0_6747]), ['final']). 4.05/4.32 cnf(c_0_11307, 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_6748, c_0_6340]), ['final']). 4.05/4.32 cnf(c_0_11308, 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_6749]), ['final']). 4.05/4.32 cnf(c_0_11309, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk32_4(X1,X2,X3,X4)),esk31_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_6750]), ['final']). 4.05/4.32 cnf(c_0_11310, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk445_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_6751]), ['final']). 4.05/4.32 cnf(c_0_11311, 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_6752]), ['final']). 4.05/4.32 cnf(c_0_11312, 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_6753, c_0_6340]), ['final']). 4.05/4.32 cnf(c_0_11313, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk284_4(X2,X3,X4,X1)),esk283_4(X2,X3,X4,X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))), inference(split_conjunct,[status(thm)],[c_0_6754]), ['final']). 4.05/4.32 cnf(c_0_11314, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk426_4(X2,X3,X4,X1)),esk425_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_6755]), ['final']). 4.05/4.32 cnf(c_0_11315, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk372_4(X2,X3,X4,X1)),esk371_4(X2,X3,X4,X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X4)))|~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)),X4))), inference(split_conjunct,[status(thm)],[c_0_6756]), ['final']). 4.05/4.32 cnf(c_0_11316, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X3),X5))=hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~c_Relation_Osingle__valued(X1,X2,hAPP(c_Relation_Oconverse(X2,X1),X3))), inference(split_conjunct,[status(thm)],[c_0_6757]), ['final']). 4.05/4.32 cnf(c_0_11317, 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_6758, c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_11318, 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_6581]), ['final']). 4.05/4.32 cnf(c_0_11319, 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_6582]), ['final']). 4.05/4.32 cnf(c_0_11320, 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_6583]), ['final']). 4.05/4.32 cnf(c_0_11321, 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_6588]), ['final']). 4.05/4.32 cnf(c_0_11322, plain, (hAPP(X1,esk296_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,esk295_3(X2,X1,X3)))),hAPP(X1,esk295_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_6759, c_0_5669]), ['final']). 4.05/4.32 cnf(c_0_11323, plain, (hAPP(X1,esk97_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,esk96_3(X2,X1,X3)))),hAPP(X1,esk96_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_6760, c_0_5669]), ['final']). 4.05/4.32 cnf(c_0_11324, 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_6761]), ['final']). 4.05/4.32 cnf(c_0_11325, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),c_Map_Omap__add(X2,X1,X3,hAPP(c_Map_Omap__of(X2,X1),X4))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_6762]), ['final']). 4.05/4.32 cnf(c_0_11326, 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_6763]), ['final']). 4.05/4.32 cnf(c_0_11327, 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_6764]), ['final']). 4.05/4.32 cnf(c_0_11328, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_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,esk361_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_6765, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11329, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_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,esk363_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_6766, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11330, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X1,X2,X3,X5)|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)),X4),X5))),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),X4)))), inference(split_conjunct,[status(thm)],[c_0_6386]), ['final']). 4.05/4.32 cnf(c_0_11331, plain, (hAPP(c_Option_Ooption_OSome(X4),esk216_5(X2,X5,X4,X3,X1))=hAPP(hAPP(c_Map_Omap__of(X1,X4),hAPP(hAPP(c_List_Ozip(X1,X4),X3),X5)),X2)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5)), inference(split_conjunct,[status(thm)],[c_0_6767]), ['final']). 4.05/4.32 cnf(c_0_11332, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X3,X1),hAPP(hAPP(c_COMBB(X1,X1,X3),hAPP(c_Groups_Otimes__class_Otimes(X1),X2)),X4)),X5))|~class_Rings_Osemiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_6768]), ['final']). 4.05/4.32 cnf(c_0_11333, 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_6769]), ['final']). 4.05/4.32 cnf(c_0_11334, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_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_6770, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11335, 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_6771]), ['final']). 4.05/4.32 cnf(c_0_11336, 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_6772]), ['final']). 4.05/4.32 cnf(c_0_11337, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_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_6773, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11338, plain, (hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(c_Orderings_Oord__class_Oless(X1),X5)),X3)),X4)=c_List_OtakeWhile(X2,hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(c_Orderings_Oord__class_Oless(X1),X5)),X3),X4)|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_6774]), ['final']). 4.05/4.32 cnf(c_0_11339, plain, (X3=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X4),hAPP(c_Option_Ooption_OSome(X2),esk43_4(X4,X3,X2,X1)))|c_Map_Odom(X1,X2,X3)!=hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5852]), ['final']). 4.05/4.32 cnf(c_0_11340, plain, (hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X6)),hAPP(X4,X5))=hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X4,X6))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6))), inference(split_conjunct,[status(thm)],[c_0_6775]), ['final']). 4.05/4.32 cnf(c_0_11341, 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_6776, c_0_4523]), c_0_5205]), ['final']). 4.05/4.32 cnf(c_0_11342, 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_6777]), ['final']). 4.05/4.32 cnf(c_0_11343, 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_6778, c_0_4519]), c_0_4519]), ['final']). 4.05/4.32 cnf(c_0_11344, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6779, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), ['final']). 4.05/4.32 cnf(c_0_11345, plain, (c_List_OtakeWhile(X1,X3,X2)=hAPP(c_List_Ofilter(X1,X3),X2)|hBOOL(hAPP(hAPP(c_member(X1),esk488_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_6780, c_0_4950]), ['final']). 4.05/4.32 cnf(c_0_11346, plain, (c_Nitpick_Ofold__graph_H(X6,X7,X1,X8,X9,hAPP(hAPP(X1,X4),X5))|hAPP(hAPP(X1,X2),X3)!=hAPP(hAPP(X1,X4),X5)|~c_Nitpick_Ofold__graph_H(X6,X7,X1,X8,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X6,tc_HOL_Obool)),X9),hAPP(hAPP(c_Set_Oinsert(X6),X2),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),X3)|~hBOOL(hAPP(hAPP(c_member(X6),X2),X9))), inference(split_conjunct,[status(thm)],[c_0_6351]), ['final']). 4.05/4.32 cnf(c_0_11347, plain, (hAPP(c_List_Oset(tc_prod(X1,X2)),X3)=hAPP(c_List_Oset(tc_prod(X1,X2)),X4)|hAPP(c_Map_Omap__of(X1,X2),X3)!=hAPP(c_Map_Omap__of(X1,X2),X4)|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4)))), inference(split_conjunct,[status(thm)],[c_0_6633]), ['final']). 4.05/4.32 cnf(c_0_11348, 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_6781]), ['final']). 4.05/4.32 cnf(c_0_11349, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),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)],[c_0_6782, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), ['final']). 4.05/4.32 cnf(c_0_11350, 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_6783]), ['final']). 4.05/4.32 cnf(c_0_11351, 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_6784]), ['final']). 4.05/4.32 cnf(c_0_11352, plain, (X5=X4|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))|~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_6785]), ['final']). 4.05/4.32 cnf(c_0_11353, plain, (c_Map_Omap__le(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X5),c_Option_Ooption_ONone(X2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X4),X5),hAPP(c_Option_Ooption_OSome(X2),X6)))|~c_Map_Omap__le(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_6786]), ['final']). 4.05/4.32 cnf(c_0_11354, 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_6787]), ['final']). 4.05/4.32 cnf(c_0_11355, 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_5087]), ['final']). 4.05/4.32 cnf(c_0_11356, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X4)),X3)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))|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)|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_6788]), ['final']). 4.05/4.32 cnf(c_0_11357, 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_6789]), ['final']). 4.05/4.32 cnf(c_0_11358, 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_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_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_6790]), ['final']). 4.05/4.32 cnf(c_0_11359, 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_6791, c_0_5942]), ['final']). 4.05/4.32 cnf(c_0_11360, 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)),esk424_3(X2,X3,X1))),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_6792]), ['final']). 4.05/4.32 cnf(c_0_11361, 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_6793]), ['final']). 4.05/4.32 cnf(c_0_11362, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X6),X5)),X4)|~c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_6794]), ['final']). 4.05/4.32 cnf(c_0_11363, 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_6795, c_0_6796]), ['final']). 4.05/4.32 cnf(c_0_11364, 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_5122]), ['final']). 4.05/4.32 cnf(c_0_11365, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))=hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X4))|hAPP(c_Map_Omap__of(X1,X2),X3)!=hAPP(c_Map_Omap__of(X1,X2),X4)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6797, c_0_5304]), c_0_5304]), ['final']). 4.05/4.32 cnf(c_0_11366, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk283_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_6754]), ['final']). 4.05/4.32 cnf(c_0_11367, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk31_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_6750]), ['final']). 4.05/4.32 cnf(c_0_11368, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk371_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_6756]), ['final']). 4.05/4.32 cnf(c_0_11369, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk425_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_6755]), ['final']). 4.05/4.32 cnf(c_0_11370, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_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_6798, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11371, plain, (hAPP(hAPP(X6,X7),X9)=hAPP(hAPP(X6,X8),X10)|~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_6799]), ['final']). 4.05/4.32 cnf(c_0_11372, 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_6800]), ['final']). 4.05/4.32 cnf(c_0_11373, 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_6801]), ['final']). 4.05/4.32 cnf(c_0_11374, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_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_6802, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11375, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6803]), ['final']). 4.05/4.32 cnf(c_0_11376, 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_6804]), ['final']). 4.05/4.32 cnf(c_0_11377, plain, (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)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),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_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[c_0_6805, c_0_4867]), ['final']). 4.05/4.32 cnf(c_0_11378, plain, (hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_OSuc,X1)),X3)=hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Otake(X2),X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(hAPP(c_List_Onth(X2),X3),X1)),c_List_Olist_ONil(X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6806]), ['final']). 4.05/4.32 cnf(c_0_11379, 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_6807]), ['final']). 4.05/4.32 cnf(c_0_11380, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk206_3(X1,X2,X3)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X2))))|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_5447]), ['final']). 4.05/4.32 cnf(c_0_11381, 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_6349]), ['final']). 4.05/4.32 cnf(c_0_11382, 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),esk9_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_6599]), ['final']). 4.05/4.32 cnf(c_0_11383, 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),esk255_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_6598]), ['final']). 4.05/4.32 cnf(c_0_11384, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,X1,tc_Nat_Onat),X3),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X1),X3),X2)|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)|~c_Nat__Transfer_Onat__set(X2)), inference(split_conjunct,[status(thm)],[c_0_6808]), ['final']). 4.05/4.32 cnf(c_0_11385, 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),esk245_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_6809]), ['final']). 4.05/4.32 cnf(c_0_11386, 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_6810, c_0_5379]), ['final']). 4.05/4.32 cnf(c_0_11387, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk45_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_6555]), ['final']). 4.05/4.32 cnf(c_0_11388, 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),esk240_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_6811, c_0_5165]), ['final']). 4.05/4.32 cnf(c_0_11389, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk316_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_6812]), ['final']). 4.05/4.32 cnf(c_0_11390, 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_6813]), ['final']). 4.05/4.32 cnf(c_0_11391, 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),esk309_4(X3,X2,X4,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6600]), ['final']). 4.05/4.32 cnf(c_0_11392, 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),esk112_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_6601]), ['final']). 4.05/4.32 cnf(c_0_11393, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_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,esk353_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_6814, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11394, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_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,esk355_3(X1,X2,X3)))), inference(rw,[status(thm)],[c_0_6815, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11395, 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),esk286_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_6816]), ['final']). 4.05/4.32 cnf(c_0_11396, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk242_3(X2,X3,X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_6817]), ['final']). 4.05/4.32 cnf(c_0_11397, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk406_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_6818]), ['final']). 4.05/4.32 cnf(c_0_11398, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk361_3(X1,X2,X3)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_6819, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11399, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk363_3(X1,X2,X3)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_6820, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11400, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk61_3(X2,X3,X1)),esk61_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_6821]), ['final']). 4.05/4.32 cnf(c_0_11401, 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|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_6822]), ['final']). 4.05/4.32 cnf(c_0_11402, 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_6823]), ['final']). 4.05/4.32 cnf(c_0_11403, 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_6824]), ['final']). 4.05/4.32 cnf(c_0_11404, 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_6825]), ['final']). 4.05/4.32 cnf(c_0_11405, 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_6826]), ['final']). 4.05/4.32 cnf(c_0_11406, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_6827]), ['final']). 4.05/4.32 cnf(c_0_11407, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X6))),c_List_Olexord(X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_5080]), ['final']). 4.05/4.32 cnf(c_0_11408, 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_Olistrel1(X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_6363]), ['final']). 4.05/4.32 cnf(c_0_11409, 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_6828]), ['final']). 4.05/4.32 cnf(c_0_11410, 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_6829]), ['final']). 4.05/4.32 cnf(c_0_11411, 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_Olex(X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_5079]), ['final']). 4.05/4.32 cnf(c_0_11412, plain, (hBOOL(hAPP(X1,esk505_4(X1,X2,X3,X4)))|hBOOL(hAPP(hAPP(c_member(X4),esk504_4(X1,X2,X3,X4)),X3))|~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))), inference(split_conjunct,[status(thm)],[c_0_6673]), ['final']). 4.05/4.32 cnf(c_0_11413, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk505_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(X2,esk504_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))), inference(split_conjunct,[status(thm)],[c_0_6673]), ['final']). 4.05/4.32 cnf(c_0_11414, 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,esk165_6(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)))|~hBOOL(hAPP(X2,X4))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6830])]), ['final']). 4.05/4.32 cnf(c_0_11415, 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_6831]), ['final']). 4.05/4.32 cnf(c_0_11416, 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_6832]), ['final']). 4.05/4.32 cnf(c_0_11417, 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_6833]), ['final']). 4.05/4.32 cnf(c_0_11418, 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_6834]), ['final']). 4.05/4.32 cnf(c_0_11419, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X2)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6835]), ['final']). 4.05/4.32 cnf(c_0_11420, 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_6836]), ['final']). 4.05/4.32 cnf(c_0_11421, 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_6837]), ['final']). 4.05/4.32 cnf(c_0_11422, plain, (hBOOL(hAPP(hAPP(c_member(X1),X6),X5))|hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X3,X6))=hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X1),X6),X5))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_6838]), ['final']). 4.05/4.32 cnf(c_0_11423, 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_6839]), ['final']). 4.05/4.32 cnf(c_0_11424, plain, (hAPP(X1,X2)=hAPP(X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5))))), inference(split_conjunct,[status(thm)],[c_0_6524]), ['final']). 4.05/4.32 cnf(c_0_11425, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6840, c_0_4795]), c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11426, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6841, c_0_4795]), c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11427, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk357_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_6842]), ['final']). 4.05/4.32 cnf(c_0_11428, 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)))|esk470_5(X1,X2,X3,X4,X5)!=esk469_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_6256]), ['final']). 4.05/4.32 cnf(c_0_11429, 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)))|esk236_5(X1,X2,X3,X4,X5)!=esk237_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_6259]), ['final']). 4.05/4.32 cnf(c_0_11430, plain, (hAPP(c_Set_Oimage(X2,X4,hAPP(c_Fun_Ocomp(X1,X4,X2,X5),X3)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))|c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X2,X1,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))|c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X1,X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_6843]), ['final']). 4.05/4.32 cnf(c_0_11431, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk74_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_6844]), ['final']). 4.05/4.32 cnf(c_0_11432, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6845, c_0_4795]), c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11433, 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_6846]), ['final']). 4.05/4.32 cnf(c_0_11434, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X3))))=c_Groups_Oone__class_Oone(X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6847, c_0_4795]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_11435, 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_Otake(X2),X1),X3)=c_List_OtakeWhile(X2,X4,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk12_4(X4,X3,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6848]), ['final']). 4.05/4.32 cnf(c_0_11436, plain, (X1=hAPP(X2,esk232_4(X1,X2,X3,X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk231_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_5104]), ['final']). 4.05/4.32 cnf(c_0_11437, plain, (X1=hAPP(X2,esk232_4(X1,X2,X3,X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk231_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_5104]), ['final']). 4.05/4.32 cnf(c_0_11438, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),hAPP(hAPP(c_List_Onth(X2),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3)=hAPP(c_List_Ofoldl(X2,X2,hAPP(c_COMBC(X2,X2,X2),c_Orderings_Oord__class_Omax(X2)),X3),hAPP(c_List_Orev(X2),X1))|~class_Orderings_Olinorder(X2)|~c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Orev(X2),X1))), inference(rw,[status(thm)],[c_0_6849, c_0_4742]), ['final']). 4.05/4.32 cnf(c_0_11439, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),hAPP(c_List_Oset(X4),X5))))|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X1,X2),X3),X5)=c_List_Olinorder__class_Oinsort__insert__key(X4,X1,X2,X3,X5)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6850]), ['final']). 4.05/4.32 cnf(c_0_11440, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_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(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.32 cnf(c_0_11441, 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,esk421_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_6851])]), ['final']). 4.05/4.32 cnf(c_0_11442, 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_6699]), ['final']). 4.05/4.32 cnf(c_0_11443, 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_6852]), ['final']). 4.05/4.32 cnf(c_0_11444, 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_6853, c_0_6520]), c_0_4920]), ['final']). 4.05/4.32 cnf(c_0_11445, 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_6854, c_0_6520]), c_0_4920]), ['final']). 4.05/4.32 cnf(c_0_11446, 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)),esk364_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk362_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_5093]), ['final']). 4.05/4.32 cnf(c_0_11447, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk350_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_5606]), ['final']). 4.05/4.32 cnf(c_0_11448, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X6),X7)),X5))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,X3,X4),X5))|hAPP(hAPP(c_Set_Oinsert(X1),X6),X7)!=hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_6855]), ['final']). 4.05/4.32 cnf(c_0_11449, plain, (hAPP(hAPP(X1,X2),X3)=X4|hAPP(hAPP(X1,esk307_7(X3,X2,X5,X4,X1,X6,X7)),esk308_7(X3,X2,X5,X4,X1,X6,X7))=hAPP(hAPP(X1,X2),X3)|~c_Nitpick_Ofold__graph_H(X7,X6,X1,X4,X5,hAPP(hAPP(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6351]), ['final']). 4.05/4.32 cnf(c_0_11450, 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_6856, c_0_6857]), c_0_6106]), ['final']). 4.05/4.32 cnf(c_0_11451, 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_6858, c_0_5205]), ['final']). 4.05/4.32 cnf(c_0_11452, 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_6859]), ['final']). 4.05/4.32 cnf(c_0_11453, 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_6860]), ['final']). 4.05/4.32 cnf(c_0_11454, 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_6861]), ['final']). 4.05/4.32 cnf(c_0_11455, 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_6862]), ['final']). 4.05/4.32 cnf(c_0_11456, 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_6863, c_0_5205]), ['final']). 4.05/4.32 cnf(c_0_11457, 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_6864, c_0_5205]), ['final']). 4.05/4.32 cnf(c_0_11458, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk263_6(X4,X3,X5,X6,X2,X1)),esk264_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_6865]), ['final']). 4.05/4.32 cnf(c_0_11459, 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_6866, c_0_4742]), ['final']). 4.05/4.32 cnf(c_0_11460, 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_6867]), ['final']). 4.05/4.32 cnf(c_0_11461, 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_6868]), ['final']). 4.05/4.32 cnf(c_0_11462, 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_6869, c_0_4427]), ['final']). 4.05/4.32 cnf(c_0_11463, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X2,X3,X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_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)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.32 cnf(c_0_11464, 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_6870]), ['final']). 4.05/4.32 cnf(c_0_11465, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(hAPP(X3,esk307_7(X4,X5,X1,X6,X3,X7,X2)),esk308_7(X4,X5,X1,X6,X3,X7,X2))=hAPP(hAPP(X3,X5),X4)|~c_Nitpick_Ofold__graph_H(X2,X7,X3,X6,X1,hAPP(hAPP(X3,X5),X4))), inference(split_conjunct,[status(thm)],[c_0_6351]), ['final']). 4.05/4.32 cnf(c_0_11466, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),esk11_5(X1,X3,X4,X5,X2)),X4)|X4=hAPP(hAPP(c_List_Oappend(X2),esk10_5(X1,X3,X4,X5,X2)),X1)|hAPP(hAPP(c_List_Oappend(X2),X3),X1)!=hAPP(hAPP(c_List_Oappend(X2),X5),X4)), inference(split_conjunct,[status(thm)],[c_0_6871]), ['final']). 4.05/4.32 cnf(c_0_11467, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),esk11_5(X1,X3,X4,X5,X2)),X4)|hAPP(hAPP(c_List_Oappend(X2),X5),esk10_5(X1,X3,X4,X5,X2))=X3|hAPP(hAPP(c_List_Oappend(X2),X3),X1)!=hAPP(hAPP(c_List_Oappend(X2),X5),X4)), inference(split_conjunct,[status(thm)],[c_0_6871]), ['final']). 4.05/4.32 cnf(c_0_11468, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk364_3(X2,X3,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk362_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_5093]), ['final']). 4.05/4.32 cnf(c_0_11469, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk247_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_6872, c_0_5165]), ['final']). 4.05/4.32 cnf(c_0_11470, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk202_3(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)=X2|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6873]), ['final']). 4.05/4.32 cnf(c_0_11471, 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_6874, c_0_5905]), ['final']). 4.05/4.32 cnf(c_0_11472, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),esk11_5(X3,X2,X4,X5,X1))=X5|X4=hAPP(hAPP(c_List_Oappend(X1),esk10_5(X3,X2,X4,X5,X1)),X3)|hAPP(hAPP(c_List_Oappend(X1),X2),X3)!=hAPP(hAPP(c_List_Oappend(X1),X5),X4)), inference(split_conjunct,[status(thm)],[c_0_6871]), ['final']). 4.05/4.32 cnf(c_0_11473, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),esk11_5(X3,X2,X4,X5,X1))=X5|hAPP(hAPP(c_List_Oappend(X1),X5),esk10_5(X3,X2,X4,X5,X1))=X2|hAPP(hAPP(c_List_Oappend(X1),X2),X3)!=hAPP(hAPP(c_List_Oappend(X1),X5),X4)), inference(split_conjunct,[status(thm)],[c_0_6871]), ['final']). 4.05/4.32 cnf(c_0_11474, 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_6875]), ['final']). 4.05/4.32 cnf(c_0_11475, 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_6876]), ['final']). 4.05/4.32 cnf(c_0_11476, 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_6877]), ['final']). 4.05/4.32 cnf(c_0_11477, 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_6878]), ['final']). 4.05/4.32 cnf(c_0_11478, 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_6879]), ['final']). 4.05/4.32 cnf(c_0_11479, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|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_6008]), ['final']). 4.05/4.32 cnf(c_0_11480, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk353_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[c_0_6880, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11481, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk355_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2))), inference(rw,[status(thm)],[c_0_6881, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11482, 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,esk304_3(X3,X2,X1)))),c_Predicate_ORangeP(X1,X1,hAPP(X2,esk305_3(X3,X2,X1))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~c_Wellfounded_OwfP(X1,hAPP(X2,esk303_3(X3,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_6882]), ['final']). 4.05/4.32 cnf(c_0_11483, 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_6883]), ['final']). 4.05/4.32 cnf(c_0_11484, 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_6884]), ['final']). 4.05/4.32 cnf(c_0_11485, 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_6885]), ['final']). 4.05/4.32 cnf(c_0_11486, 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_6886]), ['final']). 4.05/4.32 cnf(c_0_11487, 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_6887]), ['final']). 4.05/4.32 cnf(c_0_11488, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X5|hAPP(X4,hAPP(X3,X5))=hAPP(X3,hAPP(c_Set_Oimage(X1,X1,X4),X5))|~c_Finite__Set_Ofolding__one__idem(X1,X2,X3)|hAPP(X4,hAPP(hAPP(X2,esk153_5(X5,X4,X3,X2,X1)),esk154_5(X5,X4,X3,X2,X1)))!=hAPP(hAPP(X2,hAPP(X4,esk153_5(X5,X4,X3,X2,X1))),hAPP(X4,esk154_5(X5,X4,X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_6888]), ['final']). 4.05/4.32 cnf(c_0_11489, plain, (hBOOL(hAPP(X1,esk72_2(X1,X2)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk71_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,esk70_2(X1,X2)))|~hBOOL(hAPP(X1,X3))), inference(rw,[status(thm)],[c_0_6889, c_0_6492]), ['final']). 4.05/4.32 cnf(c_0_11490, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk367_4(X3,X4,X1,X2)),esk368_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_6890]), ['final']). 4.05/4.32 cnf(c_0_11491, 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_6891, c_0_6120]), c_0_5905]), c_0_6120]), ['final']). 4.05/4.32 cnf(c_0_11492, 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_6892]), ['final']). 4.05/4.32 cnf(c_0_11493, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6893, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4977]), ['final']). 4.05/4.32 cnf(c_0_11494, 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_6894, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_6641]), ['final']). 4.05/4.32 cnf(c_0_11495, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk232_4(X1,X2,X3,X4)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk231_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_5104]), ['final']). 4.05/4.32 cnf(c_0_11496, 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_6895]), ['final']). 4.05/4.32 cnf(c_0_11497, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk40_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_6896]), ['final']). 4.05/4.32 cnf(c_0_11498, 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_6897]), ['final']). 4.05/4.32 cnf(c_0_11499, 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_6898, c_0_4950]), ['final']). 4.05/4.32 cnf(c_0_11500, 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|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_6899]), ['final']). 4.05/4.32 cnf(c_0_11501, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk232_4(X2,X3,X4,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk231_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_5104]), ['final']). 4.05/4.32 cnf(c_0_11502, 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_6900]), ['final']). 4.05/4.32 cnf(c_0_11503, 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_6901]), ['final']). 4.05/4.32 cnf(c_0_11504, 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_6902, c_0_6903]), c_0_6904]), ['final']). 4.05/4.32 cnf(c_0_11505, 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,esk286_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2)))!=hAPP(X7,esk286_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_6905, c_0_6340])]), ['final']). 4.05/4.32 cnf(c_0_11506, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk184_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_5065]), ['final']). 4.05/4.32 cnf(c_0_11507, 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_6906, c_0_6151]), ['final']). 4.05/4.32 cnf(c_0_11508, 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_6907, c_0_6151]), ['final']). 4.05/4.32 cnf(c_0_11509, plain, (c_List_OtakeWhile(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),c_List_Olast(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X2)=c_List_Obutlast(X1,X2)|X2=c_List_Olist_ONil(X1)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6908, c_0_5695]), c_0_5201]), ['final']). 4.05/4.32 cnf(c_0_11510, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X4|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X5|hAPP(hAPP(X2,hAPP(X3,X4)),hAPP(X3,X5))=hAPP(X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~c_Finite__Set_Ofolding__one__idem(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_6909]), ['final']). 4.05/4.32 cnf(c_0_11511, 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_6910]), ['final']). 4.05/4.32 cnf(c_0_11512, 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_6911]), ['final']). 4.05/4.32 cnf(c_0_11513, 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_5087]), ['final']). 4.05/4.32 cnf(c_0_11514, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk287_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_6912]), ['final']). 4.05/4.32 cnf(c_0_11515, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_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)))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.32 cnf(c_0_11516, 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_6913, c_0_5981]), ['final']). 4.05/4.32 cnf(c_0_11517, plain, (hAPP(c_Finite__Set_Ocard(X1),X4)=hAPP(c_Finite__Set_Ocard(X2),X5)|~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),X5))|~c_Fun_Oinj__on(X2,X1,X6,X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X6),X5)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))), inference(split_conjunct,[status(thm)],[c_0_6914]), ['final']). 4.05/4.32 cnf(c_0_11518, 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),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X4)),X4)),c_Divides_Odiv__class_Omod(X1,X2,X4))),X3)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_6915]), ['final']). 4.05/4.32 cnf(c_0_11519, 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_6916]), ['final']). 4.05/4.32 cnf(c_0_11520, 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_6917]), ['final']). 4.05/4.32 cnf(c_0_11521, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_6918, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11522, 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_6919, c_0_6920]), ['final']). 4.05/4.32 cnf(c_0_11523, plain, (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),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_6921]), ['final']). 4.05/4.32 cnf(c_0_11524, 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_6922]), ['final']). 4.05/4.32 cnf(c_0_11525, 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_6923]), ['final']). 4.05/4.32 cnf(c_0_11526, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk353_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_5096]), ['final']). 4.05/4.32 cnf(c_0_11527, 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_6924]), ['final']). 4.05/4.32 cnf(c_0_11528, 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_6925]), ['final']). 4.05/4.32 cnf(c_0_11529, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_6926]), ['final']). 4.05/4.32 cnf(c_0_11530, 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_6927, c_0_4635]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_11531, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))|hAPP(hAPP(c_List_Onth(X2),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))=hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1)), inference(split_conjunct,[status(thm)],[c_0_6928]), ['final']). 4.05/4.32 cnf(c_0_11532, 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_6929, c_0_4519]), ['final']). 4.05/4.32 cnf(c_0_11533, 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)),esk474_5(X2,X4,X3,X3,X1)))|~c_Nat__Transfer_Onat__set(X3)|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)), inference(er,[status(thm)],[c_0_6930]), ['final']). 4.05/4.32 cnf(c_0_11534, 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)),esk139_5(X2,X4,X3,X3,X1)))|~c_Nat__Transfer_Onat__set(X3)|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)), inference(er,[status(thm)],[c_0_6931]), ['final']). 4.05/4.32 cnf(c_0_11535, 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_6932]), ['final']). 4.05/4.32 cnf(c_0_11536, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X6),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_6933]), ['final']). 4.05/4.32 cnf(c_0_11537, 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_6934]), ['final']). 4.05/4.32 cnf(c_0_11538, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk377_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_5156]), ['final']). 4.05/4.32 cnf(c_0_11539, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk198_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_5155]), ['final']). 4.05/4.32 cnf(c_0_11540, 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_6935]), ['final']). 4.05/4.32 cnf(c_0_11541, plain, (hAPP(hAPP(c_List_Otake(X1),X4),X2)=hAPP(hAPP(c_List_Otake(X1),X4),X3)|hAPP(hAPP(c_List_Onth(X1),X2),esk287_4(X3,X2,X1,X4))!=hAPP(hAPP(c_List_Onth(X1),X3),esk287_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_6912]), ['final']). 4.05/4.32 cnf(c_0_11542, 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__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_6936]), ['final']). 4.05/4.32 cnf(c_0_11543, 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_6937]), ['final']). 4.05/4.32 cnf(c_0_11544, 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_6938]), ['final']). 4.05/4.32 cnf(c_0_11545, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X6),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5),X3)|~class_Divides_Osemiring__div(X1)|c_Divides_Odiv__class_Omod(X1,X2,X3)!=c_Divides_Odiv__class_Omod(X1,X4,X3)|c_Divides_Odiv__class_Omod(X1,X5,X3)!=c_Divides_Odiv__class_Omod(X1,X6,X3)), inference(split_conjunct,[status(thm)],[c_0_6939]), ['final']). 4.05/4.32 cnf(c_0_11546, 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_6940]), ['final']). 4.05/4.32 cnf(c_0_11547, 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_6941]), ['final']). 4.05/4.32 cnf(c_0_11548, 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_6942]), ['final']). 4.05/4.32 cnf(c_0_11549, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_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(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.32 cnf(c_0_11550, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk73_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),esk70_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk71_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,esk70_2(X1,X2)))|~hBOOL(hAPP(X1,X3))), inference(rw,[status(thm)],[c_0_6943, c_0_6492]), ['final']). 4.05/4.32 cnf(c_0_11551, 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_6944]), ['final']). 4.05/4.32 cnf(c_0_11552, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_6945]), ['final']). 4.05/4.32 cnf(c_0_11553, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk353_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_5096]), ['final']). 4.05/4.32 cnf(c_0_11554, 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_6946]), ['final']). 4.05/4.32 cnf(c_0_11555, plain, (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))=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_6947]), ['final']). 4.05/4.32 cnf(c_0_11556, 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_6948]), ['final']). 4.05/4.32 cnf(c_0_11557, plain, (hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X4,X5)),hAPP(X3,X6))=hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X6)),hAPP(X4,X5))|~c_Finite__Set_Ofolding(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_6949]), ['final']). 4.05/4.32 cnf(c_0_11558, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk459_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_6950]), ['final']). 4.05/4.32 cnf(c_0_11559, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk199_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_6951]), ['final']). 4.05/4.32 cnf(c_0_11560, 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_6952, c_0_5905]), ['final']). 4.05/4.32 cnf(c_0_11561, 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_6953, c_0_4859]), c_0_4859]), ['final']). 4.05/4.32 cnf(c_0_11562, 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_6954, c_0_6955]), c_0_6955]), ['final']). 4.05/4.32 cnf(c_0_11563, 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_6956, c_0_6395]), c_0_6396]), ['final']). 4.05/4.32 cnf(c_0_11564, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)))|hAPP(hAPP(c_List_Otake(X2),X4),X3)=c_List_OtakeWhile(X2,X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk12_4(X1,X3,X2,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6848]), ['final']). 4.05/4.32 cnf(c_0_11565, 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_6957]), ['final']). 4.05/4.32 cnf(c_0_11566, plain, (hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4)),X5)=hAPP(hAPP(c_List_Olist__update(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X5)),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_6958]), ['final']). 4.05/4.32 cnf(c_0_11567, 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),esk496_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_6959]), ['final']). 4.05/4.32 cnf(c_0_11568, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk28_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_6960]), ['final']). 4.05/4.32 cnf(c_0_11569, 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_6961, c_0_6962]), c_0_6963]), ['final']). 4.05/4.32 cnf(c_0_11570, plain, (hBOOL(hAPP(hAPP(c_member(X4),esk403_4(X1,X2,X3,X4)),X3))|hBOOL(hAPP(X1,X5))|~hBOOL(hAPP(X1,esk404_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_6568]), ['final']). 4.05/4.32 cnf(c_0_11571, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk404_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(X2,esk403_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_6568]), ['final']). 4.05/4.32 cnf(c_0_11572, 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)),esk117_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))), inference(rw,[status(thm)],[c_0_6964, c_0_4767]), ['final']). 4.05/4.32 cnf(c_0_11573, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|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_6965]), ['final']). 4.05/4.32 cnf(c_0_11574, 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),esk473_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_6966, c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11575, 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_6967]), ['final']). 4.05/4.32 cnf(c_0_11576, 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,esk226_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_6706]), ['final']). 4.05/4.32 cnf(c_0_11577, 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,esk384_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_6710]), ['final']). 4.05/4.32 cnf(c_0_11578, 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)),esk116_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))), inference(rw,[status(thm)],[c_0_6968, c_0_4767]), ['final']). 4.05/4.32 cnf(c_0_11579, plain, (hAPP(hAPP(c_List_Olist__update(X1,X2),esk184_4(X3,X4,X2,X1)),esk183_4(X3,X4,X2,X1))=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel1(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_5065]), ['final']). 4.05/4.32 cnf(c_0_11580, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk248_3(X1,X2,X3)),esk247_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_6969, c_0_5165]), ['final']). 4.05/4.32 cnf(c_0_11581, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk203_3(X2,X1,X3)),esk202_3(X2,X1,X3))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)=X1|~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_6873]), ['final']). 4.05/4.32 cnf(c_0_11582, 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_6970]), ['final']). 4.05/4.32 cnf(c_0_11583, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))=c_Groups_Oone__class_Oone(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6971, c_0_4795]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_11584, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6972, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), ['final']). 4.05/4.32 cnf(c_0_11585, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6973, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), ['final']). 4.05/4.32 cnf(c_0_11586, 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_6974]), ['final']). 4.05/4.32 cnf(c_0_11587, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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__eq(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_6975]), ['final']). 4.05/4.32 cnf(c_0_11588, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk453_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_6976]), ['final']). 4.05/4.32 cnf(c_0_11589, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6977, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), ['final']). 4.05/4.32 cnf(c_0_11590, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6978, c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), ['final']). 4.05/4.32 cnf(c_0_11591, 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_6979]), ['final']). 4.05/4.32 cnf(c_0_11592, 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),esk318_2(X2,X1))),hAPP(c_List_Oset(X1),esk319_2(X2,X1)))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),esk317_2(X2,X1)))), inference(rw,[status(thm)],[c_0_6980, c_0_4767]), ['final']). 4.05/4.32 cnf(c_0_11593, 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_6981, c_0_4915]), ['final']). 4.05/4.32 cnf(c_0_11594, 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_6982, c_0_6702]), ['final']). 4.05/4.32 cnf(c_0_11595, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk68_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_6983]), ['final']). 4.05/4.32 cnf(c_0_11596, 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_6984]), ['final']). 4.05/4.32 cnf(c_0_11597, plain, (hBOOL(hAPP(hAPP(c_member(X2),X8),X7))|hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,X7))=hAPP(X6,hAPP(hAPP(c_Set_Oinsert(X2),X8),X7))|~c_Finite__Set_Ofolding__image__simple(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))), inference(split_conjunct,[status(thm)],[c_0_6985]), ['final']). 4.05/4.32 cnf(c_0_11598, plain, (hBOOL(hAPP(X1,esk496_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_6959]), ['final']). 4.05/4.32 cnf(c_0_11599, plain, (hBOOL(hAPP(X1,esk473_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_5240]), ['final']). 4.05/4.32 cnf(c_0_11600, 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_6986, c_0_5304]), ['final']). 4.05/4.32 cnf(c_0_11601, 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_5086]), ['final']). 4.05/4.32 cnf(c_0_11602, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X2,tc_HOL_Obool)),X3))=hAPP(c_Finite__Set_Ocard(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))|hAPP(c_Finite__Set_Ocard(X2),esk104_3(X1,X3,X2))!=X1|esk106_3(X1,X3,X2)!=esk105_3(X1,X3,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3)))), inference(csr,[status(thm)],[c_0_6987, c_0_6378]), ['final']). 4.05/4.32 cnf(c_0_11603, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk343_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_6647]), ['final']). 4.05/4.32 cnf(c_0_11604, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk323_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_6648]), ['final']). 4.05/4.32 cnf(c_0_11605, 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_6988]), ['final']). 4.05/4.32 cnf(c_0_11606, 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_6989, c_0_4902]), ['final']). 4.05/4.32 cnf(c_0_11607, 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_6990, c_0_5201]), ['final']). 4.05/4.32 cnf(c_0_11608, plain, (X1=X2|X3=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X4),hAPP(hAPP(c_List_Olist_OCons(X5),X1),c_List_Olist_ONil(X5)))),hAPP(hAPP(c_List_Oappend(X5),X3),hAPP(hAPP(c_List_Olist_OCons(X5),X2),c_List_Olist_ONil(X5))))),c_List_Olistrel1(X5,X6)))), inference(split_conjunct,[status(thm)],[c_0_6275]), ['final']). 4.05/4.32 cnf(c_0_11609, 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_6991, c_0_6992]), ['final']). 4.05/4.32 cnf(c_0_11610, 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|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_6993]), ['final']). 4.05/4.32 cnf(c_0_11611, 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_6994]), ['final']). 4.05/4.32 cnf(c_0_11612, 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_6995]), ['final']). 4.05/4.32 cnf(c_0_11613, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),X4)=c_Option_Ooption_ONone(X2)|hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))))), inference(rw,[status(thm)],[c_0_6996, c_0_5304]), ['final']). 4.05/4.32 cnf(c_0_11614, 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_6997, c_0_6992]), ['final']). 4.05/4.32 cnf(c_0_11615, 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_6998, c_0_6962]), c_0_6963]), ['final']). 4.05/4.32 cnf(c_0_11616, 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_6999, c_0_6903]), c_0_6904]), ['final']). 4.05/4.32 cnf(c_0_11617, 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)),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5607]), ['final']). 4.05/4.32 cnf(c_0_11618, 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,esk212_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_7000]), ['final']). 4.05/4.32 cnf(c_0_11619, 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_7001]), ['final']). 4.05/4.32 cnf(c_0_11620, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk198_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_5155]), ['final']). 4.05/4.32 cnf(c_0_11621, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk377_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_5156]), ['final']). 4.05/4.32 cnf(c_0_11622, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk65_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_7002]), ['final']). 4.05/4.32 cnf(c_0_11623, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),X5),X3)=hAPP(c_Option_Ooption_OSome(X2),X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_List_Oset(tc_prod(X1,X2)),X5)))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X5)))), inference(split_conjunct,[status(thm)],[c_0_7003]), ['final']). 4.05/4.32 cnf(c_0_11624, 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_7004]), ['final']). 4.05/4.32 cnf(c_0_11625, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X4))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7005]), ['final']). 4.05/4.32 cnf(c_0_11626, 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_7006]), ['final']). 4.05/4.32 cnf(c_0_11627, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk62_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_7007]), ['final']). 4.05/4.32 cnf(c_0_11628, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk33_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_7008]), ['final']). 4.05/4.32 cnf(c_0_11629, 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_6346]), ['final']). 4.05/4.32 cnf(c_0_11630, 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_6350]), ['final']). 4.05/4.32 cnf(c_0_11631, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk2_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_7009]), ['final']). 4.05/4.32 cnf(c_0_11632, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X4),hAPP(hAPP(c_List_Ozip(X1,X4),X3),hAPP(hAPP(c_List_Omap(X1,X4),X5),X3))),X2)=hAPP(c_Option_Ooption_OSome(X4),hAPP(X5,X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7010]), ['final']). 4.05/4.32 cnf(c_0_11633, 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_7011]), ['final']). 4.05/4.32 cnf(c_0_11634, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(esk480_2(X2,X1),hAPP(c_Nat_OSuc,X3))),hAPP(esk480_2(X2,X1),X3))),X2))|c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7012]), ['final']). 4.05/4.32 cnf(c_0_11635, 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_7013]), ['final']). 4.05/4.32 cnf(c_0_11636, plain, (hAPP(hAPP(c_List_Olist_OCons(X5),X3),hAPP(hAPP(c_List_Olist_OCons(X5),X4),X6))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X1,X2),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_6607]), ['final']). 4.05/4.32 cnf(c_0_11637, 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_7014, c_0_6151]), ['final']). 4.05/4.32 cnf(c_0_11638, 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_7015, c_0_6151]), ['final']). 4.05/4.32 cnf(c_0_11639, 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_7016]), ['final']). 4.05/4.32 cnf(c_0_11640, 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_7017, c_0_7018]), c_0_7018]), ['final']). 4.05/4.32 cnf(c_0_11641, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))=c_Divides_OposDivAlg(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_7019]), ['final']). 4.05/4.32 cnf(c_0_11642, plain, (c_Divides_OnegDivAlg(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(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_7020]), ['final']). 4.05/4.32 cnf(c_0_11643, 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_7021, c_0_7022]), ['final']). 4.05/4.32 cnf(c_0_11644, 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)),esk407_3(X2,X3,X1)),esk408_3(X2,X3,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_6541]), ['final']). 4.05/4.32 cnf(c_0_11645, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|c_Big__Operators_Olattice__class_OInf__fin(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(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_7023]), ['final']). 4.05/4.32 cnf(c_0_11646, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X3),X6)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(X6,X2)))), inference(split_conjunct,[status(thm)],[c_0_7024]), ['final']). 4.05/4.32 cnf(c_0_11647, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk181_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk180_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_7025, c_0_5131]), ['final']). 4.05/4.32 cnf(c_0_11648, 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_6413]), ['final']). 4.05/4.32 cnf(c_0_11649, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk429_3(X2,X3,X1)),X3))|X3=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))|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_7026]), ['final']). 4.05/4.32 cnf(c_0_11650, 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_7027])]), ['final']). 4.05/4.32 cnf(c_0_11651, 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_7028]), ['final']). 4.05/4.32 cnf(c_0_11652, 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),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X5))|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7029]), ['final']). 4.05/4.32 cnf(c_0_11653, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7030]), ['final']). 4.05/4.32 cnf(c_0_11654, 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))|esk407_3(X1,X2,X3)!=esk408_3(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_6541]), ['final']). 4.05/4.32 cnf(c_0_11655, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),esk325_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_7031]), ['final']). 4.05/4.32 cnf(c_0_11656, 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,esk245_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2))!=hAPP(X3,hAPP(X5,esk245_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_7032]), ['final']). 4.05/4.32 cnf(c_0_11657, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7033, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), ['final']). 4.05/4.32 cnf(c_0_11658, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7034, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), ['final']). 4.05/4.32 cnf(c_0_11659, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7035, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), ['final']). 4.05/4.32 cnf(c_0_11660, 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_7036]), ['final']). 4.05/4.32 cnf(c_0_11661, 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_7037]), ['final']). 4.05/4.32 cnf(c_0_11662, 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_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X3,X1))),X1)!=hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)), inference(rw,[status(thm)],[c_0_7038, c_0_4950]), ['final']). 4.05/4.32 cnf(c_0_11663, 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_7039]), ['final']). 4.05/4.32 cnf(c_0_11664, 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_7040]), ['final']). 4.05/4.32 cnf(c_0_11665, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7041, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), ['final']). 4.05/4.32 cnf(c_0_11666, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk364_3(X2,X3,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_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)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.32 cnf(c_0_11667, 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),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']). 4.05/4.32 cnf(c_0_11668, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|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),esk398_3(X3,X2,X1)),esk399_3(X3,X2,X1)))!=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk398_3(X3,X2,X1))),hAPP(X2,esk399_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7043]), ['final']). 4.05/4.32 cnf(c_0_11669, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|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))|~class_Lattices_Olattice(X1)|hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),esk464_3(X3,X2,X1)),esk465_3(X3,X2,X1)))!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X2,esk464_3(X3,X2,X1))),hAPP(X2,esk465_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7044]), ['final']). 4.05/4.32 cnf(c_0_11670, 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(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk141_3(X3,X2,X1))),hAPP(X2,esk142_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk141_3(X3,X2,X1)),esk142_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7045]), ['final']). 4.05/4.32 cnf(c_0_11671, 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_7046]), ['final']). 4.05/4.32 cnf(c_0_11672, 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_7047])]), ['final']). 4.05/4.32 cnf(c_0_11673, 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_7048]), ['final']). 4.05/4.32 cnf(c_0_11674, 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_7049]), ['final']). 4.05/4.32 cnf(c_0_11675, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2))|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_7050]), ['final']). 4.05/4.32 cnf(c_0_11676, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|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_7051]), ['final']). 4.05/4.32 cnf(c_0_11677, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(X2,c_Big__Operators_Olattice__class_OSup__fin(X1,X3))=c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))|~class_Lattices_Olattice(X1)|hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),esk252_3(X3,X2,X1)),esk253_3(X3,X2,X1)))!=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X2,esk252_3(X3,X2,X1))),hAPP(X2,esk253_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7052]), ['final']). 4.05/4.32 cnf(c_0_11678, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),esk422_5(X1,X3,X4,X5,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X5),esk423_5(X1,X3,X4,X5,X2)))|hAPP(c_List_Ofilter(X2,X3),X1)!=hAPP(hAPP(c_List_Olist_OCons(X2),X5),X4)), inference(split_conjunct,[status(thm)],[c_0_5138]), ['final']). 4.05/4.32 cnf(c_0_11679, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),esk163_5(X3,X4,X1,X5,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),esk164_5(X3,X4,X1,X5,X2)))|hAPP(c_List_Ofilter(X2,X5),X1)!=hAPP(hAPP(c_List_Olist_OCons(X2),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_5107]), ['final']). 4.05/4.32 cnf(c_0_11680, 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),X2),X4))),X2)|~class_Fields_Ofield(X1)), inference(split_conjunct,[status(thm)],[c_0_7053]), ['final']). 4.05/4.32 cnf(c_0_11681, 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_7054]), ['final']). 4.05/4.32 cnf(c_0_11682, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4)|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7055]), ['final']). 4.05/4.32 cnf(c_0_11683, 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_7056]), ['final']). 4.05/4.32 cnf(c_0_11684, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7057]), ['final']). 4.05/4.32 cnf(c_0_11685, 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_7058]), ['final']). 4.05/4.32 cnf(c_0_11686, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X4),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7059]), ['final']). 4.05/4.32 cnf(c_0_11687, 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_7060, c_0_7061]), ['final']). 4.05/4.32 cnf(c_0_11688, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X4,X5),X1),X3))=hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X4,X5),X1),hAPP(c_List_Ofilter(X4,X2),X3)))|hAPP(X1,esk250_5(X1,X2,X3,X4,X5))!=c_Groups_Ozero__class_Ozero(X5)|~class_Groups_Omonoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6500]), ['final']). 4.05/4.32 cnf(c_0_11689, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X5))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7062]), ['final']). 4.05/4.32 cnf(c_0_11690, 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)),esk364_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_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(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.32 cnf(c_0_11691, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_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))|~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_7063]), ['final']). 4.05/4.32 cnf(c_0_11692, 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_7064]), ['final']). 4.05/4.32 cnf(c_0_11693, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk358_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_7065]), ['final']). 4.05/4.32 cnf(c_0_11694, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk522_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_7066]), ['final']). 4.05/4.32 cnf(c_0_11695, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk378_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_7067]), ['final']). 4.05/4.32 cnf(c_0_11696, 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_7068]), ['final']). 4.05/4.32 cnf(c_0_11697, plain, (hAPP(hAPP(X1,X2),esk325_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_7031]), ['final']). 4.05/4.32 cnf(c_0_11698, 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_7069]), ['final']). 4.05/4.32 cnf(c_0_11699, 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_7070]), ['final']). 4.05/4.32 cnf(c_0_11700, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_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_7071]), ['final']). 4.05/4.32 cnf(c_0_11701, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk269_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_7072]), ['final']). 4.05/4.32 cnf(c_0_11702, 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)), inference(split_conjunct,[status(thm)],[c_0_7073]), ['final']). 4.05/4.32 cnf(c_0_11703, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X4))|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7074]), ['final']). 4.05/4.32 cnf(c_0_11704, 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_7075]), ['final']). 4.05/4.32 cnf(c_0_11705, 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_7076]), ['final']). 4.05/4.32 cnf(c_0_11706, 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_7076]), ['final']). 4.05/4.32 cnf(c_0_11707, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_7077]), ['final']). 4.05/4.32 cnf(c_0_11708, 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_7078]), ['final']). 4.05/4.32 cnf(c_0_11709, 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_7079]), ['final']). 4.05/4.32 cnf(c_0_11710, 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),esk349_2(X2,X1)),hAPP(X1,esk349_2(X2,X1))))), inference(rw,[status(thm)],[c_0_7080, c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_11711, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X4,X5),X2),X3))=hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X4,X5),X2),hAPP(c_List_Ofilter(X4,X1),X3)))|~hBOOL(hAPP(X1,esk250_5(X2,X1,X3,X4,X5)))|~class_Groups_Omonoid__add(X5)), inference(split_conjunct,[status(thm)],[c_0_6500]), ['final']). 4.05/4.32 cnf(c_0_11712, 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),esk24_4(X2,X3,X1,X4)),X3))|hAPP(X2,X4)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7081, c_0_4867]), c_0_4867]), ['final']). 4.05/4.32 cnf(c_0_11713, 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_6540]), ['final']). 4.05/4.32 cnf(c_0_11714, 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_7082]), ['final']). 4.05/4.32 cnf(c_0_11715, 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_7083]), ['final']). 4.05/4.32 cnf(c_0_11716, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk454_4(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3),X3,X2)),esk453_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_7084]), ['final']). 4.05/4.32 cnf(c_0_11717, 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_7085]), ['final']). 4.05/4.32 cnf(c_0_11718, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X2)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7086, c_0_4439]), c_0_4635]), ['final']). 4.05/4.32 cnf(c_0_11719, plain, (hBOOL(hAPP(X4,X2))|hBOOL(hAPP(hAPP(c_member(X1),esk405_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_6568]), ['final']). 4.05/4.32 cnf(c_0_11720, plain, (hBOOL(hAPP(X4,X2))|hBOOL(hAPP(hAPP(c_member(X1),esk405_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_6568]), ['final']). 4.05/4.32 cnf(c_0_11721, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),hAPP(c_Groups_Otimes__class_Otimes(X1),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X5))|~class_Rings_Osemiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_7087]), ['final']). 4.05/4.32 cnf(c_0_11722, plain, (hAPP(c_List_Ofoldl(X2,X1,hAPP(c_COMBC(X1,X2,X2),X3),X4),X5)=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),hAPP(c_List_Oset(X1),X5))|~c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7088]), ['final']). 4.05/4.32 cnf(c_0_11723, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X3,X1)),hAPP(hAPP(c_Set_Oinsert(X4),X2),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),c_Map_Odom(X4,X3,X1)),X5)|hAPP(X1,X2)!=c_Option_Ooption_ONone(X3)), inference(split_conjunct,[status(thm)],[c_0_7089]), ['final']). 4.05/4.32 cnf(c_0_11724, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk69_4(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3),X3,X2)),esk68_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_7090]), ['final']). 4.05/4.32 cnf(c_0_11725, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(hAPP(c_Map_Omap__of(X1,X4),hAPP(hAPP(c_List_Ozip(X1,X4),X3),X5)),X2)=c_Option_Ooption_ONone(X4)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)), inference(split_conjunct,[status(thm)],[c_0_7091]), ['final']). 4.05/4.32 cnf(c_0_11726, 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_7092]), ['final']). 4.05/4.32 cnf(c_0_11727, plain, (X1=X2|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6,tc_Option_Ooption(X4)),X3),X2),hAPP(c_Option_Ooption_OSome(X4),X7)),X1)=hAPP(c_Option_Ooption_OSome(X4),X5)|hAPP(X3,X1)!=hAPP(c_Option_Ooption_OSome(X4),X5)), inference(split_conjunct,[status(thm)],[c_0_7093]), ['final']). 4.05/4.32 cnf(c_0_11728, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(hAPP(c_Map_Omap__of(X1,X4),hAPP(hAPP(c_List_Ozip(X1,X4),X3),hAPP(hAPP(c_List_Omap(X1,X4),X5),X3))),X2)=c_Option_Ooption_ONone(X4)), inference(split_conjunct,[status(thm)],[c_0_7010]), ['final']). 4.05/4.32 cnf(c_0_11729, 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_7094, c_0_4902]), ['final']). 4.05/4.32 cnf(c_0_11730, 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_7095]), ['final']). 4.05/4.32 cnf(c_0_11731, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_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(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.32 cnf(c_0_11732, plain, (hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X3,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7096]), ['final']). 4.05/4.32 cnf(c_0_11733, 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_7097]), ['final']). 4.05/4.32 cnf(c_0_11734, 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_7098]), ['final']). 4.05/4.32 cnf(c_0_11735, 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_7099]), ['final']). 4.05/4.32 cnf(c_0_11736, 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_7100]), ['final']). 4.05/4.32 cnf(c_0_11737, plain, (c_Map_Omap__le(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X5),X6),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X4),X5),X6))|~c_Map_Omap__le(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_7101]), ['final']). 4.05/4.32 cnf(c_0_11738, 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_6842]), ['final']). 4.05/4.32 cnf(c_0_11739, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk26_3(X3,X2,X1)),esk27_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_5827]), ['final']). 4.05/4.32 cnf(c_0_11740, 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_7102]), ['final']). 4.05/4.32 cnf(c_0_11741, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk337_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))|X4=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_7103]), ['final']). 4.05/4.32 cnf(c_0_11742, 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_7104]), ['final']). 4.05/4.32 cnf(c_0_11743, 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_5479]), ['final']). 4.05/4.32 cnf(c_0_11744, 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_6844]), ['final']). 4.05/4.32 cnf(c_0_11745, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X2)),hAPP(c_List_Oset(tc_prod(X3,X1)),X4)))|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(hAPP(c_Map_Omap__of(X3,X1),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_7105]), ['final']). 4.05/4.32 cnf(c_0_11746, 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_5479]), ['final']). 4.05/4.32 cnf(c_0_11747, 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_7106]), ['final']). 4.05/4.32 cnf(c_0_11748, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk223_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_7107]), ['final']). 4.05/4.32 cnf(c_0_11749, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_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)))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.32 cnf(c_0_11750, 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))|~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_7108]), ['final']). 4.05/4.32 cnf(c_0_11751, 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))|~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_7108]), ['final']). 4.05/4.32 cnf(c_0_11752, 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))|~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_7108]), ['final']). 4.05/4.32 cnf(c_0_11753, 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))|~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_7108]), ['final']). 4.05/4.32 cnf(c_0_11754, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,X1,esk228_2(X2,X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),esk227_2(X2,X1)))=X2|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(rw,[status(thm)],[c_0_7109, c_0_4523]), ['final']). 4.05/4.32 cnf(c_0_11755, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7110, c_0_6203]), c_0_4795]), ['final']). 4.05/4.32 cnf(c_0_11756, 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_7111]), ['final']). 4.05/4.32 cnf(c_0_11757, 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_7112, c_0_7113]), ['final']). 4.05/4.32 cnf(c_0_11758, 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_7114]), ['final']). 4.05/4.32 cnf(c_0_11759, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk515_3(X2,X3,X1)),X3))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk514_3(X2,X3,X1)),X2))|c_Relation_Orefl__on(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_4546]), ['final']). 4.05/4.32 cnf(c_0_11760, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk149_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_7115]), ['final']). 4.05/4.32 cnf(c_0_11761, 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_7116]), ['final']). 4.05/4.32 cnf(c_0_11762, plain, (c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X2)=hAPP(c_List_Ofoldl(tc_List_Olist(X1),X1,hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1))),c_List_Olist_ONil(X1)),X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7117]), ['final']). 4.05/4.32 cnf(c_0_11763, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk181_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk180_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(rw,[status(thm)],[c_0_7118, c_0_5131]), ['final']). 4.05/4.32 cnf(c_0_11764, 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_7119]), ['final']). 4.05/4.32 cnf(c_0_11765, 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_7120]), ['final']). 4.05/4.32 cnf(c_0_11766, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X4),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(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_7121]), ['final']). 4.05/4.32 cnf(c_0_11767, 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_7122]), ['final']). 4.05/4.32 cnf(c_0_11768, 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))), inference(split_conjunct,[status(thm)],[c_0_6580]), ['final']). 4.05/4.32 cnf(c_0_11769, 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_7123]), ['final']). 4.05/4.32 cnf(c_0_11770, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X4),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7124]), ['final']). 4.05/4.32 cnf(c_0_11771, 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_7125]), ['final']). 4.05/4.32 cnf(c_0_11772, plain, (X1=hAPP(c_Relation_OImage(X2,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),esk89_4(X3,X4,X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_7126]), ['final']). 4.05/4.32 cnf(c_0_11773, plain, (hAPP(X1,esk296_3(X2,X1,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk295_3(X2,X1,X3)),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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))), inference(split_conjunct,[status(thm)],[c_0_5141]), ['final']). 4.05/4.32 cnf(c_0_11774, 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_7127, c_0_6709]), ['final']). 4.05/4.32 cnf(c_0_11775, 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_7128]), ['final']). 4.05/4.33 cnf(c_0_11776, 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_7129]), ['final']). 4.05/4.33 cnf(c_0_11777, 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_7130]), ['final']). 4.05/4.33 cnf(c_0_11778, 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_7131]), ['final']). 4.05/4.33 cnf(c_0_11779, plain, (hAPP(X1,esk97_3(X2,X1,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk96_3(X2,X1,X3)),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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))), inference(split_conjunct,[status(thm)],[c_0_5142]), ['final']). 4.05/4.33 cnf(c_0_11780, 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_7132]), ['final']). 4.05/4.33 cnf(c_0_11781, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7133]), ['final']). 4.05/4.33 cnf(c_0_11782, 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_7134]), ['final']). 4.05/4.33 cnf(c_0_11783, 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),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~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_7135]), ['final']). 4.05/4.33 cnf(c_0_11784, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk503_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_6673]), ['final']). 4.05/4.33 cnf(c_0_11785, 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)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),X2))), inference(split_conjunct,[status(thm)],[c_0_5446]), ['final']). 4.05/4.33 cnf(c_0_11786, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk263_6(X3,X4,X2,X1,X5,X6)),esk264_6(X3,X4,X2,X1,X5,X6))=X3|~hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(X6,tc_HOL_Obool)),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_6865]), ['final']). 4.05/4.33 cnf(c_0_11787, plain, (X1=X2|hAPP(hAPP(c_Map_Omap__of(X3,X4),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X2),X5)),X6)),X1)=hAPP(hAPP(c_Map_Omap__of(X3,X4),X6),X1)), inference(split_conjunct,[status(thm)],[c_0_5864]), ['final']). 4.05/4.33 cnf(c_0_11788, 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_7136, c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_11789, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk503_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_6673]), ['final']). 4.05/4.33 cnf(c_0_11790, 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_7137]), ['final']). 4.05/4.33 cnf(c_0_11791, 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_7138]), ['final']). 4.05/4.33 cnf(c_0_11792, 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_7139]), ['final']). 4.05/4.33 cnf(c_0_11793, 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),esk316_3(X2,X3,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6812]), ['final']). 4.05/4.33 cnf(c_0_11794, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk242_3(X2,X3,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_6817]), ['final']). 4.05/4.33 cnf(c_0_11795, 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),esk406_3(X2,X3,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6818]), ['final']). 4.05/4.33 cnf(c_0_11796, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk273_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_7140]), ['final']). 4.05/4.33 cnf(c_0_11797, 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_7141]), ['final']). 4.05/4.33 cnf(c_0_11798, 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_7142]), ['final']). 4.05/4.33 cnf(c_0_11799, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7143, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_11800, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk233_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_7144]), ['final']). 4.05/4.33 cnf(c_0_11801, 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_7145]), ['final']). 4.05/4.33 cnf(c_0_11802, 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,esk304_3(X2,X1,X3))!=hAPP(X1,esk305_3(X2,X1,X3))|~c_Wellfounded_OwfP(X3,hAPP(X1,esk303_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_6882]), ['final']). 4.05/4.33 cnf(c_0_11803, 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_7146]), ['final']). 4.05/4.33 cnf(c_0_11804, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7147, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_11805, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7148, c_0_4795]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), ['final']). 4.05/4.33 cnf(c_0_11806, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk483_6(X3,X4,X5,X6,X2,X1)),esk485_6(X3,X4,X5,X6,X2,X1))=X6|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),X6),hAPP(hAPP(c_Relation_Orel__comp(X1,X5,X2),X4),X3)))), inference(split_conjunct,[status(thm)],[c_0_6674]), ['final']). 4.05/4.33 cnf(c_0_11807, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk86_5(X1,X2,X3,X4,X5)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X4)))|c_List_Olist__all2(X5,X3,X1,X4,X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2)), inference(split_conjunct,[status(thm)],[c_0_7149]), ['final']). 4.05/4.33 cnf(c_0_11808, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk442_5(X1,X2,X3,X4,X5)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X2)))|c_List_Olist__all2(X5,X4,X3,X2,X1)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X1)), inference(split_conjunct,[status(thm)],[c_0_7150]), ['final']). 4.05/4.33 cnf(c_0_11809, 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_7151, c_0_5669]), ['final']). 4.05/4.33 cnf(c_0_11810, 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_7152]), ['final']). 4.05/4.33 cnf(c_0_11811, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7153, c_0_4795]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), ['final']). 4.05/4.33 cnf(c_0_11812, 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_7154]), ['final']). 4.05/4.33 cnf(c_0_11813, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7133]), ['final']). 4.05/4.33 cnf(c_0_11814, 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_7155]), ['final']). 4.05/4.33 cnf(c_0_11815, 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_7156]), ['final']). 4.05/4.33 cnf(c_0_11816, 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_7157, c_0_6268]), ['final']). 4.05/4.33 cnf(c_0_11817, 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_7158]), ['final']). 4.05/4.33 cnf(c_0_11818, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk174_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk173_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_7159, c_0_5131]), ['final']). 4.05/4.33 cnf(c_0_11819, 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_7131]), ['final']). 4.05/4.33 cnf(c_0_11820, 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_7133]), ['final']). 4.05/4.33 cnf(c_0_11821, 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_7131]), ['final']). 4.05/4.33 cnf(c_0_11822, 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_7134]), ['final']). 4.05/4.33 cnf(c_0_11823, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk243_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_7160]), ['final']). 4.05/4.33 cnf(c_0_11824, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk409_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_6613]), ['final']). 4.05/4.33 cnf(c_0_11825, 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_Otake(X2),X1),X3)=c_List_OtakeWhile(X2,X4,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk12_4(X4,X3,X2,X1)),X1))), inference(split_conjunct,[status(thm)],[c_0_6848]), ['final']). 4.05/4.33 cnf(c_0_11826, 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_7161]), ['final']). 4.05/4.33 cnf(c_0_11827, 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),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7135]), ['final']). 4.05/4.33 cnf(c_0_11828, 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_7131]), ['final']). 4.05/4.33 cnf(c_0_11829, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7133]), ['final']). 4.05/4.33 cnf(c_0_11830, 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),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)))|~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_7134]), ['final']). 4.05/4.33 cnf(c_0_11831, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(hAPP(c_List_Omap(X1,X4),X5),X3)=hAPP(hAPP(c_List_Omap(X1,X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X4),X5),X2),X6)),X3)), inference(split_conjunct,[status(thm)],[c_0_7162]), ['final']). 4.05/4.33 cnf(c_0_11832, 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_7163]), ['final']). 4.05/4.33 cnf(c_0_11833, 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_6812]), ['final']). 4.05/4.33 cnf(c_0_11834, plain, (hAPP(c_List_Orev(tc_prod(X1,X3)),hAPP(hAPP(c_List_Ozip(X1,X3),X2),X4))=hAPP(hAPP(c_List_Ozip(X1,X3),hAPP(c_List_Orev(X1),X2)),hAPP(c_List_Orev(X3),X4))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)), inference(split_conjunct,[status(thm)],[c_0_7164]), ['final']). 4.05/4.33 cnf(c_0_11835, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7134]), ['final']). 4.05/4.33 cnf(c_0_11836, 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_7135]), ['final']). 4.05/4.33 cnf(c_0_11837, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7135]), ['final']). 4.05/4.33 cnf(c_0_11838, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk284_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_6754]), ['final']). 4.05/4.33 cnf(c_0_11839, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_6817]), ['final']). 4.05/4.33 cnf(c_0_11840, 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_6818]), ['final']). 4.05/4.33 cnf(c_0_11841, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk32_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_6750]), ['final']). 4.05/4.33 cnf(c_0_11842, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk426_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_6755]), ['final']). 4.05/4.33 cnf(c_0_11843, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk372_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_6756]), ['final']). 4.05/4.33 cnf(c_0_11844, 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_7165, c_0_6903]), c_0_6904]), ['final']). 4.05/4.33 cnf(c_0_11845, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_List_Olist_OCons(X2),X3),hAPP(hAPP(c_List_Otake(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4))=hAPP(hAPP(c_List_Otake(X2),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7166]), ['final']). 4.05/4.33 cnf(c_0_11846, 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_7167]), ['final']). 4.05/4.33 cnf(c_0_11847, 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_7168, c_0_4635]), c_0_4635]), c_0_5149]), c_0_4635]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_11848, 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_7169]), ['final']). 4.05/4.33 cnf(c_0_11849, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7170, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), ['final']). 4.05/4.33 cnf(c_0_11850, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7171, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), ['final']). 4.05/4.33 cnf(c_0_11851, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7172, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), ['final']). 4.05/4.33 cnf(c_0_11852, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk174_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk173_3(X1,X2,X3)))=X2|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))), inference(rw,[status(thm)],[c_0_7173, c_0_5131]), ['final']). 4.05/4.33 cnf(c_0_11853, 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_7174]), ['final']). 4.05/4.33 cnf(c_0_11854, 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_7175]), ['final']). 4.05/4.33 cnf(c_0_11855, 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_7176]), ['final']). 4.05/4.33 cnf(c_0_11856, 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)),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)), inference(split_conjunct,[status(thm)],[c_0_5087]), ['final']). 4.05/4.33 cnf(c_0_11857, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7177, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), ['final']). 4.05/4.33 cnf(c_0_11858, 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_7178]), ['final']). 4.05/4.33 cnf(c_0_11859, 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_7131]), ['final']). 4.05/4.33 cnf(c_0_11860, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1)),X3)),X4)=hAPP(c_Option_Ooption_OSome(X2),esk143_4(X4,X3,X2,X1))|~class_Enum_Oenum(X1)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1))), inference(split_conjunct,[status(thm)],[c_0_7179]), ['final']). 4.05/4.33 cnf(c_0_11861, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk201_5(X2,X3,X4,X1,X5)),hAPP(X2,esk200_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_7180]), ['final']). 4.05/4.33 cnf(c_0_11862, 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_5253]), ['final']). 4.05/4.33 cnf(c_0_11863, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk78_3(X3,X2,X1)),esk80_3(X3,X2,X1))),X3))|c_Relation_Osingle__valued(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7181]), ['final']). 4.05/4.33 cnf(c_0_11864, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X2))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7133]), ['final']). 4.05/4.33 cnf(c_0_11865, 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_7131]), ['final']). 4.05/4.33 cnf(c_0_11866, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X2))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7133]), ['final']). 4.05/4.33 cnf(c_0_11867, 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),X2),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_7134]), ['final']). 4.05/4.33 cnf(c_0_11868, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk78_3(X3,X2,X1)),esk79_3(X3,X2,X1))),X3))|c_Relation_Osingle__valued(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7181]), ['final']). 4.05/4.33 cnf(c_0_11869, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7182]), ['final']). 4.05/4.33 cnf(c_0_11870, 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_7183]), ['final']). 4.05/4.33 cnf(c_0_11871, 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_7184]), ['final']). 4.05/4.33 cnf(c_0_11872, 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_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)|~class_Orderings_Oord(X1)|~class_Int_Onumber(X1)), inference(split_conjunct,[status(thm)],[c_0_7185]), ['final']). 4.05/4.33 cnf(c_0_11873, 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),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_7134]), ['final']). 4.05/4.33 cnf(c_0_11874, 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__eq(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),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7135]), ['final']). 4.05/4.33 cnf(c_0_11875, plain, (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)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7135]), ['final']). 4.05/4.33 cnf(c_0_11876, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk296_3(X1,X2,X3)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk295_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_5141]), ['final']). 4.05/4.33 cnf(c_0_11877, 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_7186]), ['final']). 4.05/4.33 cnf(c_0_11878, 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_7187]), ['final']). 4.05/4.33 cnf(c_0_11879, 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_Orderings_Oord(X1)|~class_Int_Onumber(X1)), inference(split_conjunct,[status(thm)],[c_0_7188]), ['final']). 4.05/4.33 cnf(c_0_11880, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk97_3(X1,X2,X3)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk96_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_5142]), ['final']). 4.05/4.33 cnf(c_0_11881, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_3(X1,X3,X2)),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,esk363_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_11882, 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)),esk364_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk361_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_11883, 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_7189]), ['final']). 4.05/4.33 cnf(c_0_11884, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk224_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_7190]), ['final']). 4.05/4.33 cnf(c_0_11885, plain, (hAPP(c_Nat_OSuc,esk389_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)))), inference(split_conjunct,[status(thm)],[c_0_6330]), ['final']). 4.05/4.33 cnf(c_0_11886, plain, (hAPP(c_Nat_OSuc,esk176_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)))), inference(split_conjunct,[status(thm)],[c_0_6327]), ['final']). 4.05/4.33 cnf(c_0_11887, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk19_3(X2,X1,X3)),X3)),X2))|c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),esk17_2(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_7191]), ['final']). 4.05/4.33 cnf(c_0_11888, 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_7192]), ['final']). 4.05/4.33 cnf(c_0_11889, 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_7193]), ['final']). 4.05/4.33 cnf(c_0_11890, 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_7194]), ['final']). 4.05/4.33 cnf(c_0_11891, 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_7195]), ['final']). 4.05/4.33 cnf(c_0_11892, 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_7196]), ['final']). 4.05/4.33 cnf(c_0_11893, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk268_4(X2,X3,X1,X4)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X2,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7197]), ['final']). 4.05/4.33 cnf(c_0_11894, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk362_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_5093]), ['final']). 4.05/4.33 cnf(c_0_11895, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),c_Groups_Oone__class_Oone(X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7198]), ['final']). 4.05/4.33 cnf(c_0_11896, 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_7199, c_0_5131]), ['final']). 4.05/4.33 cnf(c_0_11897, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk439_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_7200]), ['final']). 4.05/4.33 cnf(c_0_11898, 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_7201, c_0_6606]), ['final']). 4.05/4.33 cnf(c_0_11899, 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_7202]), ['final']). 4.05/4.33 cnf(c_0_11900, 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_7203, c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_11901, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk7_5(X2,X3,X4,X1,X5)),X4))|c_Groups_Ozero__class_Ozero(X5)=hAPP(X3,X2)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X5),X3),X4)!=c_Groups_Ozero__class_Ozero(X5)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Oordered__ab__group__add(X5)), inference(split_conjunct,[status(thm)],[c_0_7204]), ['final']). 4.05/4.33 cnf(c_0_11902, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Map_Oran(X5,X1,X2))=c_Map_Oran(X5,X1,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X1)),X2),X3),hAPP(c_Option_Ooption_OSome(X1),X4)))|c_Option_Ooption_ONone(X1)!=hAPP(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7205]), ['final']). 4.05/4.33 cnf(c_0_11903, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),c_Groups_Oone__class_Oone(X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7206]), ['final']). 4.05/4.33 cnf(c_0_11904, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X1),X6),X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X5),X3),X6))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7207]), ['final']). 4.05/4.33 cnf(c_0_11905, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X1),X6),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X5),X4),X6))|~class_Orderings_Olinorder(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7208]), ['final']). 4.05/4.33 cnf(c_0_11906, 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_7209]), ['final']). 4.05/4.33 cnf(c_0_11907, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X5),X1,c_Option_Ooption_ONone(X5),X7),hAPP(X3,X4))=hAPP(c_Option_Ooption_OSome(X5),X6)|hAPP(c_Option_Ooption_OSome(X5),X6)!=hAPP(X7,X2)|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(X3,X4)), inference(rw,[status(thm)],[c_0_7210, c_0_7211]), ['final']). 4.05/4.33 cnf(c_0_11908, plain, (X4=hAPP(c_Set_Oimage(X2,X1,esk213_4(X5,X2,X1,X4)),X5)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=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))), inference(split_conjunct,[status(thm)],[c_0_5258]), ['final']). 4.05/4.33 cnf(c_0_11909, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk472_5(X2,X3,X4,X5,X1)),hAPP(c_List_Oset(X1),X3)))|hAPP(hAPP(c_List_Omap(X1,X5),X4),X3)=hAPP(hAPP(c_List_Omap(X1,X5),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_7212]), ['final']). 4.05/4.33 cnf(c_0_11910, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_3(X2,X3,X1)),c_Groups_Ozero__class_Ozero(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,esk355_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_11911, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X2,X3,X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk362_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_5093]), ['final']). 4.05/4.33 cnf(c_0_11912, 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_7213, c_0_6561]), c_0_6610]), ['final']). 4.05/4.33 cnf(c_0_11913, 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_7214]), ['final']). 4.05/4.33 cnf(c_0_11914, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_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,esk353_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_11915, 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_7215, c_0_4635]), c_0_4635]), c_0_5149]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_11916, 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_7216]), ['final']). 4.05/4.33 cnf(c_0_11917, 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_7217]), ['final']). 4.05/4.33 cnf(c_0_11918, 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_7218]), ['final']). 4.05/4.33 cnf(c_0_11919, 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_7219]), ['final']). 4.05/4.33 cnf(c_0_11920, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk21_3(X2,X3,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X2,c_Enum_Oenum__class_Oenum(X1)))))|c_Enum_Oall__n__lists(X1,X3,X2)|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_7220]), ['final']). 4.05/4.33 cnf(c_0_11921, plain, (hAPP(c_Option_Ooption_OSome(X2),esk35_5(X5,X4,X3,X2,X1))=hAPP(hAPP(c_Map_Omap__of(X1,X2),X5),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_List_Oset(tc_prod(X1,X2)),X5)))), inference(split_conjunct,[status(thm)],[c_0_7221]), ['final']). 4.05/4.33 cnf(c_0_11922, 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(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_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(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_11923, 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_7222]), ['final']). 4.05/4.33 cnf(c_0_11924, 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_7223]), ['final']). 4.05/4.33 cnf(c_0_11925, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk222_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_7107]), ['final']). 4.05/4.33 cnf(c_0_11926, 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)),esk364_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)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_11927, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk365_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_7224]), ['final']). 4.05/4.33 cnf(c_0_11928, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk270_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_7225]), ['final']). 4.05/4.33 cnf(c_0_11929, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk527_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_7226]), ['final']). 4.05/4.33 cnf(c_0_11930, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk281_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_7227]), ['final']). 4.05/4.33 cnf(c_0_11931, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk108_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_7228]), ['final']). 4.05/4.33 cnf(c_0_11932, 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__eq(tc_Int_Oint),esk362_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)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_11933, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk364_3(X2,X3,X1)))|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)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_11934, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_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,esk363_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_11935, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk364_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,esk361_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_11936, 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_7229]), ['final']). 4.05/4.33 cnf(c_0_11937, plain, (hAPP(X4,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))|~c_Finite__Set_Ofolding__one(X1,X5,X4)), inference(split_conjunct,[status(thm)],[c_0_6385]), ['final']). 4.05/4.33 cnf(c_0_11938, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2))=hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7230]), ['final']). 4.05/4.33 cnf(c_0_11939, 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_7131]), ['final']). 4.05/4.33 cnf(c_0_11940, 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_7133]), ['final']). 4.05/4.33 cnf(c_0_11941, 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_7134]), ['final']). 4.05/4.33 cnf(c_0_11942, 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_7135]), ['final']). 4.05/4.33 cnf(c_0_11943, 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_7231, c_0_4742]), ['final']). 4.05/4.33 cnf(c_0_11944, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk312_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_6974]), ['final']). 4.05/4.33 cnf(c_0_11945, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk443_3(X2,X3,X1)),X2))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6975]), ['final']). 4.05/4.33 cnf(c_0_11946, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk443_3(X2,X3,X1)),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X3)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6975]), ['final']). 4.05/4.33 cnf(c_0_11947, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk458_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_7232]), ['final']). 4.05/4.33 cnf(c_0_11948, 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)), inference(split_conjunct,[status(thm)],[c_0_7233]), ['final']). 4.05/4.33 cnf(c_0_11949, 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_7234]), ['final']). 4.05/4.33 cnf(c_0_11950, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3)|~class_Lattices_Odistrib__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7235]), ['final']). 4.05/4.33 cnf(c_0_11951, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_7236]), ['final']). 4.05/4.33 cnf(c_0_11952, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk360_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_7237]), ['final']). 4.05/4.33 cnf(c_0_11953, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk312_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_6974]), ['final']). 4.05/4.33 cnf(c_0_11954, 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_7238]), ['final']). 4.05/4.33 cnf(c_0_11955, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7239]), ['final']). 4.05/4.33 cnf(c_0_11956, plain, (hAPP(hAPP(c_Set_Oinsert(X1),esk130_5(X2,X3,X4,X5,X1)),esk131_5(X2,X3,X4,X5,X1))=hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2))), inference(split_conjunct,[status(thm)],[c_0_7240]), ['final']). 4.05/4.33 cnf(c_0_11957, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk300_3(X2,X3,X1)),X3)),X2))|hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7241]), ['final']). 4.05/4.33 cnf(c_0_11958, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)))=hAPP(c_List_Oset(X1),X3)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(c_List_Odistinct(X1),X3))), inference(rw,[status(thm)],[c_0_7242, c_0_7243]), ['final']). 4.05/4.33 cnf(c_0_11959, 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_7244]), ['final']). 4.05/4.33 cnf(c_0_11960, 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_7245]), ['final']). 4.05/4.33 cnf(c_0_11961, 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_7246]), ['final']). 4.05/4.33 cnf(c_0_11962, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)=hAPP(hAPP(c_Set_Oinsert(X1),esk501_5(X4,X3,X2,X5,X1)),esk502_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_6855]), ['final']). 4.05/4.33 cnf(c_0_11963, plain, (c_Map_Omap__upds(X1,X4,X6,X2,hAPP(hAPP(c_List_Olist__update(X4,X5),X3),X7))=c_Map_Omap__upds(X1,X4,X6,X2,X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X5)))), inference(split_conjunct,[status(thm)],[c_0_7247]), ['final']). 4.05/4.33 cnf(c_0_11964, 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_7248, c_0_4902]), c_0_4902]), ['final']). 4.05/4.33 cnf(c_0_11965, 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_7249]), ['final']). 4.05/4.33 cnf(c_0_11966, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4)=hAPP(hAPP(c_Orderings_Oord__class_Omax(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_7250]), ['final']). 4.05/4.33 cnf(c_0_11967, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))|~class_Lattices_Odistrib__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7251]), ['final']). 4.05/4.33 cnf(c_0_11968, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))|~class_Lattices_Odistrib__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7252]), ['final']). 4.05/4.33 cnf(c_0_11969, 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_7253]), ['final']). 4.05/4.33 cnf(c_0_11970, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk353_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_5096]), ['final']). 4.05/4.33 cnf(c_0_11971, 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_7254]), ['final']). 4.05/4.33 cnf(c_0_11972, 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_7255]), ['final']). 4.05/4.33 cnf(c_0_11973, 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_7256]), ['final']). 4.05/4.33 cnf(c_0_11974, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|c_Groups_Ozero__class_Ozero(X1)!=hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~class_Groups_Ocomm__monoid__add(X1)), inference(rw,[status(thm)],[c_0_7257, c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_11975, 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)), inference(split_conjunct,[status(thm)],[c_0_7258]), ['final']). 4.05/4.33 cnf(c_0_11976, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7259, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4427]), c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_11977, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7260, c_0_4505]), c_0_4795]), c_0_5796]), ['final']). 4.05/4.33 cnf(c_0_11978, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7261, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4427]), c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_11979, plain, (hAPP(hAPP(X1,X2),X3)=X4|hBOOL(hAPP(hAPP(c_member(X5),esk307_7(X3,X2,X6,X4,X1,X7,X5)),X6))|~c_Nitpick_Ofold__graph_H(X5,X7,X1,X4,X6,hAPP(hAPP(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_6351]), ['final']). 4.05/4.33 cnf(c_0_11980, 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_7262, c_0_4635]), c_0_4635]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_11981, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7263, c_0_4505]), c_0_4795]), c_0_5796]), ['final']). 4.05/4.33 cnf(c_0_11982, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7264, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4427]), c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_11983, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7265, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4635]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_11984, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7266, c_0_4427]), c_0_4505]), c_0_4795]), c_0_5796]), c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_11985, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,X1,X2),c_Int_Oring__1__class_Oof__int(X1)),X3)),X4)=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,tc_Int_Oint),X3),X4))|~class_Rings_Oring__1(X1)|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_7267]), ['final']). 4.05/4.33 cnf(c_0_11986, plain, (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)=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))|~class_Rings_Osemiring__1(X1)|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_7268]), ['final']). 4.05/4.33 cnf(c_0_11987, 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_7269]), ['final']). 4.05/4.33 cnf(c_0_11988, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7270, c_0_4505]), c_0_4795]), c_0_5796]), ['final']). 4.05/4.33 cnf(c_0_11989, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7271, c_0_4427]), c_0_4505]), c_0_4795]), c_0_5796]), c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_11990, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7272, c_0_4505]), c_0_4795]), c_0_5796]), ['final']). 4.05/4.33 cnf(c_0_11991, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7273, c_0_4427]), c_0_4505]), c_0_4795]), c_0_5796]), c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_11992, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|c_Map_Orestrict__map(X1,X4,X5,X3)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),c_Map_Orestrict__map(X1,X4,X5,X3)),X2),c_Option_Ooption_ONone(X4))), inference(split_conjunct,[status(thm)],[c_0_6428]), ['final']). 4.05/4.33 cnf(c_0_11993, 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_7274]), ['final']). 4.05/4.33 cnf(c_0_11994, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X5))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7275]), ['final']). 4.05/4.33 cnf(c_0_11995, 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)), inference(split_conjunct,[status(thm)],[c_0_7276]), ['final']). 4.05/4.33 cnf(c_0_11996, 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_7277]), ['final']). 4.05/4.33 cnf(c_0_11997, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)))|hAPP(hAPP(c_List_Otake(X2),X4),X3)=c_List_OtakeWhile(X2,X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk12_4(X1,X3,X2,X4)),X4))), inference(split_conjunct,[status(thm)],[c_0_6848]), ['final']). 4.05/4.33 cnf(c_0_11998, plain, (hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X4|hAPP(hAPP(X2,X5),hAPP(X3,X4))=hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4))|~c_Finite__Set_Ofolding__one(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_7278]), ['final']). 4.05/4.33 cnf(c_0_11999, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk248_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_7279, c_0_5165]), ['final']). 4.05/4.33 cnf(c_0_12000, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk203_3(X1,X2,X3)),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)=X2|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))), inference(split_conjunct,[status(thm)],[c_0_6873]), ['final']). 4.05/4.33 cnf(c_0_12001, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk353_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_5096]), ['final']). 4.05/4.33 cnf(c_0_12002, 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_7280, c_0_4635]), c_0_4635]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_12003, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_7281]), ['final']). 4.05/4.33 cnf(c_0_12004, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))|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(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),X2)))=c_Random_Olog(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_7282]), ['final']). 4.05/4.33 cnf(c_0_12005, 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_7283]), ['final']). 4.05/4.33 cnf(c_0_12006, 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_7284]), ['final']). 4.05/4.33 cnf(c_0_12007, plain, (hAPP(X6,hAPP(hAPP(c_Set_Oinsert(X2),X8),X7))=hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,X7))|~c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7))), inference(split_conjunct,[status(thm)],[c_0_7285]), ['final']). 4.05/4.33 cnf(c_0_12008, plain, (X2=c_List_Olist_ONil(X1)|hAPP(c_List_Ofoldl(X1,X1,c_Groups_Otimes__class_Otimes(X1),hAPP(c_List_Ohd(X1),X2)),hAPP(c_List_Otl(X1),X2))=hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(c_List_Oset(X1),X2))|~class_Lattices_Oab__semigroup__idem__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_7286]), ['final']). 4.05/4.33 cnf(c_0_12009, 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)],[inference(rw,[status(thm)],[c_0_7287, c_0_6145]), c_0_6268]), ['final']). 4.05/4.33 cnf(c_0_12010, 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),esk353_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)))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_12011, 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_7288]), ['final']). 4.05/4.33 cnf(c_0_12012, 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_7131]), ['final']). 4.05/4.33 cnf(c_0_12013, 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_7133]), ['final']). 4.05/4.33 cnf(c_0_12014, 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_7134]), ['final']). 4.05/4.33 cnf(c_0_12015, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X1,X2,X3)))|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(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_12016, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),esk307_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_6351]), ['final']). 4.05/4.33 cnf(c_0_12017, plain, (hBOOL(hAPP(X1,esk505_4(X1,X2,X3,X4)))|hBOOL(hAPP(X1,esk504_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))), inference(split_conjunct,[status(thm)],[c_0_6673]), ['final']). 4.05/4.33 cnf(c_0_12018, 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)), inference(split_conjunct,[status(thm)],[c_0_7289]), ['final']). 4.05/4.33 cnf(c_0_12019, 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_7290, c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_12020, 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_7135]), ['final']). 4.05/4.33 cnf(c_0_12021, 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_7291]), ['final']). 4.05/4.33 cnf(c_0_12022, 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_7292]), ['final']). 4.05/4.33 cnf(c_0_12023, 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_6619]), ['final']). 4.05/4.33 cnf(c_0_12024, 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_7293, c_0_6962]), c_0_6963]), ['final']). 4.05/4.33 cnf(c_0_12025, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Divides_Odivmod__int(X1,X2)=hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_7294]), ['final']). 4.05/4.33 cnf(c_0_12026, 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_7295]), ['final']). 4.05/4.33 cnf(c_0_12027, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk361_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_12028, 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_7296, c_0_5716]), ['final']). 4.05/4.33 cnf(c_0_12029, 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_7297]), ['final']). 4.05/4.33 cnf(c_0_12030, 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_7298]), ['final']). 4.05/4.33 cnf(c_0_12031, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7299]), ['final']). 4.05/4.33 cnf(c_0_12032, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk362_3(X1,X3,X2)))|hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X1)))|~hBOOL(hAPP(X2,esk363_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_12033, 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_7300, c_0_5149]), c_0_5149]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_12034, 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_7301]), ['final']). 4.05/4.33 cnf(c_0_12035, 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_7302]), ['final']). 4.05/4.33 cnf(c_0_12036, plain, (hAPP(c_Nat_OSuc,esk389_5(X1,X2,X3,X4,X5))=X2|X3=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_6330]), ['final']). 4.05/4.33 cnf(c_0_12037, plain, (hAPP(c_Nat_OSuc,esk176_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_6327]), ['final']). 4.05/4.33 cnf(c_0_12038, 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_7303]), ['final']). 4.05/4.33 cnf(c_0_12039, 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_7304]), ['final']). 4.05/4.33 cnf(c_0_12040, 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_7305, c_0_4427]), c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_12041, 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_7306]), ['final']). 4.05/4.33 cnf(c_0_12042, 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_7307]), ['final']). 4.05/4.33 cnf(c_0_12043, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7308]), ['final']). 4.05/4.33 cnf(c_0_12044, 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))|hAPP(hAPP(c_List_Olist__update(X2,c_List_Obutlast(X2,X3)),X1),X4)=c_List_Obutlast(X2,hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4))), inference(split_conjunct,[status(thm)],[c_0_5929]), ['final']). 4.05/4.33 cnf(c_0_12045, plain, (hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X3),X4)))|c_Fun_Oinj__on(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X6),X5),X4)|~c_Fun_Oinj__on(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_7309]), ['final']). 4.05/4.33 cnf(c_0_12046, plain, (X1=c_List_Olist_ONil(tc_List_Olist(X2))|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)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X2))),c_List_Otranspose(X2,X1))|~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_7310]), ['final']). 4.05/4.33 cnf(c_0_12047, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7311]), ['final']). 4.05/4.33 cnf(c_0_12048, 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_OgreaterThanLessThan(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7312]), ['final']). 4.05/4.33 cnf(c_0_12049, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_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)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_12050, 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_7313]), ['final']). 4.05/4.33 cnf(c_0_12051, 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_7314]), ['final']). 4.05/4.33 cnf(c_0_12052, 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_7315]), ['final']). 4.05/4.33 cnf(c_0_12053, 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_7316]), ['final']). 4.05/4.33 cnf(c_0_12054, 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(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk362_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_5093]), ['final']). 4.05/4.33 cnf(c_0_12055, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7317]), ['final']). 4.05/4.33 cnf(c_0_12056, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X4)=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))|~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_7318]), ['final']). 4.05/4.33 cnf(c_0_12057, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7319]), ['final']). 4.05/4.33 cnf(c_0_12058, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7320]), ['final']). 4.05/4.33 cnf(c_0_12059, 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_7321]), ['final']). 4.05/4.33 cnf(c_0_12060, 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_7322]), ['final']). 4.05/4.33 cnf(c_0_12061, 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_7323]), ['final']). 4.05/4.33 cnf(c_0_12062, 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_7324]), ['final']). 4.05/4.33 cnf(c_0_12063, 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_7325]), ['final']). 4.05/4.33 cnf(c_0_12064, 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,esk297_6(X3,X2,X1,X4,X5,X6)),esk298_6(X3,X2,X1,X4,X5,X6))))), inference(split_conjunct,[status(thm)],[c_0_6741]), ['final']). 4.05/4.33 cnf(c_0_12065, 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)))|esk319_2(X1,X2)!=esk318_2(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1))|~hBOOL(hAPP(c_List_Odistinct(X2),esk317_2(X1,X2)))), inference(rw,[status(thm)],[c_0_7326, c_0_4767]), ['final']). 4.05/4.33 cnf(c_0_12066, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk200_5(X3,X4,X5,X2,X1)),esk201_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)))), inference(split_conjunct,[status(thm)],[c_0_7180]), ['final']). 4.05/4.33 cnf(c_0_12067, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7327]), ['final']). 4.05/4.33 cnf(c_0_12068, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X4)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7328]), ['final']). 4.05/4.33 cnf(c_0_12069, 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_7308]), ['final']). 4.05/4.33 cnf(c_0_12070, 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_7329]), ['final']). 4.05/4.33 cnf(c_0_12071, plain, (X5=X2|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)),X4)|~hBOOL(hAPP(c_List_Odistinct(X3),X4))|hAPP(c_Map_Omap__of(X3,X1),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2))!=hAPP(c_Map_Omap__of(X3,X1),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_7330]), ['final']). 4.05/4.33 cnf(c_0_12072, 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_7331]), ['final']). 4.05/4.33 cnf(c_0_12073, 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,esk199_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_7332]), ['final']). 4.05/4.33 cnf(c_0_12074, 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_7333]), ['final']). 4.05/4.33 cnf(c_0_12075, 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_7334]), ['final']). 4.05/4.33 cnf(c_0_12076, 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_7335]), ['final']). 4.05/4.33 cnf(c_0_12077, 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_7336]), ['final']). 4.05/4.33 cnf(c_0_12078, plain, (hAPP(hAPP(X3,X5),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X5),X6)),X4)|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_7337]), ['final']). 4.05/4.33 cnf(c_0_12079, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk487_3(X2,X3,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X2,c_Enum_Oenum__class_Oenum(X1)))))|~c_Enum_Oex__n__lists(X1,X3,X2)|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_7338]), ['final']). 4.05/4.33 cnf(c_0_12080, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7339]), ['final']). 4.05/4.33 cnf(c_0_12081, 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),esk353_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(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_12082, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_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))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_12083, 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_7340]), ['final']). 4.05/4.33 cnf(c_0_12084, 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)), inference(split_conjunct,[status(thm)],[c_0_7341]), ['final']). 4.05/4.33 cnf(c_0_12085, 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_7342]), ['final']). 4.05/4.33 cnf(c_0_12086, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|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_7343]), ['final']). 4.05/4.33 cnf(c_0_12087, plain, (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,X3)),c_Big__Operators_Olattice__class_OInf__fin(X1,X2))=c_Big__Operators_Olattice__class_OInf__fin(X1,X2)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7344]), ['final']). 4.05/4.33 cnf(c_0_12088, plain, (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),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_7345]), ['final']). 4.05/4.33 cnf(c_0_12089, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7346]), ['final']). 4.05/4.33 cnf(c_0_12090, 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)), inference(split_conjunct,[status(thm)],[c_0_7347]), ['final']). 4.05/4.33 cnf(c_0_12091, 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_7348]), ['final']). 4.05/4.33 cnf(c_0_12092, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_7349]), ['final']). 4.05/4.33 cnf(c_0_12093, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7350]), ['final']). 4.05/4.33 cnf(c_0_12094, plain, (X3=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),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_7351]), ['final']). 4.05/4.33 cnf(c_0_12095, 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_7352]), ['final']). 4.05/4.33 cnf(c_0_12096, 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_7353]), ['final']). 4.05/4.33 cnf(c_0_12097, 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_7354]), ['final']). 4.05/4.33 cnf(c_0_12098, plain, (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_7355]), ['final']). 4.05/4.33 cnf(c_0_12099, 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_7356]), ['final']). 4.05/4.33 cnf(c_0_12100, 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_7357]), ['final']). 4.05/4.33 cnf(c_0_12101, 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_7358]), ['final']). 4.05/4.33 cnf(c_0_12102, plain, (c_Big__Operators_Olattice__class_OInf__fin(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_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6415]), ['final']). 4.05/4.33 cnf(c_0_12103, plain, (X3=c_Big__Operators_Olinorder__class_OMax(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_6429]), ['final']). 4.05/4.33 cnf(c_0_12104, 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_7359, c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_12105, 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_4647]), ['final']). 4.05/4.33 cnf(c_0_12106, 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_7360, c_0_7022]), ['final']). 4.05/4.33 cnf(c_0_12107, 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_7361, c_0_4519]), c_0_4519]), ['final']). 4.05/4.33 cnf(c_0_12108, 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_6442]), ['final']). 4.05/4.33 cnf(c_0_12109, 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_6422]), ['final']). 4.05/4.33 cnf(c_0_12110, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7362, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), ['final']). 4.05/4.33 cnf(c_0_12111, plain, (X3=X2|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_7363]), ['final']). 4.05/4.33 cnf(c_0_12112, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_3(X2,X3,X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,esk355_3(X2,X3,X1)))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_12113, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk353_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_12114, plain, (hAPP(hAPP(c_List_Oappend(X1),esk369_3(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),esk370_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_7364]), ['final']). 4.05/4.33 cnf(c_0_12115, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),esk382_3(X1,X3,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk383_3(X1,X3,X2)))|~hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_7365]), ['final']). 4.05/4.33 cnf(c_0_12116, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk509_3(X2,X3,X1)),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5446]), ['final']). 4.05/4.33 cnf(c_0_12117, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X2))=hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~class_Lattices_Oab__semigroup__idem__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7366]), ['final']). 4.05/4.33 cnf(c_0_12118, 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_7367, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_12119, 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_7368]), ['final']). 4.05/4.33 cnf(c_0_12120, 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_7369]), ['final']). 4.05/4.33 cnf(c_0_12121, 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_7370, c_0_5131])])]), c_0_7371]), c_0_7372]), ['final']). 4.05/4.33 cnf(c_0_12122, 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),esk37_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))), inference(rw,[status(thm)],[c_0_7373, c_0_4950]), ['final']). 4.05/4.33 cnf(c_0_12123, plain, (X3=hAPP(hAPP(c_List_Oappend(X1),esk271_3(X3,X2,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk272_3(X3,X2,X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_5927]), ['final']). 4.05/4.33 cnf(c_0_12124, 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_7374]), ['final']). 4.05/4.33 cnf(c_0_12125, 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))), inference(split_conjunct,[status(thm)],[c_0_7375]), ['final']). 4.05/4.33 cnf(c_0_12126, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Olist_OCons(X2),hAPP(c_List_Ohd(X2),X1)),hAPP(hAPP(c_List_Otake(X2),X3),hAPP(c_List_Otl(X2),X1)))=hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_OSuc,X3)),X1)), inference(split_conjunct,[status(thm)],[c_0_7376]), ['final']). 4.05/4.33 cnf(c_0_12127, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Nat_OSuc,esk494_3(X3,X2,X1)))))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_5569]), ['final']). 4.05/4.33 cnf(c_0_12128, 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_7377, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), ['final']). 4.05/4.33 cnf(c_0_12129, 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_7378]), ['final']). 4.05/4.33 cnf(c_0_12130, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk501_5(X3,X4,X5,X2,X1),esk502_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_6855]), ['final']). 4.05/4.33 cnf(c_0_12131, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk130_5(X3,X4,X5,X2,X1),esk131_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_7240]), ['final']). 4.05/4.33 cnf(c_0_12132, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk479_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_7379]), ['final']). 4.05/4.33 cnf(c_0_12133, 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_7380]), ['final']). 4.05/4.33 cnf(c_0_12134, 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_7381]), ['final']). 4.05/4.33 cnf(c_0_12135, 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_7382, c_0_4867]), c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_12136, 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_7383, c_0_4867]), c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_12137, 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_7384]), ['final']). 4.05/4.33 cnf(c_0_12138, 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_7385]), ['final']). 4.05/4.33 cnf(c_0_12139, 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_Otake(X2),X1),X3)=c_List_OtakeWhile(X2,X4,X3)|~hBOOL(hAPP(X4,hAPP(hAPP(c_List_Onth(X2),X3),esk12_4(X4,X3,X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_6848]), ['final']). 4.05/4.33 cnf(c_0_12140, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk347_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_7386]), ['final']). 4.05/4.33 cnf(c_0_12141, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|c_Map_Orestrict__map(X1,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X4)),X5),X2),X6),X3)=c_Map_Orestrict__map(X1,X4,X5,X3)), inference(split_conjunct,[status(thm)],[c_0_5068]), ['final']). 4.05/4.33 cnf(c_0_12142, 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_7185]), ['final']). 4.05/4.33 cnf(c_0_12143, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X4),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),hAPP(c_List_Oset(X2),X3))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_List_Odistinct(X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7387]), ['final']). 4.05/4.33 cnf(c_0_12144, 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_5569]), ['final']). 4.05/4.33 cnf(c_0_12145, 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_7388]), ['final']). 4.05/4.33 cnf(c_0_12146, plain, (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))=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)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7389]), ['final']). 4.05/4.33 cnf(c_0_12147, 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_7390]), ['final']). 4.05/4.33 cnf(c_0_12148, plain, (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))|~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_7188]), ['final']). 4.05/4.33 cnf(c_0_12149, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk159_3(X1,X2,X3)))=X3|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7391]), ['final']). 4.05/4.33 cnf(c_0_12150, 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)),esk277_3(X1,X3,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk276_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_7392]), ['final']). 4.05/4.33 cnf(c_0_12151, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_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)))|~hBOOL(hAPP(X3,esk353_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_12152, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_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)))|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_5096]), ['final']). 4.05/4.33 cnf(c_0_12153, 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_7393]), ['final']). 4.05/4.33 cnf(c_0_12154, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,esk494_3(X1,X2,X3)))))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_5569]), ['final']). 4.05/4.33 cnf(c_0_12155, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X2,X3,X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1,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_5093]), ['final']). 4.05/4.33 cnf(c_0_12156, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk353_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_5096]), ['final']). 4.05/4.33 cnf(c_0_12157, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk353_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,esk355_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_12158, 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_7394, c_0_4915]), ['final']). 4.05/4.33 cnf(c_0_12159, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk107_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_7395]), ['final']). 4.05/4.33 cnf(c_0_12160, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk16_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_7068]), ['final']). 4.05/4.33 cnf(c_0_12161, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk356_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),c_List_Oreplicate(X1,X4,X3))))|hBOOL(hAPP(X2,X3))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X4), inference(split_conjunct,[status(thm)],[c_0_7396]), ['final']). 4.05/4.33 cnf(c_0_12162, 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(tc_Int_Oint),X2),esk362_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_5093]), ['final']). 4.05/4.33 cnf(c_0_12163, 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_7397]), ['final']). 4.05/4.33 cnf(c_0_12164, 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_7398]), ['final']). 4.05/4.33 cnf(c_0_12165, 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_7399]), ['final']). 4.05/4.33 cnf(c_0_12166, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(c_Set_Oimage(X1,X4,X5),X3)=hAPP(c_Set_Oimage(X1,X4,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X4),X5),X2),X6)),X3)), inference(split_conjunct,[status(thm)],[c_0_6473]), ['final']). 4.05/4.33 cnf(c_0_12167, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk265_4(X2,X3,X4,X1)),X3))|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Wellfounded_Omax__extp(X1,X4,X3,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_5611]), ['final']). 4.05/4.33 cnf(c_0_12168, 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_7400, c_0_6268]), ['final']). 4.05/4.33 cnf(c_0_12169, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_7401]), ['final']). 4.05/4.33 cnf(c_0_12170, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk127_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,X3)|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7274]), ['final']). 4.05/4.33 cnf(c_0_12171, 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_7402]), ['final']). 4.05/4.33 cnf(c_0_12172, 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_7403]), ['final']). 4.05/4.33 cnf(c_0_12173, 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_7404]), ['final']). 4.05/4.33 cnf(c_0_12174, 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_7405]), ['final']). 4.05/4.33 cnf(c_0_12175, 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_7178]), ['final']). 4.05/4.33 cnf(c_0_12176, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk126_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,X3)|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7274]), ['final']). 4.05/4.33 cnf(c_0_12177, plain, (hAPP(X1,X2)=c_Option_Ooption_ONone(X3)|hAPP(X1,X2)=hAPP(c_Option_Ooption_OSome(X3),esk208_6(X2,X1,X4,X5,X6,X3))|c_Option_Ooption_ONone(X6)!=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X3,c_Option_Ooption_ONone(X6),X4),hAPP(X1,X2))), inference(rw,[status(thm)],[c_0_7406, c_0_7211]), ['final']). 4.05/4.33 cnf(c_0_12178, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk23_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_7407, c_0_6268]), ['final']). 4.05/4.33 cnf(c_0_12179, 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_7408]), ['final']). 4.05/4.33 cnf(c_0_12180, 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_7409]), ['final']). 4.05/4.33 cnf(c_0_12181, 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_7410]), ['final']). 4.05/4.33 cnf(c_0_12182, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),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_7411]), ['final']). 4.05/4.33 cnf(c_0_12183, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))|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)),esk429_3(X2,X3,X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7026]), ['final']). 4.05/4.33 cnf(c_0_12184, 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))|~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_6352]), ['final']). 4.05/4.33 cnf(c_0_12185, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__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_6347]), ['final']). 4.05/4.33 cnf(c_0_12186, 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_7412]), ['final']). 4.05/4.33 cnf(c_0_12187, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk454_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_7413]), ['final']). 4.05/4.33 cnf(c_0_12188, 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_7414]), ['final']). 4.05/4.33 cnf(c_0_12189, 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_7415]), ['final']). 4.05/4.33 cnf(c_0_12190, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_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,esk361_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_12191, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk362_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,esk363_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_12192, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X2),c_Lazy__Sequence_Osmall__lazy_H(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Lazy__Sequence_Osmall__lazy_H(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7416]), ['final']). 4.05/4.33 cnf(c_0_12193, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk144_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_7417]), ['final']). 4.05/4.33 cnf(c_0_12194, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk276_3(X2,X3,X1)),esk277_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_7392]), ['final']). 4.05/4.33 cnf(c_0_12195, 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_7418]), ['final']). 4.05/4.33 cnf(c_0_12196, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk69_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_7419]), ['final']). 4.05/4.33 cnf(c_0_12197, 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_7420]), ['final']). 4.05/4.33 cnf(c_0_12198, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7421]), ['final']). 4.05/4.33 cnf(c_0_12199, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk135_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_7422]), ['final']). 4.05/4.33 cnf(c_0_12200, 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_7423]), ['final']). 4.05/4.33 cnf(c_0_12201, 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),esk107_3(X2,X3,X1)),esk107_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_7395]), ['final']). 4.05/4.33 cnf(c_0_12202, 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),esk16_3(X2,X3,X1)),esk16_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_7068]), ['final']). 4.05/4.33 cnf(c_0_12203, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk514_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),esk515_3(X2,X3,X1)),esk515_3(X2,X3,X1))),X2))), inference(split_conjunct,[status(thm)],[c_0_4546]), ['final']). 4.05/4.33 cnf(c_0_12204, 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))), inference(split_conjunct,[status(thm)],[c_0_7424]), ['final']). 4.05/4.33 cnf(c_0_12205, 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_7425]), ['final']). 4.05/4.33 cnf(c_0_12206, 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_7426, c_0_5670]), ['final']). 4.05/4.33 cnf(c_0_12207, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X3),X4))=hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)|~class_Groups_Osemigroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7427]), ['final']). 4.05/4.33 cnf(c_0_12208, 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_7428]), ['final']). 4.05/4.33 cnf(c_0_12209, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk59_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_7429]), ['final']). 4.05/4.33 cnf(c_0_12210, plain, (hBOOL(hAPP(X1,esk73_2(X1,X2)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk71_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,esk70_2(X1,X2)))|~hBOOL(hAPP(X1,X3))), inference(rw,[status(thm)],[c_0_7430, c_0_6492]), ['final']). 4.05/4.33 cnf(c_0_12211, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|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))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_7431]), ['final']). 4.05/4.33 cnf(c_0_12212, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_List_Odrop(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)=hAPP(hAPP(c_List_Odrop(X2),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7432]), ['final']). 4.05/4.33 cnf(c_0_12213, 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_7150]), ['final']). 4.05/4.33 cnf(c_0_12214, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X2)),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7433]), ['final']). 4.05/4.33 cnf(c_0_12215, 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_7434]), ['final']). 4.05/4.33 cnf(c_0_12216, plain, (c_List_Olist_ONil(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)))=hAPP(c_List_Orotate1(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_7435]), ['final']). 4.05/4.33 cnf(c_0_12217, 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_7436, c_0_4742]), ['final']). 4.05/4.33 cnf(c_0_12218, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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),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_7437]), ['final']). 4.05/4.33 cnf(c_0_12219, 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_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_7438]), ['final']). 4.05/4.33 cnf(c_0_12220, 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_7439]), ['final']). 4.05/4.33 cnf(c_0_12221, 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_7437]), ['final']). 4.05/4.33 cnf(c_0_12222, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(c_List_Onth(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7440]), ['final']). 4.05/4.33 cnf(c_0_12223, 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),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_7441]), ['final']). 4.05/4.33 cnf(c_0_12224, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7308]), ['final']). 4.05/4.33 cnf(c_0_12225, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7442, c_0_4795]), c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_12226, plain, (X5=X3|X2=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),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_7443]), ['final']). 4.05/4.33 cnf(c_0_12227, 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_7294]), ['final']). 4.05/4.33 cnf(c_0_12228, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7444, c_0_4795]), c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_12229, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7445, c_0_4795]), c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_12230, 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_7446]), ['final']). 4.05/4.33 cnf(c_0_12231, 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_7447]), ['final']). 4.05/4.33 cnf(c_0_12232, plain, (hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,X1)),X4),X5),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X4),hAPP(hAPP(c_COMBC(X2,X3,X1),X5),X6))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7448]), ['final']). 4.05/4.33 cnf(c_0_12233, 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_7449])]), ['final']). 4.05/4.33 cnf(c_0_12234, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk437_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_7450]), ['final']). 4.05/4.33 cnf(c_0_12235, 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),X2),X1)),X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(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))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7451]), ['final']). 4.05/4.33 cnf(c_0_12236, 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_7452]), ['final']). 4.05/4.33 cnf(c_0_12237, 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_7453]), ['final']). 4.05/4.33 cnf(c_0_12238, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk177_2(X2,X1)),esk177_2(X2,X1))),X2))|c_Relation_Oirrefl(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7454]), ['final']). 4.05/4.33 cnf(c_0_12239, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)=X4|X3=hAPP(hAPP(c_List_Oappend(X1),esk3_5(X4,X5,X3,X2,X1)),X4)|hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=hAPP(hAPP(c_List_Oappend(X1),X5),X4)), inference(split_conjunct,[status(thm)],[c_0_7455]), ['final']). 4.05/4.33 cnf(c_0_12240, plain, (hAPP(hAPP(c_List_Oappend(X1),esk428_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)), inference(split_conjunct,[status(thm)],[c_0_7456]), ['final']). 4.05/4.33 cnf(c_0_12241, 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_7001]), ['final']). 4.05/4.33 cnf(c_0_12242, 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_7457]), ['final']). 4.05/4.33 cnf(c_0_12243, 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_7458]), ['final']). 4.05/4.33 cnf(c_0_12244, 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_7459]), ['final']). 4.05/4.33 cnf(c_0_12245, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk261_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_7460]), ['final']). 4.05/4.33 cnf(c_0_12246, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)=X4|X5=hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk3_5(X4,X5,X3,X2,X1))|hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=hAPP(hAPP(c_List_Oappend(X1),X5),X4)), inference(split_conjunct,[status(thm)],[c_0_7455]), ['final']). 4.05/4.33 cnf(c_0_12247, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk428_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)), inference(split_conjunct,[status(thm)],[c_0_7456]), ['final']). 4.05/4.33 cnf(c_0_12248, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk359_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_7461]), ['final']). 4.05/4.33 cnf(c_0_12249, 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_6994]), ['final']). 4.05/4.33 cnf(c_0_12250, 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_7462]), ['final']). 4.05/4.33 cnf(c_0_12251, 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_7463]), ['final']). 4.05/4.33 cnf(c_0_12252, 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_7464]), ['final']). 4.05/4.33 cnf(c_0_12253, 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_7465, c_0_4523]), c_0_4523]), ['final']). 4.05/4.33 cnf(c_0_12254, 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),c_List_Oremdups(X1,X5))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7466]), ['final']). 4.05/4.33 cnf(c_0_12255, 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_6014]), ['final']). 4.05/4.33 cnf(c_0_12256, 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_7467]), ['final']). 4.05/4.33 cnf(c_0_12257, 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_7065]), ['final']). 4.05/4.33 cnf(c_0_12258, plain, (hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X3))),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))), inference(rw,[status(thm)],[c_0_7468, c_0_4519]), ['final']). 4.05/4.33 cnf(c_0_12259, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_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))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_12260, plain, (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)))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_7469]), ['final']). 4.05/4.33 cnf(c_0_12261, 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_7066]), ['final']). 4.05/4.33 cnf(c_0_12262, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)|~class_Divides_Oring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7470]), ['final']). 4.05/4.33 cnf(c_0_12263, 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),esk353_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_5096]), ['final']). 4.05/4.33 cnf(c_0_12264, plain, (hBOOL(hAPP(X2,c_Option_Ooption_ONone(X1)))|hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1))))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X1)),X2))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_7471]), ['final']). 4.05/4.33 cnf(c_0_12265, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|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_7472]), ['final']). 4.05/4.33 cnf(c_0_12266, plain, (hBOOL(hAPP(X4,X2))|c_List_OtakeWhile(X1,X4,X3)=c_List_OtakeWhile(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_7473]), ['final']). 4.05/4.33 cnf(c_0_12267, 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,esk2_4(X2,X1,X3,X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7009]), ['final']). 4.05/4.33 cnf(c_0_12268, 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_7474]), ['final']). 4.05/4.33 cnf(c_0_12269, 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_7475]), ['final']). 4.05/4.33 cnf(c_0_12270, 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_7475]), ['final']). 4.05/4.33 cnf(c_0_12271, 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),esk445_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_6751]), ['final']). 4.05/4.33 cnf(c_0_12272, 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_7476, c_0_4915]), ['final']). 4.05/4.33 cnf(c_0_12273, 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_7477]), ['final']). 4.05/4.33 cnf(c_0_12274, 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),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_5253]), ['final']). 4.05/4.33 cnf(c_0_12275, 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_7478, c_0_4635]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_12276, 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_7002]), ['final']). 4.05/4.33 cnf(c_0_12277, 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_7479, c_0_4867]), c_0_4867]), c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_12278, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7480, c_0_4867]), c_0_4867]), c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_12279, 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,esk474_5(X4,X2,X3,X3,X1))!=hAPP(X4,esk474_5(X4,X2,X3,X3,X1))|~c_Nat__Transfer_Onat__set(X3)|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)), inference(er,[status(thm)],[c_0_7481]), ['final']). 4.05/4.33 cnf(c_0_12280, 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,esk139_5(X4,X2,X3,X3,X1))!=hAPP(X4,esk139_5(X4,X2,X3,X3,X1))|~c_Nat__Transfer_Onat__set(X3)|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1)), inference(er,[status(thm)],[c_0_7482]), ['final']). 4.05/4.33 cnf(c_0_12281, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7483]), ['final']). 4.05/4.33 cnf(c_0_12282, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk120_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_7484]), ['final']). 4.05/4.33 cnf(c_0_12283, 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_7485]), ['final']). 4.05/4.33 cnf(c_0_12284, plain, (X4=X2|~class_Rings_Olinordered__semidom(X1)|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))), inference(split_conjunct,[status(thm)],[c_0_7486]), ['final']). 4.05/4.33 cnf(c_0_12285, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk87_2(X2,X1)),esk87_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_7487, c_0_5716]), ['final']). 4.05/4.33 cnf(c_0_12286, 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_7488]), ['final']). 4.05/4.33 cnf(c_0_12287, 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_7489]), ['final']). 4.05/4.33 cnf(c_0_12288, 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_7490]), ['final']). 4.05/4.33 cnf(c_0_12289, 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_7491]), ['final']). 4.05/4.33 cnf(c_0_12290, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X3|c_List_Olast(X1,X2)=c_List_Olast(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))|c_List_Olist_ONil(X1)=X2), inference(split_conjunct,[status(thm)],[c_0_5462]), ['final']). 4.05/4.33 cnf(c_0_12291, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2)),X3)|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7492]), ['final']). 4.05/4.33 cnf(c_0_12292, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7493]), ['final']). 4.05/4.33 cnf(c_0_12293, 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_7494]), ['final']). 4.05/4.33 cnf(c_0_12294, 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_7495, c_0_4427]), c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_12295, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X5),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_7496]), ['final']). 4.05/4.33 cnf(c_0_12296, plain, (c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7497]), ['final']). 4.05/4.33 cnf(c_0_12297, 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_7498]), ['final']). 4.05/4.33 cnf(c_0_12298, 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_7499]), ['final']). 4.05/4.33 cnf(c_0_12299, 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_7500]), ['final']). 4.05/4.33 cnf(c_0_12300, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(hAPP(c_List_Oappend(X1),X3),c_List_Oremove1(X1,X2,X4))=c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_7501]), ['final']). 4.05/4.33 cnf(c_0_12301, 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_7502]), ['final']). 4.05/4.33 cnf(c_0_12302, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk339_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_7503]), ['final']). 4.05/4.33 cnf(c_0_12303, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk93_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_7218]), ['final']). 4.05/4.33 cnf(c_0_12304, 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_7504, c_0_4635]), c_0_5149]), c_0_4867]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_12305, plain, (X3=hAPP(X4,X2)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Finite__Set_Ofolding__one(X1,X5,X4)), inference(split_conjunct,[status(thm)],[c_0_6376]), ['final']). 4.05/4.33 cnf(c_0_12306, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk41_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_7505]), ['final']). 4.05/4.33 cnf(c_0_12307, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk468_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_7506]), ['final']). 4.05/4.33 cnf(c_0_12308, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk460_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_7507]), ['final']). 4.05/4.33 cnf(c_0_12309, 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)), inference(split_conjunct,[status(thm)],[c_0_7508]), ['final']). 4.05/4.33 cnf(c_0_12310, plain, (X1=hAPP(c_List_Orev(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4))|hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)!=hAPP(c_List_Orev(X2),X1)), inference(rw,[status(thm)],[c_0_7509, c_0_7510]), ['final']). 4.05/4.33 cnf(c_0_12311, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk494_3(X2,X3,X1))),X3))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_5569]), ['final']). 4.05/4.33 cnf(c_0_12312, 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_7511]), ['final']). 4.05/4.33 cnf(c_0_12313, 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_7288]), ['final']). 4.05/4.33 cnf(c_0_12314, 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)), inference(split_conjunct,[status(thm)],[c_0_7512]), ['final']). 4.05/4.33 cnf(c_0_12315, 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)), inference(split_conjunct,[status(thm)],[c_0_7513]), ['final']). 4.05/4.33 cnf(c_0_12316, 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_7514]), ['final']). 4.05/4.33 cnf(c_0_12317, 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_7515]), ['final']). 4.05/4.33 cnf(c_0_12318, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7516]), ['final']). 4.05/4.33 cnf(c_0_12319, 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_7517]), ['final']). 4.05/4.33 cnf(c_0_12320, 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_6361]), ['final']). 4.05/4.33 cnf(c_0_12321, 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_6366]), ['final']). 4.05/4.33 cnf(c_0_12322, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7518]), ['final']). 4.05/4.33 cnf(c_0_12323, 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_7519]), ['final']). 4.05/4.33 cnf(c_0_12324, 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_7520]), ['final']). 4.05/4.33 cnf(c_0_12325, plain, (X1=c_Option_Ooption_ONone(X2)|c_Map_Odom(X3,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X2)),X4),X5),X1))=hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Map_Odom(X3,X2,X4))), inference(split_conjunct,[status(thm)],[c_0_5660]), ['final']). 4.05/4.33 cnf(c_0_12326, 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))), inference(split_conjunct,[status(thm)],[c_0_7521]), ['final']). 4.05/4.33 cnf(c_0_12327, 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_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7522]), ['final']). 4.05/4.33 cnf(c_0_12328, 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)), inference(split_conjunct,[status(thm)],[c_0_7523]), ['final']). 4.05/4.33 cnf(c_0_12329, 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)), inference(split_conjunct,[status(thm)],[c_0_7524]), ['final']). 4.05/4.33 cnf(c_0_12330, 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_7525, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), ['final']). 4.05/4.33 cnf(c_0_12331, 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_7526, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_12332, 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_7527]), ['final']). 4.05/4.33 cnf(c_0_12333, 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_7528]), ['final']). 4.05/4.33 cnf(c_0_12334, 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_7529, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), ['final']). 4.05/4.33 cnf(c_0_12335, 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_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7530]), ['final']). 4.05/4.33 cnf(c_0_12336, 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_7531]), ['final']). 4.05/4.33 cnf(c_0_12337, plain, (hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7532]), ['final']). 4.05/4.33 cnf(c_0_12338, 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_7533, c_0_5149]), c_0_6120]), ['final']). 4.05/4.33 cnf(c_0_12339, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(X2,X3)),hAPP(X4,X3))=hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,X1)),X2),X4),X3)|~class_Groups_Ominus(X1)), inference(split_conjunct,[status(thm)],[c_0_7534]), ['final']). 4.05/4.33 cnf(c_0_12340, 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_7535]), ['final']). 4.05/4.33 cnf(c_0_12341, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X2,X3)),hAPP(X4,X3))=hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,X1)),X2),X4),X3)|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7536]), ['final']). 4.05/4.33 cnf(c_0_12342, 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_7537]), ['final']). 4.05/4.33 cnf(c_0_12343, 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)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7538]), ['final']). 4.05/4.33 cnf(c_0_12344, 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_7539, c_0_7540]), ['final']). 4.05/4.33 cnf(c_0_12345, 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_7541]), ['final']). 4.05/4.33 cnf(c_0_12346, 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))|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(tc_Int_Oint),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_7542]), ['final']). 4.05/4.33 cnf(c_0_12347, 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),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7441]), ['final']). 4.05/4.33 cnf(c_0_12348, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7308]), ['final']). 4.05/4.33 cnf(c_0_12349, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7308]), ['final']). 4.05/4.33 cnf(c_0_12350, 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,esk357_5(X3,X2,X4,X5,X1))),X3))), inference(split_conjunct,[status(thm)],[c_0_6842]), ['final']). 4.05/4.33 cnf(c_0_12351, 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,esk74_5(X3,X4,X5,X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_6844]), ['final']). 4.05/4.33 cnf(c_0_12352, 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_7543]), ['final']). 4.05/4.33 cnf(c_0_12353, 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_7544]), ['final']). 4.05/4.33 cnf(c_0_12354, 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),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_7441]), ['final']). 4.05/4.33 cnf(c_0_12355, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk494_3(X1,X2,X3))),X2))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_5569]), ['final']). 4.05/4.33 cnf(c_0_12356, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))), inference(split_conjunct,[status(thm)],[c_0_5438]), ['final']). 4.05/4.33 cnf(c_0_12357, 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_7545]), ['final']). 4.05/4.33 cnf(c_0_12358, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk211_2(X2,X1)),hAPP(c_Relation_OImage(X1,X1,X2),esk211_2(X2,X1))))|c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7546]), ['final']). 4.05/4.33 cnf(c_0_12359, 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_7547]), ['final']). 4.05/4.33 cnf(c_0_12360, 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_7548]), ['final']). 4.05/4.33 cnf(c_0_12361, 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_7549, c_0_7550]), ['final']). 4.05/4.33 cnf(c_0_12362, plain, (c_Groups_Oone__class_Oone(X4)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X3,c_Groups_Otimes__class_Otimes(X4)),X1),c_Groups_Oone__class_Oone(X4)),X2)|hAPP(X1,esk40_4(X1,X2,X3,X4))!=c_Groups_Oone__class_Oone(X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))|~class_Groups_Ocomm__monoid__mult(X4)), inference(split_conjunct,[status(thm)],[c_0_6896]), ['final']). 4.05/4.33 cnf(c_0_12363, plain, (c_Enum_Oenum__class_Oenum(tc_Option_Ooption(X1))=hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(X1)),c_Option_Ooption_ONone(X1)),hAPP(hAPP(c_List_Omap(X1,tc_Option_Ooption(X1)),c_Option_Ooption_OSome(X1)),c_Enum_Oenum__class_Oenum(X1)))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_7551]), ['final']). 4.05/4.33 cnf(c_0_12364, 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_7552]), ['final']). 4.05/4.33 cnf(c_0_12365, 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_7553]), ['final']). 4.05/4.33 cnf(c_0_12366, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk310_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_7554]), ['final']). 4.05/4.33 cnf(c_0_12367, 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_7555]), ['final']). 4.05/4.33 cnf(c_0_12368, 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_7556]), ['final']). 4.05/4.33 cnf(c_0_12369, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4))=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7557]), ['final']). 4.05/4.33 cnf(c_0_12370, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk400_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_7558]), ['final']). 4.05/4.33 cnf(c_0_12371, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_7559, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_12372, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk56_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_7560]), ['final']). 4.05/4.33 cnf(c_0_12373, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7561, c_0_4795]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_12374, 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_7562]), ['final']). 4.05/4.33 cnf(c_0_12375, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))), inference(split_conjunct,[status(thm)],[c_0_7563]), ['final']). 4.05/4.33 cnf(c_0_12376, 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_7564]), ['final']). 4.05/4.33 cnf(c_0_12377, 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_7565]), ['final']). 4.05/4.33 cnf(c_0_12378, 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_7566]), ['final']). 4.05/4.33 cnf(c_0_12379, 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_7567]), ['final']). 4.05/4.33 cnf(c_0_12380, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk353_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_12381, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),esk353_3(X2,X3,X1)))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,esk355_3(X2,X3,X1)))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_12382, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk446_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)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_7568]), ['final']). 4.05/4.33 cnf(c_0_12383, 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_7569]), ['final']). 4.05/4.33 cnf(c_0_12384, 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_7570]), ['final']). 4.05/4.33 cnf(c_0_12385, 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_7571]), ['final']). 4.05/4.33 cnf(c_0_12386, 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_7572]), ['final']). 4.05/4.33 cnf(c_0_12387, 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_7573]), ['final']). 4.05/4.33 cnf(c_0_12388, 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_7574]), ['final']). 4.05/4.33 cnf(c_0_12389, 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_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7573]), ['final']). 4.05/4.33 cnf(c_0_12390, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Rings_Oordered__cancel__semiring(X1)), inference(split_conjunct,[status(thm)],[c_0_7575]), ['final']). 4.05/4.33 cnf(c_0_12391, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X2)=c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7576]), ['final']). 4.05/4.33 cnf(c_0_12392, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X2)=c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7577]), ['final']). 4.05/4.33 cnf(c_0_12393, 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_7578]), ['final']). 4.05/4.33 cnf(c_0_12394, plain, (c_List_Olist__all2(X2,X5,X1,X3,X4)|~hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk442_5(X4,X3,X1,X5,X2))),hAPP(hAPP(c_List_Onth(X5),X4),esk442_5(X4,X3,X1,X5,X2))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X4)), inference(split_conjunct,[status(thm)],[c_0_7150]), ['final']). 4.05/4.33 cnf(c_0_12395, 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_7579]), ['final']). 4.05/4.33 cnf(c_0_12396, 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_7575]), ['final']). 4.05/4.33 cnf(c_0_12397, 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_7580]), ['final']). 4.05/4.33 cnf(c_0_12398, 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_7581]), ['final']). 4.05/4.33 cnf(c_0_12399, plain, (c_List_Olist__all2(X2,X5,X1,X3,X4)|~hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk86_5(X1,X4,X5,X3,X2))),hAPP(hAPP(c_List_Onth(X5),X4),esk86_5(X1,X4,X5,X3,X2))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X4)), inference(split_conjunct,[status(thm)],[c_0_7149]), ['final']). 4.05/4.33 cnf(c_0_12400, 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_7582]), ['final']). 4.05/4.33 cnf(c_0_12401, 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_7583]), ['final']). 4.05/4.33 cnf(c_0_12402, 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_7584]), ['final']). 4.05/4.33 cnf(c_0_12403, 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_7585]), ['final']). 4.05/4.33 cnf(c_0_12404, 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_7586]), ['final']). 4.05/4.33 cnf(c_0_12405, 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_7587]), ['final']). 4.05/4.33 cnf(c_0_12406, 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_7588]), ['final']). 4.05/4.33 cnf(c_0_12407, 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))),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7589]), ['final']). 4.05/4.33 cnf(c_0_12408, 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_7590]), ['final']). 4.05/4.33 cnf(c_0_12409, plain, (hAPP(c_Option_Ooption_OSome(X1),esk477_7(X2,X3,X4,X5,X6,X7,X1))=hAPP(X4,X3)|hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X7),X1,c_Option_Ooption_ONone(X7),X5),hAPP(X4,X3))!=hAPP(c_Option_Ooption_OSome(X7),X2)), inference(rw,[status(thm)],[c_0_7591, c_0_7211]), ['final']). 4.05/4.33 cnf(c_0_12410, plain, (c_List_Olist_ONil(X1)=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)|~hBOOL(hAPP(X2,hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7592, c_0_4950]), c_0_4950]), ['final']). 4.05/4.33 cnf(c_0_12411, 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_5906]), ['final']). 4.05/4.33 cnf(c_0_12412, 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_7593]), ['final']). 4.05/4.33 cnf(c_0_12413, 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_7594]), ['final']). 4.05/4.33 cnf(c_0_12414, 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_7595]), ['final']). 4.05/4.33 cnf(c_0_12415, 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_7596, c_0_5149]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_12416, 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_7597]), ['final']). 4.05/4.33 cnf(c_0_12417, plain, (hAPP(c_Product__Type_Osnd(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)|~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_6895]), ['final']). 4.05/4.33 cnf(c_0_12418, plain, (X2=X4|~class_Rings_Olinordered__semidom(X1)|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),hAPP(c_Nat_OSuc,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),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_7598]), ['final']). 4.05/4.33 cnf(c_0_12419, 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_7599, c_0_5201]), ['final']). 4.05/4.33 cnf(c_0_12420, 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_7600]), ['final']). 4.05/4.33 cnf(c_0_12421, 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_7601]), ['final']). 4.05/4.33 cnf(c_0_12422, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7602]), ['final']). 4.05/4.33 cnf(c_0_12423, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Rings_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7603]), ['final']). 4.05/4.33 cnf(c_0_12424, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk306_5(X2,X3,X4,X1,X5)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X5),X4),X3)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X5)|~class_Orderings_Olinorder(X5)), inference(split_conjunct,[status(thm)],[c_0_7207]), ['final']). 4.05/4.33 cnf(c_0_12425, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk122_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_Orderings_Olinorder(X5)|~class_Complete__Lattice_Ocomplete__lattice(X5)), inference(split_conjunct,[status(thm)],[c_0_7208]), ['final']). 4.05/4.33 cnf(c_0_12426, plain, (hAPP(X1,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|esk25_3(X1,X3,X4)=X2|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X3)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X4),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(rw,[status(thm)],[c_0_7604, c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_12427, plain, (hBOOL(hAPP(hAPP(hAPP(X1,esk440_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_7605]), ['final']). 4.05/4.33 cnf(c_0_12428, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3)),c_Divides_Odiv__class_Omod(X1,X2,X3))|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7606]), ['final']). 4.05/4.33 cnf(c_0_12429, 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_7607]), ['final']). 4.05/4.33 cnf(c_0_12430, 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_7608]), ['final']). 4.05/4.33 cnf(c_0_12431, 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_7609]), ['final']). 4.05/4.33 cnf(c_0_12432, 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)), inference(split_conjunct,[status(thm)],[c_0_7610]), ['final']). 4.05/4.33 cnf(c_0_12433, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X5),X1),X3)|hAPP(X1,esk493_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_6530]), ['final']). 4.05/4.33 cnf(c_0_12434, 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,esk518_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_6532]), ['final']). 4.05/4.33 cnf(c_0_12435, plain, (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,esk238_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_6531]), ['final']). 4.05/4.33 cnf(c_0_12436, plain, (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,esk178_5(X2,X3,X4,X5,X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_6533]), ['final']). 4.05/4.33 cnf(c_0_12437, 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_7611]), ['final']). 4.05/4.33 cnf(c_0_12438, 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_7612]), ['final']). 4.05/4.33 cnf(c_0_12439, 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_7613]), ['final']). 4.05/4.33 cnf(c_0_12440, 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_Oordered__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7603]), ['final']). 4.05/4.33 cnf(c_0_12441, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7602]), ['final']). 4.05/4.33 cnf(c_0_12442, 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),esk60_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_List_Oset(tc_Nat_Onat),X1)))), inference(er,[status(thm)],[c_0_7614]), ['final']). 4.05/4.33 cnf(c_0_12443, 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_7615]), ['final']). 4.05/4.33 cnf(c_0_12444, 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_7616]), ['final']). 4.05/4.33 cnf(c_0_12445, 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_7617]), ['final']). 4.05/4.33 cnf(c_0_12446, 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_7618, c_0_5149]), c_0_5149]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_12447, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7619]), ['final']). 4.05/4.33 cnf(c_0_12448, plain, (hAPP(X4,X3)=c_Option_Ooption_ONone(X6)|c_Option_Ooption_ONone(X1)=hAPP(X2,esk208_6(X3,X4,X2,X5,X1,X6))|c_Option_Ooption_ONone(X1)!=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X6,c_Option_Ooption_ONone(X1),X2),hAPP(X4,X3))), inference(rw,[status(thm)],[c_0_7620, c_0_7211]), ['final']). 4.05/4.33 cnf(c_0_12449, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk452_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_7222]), ['final']). 4.05/4.33 cnf(c_0_12450, 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_6677]), ['final']). 4.05/4.33 cnf(c_0_12451, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk368_4(X3,X4,X2,X1)),esk367_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_6890]), ['final']). 4.05/4.33 cnf(c_0_12452, 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_7621]), ['final']). 4.05/4.33 cnf(c_0_12453, 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_7622]), ['final']). 4.05/4.33 cnf(c_0_12454, 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_7623]), ['final']). 4.05/4.33 cnf(c_0_12455, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X4),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))|~class_Orderings_Oord(X2)), inference(split_conjunct,[status(thm)],[c_0_7624]), ['final']). 4.05/4.33 cnf(c_0_12456, 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),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_7625]), ['final']). 4.05/4.33 cnf(c_0_12457, 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_7626]), ['final']). 4.05/4.33 cnf(c_0_12458, 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_7627]), ['final']). 4.05/4.33 cnf(c_0_12459, 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_7628]), ['final']). 4.05/4.33 cnf(c_0_12460, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X1))), inference(er,[status(thm)],[c_0_7629]), ['final']). 4.05/4.33 cnf(c_0_12461, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk306_5(X3,X2,X4,X5,X1))),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X1),X4),X2)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7207]), ['final']). 4.05/4.33 cnf(c_0_12462, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(X3,esk122_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_Orderings_Olinorder(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7208]), ['final']). 4.05/4.33 cnf(c_0_12463, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)))|hAPP(hAPP(c_List_Otake(X2),X4),X3)=c_List_OtakeWhile(X2,X1,X3)|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk12_4(X1,X3,X2,X4))))), inference(split_conjunct,[status(thm)],[c_0_6848]), ['final']). 4.05/4.33 cnf(c_0_12464, 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_7630]), ['final']). 4.05/4.33 cnf(c_0_12465, 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_7631]), ['final']). 4.05/4.33 cnf(c_0_12466, plain, (c_List_Olist__all2(X4,X5,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X6),hAPP(hAPP(c_List_Olist_OCons(X5),X3),X7))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~c_List_Olist__all2(X4,X5,X1,X6,X7)), inference(split_conjunct,[status(thm)],[c_0_7632]), ['final']). 4.05/4.33 cnf(c_0_12467, 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_7633]), ['final']). 4.05/4.33 cnf(c_0_12468, 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_7634]), ['final']). 4.05/4.33 cnf(c_0_12469, 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_7008]), ['final']). 4.05/4.33 cnf(c_0_12470, 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_7635]), ['final']). 4.05/4.33 cnf(c_0_12471, 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_7636]), ['final']). 4.05/4.33 cnf(c_0_12472, 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_7637]), ['final']). 4.05/4.33 cnf(c_0_12473, 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_7638]), ['final']). 4.05/4.33 cnf(c_0_12474, 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_7639]), ['final']). 4.05/4.33 cnf(c_0_12475, plain, (hBOOL(hAPP(hAPP(c_member(X3),X6),hAPP(c_List_Oset(X3),X4)))|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(hAPP(c_Map_Omap__of(X3,X1),hAPP(hAPP(c_List_Ozip(X3,X1),X4),X5)),X6)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5)), inference(split_conjunct,[status(thm)],[c_0_6767]), ['final']). 4.05/4.33 cnf(c_0_12476, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk172_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_5090]), ['final']). 4.05/4.33 cnf(c_0_12477, 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_7640])]), ['final']). 4.05/4.33 cnf(c_0_12478, 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_7641]), ['final']). 4.05/4.33 cnf(c_0_12479, 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_7642]), ['final']). 4.05/4.33 cnf(c_0_12480, 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_7643]), ['final']). 4.05/4.33 cnf(c_0_12481, 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_7644]), ['final']). 4.05/4.33 cnf(c_0_12482, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk200_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_7180]), ['final']). 4.05/4.33 cnf(c_0_12483, 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_7645]), ['final']). 4.05/4.33 cnf(c_0_12484, 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_7646]), ['final']). 4.05/4.33 cnf(c_0_12485, 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_7647, c_0_4523]), ['final']). 4.05/4.33 cnf(c_0_12486, 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_7648]), ['final']). 4.05/4.33 cnf(c_0_12487, 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_7649]), ['final']). 4.05/4.33 cnf(c_0_12488, 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_7650]), ['final']). 4.05/4.33 cnf(c_0_12489, 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_7651]), ['final']). 4.05/4.33 cnf(c_0_12490, 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_7652]), ['final']). 4.05/4.33 cnf(c_0_12491, 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_7653]), ['final']). 4.05/4.33 cnf(c_0_12492, 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_7654, c_0_5379]), c_0_7655]), c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_12493, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),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),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7656]), ['final']). 4.05/4.33 cnf(c_0_12494, 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_7657, c_0_4635]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_12495, 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_7658]), ['final']). 4.05/4.33 cnf(c_0_12496, 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_7659]), ['final']). 4.05/4.33 cnf(c_0_12497, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),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)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3))|~hBOOL(hAPP(c_List_Odistinct(X1),X3))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7420]), ['final']). 4.05/4.33 cnf(c_0_12498, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X2),hAPP(c_Int_Oring__1__class_Oof__int(X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)))=hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)|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)))|~class_Rings_Oring__1(X2)), inference(split_conjunct,[status(thm)],[c_0_4500]), ['final']). 4.05/4.33 cnf(c_0_12499, 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_7660]), ['final']). 4.05/4.33 cnf(c_0_12500, 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_7661]), ['final']). 4.05/4.33 cnf(c_0_12501, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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),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))))), inference(split_conjunct,[status(thm)],[c_0_7545]), ['final']). 4.05/4.33 cnf(c_0_12502, 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_7662, c_0_4635]), c_0_5149]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_12503, plain, (c_List_Obutlast(X2,hAPP(hAPP(c_List_Otake(X2),X1),X3))=hAPP(hAPP(c_List_Otake(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_7663]), ['final']). 4.05/4.33 cnf(c_0_12504, 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),X2),X4)),hAPP(hAPP(c_List_Olist_OCons(X5),X1),X3))),c_List_Olistrel1(X5,X6)))), inference(split_conjunct,[status(thm)],[c_0_6363]), ['final']). 4.05/4.33 cnf(c_0_12505, plain, (X2=esk267_3(X4,X3,X1)|hAPP(X4,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7197]), ['final']). 4.05/4.33 cnf(c_0_12506, plain, (hAPP(c_Option_Ooption_OSome(X1),X2)=hAPP(X3,esk477_7(X2,X4,X5,X3,X6,X1,X7))|hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X7,c_Option_Ooption_ONone(X1),X3),hAPP(X5,X4))!=hAPP(c_Option_Ooption_OSome(X1),X2)), inference(rw,[status(thm)],[c_0_7664, c_0_7211]), ['final']). 4.05/4.33 cnf(c_0_12507, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7308]), ['final']). 4.05/4.33 cnf(c_0_12508, 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),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7441]), ['final']). 4.05/4.33 cnf(c_0_12509, 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_7665, c_0_4635]), c_0_4635]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_12510, 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_7666]), ['final']). 4.05/4.33 cnf(c_0_12511, 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_7667]), ['final']). 4.05/4.33 cnf(c_0_12512, 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_7668, c_0_4902]), ['final']). 4.05/4.33 cnf(c_0_12513, 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_7669]), ['final']). 4.05/4.33 cnf(c_0_12514, 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_7670]), ['final']). 4.05/4.33 cnf(c_0_12515, 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_7671]), ['final']). 4.05/4.33 cnf(c_0_12516, 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_7672]), ['final']). 4.05/4.33 cnf(c_0_12517, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk513_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_7673]), ['final']). 4.05/4.33 cnf(c_0_12518, 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_7674]), ['final']). 4.05/4.33 cnf(c_0_12519, 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_7674]), ['final']). 4.05/4.33 cnf(c_0_12520, 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_7675, c_0_4902]), ['final']). 4.05/4.33 cnf(c_0_12521, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7676]), ['final']). 4.05/4.33 cnf(c_0_12522, 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_4647]), ['final']). 4.05/4.33 cnf(c_0_12523, 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_7677]), ['final']). 4.05/4.33 cnf(c_0_12524, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk436_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_7450]), ['final']). 4.05/4.33 cnf(c_0_12525, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Odrop(X2),X3),X1))=hAPP(hAPP(c_List_Onth(X2),X1),X3)|~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_7678]), ['final']). 4.05/4.33 cnf(c_0_12526, 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_7011]), ['final']). 4.05/4.33 cnf(c_0_12527, 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_7679]), ['final']). 4.05/4.33 cnf(c_0_12528, 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_7680]), ['final']). 4.05/4.33 cnf(c_0_12529, 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_7681, c_0_4902]), ['final']). 4.05/4.33 cnf(c_0_12530, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),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_7682]), ['final']). 4.05/4.33 cnf(c_0_12531, 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_7683]), ['final']). 4.05/4.33 cnf(c_0_12532, 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_7684, c_0_5149]), c_0_5149]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_12533, 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_6402]), ['final']). 4.05/4.33 cnf(c_0_12534, plain, (c_Big__Operators_Olattice__class_OInf__fin(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_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6405]), ['final']). 4.05/4.33 cnf(c_0_12535, plain, (X3=c_Big__Operators_Olattice__class_OSup__fin(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_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_6408]), ['final']). 4.05/4.33 cnf(c_0_12536, 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_7685, c_0_4902]), ['final']). 4.05/4.33 cnf(c_0_12537, 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_7686]), ['final']). 4.05/4.33 cnf(c_0_12538, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7686]), ['final']). 4.05/4.33 cnf(c_0_12539, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7687]), ['final']). 4.05/4.33 cnf(c_0_12540, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7687]), ['final']). 4.05/4.33 cnf(c_0_12541, plain, (X3=c_Big__Operators_Olinorder__class_OMax(X1,X2)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_6397]), ['final']). 4.05/4.33 cnf(c_0_12542, 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_7688, c_0_4859]), c_0_4859]), ['final']). 4.05/4.33 cnf(c_0_12543, 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_7689, c_0_6955]), c_0_6955]), ['final']). 4.05/4.33 cnf(c_0_12544, 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_7690]), ['final']). 4.05/4.33 cnf(c_0_12545, 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_7691]), ['final']). 4.05/4.33 cnf(c_0_12546, 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_7692]), ['final']). 4.05/4.33 cnf(c_0_12547, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk145_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_7417]), ['final']). 4.05/4.33 cnf(c_0_12548, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk189_3(X2,X3,X1)),c_List_Olists(X1,X2)))|c_List_Olist_ONil(X1)=X3|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7693]), ['final']). 4.05/4.33 cnf(c_0_12549, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_Fun_Oid(X1)),hAPP(c_Set_Oimage(X2,X1,X3),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)|~class_Groups_Ocomm__monoid__add(X1)|~c_Fun_Oinj__on(X2,X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_7694]), ['final']). 4.05/4.33 cnf(c_0_12550, 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_7695]), ['final']). 4.05/4.33 cnf(c_0_12551, 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_7696, c_0_5201]), ['final']). 4.05/4.33 cnf(c_0_12552, 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_7697, c_0_4902]), ['final']). 4.05/4.33 cnf(c_0_12553, 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_7698]), ['final']). 4.05/4.33 cnf(c_0_12554, 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_7699]), ['final']). 4.05/4.33 cnf(c_0_12555, plain, (hAPP(X1,X2)=X3|~hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,X4),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X1)))), inference(rw,[status(thm)],[c_0_7700, c_0_4902]), ['final']). 4.05/4.33 cnf(c_0_12556, 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_7701, c_0_4902]), ['final']). 4.05/4.33 cnf(c_0_12557, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(c_Map_Omap__upds(X1,X4,X5,X3,X6),X2)=hAPP(X5,X2)), inference(split_conjunct,[status(thm)],[c_0_7702]), ['final']). 4.05/4.33 cnf(c_0_12558, 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_7703]), ['final']). 4.05/4.33 cnf(c_0_12559, plain, (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)|~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))), inference(split_conjunct,[status(thm)],[c_0_7704]), ['final']). 4.05/4.33 cnf(c_0_12560, 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_7705, c_0_4902]), ['final']). 4.05/4.33 cnf(c_0_12561, 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_7706, c_0_4902]), ['final']). 4.05/4.33 cnf(c_0_12562, 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_6860]), ['final']). 4.05/4.33 cnf(c_0_12563, 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_6995]), ['final']). 4.05/4.33 cnf(c_0_12564, 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_7707]), ['final']). 4.05/4.33 cnf(c_0_12565, 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_7708]), ['final']). 4.05/4.33 cnf(c_0_12566, 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_7709]), ['final']). 4.05/4.33 cnf(c_0_12567, 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_7708]), ['final']). 4.05/4.33 cnf(c_0_12568, 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_7709]), ['final']). 4.05/4.33 cnf(c_0_12569, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Onth(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_List_Olast(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7710]), ['final']). 4.05/4.33 cnf(c_0_12570, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7483]), ['final']). 4.05/4.33 cnf(c_0_12571, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))=hAPP(c_Set_Oimage(X1,X3,hAPP(c_COMBK(X3,X1),X4)),X2)), inference(split_conjunct,[status(thm)],[c_0_7711]), ['final']). 4.05/4.33 cnf(c_0_12572, 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_7573]), ['final']). 4.05/4.33 cnf(c_0_12573, 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_7573]), ['final']). 4.05/4.33 cnf(c_0_12574, 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_7573]), ['final']). 4.05/4.33 cnf(c_0_12575, 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_7573]), ['final']). 4.05/4.33 cnf(c_0_12576, 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(c_COMBK(tc_fun(X3,tc_HOL_Obool),X1),X4))=X4), inference(split_conjunct,[status(thm)],[c_0_7712]), ['final']). 4.05/4.33 cnf(c_0_12577, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,esk452_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_7222]), ['final']). 4.05/4.33 cnf(c_0_12578, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Oone__class_Oone(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7713, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_6641]), ['final']). 4.05/4.33 cnf(c_0_12579, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Oone__class_Oone(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7714, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4977]), ['final']). 4.05/4.33 cnf(c_0_12580, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X2),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X1),X4))=X4), inference(split_conjunct,[status(thm)],[c_0_5876]), ['final']). 4.05/4.33 cnf(c_0_12581, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))=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))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_7715, c_0_4434]), ['final']). 4.05/4.33 cnf(c_0_12582, 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_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7602]), ['final']). 4.05/4.33 cnf(c_0_12583, 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_Groups_Otimes__class_Otimes(X1),X3),X2)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7602]), ['final']). 4.05/4.33 cnf(c_0_12584, 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_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7602]), ['final']). 4.05/4.33 cnf(c_0_12585, 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_Groups_Otimes__class_Otimes(X1),X3),X2)))|~class_Rings_Olinordered__ring__strict(X1)), inference(split_conjunct,[status(thm)],[c_0_7602]), ['final']). 4.05/4.33 cnf(c_0_12586, 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_7716]), ['final']). 4.05/4.33 cnf(c_0_12587, 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_7225]), ['final']). 4.05/4.33 cnf(c_0_12588, plain, (c_Option_Ooption_ONone(X5)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X5),X3,c_Option_Ooption_ONone(X5),X6),hAPP(X1,X2))|c_Option_Ooption_ONone(X5)!=hAPP(X6,X4)|hAPP(X1,X2)!=hAPP(c_Option_Ooption_OSome(X3),X4)), inference(rw,[status(thm)],[c_0_7717, c_0_7211]), ['final']). 4.05/4.33 cnf(c_0_12589, 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),esk171_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_7718]), ['final']). 4.05/4.33 cnf(c_0_12590, 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_7719]), ['final']). 4.05/4.33 cnf(c_0_12591, 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_7134]), ['final']). 4.05/4.33 cnf(c_0_12592, plain, (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(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))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7135]), ['final']). 4.05/4.33 cnf(c_0_12593, 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_7131]), ['final']). 4.05/4.33 cnf(c_0_12594, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7133]), ['final']). 4.05/4.33 cnf(c_0_12595, 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),esk146_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_7720]), ['final']). 4.05/4.33 cnf(c_0_12596, 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,esk197_3(X2,X1,X3)),esk198_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_5155]), ['final']). 4.05/4.33 cnf(c_0_12597, 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,esk376_3(X2,X1,X3)),esk377_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_5156]), ['final']). 4.05/4.33 cnf(c_0_12598, 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_7721, c_0_5149]), c_0_5149]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_12599, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|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_7722]), ['final']). 4.05/4.33 cnf(c_0_12600, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk260_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_7460]), ['final']). 4.05/4.33 cnf(c_0_12601, 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,esk339_3(X1,X2,X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7503]), ['final']). 4.05/4.33 cnf(c_0_12602, 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,esk93_3(X1,X2,X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7218]), ['final']). 4.05/4.33 cnf(c_0_12603, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk530_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_7723]), ['final']). 4.05/4.33 cnf(c_0_12604, 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_7724, c_0_4977]), ['final']). 4.05/4.33 cnf(c_0_12605, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X2))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_6835]), ['final']). 4.05/4.33 cnf(c_0_12606, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk440_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_7605]), ['final']). 4.05/4.33 cnf(c_0_12607, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2,X1),tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_7725]), ['final']). 4.05/4.33 cnf(c_0_12608, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))), inference(split_conjunct,[status(thm)],[c_0_7726]), ['final']). 4.05/4.33 cnf(c_0_12609, 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_7727]), ['final']). 4.05/4.33 cnf(c_0_12610, 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_7728, c_0_4635]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_12611, 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_7729, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_12612, 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_7730]), ['final']). 4.05/4.33 cnf(c_0_12613, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7731]), ['final']). 4.05/4.33 cnf(c_0_12614, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7732]), ['final']). 4.05/4.33 cnf(c_0_12615, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|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_7733]), ['final']). 4.05/4.33 cnf(c_0_12616, 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_7734]), ['final']). 4.05/4.33 cnf(c_0_12617, 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)],[c_0_7735, c_0_5796]), ['final']). 4.05/4.33 cnf(c_0_12618, 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)],[c_0_7736, c_0_5796]), ['final']). 4.05/4.33 cnf(c_0_12619, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))), inference(rw,[status(thm)],[c_0_7737, c_0_5796]), ['final']). 4.05/4.33 cnf(c_0_12620, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2))=c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),X2))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7738]), ['final']). 4.05/4.33 cnf(c_0_12621, 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,esk7_5(X3,X2,X4,X5,X1))))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X1),X2),X4)!=c_Groups_Ozero__class_Ozero(X1)|~hBOOL(hAPP(hAPP(c_member(X5),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7204]), ['final']). 4.05/4.33 cnf(c_0_12622, 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_7739]), ['final']). 4.05/4.33 cnf(c_0_12623, plain, (hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))=hAPP(c_Set_Oimage(X1,X4,hAPP(c_COMBK(X4,X1),X5)),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_7740]), ['final']). 4.05/4.33 cnf(c_0_12624, 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)],[c_0_7741, c_0_5796]), ['final']). 4.05/4.33 cnf(c_0_12625, 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)],[c_0_7742, c_0_5796]), ['final']). 4.05/4.33 cnf(c_0_12626, 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_7743, c_0_5796]), ['final']). 4.05/4.33 cnf(c_0_12627, 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_7744, c_0_5796]), ['final']). 4.05/4.33 cnf(c_0_12628, 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_7745, c_0_5796]), ['final']). 4.05/4.33 cnf(c_0_12629, 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_7746, c_0_5796]), ['final']). 4.05/4.33 cnf(c_0_12630, 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_7747]), ['final']). 4.05/4.33 cnf(c_0_12631, 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_7748]), ['final']). 4.05/4.33 cnf(c_0_12632, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_7749, c_0_5796]), ['final']). 4.05/4.33 cnf(c_0_12633, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_7750, c_0_5796]), ['final']). 4.05/4.33 cnf(c_0_12634, 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)],[c_0_7751, c_0_5796]), ['final']). 4.05/4.33 cnf(c_0_12635, 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_7752, c_0_4523]), ['final']). 4.05/4.33 cnf(c_0_12636, 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_7212]), ['final']). 4.05/4.33 cnf(c_0_12637, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk430_5(X2,X3,X1,X4,X5)),X2))|~hBOOL(hAPP(hAPP(c_member(X5),X4),c_Map_Oran(X1,X5,c_Map_Orestrict__map(X1,X5,X3,X2))))), inference(split_conjunct,[status(thm)],[c_0_7753]), ['final']). 4.05/4.33 cnf(c_0_12638, 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_6460]), ['final']). 4.05/4.33 cnf(c_0_12639, 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_7754]), ['final']). 4.05/4.33 cnf(c_0_12640, 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_7755]), ['final']). 4.05/4.33 cnf(c_0_12641, 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_7756]), ['final']). 4.05/4.33 cnf(c_0_12642, 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_7757]), ['final']). 4.05/4.33 cnf(c_0_12643, 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_7758]), ['final']). 4.05/4.33 cnf(c_0_12644, 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_7547]), ['final']). 4.05/4.33 cnf(c_0_12645, 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_7759, c_0_6268]), ['final']). 4.05/4.33 cnf(c_0_12646, 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_OSup__fin(X1,X2))=c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7760]), ['final']). 4.05/4.33 cnf(c_0_12647, 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_7761]), ['final']). 4.05/4.33 cnf(c_0_12648, 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_7762]), ['final']). 4.05/4.33 cnf(c_0_12649, 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_7763]), ['final']). 4.05/4.33 cnf(c_0_12650, 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_7764]), ['final']). 4.05/4.33 cnf(c_0_12651, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X3),X4),X2)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X1,c_Groups_Otimes__class_Otimes(X3)),X4),c_Groups_Oone__class_Oone(X3)),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Groups_Ocomm__monoid__mult(X3)), inference(split_conjunct,[status(thm)],[c_0_4982]), ['final']). 4.05/4.33 cnf(c_0_12652, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X4),X2)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X1,c_Groups_Oplus__class_Oplus(X3)),X4),c_Groups_Ozero__class_Ozero(X3)),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Groups_Ocomm__monoid__add(X3)), inference(split_conjunct,[status(thm)],[c_0_4984]), ['final']). 4.05/4.33 cnf(c_0_12653, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk194_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_7765]), ['final']). 4.05/4.33 cnf(c_0_12654, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|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,X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7766]), ['final']). 4.05/4.33 cnf(c_0_12655, 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_7767]), ['final']). 4.05/4.33 cnf(c_0_12656, 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(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)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_12657, plain, (esk109_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_7768]), c_0_7769])]), ['final']). 4.05/4.33 cnf(c_0_12658, 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_7770]), ['final']). 4.05/4.33 cnf(c_0_12659, 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_7771]), ['final']). 4.05/4.33 cnf(c_0_12660, plain, (X3=X4|~hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hAPP(hAPP(c_List_Onth(X1),X2),X3)!=hAPP(hAPP(c_List_Onth(X1),X2),X4)), inference(split_conjunct,[status(thm)],[c_0_7772]), ['final']). 4.05/4.33 cnf(c_0_12661, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7773]), ['final']). 4.05/4.33 cnf(c_0_12662, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|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,X2))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7774]), ['final']). 4.05/4.33 cnf(c_0_12663, 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_7775]), ['final']). 4.05/4.33 cnf(c_0_12664, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3))|~class_Groups_Olinordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7776]), ['final']). 4.05/4.33 cnf(c_0_12665, 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_7777]), ['final']). 4.05/4.33 cnf(c_0_12666, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7778]), ['final']). 4.05/4.33 cnf(c_0_12667, plain, (hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),esk144_4(X1,X3,X4,X2)),esk145_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_7417]), ['final']). 4.05/4.33 cnf(c_0_12668, 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_7779]), ['final']). 4.05/4.33 cnf(c_0_12669, 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_7780]), ['final']). 4.05/4.33 cnf(c_0_12670, 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_7781]), ['final']). 4.05/4.33 cnf(c_0_12671, 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_7782]), ['final']). 4.05/4.33 cnf(c_0_12672, 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_7783]), ['final']). 4.05/4.33 cnf(c_0_12673, 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_7784]), ['final']). 4.05/4.33 cnf(c_0_12674, 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_6370]), ['final']). 4.05/4.33 cnf(c_0_12675, 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_7785]), ['final']). 4.05/4.33 cnf(c_0_12676, plain, (X1=hAPP(hAPP(c_List_Olist_OCons(X2),esk188_3(X3,X1,X2)),esk189_3(X3,X1,X2))|c_List_Olist_ONil(X2)=X1|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X1),c_List_Olists(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_7693]), ['final']). 4.05/4.33 cnf(c_0_12677, 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_7786]), ['final']). 4.05/4.33 cnf(c_0_12678, 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_7621]), ['final']). 4.05/4.33 cnf(c_0_12679, 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_7686]), ['final']). 4.05/4.33 cnf(c_0_12680, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7687]), ['final']). 4.05/4.33 cnf(c_0_12681, 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_7686]), ['final']). 4.05/4.33 cnf(c_0_12682, 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_7622]), ['final']). 4.05/4.33 cnf(c_0_12683, 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_7787]), ['final']). 4.05/4.33 cnf(c_0_12684, 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_7788]), ['final']). 4.05/4.33 cnf(c_0_12685, 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_7789]), ['final']). 4.05/4.33 cnf(c_0_12686, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))|hAPP(c_Map_Omap__add(X1,X3,X5,X4),X2)=hAPP(X5,X2)), inference(split_conjunct,[status(thm)],[c_0_7790]), ['final']). 4.05/4.33 cnf(c_0_12687, 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_7791]), ['final']). 4.05/4.33 cnf(c_0_12688, 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_7686]), ['final']). 4.05/4.33 cnf(c_0_12689, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7687]), ['final']). 4.05/4.33 cnf(c_0_12690, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7687]), ['final']). 4.05/4.33 cnf(c_0_12691, 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_7686]), ['final']). 4.05/4.33 cnf(c_0_12692, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))|hAPP(X5,X2)=hAPP(c_Map_Omap__add(X1,X3,X4,X5),X2)), inference(split_conjunct,[status(thm)],[c_0_7792]), ['final']). 4.05/4.33 cnf(c_0_12693, 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_7793]), ['final']). 4.05/4.33 cnf(c_0_12694, 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_7636]), ['final']). 4.05/4.33 cnf(c_0_12695, 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_7637]), ['final']). 4.05/4.33 cnf(c_0_12696, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_7687]), ['final']). 4.05/4.33 cnf(c_0_12697, 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_7708]), ['final']). 4.05/4.33 cnf(c_0_12698, 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_7708]), ['final']). 4.05/4.33 cnf(c_0_12699, 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_7794, c_0_6709]), ['final']). 4.05/4.33 cnf(c_0_12700, 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_7795]), ['final']). 4.05/4.33 cnf(c_0_12701, 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_7796]), ['final']). 4.05/4.33 cnf(c_0_12702, plain, (hAPP(X1,X2)=hAPP(X3,X2)|~class_HOL_Oequal(X4)|~class_Enum_Oenum(X5)|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X5,X4)),X1),X3))), inference(csr,[status(thm)],[c_0_7797, c_0_7798]), ['final']). 4.05/4.33 cnf(c_0_12703, 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_7708]), ['final']). 4.05/4.33 cnf(c_0_12704, 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_7708]), ['final']). 4.05/4.33 cnf(c_0_12705, 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_7709]), ['final']). 4.05/4.33 cnf(c_0_12706, 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_7709]), ['final']). 4.05/4.33 cnf(c_0_12707, 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_7799, c_0_7800]), ['final']). 4.05/4.33 cnf(c_0_12708, 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_7801, c_0_7800]), ['final']). 4.05/4.33 cnf(c_0_12709, 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_7802]), ['final']). 4.05/4.33 cnf(c_0_12710, plain, (hAPP(hAPP(X1,X2),esk390_7(X2,X3,X4,X5,X1,X6,X7))=X3|~hBOOL(hAPP(hAPP(c_member(X7),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X6,X1,X5,X4),X3))|~c_Finite__Set_Ofun__left__comm(X7,X6,X1)), inference(split_conjunct,[status(thm)],[c_0_6440]), ['final']). 4.05/4.33 cnf(c_0_12711, 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_7709]), ['final']). 4.05/4.33 cnf(c_0_12712, 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_7709]), ['final']). 4.05/4.33 cnf(c_0_12713, 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_7803, c_0_7804]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_12714, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X6),X4))|c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X6|~c_Fun_Oinj__on(X1,X2,X3,hAPP(X4,esk85_6(X4,X3,X2,X1,X5,X6)))), inference(split_conjunct,[status(thm)],[c_0_6747]), ['final']). 4.05/4.33 cnf(c_0_12715, 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,esk28_4(X2,X1,X3,X4))),hAPP(X2,esk28_4(X2,X1,X3,X4))))), inference(split_conjunct,[status(thm)],[c_0_6960]), ['final']). 4.05/4.33 cnf(c_0_12716, 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,esk37_3(X2,X1,X3)))), inference(rw,[status(thm)],[c_0_7805, c_0_4950]), ['final']). 4.05/4.33 cnf(c_0_12717, 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_7806, c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_12718, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk507_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_7807]), ['final']). 4.05/4.33 cnf(c_0_12719, 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_7808]), ['final']). 4.05/4.33 cnf(c_0_12720, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),X2)=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_7809]), ['final']). 4.05/4.33 cnf(c_0_12721, 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_7810]), ['final']). 4.05/4.33 cnf(c_0_12722, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk491_4(X2,X3,X4,X1)),X3))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X2)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_7811]), ['final']). 4.05/4.33 cnf(c_0_12723, 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_7812]), ['final']). 4.05/4.33 cnf(c_0_12724, 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)), inference(split_conjunct,[status(thm)],[c_0_7813]), ['final']). 4.05/4.33 cnf(c_0_12725, 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_7814]), ['final']). 4.05/4.33 cnf(c_0_12726, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk219_4(X2,X3,X1,X4)),X3))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X2)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_7815]), ['final']). 4.05/4.33 cnf(c_0_12727, 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_7816]), ['final']). 4.05/4.33 cnf(c_0_12728, plain, (X1=X2|X2=X3|hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_7817]), ['final']). 4.05/4.33 cnf(c_0_12729, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk282_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_7818]), ['final']). 4.05/4.33 cnf(c_0_12730, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_7819]), ['final']). 4.05/4.33 cnf(c_0_12731, 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_7820]), ['final']). 4.05/4.33 cnf(c_0_12732, 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)), inference(split_conjunct,[status(thm)],[c_0_7821]), ['final']). 4.05/4.33 cnf(c_0_12733, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4)|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_7822]), ['final']). 4.05/4.33 cnf(c_0_12734, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk196_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_7823]), ['final']). 4.05/4.33 cnf(c_0_12735, plain, (X1=X2|X3=X2|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))))), inference(split_conjunct,[status(thm)],[c_0_7817]), ['final']). 4.05/4.33 cnf(c_0_12736, 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_7824]), ['final']). 4.05/4.33 cnf(c_0_12737, 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_7825]), ['final']). 4.05/4.33 cnf(c_0_12738, 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,esk243_7(X2,X3,X1,X4,X5,X6,X7)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7160]), ['final']). 4.05/4.33 cnf(c_0_12739, 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_7826]), ['final']). 4.05/4.33 cnf(c_0_12740, 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_7827]), ['final']). 4.05/4.33 cnf(c_0_12741, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)|~class_Groups_Oab__semigroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7828]), ['final']). 4.05/4.33 cnf(c_0_12742, 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_7829]), ['final']). 4.05/4.33 cnf(c_0_12743, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X2)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_7830, c_0_5942]), ['final']). 4.05/4.33 cnf(c_0_12744, plain, (hBOOL(hAPP(X2,X3))|hAPP(c_List_Ofilter(X4,X2),X5)=hAPP(c_List_Ofilter(X4,X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X1,X6),X3),X5))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7831]), ['final']). 4.05/4.33 cnf(c_0_12745, plain, (hAPP(X5,X4)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X3,c_Option_Ooption_ONone(X6),X5),hAPP(X1,X2))|hAPP(X1,X2)!=hAPP(c_Option_Ooption_OSome(X3),X4)), inference(rw,[status(thm)],[c_0_7832, c_0_7211]), ['final']). 4.05/4.33 cnf(c_0_12746, plain, (hAPP(hAPP(c_List_Oappend(X1),esk428_5(X2,X3,X4,X5,X1)),X4)=X2|X5=c_List_Olist_ONil(X1)|hAPP(hAPP(c_List_Oappend(X1),X5),X4)!=hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_7456]), ['final']). 4.05/4.33 cnf(c_0_12747, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5)|c_Groups_Ozero__class_Ozero(X1)=X5|c_Groups_Ozero__class_Ozero(X1)=X3|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_7833]), ['final']). 4.05/4.33 cnf(c_0_12748, 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_7834]), ['final']). 4.05/4.33 cnf(c_0_12749, 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_7835]), ['final']). 4.05/4.33 cnf(c_0_12750, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[c_0_7836, c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_12751, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[c_0_7837, c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_12752, plain, (X1=c_List_Olist_ONil(X2)|X3=hAPP(hAPP(c_List_Oappend(X2),esk3_5(X4,X1,X3,X5,X2)),X4)|hAPP(hAPP(c_List_Olist_OCons(X2),X5),X3)!=hAPP(hAPP(c_List_Oappend(X2),X1),X4)), inference(split_conjunct,[status(thm)],[c_0_7455]), ['final']). 4.05/4.33 cnf(c_0_12753, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk428_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)), inference(split_conjunct,[status(thm)],[c_0_7456]), ['final']). 4.05/4.33 cnf(c_0_12754, plain, (X1=c_List_Olist_ONil(X2)|X1=hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk3_5(X4,X1,X5,X3,X2))|hAPP(hAPP(c_List_Olist_OCons(X2),X3),X5)!=hAPP(hAPP(c_List_Oappend(X2),X1),X4)), inference(split_conjunct,[status(thm)],[c_0_7455]), ['final']). 4.05/4.33 cnf(c_0_12755, plain, (hAPP(X1,esk109_4(X2,X1,X3,X4))=X2|~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)))))|~c_Fun_Oinj__on(X4,X3,X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_5412]), ['final']). 4.05/4.33 cnf(c_0_12756, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)|c_Groups_Ozero__class_Ozero(X1)=X5|c_Groups_Ozero__class_Ozero(X1)=X3|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_7833]), ['final']). 4.05/4.33 cnf(c_0_12757, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7838, c_0_4795]), c_0_4427]), c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_12758, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))), inference(rw,[status(thm)],[c_0_7839, c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_12759, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7840, c_0_4795]), c_0_4427]), c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_12760, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7841, c_0_4795]), c_0_4635]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_12761, 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_7842, c_0_6268]), ['final']). 4.05/4.33 cnf(c_0_12762, 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_7843]), ['final']). 4.05/4.33 cnf(c_0_12763, 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_7844]), ['final']). 4.05/4.33 cnf(c_0_12764, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[c_0_7845, c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_12765, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[c_0_7846, c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_12766, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7847, c_0_4427]), c_0_4795]), c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_12767, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1))), inference(rw,[status(thm)],[c_0_7848, c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_12768, 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_7849]), ['final']). 4.05/4.33 cnf(c_0_12769, 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_7850]), ['final']). 4.05/4.33 cnf(c_0_12770, 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,esk24_4(X2,X3,X1,X4))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(X2,X4)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7851, c_0_4867]), c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_12771, plain, (hAPP(X6,X7)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3),X5),X4),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_7852]), ['final']). 4.05/4.33 cnf(c_0_12772, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)=hAPP(c_Nat_OSuc,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_7853]), ['final']). 4.05/4.33 cnf(c_0_12773, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7854, c_0_4427]), c_0_4795]), c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_12774, 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_7855]), ['final']). 4.05/4.33 cnf(c_0_12775, plain, (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X6,tc_HOL_Obool)),X3),X4),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(X4,X2),X5))), inference(split_conjunct,[status(thm)],[c_0_7856]), ['final']). 4.05/4.33 cnf(c_0_12776, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7857, c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), ['final']). 4.05/4.33 cnf(c_0_12777, plain, (hBOOL(hAPP(X1,X5))|~hBOOL(hAPP(X1,esk404_4(X1,X2,X3,X4)))|~hBOOL(hAPP(X1,esk403_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_6568]), ['final']). 4.05/4.33 cnf(c_0_12778, plain, (hBOOL(hAPP(X1,esk145_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_7417]), ['final']). 4.05/4.33 cnf(c_0_12779, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)=hAPP(hAPP(c_Finite__Set_Ofold(X1,tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1)),X3),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7858]), ['final']). 4.05/4.33 cnf(c_0_12780, 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_7859]), ['final']). 4.05/4.33 cnf(c_0_12781, 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)), inference(split_conjunct,[status(thm)],[c_0_7860]), ['final']). 4.05/4.33 cnf(c_0_12782, 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_7861, c_0_5905]), ['final']). 4.05/4.33 cnf(c_0_12783, 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_7862]), ['final']). 4.05/4.33 cnf(c_0_12784, 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_7863]), ['final']). 4.05/4.33 cnf(c_0_12785, 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_7864]), ['final']). 4.05/4.33 cnf(c_0_12786, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7865]), ['final']). 4.05/4.33 cnf(c_0_12787, 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_7866]), ['final']). 4.05/4.33 cnf(c_0_12788, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),c_List_Oremove1(X1,X2,X3))=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_7867]), ['final']). 4.05/4.33 cnf(c_0_12789, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7868]), ['final']). 4.05/4.33 cnf(c_0_12790, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk311_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_7554]), ['final']). 4.05/4.33 cnf(c_0_12791, plain, (hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Oappend(X2),X3),X4)),X1)=hAPP(hAPP(c_List_Onth(X2),X3),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)))), inference(split_conjunct,[status(thm)],[c_0_6928]), ['final']). 4.05/4.33 cnf(c_0_12792, 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_7869]), ['final']). 4.05/4.33 cnf(c_0_12793, 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_7870]), ['final']). 4.05/4.33 cnf(c_0_12794, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk273_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_7140]), ['final']). 4.05/4.33 cnf(c_0_12795, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk233_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_7144]), ['final']). 4.05/4.33 cnf(c_0_12796, 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,esk108_4(X2,X1,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_7228]), ['final']). 4.05/4.33 cnf(c_0_12797, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk456_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_7871]), ['final']). 4.05/4.33 cnf(c_0_12798, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7872]), ['final']). 4.05/4.33 cnf(c_0_12799, 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_7873]), ['final']). 4.05/4.33 cnf(c_0_12800, 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_7874, c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_12801, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),X3))=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7875]), ['final']). 4.05/4.33 cnf(c_0_12802, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk57_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_7560]), ['final']). 4.05/4.33 cnf(c_0_12803, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7876]), ['final']). 4.05/4.33 cnf(c_0_12804, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk524_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_7877]), ['final']). 4.05/4.33 cnf(c_0_12805, 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_7878]), ['final']). 4.05/4.33 cnf(c_0_12806, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))=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))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7879]), ['final']). 4.05/4.33 cnf(c_0_12807, 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_7880]), ['final']). 4.05/4.33 cnf(c_0_12808, 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_7881]), ['final']). 4.05/4.33 cnf(c_0_12809, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3),X4)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7882]), ['final']). 4.05/4.33 cnf(c_0_12810, 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_7765]), ['final']). 4.05/4.33 cnf(c_0_12811, 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_7883]), ['final']). 4.05/4.33 cnf(c_0_12812, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7884]), ['final']). 4.05/4.33 cnf(c_0_12813, 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_7885]), ['final']). 4.05/4.33 cnf(c_0_12814, 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))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_12815, 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_7886]), ['final']). 4.05/4.33 cnf(c_0_12816, 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_7887]), ['final']). 4.05/4.33 cnf(c_0_12817, 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)), inference(split_conjunct,[status(thm)],[c_0_7888]), ['final']). 4.05/4.33 cnf(c_0_12818, 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),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)|~class_Divides_Oring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7889]), ['final']). 4.05/4.33 cnf(c_0_12819, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|X3=X5|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5),X6)))), inference(split_conjunct,[status(thm)],[c_0_7890]), ['final']). 4.05/4.33 cnf(c_0_12820, 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)), inference(split_conjunct,[status(thm)],[c_0_7891]), ['final']). 4.05/4.33 cnf(c_0_12821, 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_7892]), ['final']). 4.05/4.33 cnf(c_0_12822, 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_7893]), ['final']). 4.05/4.33 cnf(c_0_12823, 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_7894]), ['final']). 4.05/4.33 cnf(c_0_12824, 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_7474]), ['final']). 4.05/4.33 cnf(c_0_12825, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X3))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_7895]), ['final']). 4.05/4.33 cnf(c_0_12826, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|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_7896]), ['final']). 4.05/4.33 cnf(c_0_12827, 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_7897]), ['final']). 4.05/4.33 cnf(c_0_12828, 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_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_7898]), ['final']). 4.05/4.33 cnf(c_0_12829, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Wellfounded_Omax__extp(X1,X4,X5,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(X4,esk265_4(X3,X5,X4,X1)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_5611]), ['final']). 4.05/4.33 cnf(c_0_12830, 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_7899]), ['final']). 4.05/4.33 cnf(c_0_12831, 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_7900]), ['final']). 4.05/4.33 cnf(c_0_12832, 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_7901]), ['final']). 4.05/4.33 cnf(c_0_12833, 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_7131]), ['final']). 4.05/4.33 cnf(c_0_12834, 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)), inference(split_conjunct,[status(thm)],[c_0_7902]), ['final']). 4.05/4.33 cnf(c_0_12835, 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_7903]), ['final']). 4.05/4.33 cnf(c_0_12836, 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_7904]), ['final']). 4.05/4.33 cnf(c_0_12837, 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)), inference(split_conjunct,[status(thm)],[c_0_7905]), ['final']). 4.05/4.33 cnf(c_0_12838, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7906]), ['final']). 4.05/4.33 cnf(c_0_12839, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_7907]), ['final']). 4.05/4.33 cnf(c_0_12840, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),X2)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_7908]), ['final']). 4.05/4.33 cnf(c_0_12841, 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_7133]), ['final']). 4.05/4.33 cnf(c_0_12842, 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_7134]), ['final']). 4.05/4.33 cnf(c_0_12843, 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_7135]), ['final']). 4.05/4.33 cnf(c_0_12844, 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_7909]), ['final']). 4.05/4.33 cnf(c_0_12845, 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)), inference(split_conjunct,[status(thm)],[c_0_7910]), ['final']). 4.05/4.33 cnf(c_0_12846, 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_7911]), ['final']). 4.05/4.33 cnf(c_0_12847, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7912]), ['final']). 4.05/4.33 cnf(c_0_12848, 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_7913]), ['final']). 4.05/4.33 cnf(c_0_12849, 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_7914]), ['final']). 4.05/4.33 cnf(c_0_12850, 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_7915, c_0_4427]), c_0_7916]), ['final']). 4.05/4.33 cnf(c_0_12851, 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_7917, c_0_4427]), c_0_7918]), c_0_4865]), ['final']). 4.05/4.33 cnf(c_0_12852, 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_7919, c_0_5149]), c_0_7920]), ['final']). 4.05/4.33 cnf(c_0_12853, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)|~class_Rings_Ocomm__semiring__1(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(hAPP(c_member(X2),X4),X3))|c_Groups_Ozero__class_Ozero(X1)!=hAPP(X5,X4)), inference(split_conjunct,[status(thm)],[c_0_7921]), ['final']). 4.05/4.33 cnf(c_0_12854, 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_7922]), ['final']). 4.05/4.33 cnf(c_0_12855, 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_7923]), ['final']). 4.05/4.33 cnf(c_0_12856, 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_7924]), ['final']). 4.05/4.33 cnf(c_0_12857, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7925, c_0_4439]), c_0_7804]), c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_12858, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk338_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_7926]), ['final']). 4.05/4.33 cnf(c_0_12859, 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_7927]), ['final']). 4.05/4.33 cnf(c_0_12860, 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_7928]), ['final']). 4.05/4.33 cnf(c_0_12861, 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_7314]), ['final']). 4.05/4.33 cnf(c_0_12862, 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_7929]), ['final']). 4.05/4.33 cnf(c_0_12863, 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_7930]), ['final']). 4.05/4.33 cnf(c_0_12864, 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_7322]), ['final']). 4.05/4.33 cnf(c_0_12865, 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_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_5279]), ['final']). 4.05/4.33 cnf(c_0_12866, 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_7931]), ['final']). 4.05/4.33 cnf(c_0_12867, 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_7932]), ['final']). 4.05/4.33 cnf(c_0_12868, 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_7933]), ['final']). 4.05/4.33 cnf(c_0_12869, 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_7934]), ['final']). 4.05/4.33 cnf(c_0_12870, 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_7935]), ['final']). 4.05/4.33 cnf(c_0_12871, 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_7936]), ['final']). 4.05/4.33 cnf(c_0_12872, 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_7335]), ['final']). 4.05/4.33 cnf(c_0_12873, 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),esk509_3(X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(rw,[status(thm)],[c_0_7937, c_0_6145]), ['final']). 4.05/4.33 cnf(c_0_12874, 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_7938]), ['final']). 4.05/4.33 cnf(c_0_12875, 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_7939]), ['final']). 4.05/4.33 cnf(c_0_12876, 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_7940]), ['final']). 4.05/4.33 cnf(c_0_12877, 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_7941]), ['final']). 4.05/4.33 cnf(c_0_12878, plain, (hAPP(X4,X5)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|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),X5),X3))), inference(split_conjunct,[status(thm)],[c_0_7815]), ['final']). 4.05/4.33 cnf(c_0_12879, plain, (hAPP(X4,X5)=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|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_7818]), ['final']). 4.05/4.33 cnf(c_0_12880, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1))))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X1)),X2))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_7942]), ['final']). 4.05/4.33 cnf(c_0_12881, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7943]), ['final']). 4.05/4.33 cnf(c_0_12882, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X2)=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7944]), ['final']). 4.05/4.33 cnf(c_0_12883, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X3)=c_Divides_Odiv__class_Omod(X1,X2,X3)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_7945]), ['final']). 4.05/4.33 cnf(c_0_12884, 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_7946]), ['final']). 4.05/4.33 cnf(c_0_12885, 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_7947]), ['final']). 4.05/4.33 cnf(c_0_12886, 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_7948]), ['final']). 4.05/4.33 cnf(c_0_12887, 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_7949]), ['final']). 4.05/4.33 cnf(c_0_12888, plain, (hBOOL(hAPP(X2,X4))|~hBOOL(hAPP(hAPP(c_member(X1),esk144_4(X2,X3,X4,X1)),esk145_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_7417]), ['final']). 4.05/4.33 cnf(c_0_12889, 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_7950]), ['final']). 4.05/4.33 cnf(c_0_12890, 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_7951]), ['final']). 4.05/4.33 cnf(c_0_12891, 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_7952]), ['final']). 4.05/4.33 cnf(c_0_12892, 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_7953]), ['final']). 4.05/4.33 cnf(c_0_12893, 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_7954]), ['final']). 4.05/4.33 cnf(c_0_12894, 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_7955]), ['final']). 4.05/4.33 cnf(c_0_12895, 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_7956]), ['final']). 4.05/4.33 cnf(c_0_12896, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),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(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_7957]), ['final']). 4.05/4.33 cnf(c_0_12897, 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_7958]), ['final']). 4.05/4.33 cnf(c_0_12898, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),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(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_7959]), ['final']). 4.05/4.33 cnf(c_0_12899, plain, (hAPP(hAPP(c_List_Onth(X2),X4),X1)=hAPP(hAPP(c_List_Onth(X2),c_List_OtakeWhile(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)),c_List_OtakeWhile(X2,X3,X4))))), inference(split_conjunct,[status(thm)],[c_0_7960]), ['final']). 4.05/4.33 cnf(c_0_12900, 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,esk378_4(X2,X3,X4,X1))))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_7067]), ['final']). 4.05/4.33 cnf(c_0_12901, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk482_4(X2,X3,hAPP(c_Option_Ooption_OSome(X1),X2),X1)),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(er,[status(thm)],[c_0_7961]), c_0_7962]), ['final']). 4.05/4.33 cnf(c_0_12902, 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_7963]), ['final']). 4.05/4.33 cnf(c_0_12903, 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_7964]), ['final']). 4.05/4.33 cnf(c_0_12904, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk441_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_7965]), ['final']). 4.05/4.33 cnf(c_0_12905, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk285_3(X2,X3,X1)),X3))|c_Groups_Oone__class_Oone(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_7966]), ['final']). 4.05/4.33 cnf(c_0_12906, 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,esk269_4(X2,X3,X4,X1))))|~class_Rings_Olinordered__semidom(X1)), inference(split_conjunct,[status(thm)],[c_0_7072]), ['final']). 4.05/4.33 cnf(c_0_12907, plain, (c_Map_Omap__upds(X1,X3,X5,X2,X4)=c_Map_Omap__upds(X1,X3,X5,hAPP(hAPP(c_List_Oappend(X1),X2),X6),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_7967]), ['final']). 4.05/4.33 cnf(c_0_12908, plain, (c_Map_Omap__upds(X1,X3,X5,X2,X4)=c_Map_Omap__upds(X1,X3,X5,X2,hAPP(hAPP(c_List_Oappend(X3),X4),X6))|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_7968]), ['final']). 4.05/4.33 cnf(c_0_12909, 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_7969]), ['final']). 4.05/4.33 cnf(c_0_12910, 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_7970, c_0_5149]), c_0_5149]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_12911, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),X1))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),X1),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_7971, c_0_7972])]), ['final']). 4.05/4.33 cnf(c_0_12912, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),c_List_Olinorder__class_Osort__key(X2,X1,X3,X5))=c_List_Olinorder__class_Osort__key(X2,X1,X3,hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7973]), ['final']). 4.05/4.33 cnf(c_0_12913, 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)))), inference(split_conjunct,[status(thm)],[c_0_7501]), ['final']). 4.05/4.33 cnf(c_0_12914, plain, (hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2))=c_List_Osublist(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)),X1)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_7974]), ['final']). 4.05/4.33 cnf(c_0_12915, 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_7975, c_0_5942]), ['final']). 4.05/4.33 cnf(c_0_12916, 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_7976]), ['final']). 4.05/4.33 cnf(c_0_12917, 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_7977]), ['final']). 4.05/4.33 cnf(c_0_12918, 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_7978]), ['final']). 4.05/4.33 cnf(c_0_12919, 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,esk65_5(X3,X4,X5,X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_7002]), ['final']). 4.05/4.33 cnf(c_0_12920, 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_7979]), ['final']). 4.05/4.33 cnf(c_0_12921, 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_7980]), ['final']). 4.05/4.33 cnf(c_0_12922, 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_7981]), ['final']). 4.05/4.33 cnf(c_0_12923, 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_7982]), ['final']). 4.05/4.33 cnf(c_0_12924, 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_7983]), ['final']). 4.05/4.33 cnf(c_0_12925, 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_7984]), ['final']). 4.05/4.33 cnf(c_0_12926, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))))), inference(split_conjunct,[status(thm)],[c_0_7985]), ['final']). 4.05/4.33 cnf(c_0_12927, plain, (X1=hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk166_3(X3,X1,X2)),esk166_3(X3,X1,X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X1),c_Relation_OId__on(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_7986]), ['final']). 4.05/4.33 cnf(c_0_12928, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),esk171_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_7718]), ['final']). 4.05/4.33 cnf(c_0_12929, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),esk146_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_7720]), ['final']). 4.05/4.33 cnf(c_0_12930, 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)))), inference(split_conjunct,[status(thm)],[c_0_7545]), ['final']). 4.05/4.33 cnf(c_0_12931, 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_7987]), ['final']). 4.05/4.33 cnf(c_0_12932, plain, (c_List_Olast(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_7988, c_0_4519]), ['final']). 4.05/4.33 cnf(c_0_12933, 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_7989]), ['final']). 4.05/4.33 cnf(c_0_12934, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|c_Option_Ooption_ONone(X2)=hAPP(X3,esk418_3(X3,X2,X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Map_Odom(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_7990]), ['final']). 4.05/4.33 cnf(c_0_12935, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk113_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_7991]), ['final']). 4.05/4.33 cnf(c_0_12936, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|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)), inference(split_conjunct,[status(thm)],[c_0_7802]), ['final']). 4.05/4.33 cnf(c_0_12937, 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_7992]), ['final']). 4.05/4.33 cnf(c_0_12938, 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_7507]), ['final']). 4.05/4.33 cnf(c_0_12939, plain, (hAPP(hAPP(c_List_Omap(X5,X4),X3),X2)=hAPP(hAPP(c_List_Omap(X5,X4),X1),X2)|hAPP(X1,esk472_5(X1,X2,X3,X4,X5))!=hAPP(X3,esk472_5(X1,X2,X3,X4,X5))), inference(split_conjunct,[status(thm)],[c_0_7212]), ['final']). 4.05/4.33 cnf(c_0_12940, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=X4|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)), inference(er,[status(thm)],[c_0_7993]), ['final']). 4.05/4.33 cnf(c_0_12941, 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_7994, c_0_4915]), ['final']). 4.05/4.33 cnf(c_0_12942, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk19_3(X2,X1,X3)),esk17_2(X2,X1)))|c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),esk17_2(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_7191]), ['final']). 4.05/4.33 cnf(c_0_12943, 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_7995]), ['final']). 4.05/4.33 cnf(c_0_12944, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4)), inference(split_conjunct,[status(thm)],[c_0_7996]), ['final']). 4.05/4.33 cnf(c_0_12945, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X6),X5)=hAPP(hAPP(X4,X5),X6)|~c_Finite__Set_Ofolding(X1,X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))), inference(split_conjunct,[status(thm)],[c_0_7997]), ['final']). 4.05/4.33 cnf(c_0_12946, 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_7998, c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_12947, 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_7999]), ['final']). 4.05/4.33 cnf(c_0_12948, 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_8000, c_0_8001]), ['final']). 4.05/4.33 cnf(c_0_12949, 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)))), inference(split_conjunct,[status(thm)],[c_0_8002]), ['final']). 4.05/4.33 cnf(c_0_12950, 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_8003]), ['final']). 4.05/4.33 cnf(c_0_12951, 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_8004]), ['final']). 4.05/4.33 cnf(c_0_12952, plain, (hAPP(X7,hAPP(X8,X9))=hAPP(X4,hAPP(X5,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_8005]), ['final']). 4.05/4.33 cnf(c_0_12953, 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_5606]), ['final']). 4.05/4.33 cnf(c_0_12954, 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_8006, c_0_5695]), ['final']). 4.05/4.33 cnf(c_0_12955, 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_8007]), ['final']). 4.05/4.33 cnf(c_0_12956, 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_8008]), ['final']). 4.05/4.33 cnf(c_0_12957, 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_5606]), ['final']). 4.05/4.33 cnf(c_0_12958, 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_8009]), ['final']). 4.05/4.33 cnf(c_0_12959, 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_8010]), ['final']). 4.05/4.33 cnf(c_0_12960, 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_8011]), ['final']). 4.05/4.33 cnf(c_0_12961, 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_8012, c_0_6340]), ['final']). 4.05/4.33 cnf(c_0_12962, 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_8013, c_0_6340]), ['final']). 4.05/4.33 cnf(c_0_12963, 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_8014]), ['final']). 4.05/4.33 cnf(c_0_12964, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk128_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_8015]), ['final']). 4.05/4.33 cnf(c_0_12965, 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_Int_Onumber__ring(X3)|~class_Rings_Olinordered__idom(X3)), inference(split_conjunct,[status(thm)],[c_0_8016]), ['final']). 4.05/4.33 cnf(c_0_12966, 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_8017]), ['final']). 4.05/4.33 cnf(c_0_12967, 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_8018]), ['final']). 4.05/4.33 cnf(c_0_12968, 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_8019]), ['final']). 4.05/4.33 cnf(c_0_12969, 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_8020, c_0_4523]), c_0_4523]), ['final']). 4.05/4.33 cnf(c_0_12970, 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_8021]), ['final']). 4.05/4.33 cnf(c_0_12971, 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_8022]), ['final']). 4.05/4.33 cnf(c_0_12972, 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,esk361_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_12973, 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,esk363_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_12974, 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_8023]), ['final']). 4.05/4.33 cnf(c_0_12975, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk181_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_5265]), ['final']). 4.05/4.33 cnf(c_0_12976, plain, (X3=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X2),tc_List_Olist(X2)),X1),c_List_Orotate1(X2)),X3)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))), inference(rw,[status(thm)],[c_0_8024, c_0_5942]), ['final']). 4.05/4.33 cnf(c_0_12977, 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_8025]), ['final']). 4.05/4.33 cnf(c_0_12978, 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_8026]), ['final']). 4.05/4.33 cnf(c_0_12979, 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_8027]), ['final']). 4.05/4.33 cnf(c_0_12980, 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_8028]), ['final']). 4.05/4.33 cnf(c_0_12981, 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_8029]), ['final']). 4.05/4.33 cnf(c_0_12982, 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_8030]), ['final']). 4.05/4.33 cnf(c_0_12983, 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_8031]), ['final']). 4.05/4.33 cnf(c_0_12984, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk467_4(X2,X3,X1,X4)),X3))|c_Groups_Ozero__class_Ozero(X4)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X2),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~class_Rings_Ono__zero__divisors(X4)|~class_Rings_Ocomm__semiring__1(X4)), inference(split_conjunct,[status(thm)],[c_0_8032]), ['final']). 4.05/4.33 cnf(c_0_12985, 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_8033]), ['final']). 4.05/4.33 cnf(c_0_12986, 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_8034]), ['final']). 4.05/4.33 cnf(c_0_12987, 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_8035]), ['final']). 4.05/4.33 cnf(c_0_12988, 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_7670]), ['final']). 4.05/4.33 cnf(c_0_12989, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk91_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_8036]), ['final']). 4.05/4.33 cnf(c_0_12990, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),c_Map_Odom(X1,X2,X4)))|~c_Map_Omap__le(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8037]), ['final']). 4.05/4.33 cnf(c_0_12991, 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_8038]), ['final']). 4.05/4.33 cnf(c_0_12992, plain, (hAPP(c_Option_Ooption_OSome(X1),X2)=hAPP(X3,esk430_5(X4,X3,X5,X2,X1))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Oran(X5,X1,c_Map_Orestrict__map(X5,X1,X3,X4))))), inference(split_conjunct,[status(thm)],[c_0_7753]), ['final']). 4.05/4.33 cnf(c_0_12993, 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_8039]), ['final']). 4.05/4.33 cnf(c_0_12994, 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_8040]), ['final']). 4.05/4.33 cnf(c_0_12995, 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_8041]), ['final']). 4.05/4.33 cnf(c_0_12996, 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_8042]), ['final']). 4.05/4.33 cnf(c_0_12997, 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_8043]), ['final']). 4.05/4.33 cnf(c_0_12998, 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_8044]), ['final']). 4.05/4.33 cnf(c_0_12999, 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_8045, c_0_5905]), ['final']). 4.05/4.33 cnf(c_0_13000, 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_8046, c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_13001, 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_8047]), ['final']). 4.05/4.33 cnf(c_0_13002, 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_8048]), ['final']). 4.05/4.33 cnf(c_0_13003, 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_8049, c_0_4950]), ['final']). 4.05/4.33 cnf(c_0_13004, 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),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8050]), ['final']). 4.05/4.33 cnf(c_0_13005, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~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)), inference(split_conjunct,[status(thm)],[c_0_8051]), ['final']). 4.05/4.33 cnf(c_0_13006, 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_8052, c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_13007, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk471_4(X2,X3,X4,X1)),c_Map_Odom(X1,X4,X3)))|c_Map_Omap__le(X1,X4,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8053]), ['final']). 4.05/4.33 cnf(c_0_13008, plain, (hBOOL(hAPP(X1,esk347_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_7386]), ['final']). 4.05/4.33 cnf(c_0_13009, 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_6180]), ['final']). 4.05/4.33 cnf(c_0_13010, plain, (hAPP(c_Option_Ooption_OSome(X1),X4)=hAPP(c_Map_Omap__add(X6,X1,X5,X2),X3)|c_Option_Ooption_ONone(X1)!=hAPP(X2,X3)|hAPP(c_Option_Ooption_OSome(X1),X4)!=hAPP(X5,X3)), inference(split_conjunct,[status(thm)],[c_0_8054]), ['final']). 4.05/4.33 cnf(c_0_13011, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)),X2)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)!=hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber(X1)), inference(split_conjunct,[status(thm)],[c_0_8055]), ['final']). 4.05/4.33 cnf(c_0_13012, 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_8056]), ['final']). 4.05/4.33 cnf(c_0_13013, 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|hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)))|~hBOOL(hAPP(X2,esk353_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_13014, plain, (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)=X2|hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,esk355_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_13015, 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_8057, c_0_4867]), c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_13016, 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_8058, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), ['final']). 4.05/4.33 cnf(c_0_13017, 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_6677]), ['final']). 4.05/4.33 cnf(c_0_13018, plain, (X4=hAPP(c_Set_Oimage(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_8059]), ['final']). 4.05/4.33 cnf(c_0_13019, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(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_OgreaterThanAtMost(X1,X3,X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8060]), ['final']). 4.05/4.33 cnf(c_0_13020, 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_8061])]), ['final']). 4.05/4.33 cnf(c_0_13021, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk320_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_8062]), ['final']). 4.05/4.33 cnf(c_0_13022, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk229_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_8063]), ['final']). 4.05/4.33 cnf(c_0_13023, 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_8064]), ['final']). 4.05/4.33 cnf(c_0_13024, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk280_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_8065]), ['final']). 4.05/4.33 cnf(c_0_13025, 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_5528]), ['final']). 4.05/4.33 cnf(c_0_13026, plain, (hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X6,X7,X8,X4,X1),X5),X3))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(X4,X5),X2))), inference(split_conjunct,[status(thm)],[c_0_8066]), ['final']). 4.05/4.33 cnf(c_0_13027, plain, (hBOOL(hAPP(X1,X7))|~hBOOL(hAPP(X1,esk411_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_6613]), ['final']). 4.05/4.33 cnf(c_0_13028, 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_8067]), ['final']). 4.05/4.33 cnf(c_0_13029, plain, (X1=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X3),X4)),hAPP(c_List_Olexn(X2,X5),X1)))), inference(split_conjunct,[status(thm)],[c_0_8067]), ['final']). 4.05/4.33 cnf(c_0_13030, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), inference(split_conjunct,[status(thm)],[c_0_8068]), ['final']). 4.05/4.33 cnf(c_0_13031, 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_8069]), ['final']). 4.05/4.33 cnf(c_0_13032, 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_7670]), ['final']). 4.05/4.33 cnf(c_0_13033, 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_7597]), ['final']). 4.05/4.33 cnf(c_0_13034, 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_8070]), ['final']). 4.05/4.33 cnf(c_0_13035, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk521_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_5513]), ['final']). 4.05/4.33 cnf(c_0_13036, 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_7669]), ['final']). 4.05/4.33 cnf(c_0_13037, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk181_3(X2,X3,X1)),X2))|hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_5265]), ['final']). 4.05/4.33 cnf(c_0_13038, 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_8071, c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_13039, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk520_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_5513]), ['final']). 4.05/4.33 cnf(c_0_13040, 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)|esk24_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_8072, c_0_4867]), c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_13041, plain, (hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X1,X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(split_conjunct,[status(thm)],[c_0_8073]), ['final']). 4.05/4.33 cnf(c_0_13042, 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_8074]), ['final']). 4.05/4.33 cnf(c_0_13043, plain, (X1=X2|hAPP(X3,X2)=hAPP(c_Option_Ooption_OSome(X4),X5)|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6,tc_Option_Ooption(X4)),X3),X1),hAPP(c_Option_Ooption_OSome(X4),X7)),X2)!=hAPP(c_Option_Ooption_OSome(X4),X5)), inference(split_conjunct,[status(thm)],[c_0_7093]), ['final']). 4.05/4.33 cnf(c_0_13044, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk36_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_8075]), ['final']). 4.05/4.33 cnf(c_0_13045, 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_8076]), ['final']). 4.05/4.33 cnf(c_0_13046, 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_8077, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13047, 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_8078, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13048, 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_8079]), ['final']). 4.05/4.33 cnf(c_0_13049, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk88_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_8080]), ['final']). 4.05/4.33 cnf(c_0_13050, plain, (X1=X2|hAPP(X3,X4)=hAPP(c_Option_Ooption_OSome(X5),X1)|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6,tc_Option_Ooption(X5)),X3),X7),hAPP(c_Option_Ooption_OSome(X5),X2)),X4)!=hAPP(c_Option_Ooption_OSome(X5),X1)), inference(split_conjunct,[status(thm)],[c_0_7093]), ['final']). 4.05/4.33 cnf(c_0_13051, 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,esk358_5(X3,X2,X4,X5,X1))),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7065]), ['final']). 4.05/4.33 cnf(c_0_13052, 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,esk522_5(X3,X4,X5,X2,X1))))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_7066]), ['final']). 4.05/4.33 cnf(c_0_13053, plain, (X4=hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist__update(X2,X3),X1),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_8081]), ['final']). 4.05/4.33 cnf(c_0_13054, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X5,tc_Option_Ooption(X3)),X1),X2),hAPP(c_Option_Ooption_OSome(X3),X4))=X1|hAPP(X1,X2)!=hAPP(c_Option_Ooption_OSome(X3),X4)), inference(split_conjunct,[status(thm)],[c_0_8082]), ['final']). 4.05/4.33 cnf(c_0_13055, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8083]), ['final']). 4.05/4.33 cnf(c_0_13056, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk193_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_8084]), ['final']). 4.05/4.33 cnf(c_0_13057, 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_7115]), ['final']). 4.05/4.33 cnf(c_0_13058, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk217_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_8085]), ['final']). 4.05/4.33 cnf(c_0_13059, 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_8086, c_0_7800]), ['final']). 4.05/4.33 cnf(c_0_13060, 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_8087, c_0_7800]), ['final']). 4.05/4.33 cnf(c_0_13061, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk169_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_7106]), ['final']). 4.05/4.33 cnf(c_0_13062, 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_8088]), ['final']). 4.05/4.33 cnf(c_0_13063, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))|~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_8089]), ['final']). 4.05/4.33 cnf(c_0_13064, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk174_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_5288]), ['final']). 4.05/4.33 cnf(c_0_13065, 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_8090, c_0_7800]), ['final']). 4.05/4.33 cnf(c_0_13066, 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_8091, c_0_7800]), ['final']). 4.05/4.33 cnf(c_0_13067, 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_5887]), ['final']). 4.05/4.33 cnf(c_0_13068, 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)|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_8092]), ['final']). 4.05/4.33 cnf(c_0_13069, 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))), inference(split_conjunct,[status(thm)],[c_0_8093]), ['final']). 4.05/4.33 cnf(c_0_13070, 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_8094]), ['final']). 4.05/4.33 cnf(c_0_13071, 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_8095]), ['final']). 4.05/4.33 cnf(c_0_13072, 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,esk62_4(X2,X1,X3,X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7007]), ['final']). 4.05/4.33 cnf(c_0_13073, 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,esk33_4(X2,X1,X3,X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_7008]), ['final']). 4.05/4.33 cnf(c_0_13074, 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_4647]), ['final']). 4.05/4.33 cnf(c_0_13075, 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_8096]), ['final']). 4.05/4.33 cnf(c_0_13076, 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_8097]), ['final']). 4.05/4.33 cnf(c_0_13077, 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_8098]), ['final']). 4.05/4.33 cnf(c_0_13078, 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_8099]), ['final']). 4.05/4.33 cnf(c_0_13079, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk402_2(X3,X1)),X2))|c_List_Olist_ONil(X1)=X3|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk401_2(X3,X1))))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5366]), ['final']). 4.05/4.33 cnf(c_0_13080, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),X3)|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8100]), ['final']). 4.05/4.33 cnf(c_0_13081, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(X1,esk268_4(X1,X2,X3,X4))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X3),X4),X2))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X1,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7197]), ['final']). 4.05/4.33 cnf(c_0_13082, plain, (c_Fun_Oinj__on(X1,X2,esk459_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_6950]), ['final']). 4.05/4.33 cnf(c_0_13083, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8101]), ['final']). 4.05/4.33 cnf(c_0_13084, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),X3)|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8102]), ['final']). 4.05/4.33 cnf(c_0_13085, 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_8103]), ['final']). 4.05/4.33 cnf(c_0_13086, 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_8062]), ['final']). 4.05/4.33 cnf(c_0_13087, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2)=c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_List_Oset(X1),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8104]), ['final']). 4.05/4.33 cnf(c_0_13088, 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_8105, c_0_4635]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_13089, 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_8106]), ['final']). 4.05/4.33 cnf(c_0_13090, 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_8107]), ['final']). 4.05/4.33 cnf(c_0_13091, 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_8108]), ['final']). 4.05/4.33 cnf(c_0_13092, 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_8063]), ['final']). 4.05/4.33 cnf(c_0_13093, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_COMBI(X1)),hAPP(c_List_Oset(X1),X2))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8109]), ['final']). 4.05/4.33 cnf(c_0_13094, 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_8110]), ['final']). 4.05/4.33 cnf(c_0_13095, 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_8111]), ['final']). 4.05/4.33 cnf(c_0_13096, 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_8112]), ['final']). 4.05/4.33 cnf(c_0_13097, 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_8113]), ['final']). 4.05/4.33 cnf(c_0_13098, 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,esk251_4(X3,X2,X4,X1))),hAPP(X3,esk251_4(X3,X2,X4,X1))))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_8114]), ['final']). 4.05/4.33 cnf(c_0_13099, plain, (hBOOL(hAPP(X1,X6))|~hBOOL(hAPP(X1,esk410_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_6613]), ['final']). 4.05/4.33 cnf(c_0_13100, 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_8115]), ['final']). 4.05/4.33 cnf(c_0_13101, 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_8116]), ['final']). 4.05/4.33 cnf(c_0_13102, 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_8117, c_0_5149]), c_0_5149]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_13103, 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_8118, c_0_5149]), c_0_5149]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_13104, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X2),X4)))|~hBOOL(hAPP(X1,esk223_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_7107]), ['final']). 4.05/4.33 cnf(c_0_13105, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk67_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_8119]), ['final']). 4.05/4.33 cnf(c_0_13106, plain, (hBOOL(hAPP(X1,esk152_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_8120]), ['final']). 4.05/4.33 cnf(c_0_13107, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk195_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_8121]), ['final']). 4.05/4.33 cnf(c_0_13108, 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,esk224_5(X3,X2,X4,X5,X1))))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7190]), ['final']). 4.05/4.33 cnf(c_0_13109, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk20_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_7191]), ['final']). 4.05/4.33 cnf(c_0_13110, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|c_List_Osublist(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)),X1)=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_7974]), ['final']). 4.05/4.33 cnf(c_0_13111, 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_8122]), ['final']). 4.05/4.33 cnf(c_0_13112, 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_8123]), ['final']). 4.05/4.33 cnf(c_0_13113, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk277_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_7392]), ['final']). 4.05/4.33 cnf(c_0_13114, 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_8124]), ['final']). 4.05/4.33 cnf(c_0_13115, plain, (c_Groups_Ozero__class_Ozero(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),X2)),X1))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2))), inference(csr,[status(thm)],[c_0_8125, c_0_6624]), ['final']). 4.05/4.33 cnf(c_0_13116, 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_7999]), ['final']). 4.05/4.33 cnf(c_0_13117, 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_8126]), ['final']). 4.05/4.33 cnf(c_0_13118, plain, (c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,esk225_4(X3,X4,X2,X1),X3)|~c_Natural_Oevaln(c_Com_Ocom_OBODY(X1),X2,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_8127]), ['final']). 4.05/4.33 cnf(c_0_13119, 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_8128]), ['final']). 4.05/4.33 cnf(c_0_13120, 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_8129, c_0_4867]), c_0_4867]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_13121, 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_8130]), ['final']). 4.05/4.33 cnf(c_0_13122, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk103_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_8131]), ['final']). 4.05/4.33 cnf(c_0_13123, 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_8132]), ['final']). 4.05/4.33 cnf(c_0_13124, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3))=c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8133]), ['final']). 4.05/4.33 cnf(c_0_13125, plain, (X1=hAPP(c_Set_Oimage(X2,X3,X4),esk479_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_7379]), ['final']). 4.05/4.33 cnf(c_0_13126, 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_8134, c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_13127, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk475_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_8135]), ['final']). 4.05/4.33 cnf(c_0_13128, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk103_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_8131]), ['final']). 4.05/4.33 cnf(c_0_13129, 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_8136]), ['final']). 4.05/4.33 cnf(c_0_13130, 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_8137]), ['final']). 4.05/4.33 cnf(c_0_13131, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8138]), ['final']). 4.05/4.33 cnf(c_0_13132, 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_8114]), ['final']). 4.05/4.33 cnf(c_0_13133, 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,esk361_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_13134, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),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_8139]), ['final']). 4.05/4.33 cnf(c_0_13135, 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_8140]), ['final']). 4.05/4.33 cnf(c_0_13136, 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_8141]), ['final']). 4.05/4.33 cnf(c_0_13137, 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,esk363_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_13138, 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),X2),X1))|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_8142]), ['final']). 4.05/4.33 cnf(c_0_13139, 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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|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_8142]), ['final']). 4.05/4.33 cnf(c_0_13140, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk373_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_8143]), ['final']). 4.05/4.33 cnf(c_0_13141, 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_8144]), ['final']). 4.05/4.33 cnf(c_0_13142, 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_8145]), ['final']). 4.05/4.33 cnf(c_0_13143, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk486_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_7856]), ['final']). 4.05/4.33 cnf(c_0_13144, 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_8146]), ['final']). 4.05/4.33 cnf(c_0_13145, 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_8147]), ['final']). 4.05/4.33 cnf(c_0_13146, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk89_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_7126]), ['final']). 4.05/4.33 cnf(c_0_13147, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk427_4(X2,X3,X4,X1)),X3))|c_Equiv__Relations_Ocongruent(X1,X4,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_6187]), ['final']). 4.05/4.33 cnf(c_0_13148, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk188_3(X2,X3,X1)),X2))|c_List_Olist_ONil(X1)=X3|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7693]), ['final']). 4.05/4.33 cnf(c_0_13149, 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_8148]), ['final']). 4.05/4.33 cnf(c_0_13150, 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_8149]), ['final']). 4.05/4.33 cnf(c_0_13151, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X3))))), inference(er,[status(thm)],[c_0_8150]), ['final']). 4.05/4.33 cnf(c_0_13152, 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_8151]), ['final']). 4.05/4.33 cnf(c_0_13153, 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_8152]), ['final']). 4.05/4.33 cnf(c_0_13154, 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_7965]), ['final']). 4.05/4.33 cnf(c_0_13155, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=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)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7966]), ['final']). 4.05/4.33 cnf(c_0_13156, plain, (hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Otake(X3),X2),X4)),X1)=hAPP(hAPP(c_List_Onth(X3),X4),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8153]), ['final']). 4.05/4.33 cnf(c_0_13157, 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_8154]), ['final']). 4.05/4.33 cnf(c_0_13158, plain, (X2=hAPP(hAPP(c_List_Onth(X3),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|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_8155]), ['final']). 4.05/4.33 cnf(c_0_13159, plain, (hBOOL(hAPP(hAPP(c_member(X6),X2),c_SetInterval_Oord_OatLeastLessThan(X6,X4,X1,X5,X3)))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(X4,X5),X2))), inference(split_conjunct,[status(thm)],[c_0_8156]), ['final']). 4.05/4.33 cnf(c_0_13160, 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_8157]), ['final']). 4.05/4.33 cnf(c_0_13161, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk166_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_7986]), ['final']). 4.05/4.33 cnf(c_0_13162, 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_8158]), ['final']). 4.05/4.33 cnf(c_0_13163, 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_8159]), ['final']). 4.05/4.33 cnf(c_0_13164, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk266_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_5611]), ['final']). 4.05/4.33 cnf(c_0_13165, plain, (c_List_Olinorder__class_Oinsort__insert__key(X4,X1,X2,X3,X5)=X5|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),hAPP(c_List_Oset(X4),X5))))), inference(split_conjunct,[status(thm)],[c_0_8160]), ['final']). 4.05/4.33 cnf(c_0_13166, 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_8161]), ['final']). 4.05/4.33 cnf(c_0_13167, 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_8162]), ['final']). 4.05/4.33 cnf(c_0_13168, 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_8163]), ['final']). 4.05/4.33 cnf(c_0_13169, 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)), inference(split_conjunct,[status(thm)],[c_0_8164]), ['final']). 4.05/4.33 cnf(c_0_13170, 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_5253]), ['final']). 4.05/4.33 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__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_7437]), ['final']). 4.05/4.33 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),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_5253]), ['final']). 4.05/4.33 cnf(c_0_13173, 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_8165]), ['final']). 4.05/4.33 cnf(c_0_13174, 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_5456]), ['final']). 4.05/4.33 cnf(c_0_13175, 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_8166]), ['final']). 4.05/4.33 cnf(c_0_13176, 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,esk495_2(X2,X1))))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5962]), ['final']). 4.05/4.33 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_7437]), ['final']). 4.05/4.33 cnf(c_0_13178, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Oordered__comm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5374]), ['final']). 4.05/4.33 cnf(c_0_13179, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Groups_Oordered__comm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_5374]), ['final']). 4.05/4.33 cnf(c_0_13180, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8167]), ['final']). 4.05/4.33 cnf(c_0_13181, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8168]), ['final']). 4.05/4.33 cnf(c_0_13182, 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_8169, c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_13183, 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_8170]), ['final']). 4.05/4.33 cnf(c_0_13184, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),X2)), inference(split_conjunct,[status(thm)],[c_0_8171]), ['final']). 4.05/4.33 cnf(c_0_13185, 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_8172]), ['final']). 4.05/4.33 cnf(c_0_13186, 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_8173, c_0_4635]), c_0_5165]), ['final']). 4.05/4.33 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_8174]), ['final']). 4.05/4.33 cnf(c_0_13188, plain, (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))))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_7545]), ['final']). 4.05/4.33 cnf(c_0_13189, 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_8175]), ['final']). 4.05/4.33 cnf(c_0_13190, plain, (c_List_Olist_ONil(X1)=X2|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))), inference(split_conjunct,[status(thm)],[c_0_8176]), ['final']). 4.05/4.33 cnf(c_0_13191, 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,esk212_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_8177]), ['final']). 4.05/4.33 cnf(c_0_13192, 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_8178]), ['final']). 4.05/4.33 cnf(c_0_13193, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk174_3(X3,X2,X1)),X3))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5288]), ['final']). 4.05/4.33 cnf(c_0_13194, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk397_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|c_List_OtakeWhile(X1,X3,X2)=X2), inference(split_conjunct,[status(thm)],[c_0_8179]), ['final']). 4.05/4.33 cnf(c_0_13195, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8180]), ['final']). 4.05/4.33 cnf(c_0_13196, 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_8181]), ['final']). 4.05/4.33 cnf(c_0_13197, 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_8182]), ['final']). 4.05/4.33 cnf(c_0_13198, 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_8183]), ['final']). 4.05/4.33 cnf(c_0_13199, plain, (hAPP(c_Option_Ooption_OSome(X1),X2)=hAPP(X3,X4)|hAPP(X5,X4)=hAPP(c_Option_Ooption_OSome(X1),X2)|hAPP(c_Map_Omap__add(X6,X1,X3,X5),X4)!=hAPP(c_Option_Ooption_OSome(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_8184]), ['final']). 4.05/4.33 cnf(c_0_13200, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8185, c_0_4795]), c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_13201, 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_8186])]), ['final']). 4.05/4.33 cnf(c_0_13202, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_8187]), ['final']). 4.05/4.33 cnf(c_0_13203, 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_8188]), ['final']). 4.05/4.33 cnf(c_0_13204, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8189]), ['final']). 4.05/4.33 cnf(c_0_13205, 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_8190, c_0_4915]), ['final']). 4.05/4.33 cnf(c_0_13206, plain, (c_Fun_Oinj__on(X1,X2,X3,c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X4))|X4=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))|~c_Fun_Oinj__on(X1,X2,X3,esk337_4(X3,X2,X1,X4))), inference(split_conjunct,[status(thm)],[c_0_7103]), ['final']). 4.05/4.33 cnf(c_0_13207, plain, (c_Enum_Oenum__the(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))), inference(rw,[status(thm)],[c_0_8191, c_0_6300]), ['final']). 4.05/4.33 cnf(c_0_13208, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk66_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))|c_List_Olist__all(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8192]), ['final']). 4.05/4.33 cnf(c_0_13209, 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_8193]), ['final']). 4.05/4.33 cnf(c_0_13210, 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_8194]), ['final']). 4.05/4.33 cnf(c_0_13211, 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_8195]), ['final']). 4.05/4.33 cnf(c_0_13212, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),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_8196]), ['final']). 4.05/4.33 cnf(c_0_13213, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk138_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|c_List_Olist__all(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8197]), ['final']). 4.05/4.33 cnf(c_0_13214, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Oreplicate(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)=hAPP(c_List_Otl(X2),c_List_Oreplicate(X2,X1,X3))), inference(split_conjunct,[status(thm)],[c_0_8198]), ['final']). 4.05/4.33 cnf(c_0_13215, 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_5266]), ['final']). 4.05/4.33 cnf(c_0_13216, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3))),c_Groups_Ozero__class_Ozero(X2)))|~class_Rings_Olinordered__ring__strict(X2)), inference(split_conjunct,[status(thm)],[c_0_5266]), ['final']). 4.05/4.33 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_8199])]), ['final']). 4.05/4.33 cnf(c_0_13218, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk92_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|c_List_Olist__all(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8200]), ['final']). 4.05/4.33 cnf(c_0_13219, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8201]), ['final']). 4.05/4.33 cnf(c_0_13220, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~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_8202]), ['final']). 4.05/4.33 cnf(c_0_13221, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8203]), ['final']). 4.05/4.33 cnf(c_0_13222, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),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)))=c_SMT_Oz3div(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8204]), ['final']). 4.05/4.33 cnf(c_0_13223, 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_8205]), ['final']). 4.05/4.33 cnf(c_0_13224, plain, (X1=X2|hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_Oremove1(X3,X1,X4))=c_List_Oremove1(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_5998]), ['final']). 4.05/4.33 cnf(c_0_13225, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8206]), ['final']). 4.05/4.33 cnf(c_0_13226, 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_8207]), ['final']). 4.05/4.33 cnf(c_0_13227, plain, (hAPP(c_Finite__Set_Ocard(X1),X3)=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7875]), ['final']). 4.05/4.33 cnf(c_0_13228, 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_8208]), ['final']). 4.05/4.33 cnf(c_0_13229, plain, (c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8209]), ['final']). 4.05/4.33 cnf(c_0_13230, plain, (hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk222_3(X1,X3,X2))))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_7107]), ['final']). 4.05/4.33 cnf(c_0_13231, 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_8210]), ['final']). 4.05/4.33 cnf(c_0_13232, plain, (X1=hAPP(hAPP(c_Set_Oinsert(X2),esk48_3(X3,X1,X2)),esk49_3(X3,X1,X2))|hAPP(c_Nat_OSuc,X3)!=hAPP(c_Finite__Set_Ocard(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_5466]), ['final']). 4.05/4.33 cnf(c_0_13233, plain, (X1=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X1))|~c_List_Onat__list(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8211, c_0_5829]), c_0_5830]), ['final']). 4.05/4.33 cnf(c_0_13234, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_8212, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13235, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_8213, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13236, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[c_0_8214, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13237, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[c_0_8215, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13238, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk516_3(X1,X2,X3)),esk517_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_5123]), ['final']). 4.05/4.33 cnf(c_0_13239, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk499_3(X1,X2,X3)),esk500_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_4535]), ['final']). 4.05/4.33 cnf(c_0_13240, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk214_3(X1,X2,X3)),esk215_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_4526]), ['final']). 4.05/4.33 cnf(c_0_13241, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk81_3(X1,X2,X3)),esk82_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_6684]), ['final']). 4.05/4.33 cnf(c_0_13242, 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),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))|~class_Rings_Oring(X1)), inference(split_conjunct,[status(thm)],[c_0_8216]), ['final']). 4.05/4.33 cnf(c_0_13243, 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_7927]), ['final']). 4.05/4.33 cnf(c_0_13244, 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_7928]), ['final']). 4.05/4.33 cnf(c_0_13245, 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_8217]), ['final']). 4.05/4.33 cnf(c_0_13246, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__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_7939]), ['final']). 4.05/4.33 cnf(c_0_13247, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk38_3(X1,X2,X3)),esk39_3(X1,X2,X3)))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_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_5102]), ['final']). 4.05/4.33 cnf(c_0_13248, plain, (hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(hAPP(X1,esk29_3(X1,X2,X3)),esk30_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_6627]), ['final']). 4.05/4.33 cnf(c_0_13249, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk25_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_8218, c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_13250, plain, (c_List_OtakeWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))=hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_OtakeWhile(X3,X1,X4))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_8219]), ['final']). 4.05/4.33 cnf(c_0_13251, 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_7941]), ['final']). 4.05/4.33 cnf(c_0_13252, 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_8220, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13253, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk50_2(X2,X1))))|hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,X2))), inference(rw,[status(thm)],[c_0_8221, c_0_5669]), ['final']). 4.05/4.33 cnf(c_0_13254, 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_8222, c_0_4767]), ['final']). 4.05/4.33 cnf(c_0_13255, 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_7703]), ['final']). 4.05/4.33 cnf(c_0_13256, 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_8223, c_0_4523]), ['final']). 4.05/4.33 cnf(c_0_13257, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_8224, c_0_4439]), ['final']). 4.05/4.33 cnf(c_0_13258, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk55_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_7772]), ['final']). 4.05/4.33 cnf(c_0_13259, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk54_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_7772]), ['final']). 4.05/4.33 cnf(c_0_13260, 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_8225, c_0_6268]), ['final']). 4.05/4.33 cnf(c_0_13261, 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,esk353_3(X1,X3,X2)))|~hBOOL(hAPP(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_13262, 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_8226, c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_13263, 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_8227, c_0_6268]), ['final']). 4.05/4.33 cnf(c_0_13264, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,esk355_3(X2,X3,X1)))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_13265, 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_8228, c_0_6268]), ['final']). 4.05/4.33 cnf(c_0_13266, 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_8229]), ['final']). 4.05/4.33 cnf(c_0_13267, plain, (c_Nitpick_Onorm__frac(X2,X1)=c_Nitpick_Onorm__frac(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(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5491]), ['final']). 4.05/4.33 cnf(c_0_13268, 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)), inference(split_conjunct,[status(thm)],[c_0_8230]), ['final']). 4.05/4.33 cnf(c_0_13269, plain, (X5=X7|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5))!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X6),X4),hAPP(c_Option_Ooption_OSome(X2),X7))), inference(split_conjunct,[status(thm)],[c_0_8231]), ['final']). 4.05/4.33 cnf(c_0_13270, 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_8232]), ['final']). 4.05/4.33 cnf(c_0_13271, 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_8232]), ['final']). 4.05/4.33 cnf(c_0_13272, 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_8233]), ['final']). 4.05/4.33 cnf(c_0_13273, 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_8234]), ['final']). 4.05/4.33 cnf(c_0_13274, 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_8235]), ['final']). 4.05/4.33 cnf(c_0_13275, plain, (c_Map_Omap__le(X1,X2,c_Map_Omap__add(X1,X2,X3,X5),X4)|~c_Map_Omap__le(X1,X2,X3,X4)|~c_Map_Omap__le(X1,X2,X5,X4)|~c_Map_Omap__le(X1,X2,X3,c_Map_Omap__add(X1,X2,X3,X5))), inference(split_conjunct,[status(thm)],[c_0_8236]), ['final']). 4.05/4.33 cnf(c_0_13276, 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_8237]), ['final']). 4.05/4.33 cnf(c_0_13277, 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_8238]), ['final']). 4.05/4.33 cnf(c_0_13278, plain, (c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))!=hAPP(c_Set_Oimage(X1,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_8239]), ['final']). 4.05/4.33 cnf(c_0_13279, 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_8240]), ['final']). 4.05/4.33 cnf(c_0_13280, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3))|~class_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_8241]), ['final']). 4.05/4.33 cnf(c_0_13281, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk490_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_8242]), ['final']). 4.05/4.33 cnf(c_0_13282, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),X2))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_8243]), ['final']). 4.05/4.33 cnf(c_0_13283, 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_8244]), ['final']). 4.05/4.33 cnf(c_0_13284, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk385_2(X1,X2)),c_Int_OInteg))|hBOOL(hAPP(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_8245]), ['final']). 4.05/4.33 cnf(c_0_13285, plain, (c_Map_Odom(X5,X1,X3)=hAPP(hAPP(c_Set_Oinsert(X5),X4),c_Map_Odom(X5,X1,X3))|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8246]), ['final']). 4.05/4.33 cnf(c_0_13286, plain, (hBOOL(hAPP(X2,X4))|~c_Enum_Oall__n__lists(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X3,c_Enum_Oenum__class_Oenum(X1)))))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_7220]), ['final']). 4.05/4.33 cnf(c_0_13287, 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_8247]), ['final']). 4.05/4.33 cnf(c_0_13288, 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_8248]), ['final']). 4.05/4.33 cnf(c_0_13289, 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_8249]), ['final']). 4.05/4.33 cnf(c_0_13290, 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_8250]), ['final']). 4.05/4.33 cnf(c_0_13291, 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_8251]), ['final']). 4.05/4.33 cnf(c_0_13292, 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_8252]), ['final']). 4.05/4.33 cnf(c_0_13293, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2))=hAPP(c_SetInterval_Oord__class_OatLeast(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8253]), ['final']). 4.05/4.33 cnf(c_0_13294, plain, (hAPP(c_SetInterval_Oord__class_OatMost(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_OatLeast(X1),X2))|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8254]), ['final']). 4.05/4.33 cnf(c_0_13295, plain, (hBOOL(hAPP(hAPP(X1,esk395_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_8066]), ['final']). 4.05/4.33 cnf(c_0_13296, plain, (hBOOL(hAPP(hAPP(X1,X2),esk395_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_8066]), ['final']). 4.05/4.33 cnf(c_0_13297, plain, (c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=X3|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),hAPP(c_COMBK(X1,X2),X4))=X4|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8255]), ['final']). 4.05/4.33 cnf(c_0_13298, 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_8256]), ['final']). 4.05/4.33 cnf(c_0_13299, 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_8257]), ['final']). 4.05/4.33 cnf(c_0_13300, 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_8258]), ['final']). 4.05/4.33 cnf(c_0_13301, 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_8259]), ['final']). 4.05/4.33 cnf(c_0_13302, 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_8260]), ['final']). 4.05/4.33 cnf(c_0_13303, 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_8261]), ['final']). 4.05/4.33 cnf(c_0_13304, plain, (c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),c_Map_Omap__add(X1,X2,X4,X3),c_Map_Odom(X1,X2,X3))|~c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),X3,c_Map_Odom(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_8262]), ['final']). 4.05/4.33 cnf(c_0_13305, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|X4=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1),X2),hAPP(c_COMBK(X1,X3),X4))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8263]), ['final']). 4.05/4.33 cnf(c_0_13306, 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_8264]), ['final']). 4.05/4.33 cnf(c_0_13307, 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_8265]), ['final']). 4.05/4.33 cnf(c_0_13308, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2))|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8266]), ['final']). 4.05/4.33 cnf(c_0_13309, 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_8267]), ['final']). 4.05/4.33 cnf(c_0_13310, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),c_Big__Operators_Olinorder__class_OMin(X1,X2))=c_Big__Operators_Olinorder__class_OMin(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8268]), ['final']). 4.05/4.33 cnf(c_0_13311, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),c_Big__Operators_Olinorder__class_OMax(X1,X2))=c_Big__Operators_Olinorder__class_OMax(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8269]), ['final']). 4.05/4.33 cnf(c_0_13312, 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_8270, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13313, 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_8271]), ['final']). 4.05/4.33 cnf(c_0_13314, 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_8272]), ['final']). 4.05/4.33 cnf(c_0_13315, 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_8273]), ['final']). 4.05/4.33 cnf(c_0_13316, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|esk268_4(X1,X2,X3,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X3),X4),X2))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X1,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7197]), ['final']). 4.05/4.33 cnf(c_0_13317, 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_7229]), ['final']). 4.05/4.33 cnf(c_0_13318, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk254_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_8274, c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_13319, plain, (hAPP(hAPP(c_List_Onth(X1),X2),esk54_2(X2,X1))=hAPP(hAPP(c_List_Onth(X1),X2),esk55_2(X2,X1))|hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7772]), ['final']). 4.05/4.33 cnf(c_0_13320, 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))|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_8142]), ['final']). 4.05/4.33 cnf(c_0_13321, 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_7229]), ['final']). 4.05/4.33 cnf(c_0_13322, 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_7433]), ['final']). 4.05/4.33 cnf(c_0_13323, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk267_3(X2,X3,X1)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_7197]), ['final']). 4.05/4.33 cnf(c_0_13324, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8275]), ['final']). 4.05/4.33 cnf(c_0_13325, 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_8276]), ['final']). 4.05/4.33 cnf(c_0_13326, 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_8277]), ['final']). 4.05/4.33 cnf(c_0_13327, plain, (hAPP(c_Option_Ooption_OSome(X1),X2)=hAPP(c_Map_Omap__add(X5,X1,X6,X3),X4)|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8054]), ['final']). 4.05/4.33 cnf(c_0_13328, plain, (c_Map_Omap__le(X1,X2,c_Map_Omap__upds(X1,X2,X3,X5,X6),c_Map_Omap__upds(X1,X2,X4,X5,X6))|~c_Map_Omap__le(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8278]), ['final']). 4.05/4.33 cnf(c_0_13329, 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_8277]), ['final']). 4.05/4.33 cnf(c_0_13330, 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_8075]), ['final']). 4.05/4.33 cnf(c_0_13331, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),hAPP(c_List_Oset(tc_prod(X3,X3)),hAPP(hAPP(c_List_Ozip(X3,X3),X4),X4))))), inference(split_conjunct,[status(thm)],[c_0_5172]), ['final']). 4.05/4.33 cnf(c_0_13332, plain, (c_Enum_Oex__n__lists(X3,X1,X4)|~hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3)),X2),hAPP(c_List_Oset(tc_List_Olist(X3)),c_Enum_On__lists(X3,X4,c_Enum_Oenum__class_Oenum(X3)))))|~class_Enum_Oenum(X3)), inference(split_conjunct,[status(thm)],[c_0_7338]), ['final']). 4.05/4.33 cnf(c_0_13333, plain, (c_Map_Omap__add(X1,X2,X4,X3)=c_Map_Omap__add(X1,X2,X3,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)),c_Map_Odom(X1,X2,X3)),c_Map_Odom(X1,X2,X4))), inference(split_conjunct,[status(thm)],[c_0_8279]), ['final']). 4.05/4.33 cnf(c_0_13334, 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),esk113_2(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7991]), ['final']). 4.05/4.33 cnf(c_0_13335, 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))|c_Groups_Ozero__class_Ozero(X1)=X2|~class_Groups_Osgn__if(X1)), inference(split_conjunct,[status(thm)],[c_0_8280]), ['final']). 4.05/4.33 cnf(c_0_13336, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8281]), ['final']). 4.05/4.33 cnf(c_0_13337, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2)=X3|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8282]), ['final']). 4.05/4.33 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_8283]), ['final']). 4.05/4.33 cnf(c_0_13339, 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_7734]), ['final']). 4.05/4.33 cnf(c_0_13340, 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_8284]), ['final']). 4.05/4.33 cnf(c_0_13341, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_8285]), ['final']). 4.05/4.33 cnf(c_0_13342, 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_7758]), ['final']). 4.05/4.33 cnf(c_0_13343, plain, (hAPP(X1,esk98_1(X1))=hAPP(X1,esk99_1(X1))|hBOOL(hAPP(hAPP(X1,esk98_1(X1)),esk99_1(X1)))|c_Equiv__Relations_Oequivp(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8286]), ['final']). 4.05/4.33 cnf(c_0_13344, 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_8287]), ['final']). 4.05/4.33 cnf(c_0_13345, 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_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_7762]), ['final']). 4.05/4.33 cnf(c_0_13346, 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_8288]), ['final']). 4.05/4.33 cnf(c_0_13347, 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,esk363_3(X1,X3,X2)))|~hBOOL(hAPP(X2,esk361_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_13348, 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_8289]), ['final']). 4.05/4.33 cnf(c_0_13349, 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_8290]), ['final']). 4.05/4.33 cnf(c_0_13350, 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_8291]), ['final']). 4.05/4.33 cnf(c_0_13351, 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)), inference(split_conjunct,[status(thm)],[c_0_8292]), ['final']). 4.05/4.33 cnf(c_0_13352, 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,esk481_3(X2,X1,X3)))),hAPP(X3,esk481_3(X2,X1,X3)))),X2))), inference(split_conjunct,[status(thm)],[c_0_7012]), ['final']). 4.05/4.33 cnf(c_0_13353, 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,esk387_3(X3,X2,X1)))),hAPP(X3,esk387_3(X3,X2,X1)))),X2))), inference(split_conjunct,[status(thm)],[c_0_8293]), ['final']). 4.05/4.33 cnf(c_0_13354, 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_8294]), ['final']). 4.05/4.33 cnf(c_0_13355, plain, (hBOOL(hAPP(X1,esk311_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_7554]), ['final']). 4.05/4.33 cnf(c_0_13356, 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_8295]), ['final']). 4.05/4.33 cnf(c_0_13357, 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_8296]), ['final']). 4.05/4.33 cnf(c_0_13358, plain, (hBOOL(hAPP(hAPP(X1,esk486_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_7856]), ['final']). 4.05/4.33 cnf(c_0_13359, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk20_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_7191]), ['final']). 4.05/4.33 cnf(c_0_13360, 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),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_8297]), ['final']). 4.05/4.33 cnf(c_0_13361, 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_8298]), ['final']). 4.05/4.33 cnf(c_0_13362, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5)|~class_Groups_Oordered__ab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8299]), ['final']). 4.05/4.33 cnf(c_0_13363, plain, (X3=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Lattices_Oboolean__algebra(X1)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)!=c_Orderings_Obot__class_Obot(X1)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)!=c_Orderings_Otop__class_Otop(X1)), inference(split_conjunct,[status(thm)],[c_0_8300]), ['final']). 4.05/4.33 cnf(c_0_13364, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk507_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_7807]), ['final']). 4.05/4.33 cnf(c_0_13365, plain, (c_List_Olist_ONil(X1)=X2|hAPP(X3,hAPP(c_List_Ohd(X1),X2))=hAPP(c_List_Ohd(X4),hAPP(hAPP(c_List_Omap(X1,X4),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8301]), ['final']). 4.05/4.33 cnf(c_0_13366, 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))), inference(split_conjunct,[status(thm)],[c_0_8302]), ['final']). 4.05/4.33 cnf(c_0_13367, 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_8303]), ['final']). 4.05/4.33 cnf(c_0_13368, plain, (hBOOL(hAPP(hAPP(c_member(X5),X3),c_SetInterval_Oord_OgreaterThanLessThan(X5,X1,X2,X4)))|~hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(X1,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8304]), ['final']). 4.05/4.33 cnf(c_0_13369, plain, (c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,hAPP(c_Nat_OSuc,X3),X4)=c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,X3,hAPP(X2,X4))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8305]), ['final']). 4.05/4.33 cnf(c_0_13370, 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_8306]), ['final']). 4.05/4.33 cnf(c_0_13371, plain, (c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk53_5(X3,X4,X5,X2,X1),X4,X3)|X5=X3|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X5,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_8307]), ['final']). 4.05/4.33 cnf(c_0_13372, 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_8308]), ['final']). 4.05/4.33 cnf(c_0_13373, 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_7660]), ['final']). 4.05/4.33 cnf(c_0_13374, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|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)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_8309]), ['final']). 4.05/4.33 cnf(c_0_13375, 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_8310]), ['final']). 4.05/4.33 cnf(c_0_13376, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk476_3(X2,X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7865]), ['final']). 4.05/4.33 cnf(c_0_13377, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk476_3(X2,X3,X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7865]), ['final']). 4.05/4.33 cnf(c_0_13378, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk455_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_7866]), ['final']). 4.05/4.33 cnf(c_0_13379, 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_8311]), ['final']). 4.05/4.33 cnf(c_0_13380, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk346_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex1(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_7386]), ['final']). 4.05/4.33 cnf(c_0_13381, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk218_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8312]), ['final']). 4.05/4.33 cnf(c_0_13382, 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_8313]), ['final']). 4.05/4.33 cnf(c_0_13383, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),esk455_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_7866]), ['final']). 4.05/4.33 cnf(c_0_13384, 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_8314]), ['final']). 4.05/4.33 cnf(c_0_13385, 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_8315]), ['final']). 4.05/4.33 cnf(c_0_13386, plain, (c_Complete__Lattice_OInf__class_OInf(X1,X2)=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),c_Orderings_Otop__class_Otop(X1)),X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8316]), ['final']). 4.05/4.33 cnf(c_0_13387, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4))), inference(split_conjunct,[status(thm)],[c_0_7517]), ['final']). 4.05/4.33 cnf(c_0_13388, 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_8317, c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_13389, plain, (hBOOL(hAPP(X1,esk277_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_7392]), ['final']). 4.05/4.33 cnf(c_0_13390, 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_8318]), ['final']). 4.05/4.33 cnf(c_0_13391, 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_8319]), ['final']). 4.05/4.33 cnf(c_0_13392, 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_8320]), ['final']). 4.05/4.33 cnf(c_0_13393, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(tc_sum(X3,X1)),c_Sum__Type_OPlus(X3,X1,X4,X2))), inference(split_conjunct,[status(thm)],[c_0_7517]), ['final']). 4.05/4.33 cnf(c_0_13394, 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_8321]), ['final']). 4.05/4.33 cnf(c_0_13395, 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_8322]), ['final']). 4.05/4.33 cnf(c_0_13396, plain, (hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),esk489_3(X1,X3,X2)),esk490_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_8242]), ['final']). 4.05/4.33 cnf(c_0_13397, 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_7649]), ['final']). 4.05/4.33 cnf(c_0_13398, plain, (hBOOL(hAPP(X1,X2))|hAPP(c_List_Ofilter(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))=hAPP(c_List_Ofilter(X3,X1),X4)), inference(split_conjunct,[status(thm)],[c_0_7541]), ['final']). 4.05/4.33 cnf(c_0_13399, 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_8323]), ['final']). 4.05/4.33 cnf(c_0_13400, 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_8324]), ['final']). 4.05/4.33 cnf(c_0_13401, 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_8325, c_0_5149]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_13402, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)),X5)!=c_Option_Ooption_ONone(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),X3)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)), inference(split_conjunct,[status(thm)],[c_0_7091]), ['final']). 4.05/4.33 cnf(c_0_13403, plain, (hBOOL(hAPP(hAPP(X1,X2),esk266_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_5611]), ['final']). 4.05/4.33 cnf(c_0_13404, plain, (c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk53_5(X3,X4,X5,X2,X1),X4,X3)|~hBOOL(hAPP(X1,X5))|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X5,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_8307]), ['final']). 4.05/4.33 cnf(c_0_13405, 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_8326]), ['final']). 4.05/4.33 cnf(c_0_13406, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Ois__nat(X1)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))), inference(rw,[status(thm)],[c_0_8327, c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_13407, 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_8328]), ['final']). 4.05/4.33 cnf(c_0_13408, 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),esk126_3(X2,X3,X1)),esk127_3(X2,X3,X1)))|~c_List_Olinorder__class_Osorted(X1,X3)|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7274]), ['final']). 4.05/4.33 cnf(c_0_13409, 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_8329]), ['final']). 4.05/4.33 cnf(c_0_13410, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8330]), ['final']). 4.05/4.33 cnf(c_0_13411, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8331]), ['final']). 4.05/4.33 cnf(c_0_13412, 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_8332]), ['final']). 4.05/4.33 cnf(c_0_13413, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X3,X1)),c_Sum__Type_OPlus(X3,X1,X4,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8333]), ['final']). 4.05/4.33 cnf(c_0_13414, 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_8334]), ['final']). 4.05/4.33 cnf(c_0_13415, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1)=c_List_Olist_ONil(X2)|esk117_2(X1,X2)!=c_List_Olist_ONil(X2)), inference(rw,[status(thm)],[c_0_8335, c_0_4767]), ['final']). 4.05/4.33 cnf(c_0_13416, 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)!=esk116_2(X2,X1)), inference(rw,[status(thm)],[c_0_8336, c_0_4767]), ['final']). 4.05/4.33 cnf(c_0_13417, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Oappend(X1),X3),c_List_Obutlast(X1,X2))=c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8337]), ['final']). 4.05/4.33 cnf(c_0_13418, plain, (X1=hAPP(hAPP(c_List_Olist_OCons(X2),esk402_2(X1,X2)),esk401_2(X1,X2))|c_List_Olist_ONil(X2)=X1|~c_List_Olinorder__class_Osorted(X2,X1)|~class_Orderings_Olinorder(X2)), inference(split_conjunct,[status(thm)],[c_0_5366]), ['final']). 4.05/4.33 cnf(c_0_13419, 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_8217]), ['final']). 4.05/4.33 cnf(c_0_13420, 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_7987]), ['final']). 4.05/4.33 cnf(c_0_13421, 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_8309]), ['final']). 4.05/4.33 cnf(c_0_13422, 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_5995]), ['final']). 4.05/4.33 cnf(c_0_13423, plain, (X2=X3|hAPP(hAPP(c_List_Onth(X1),X2),esk446_3(X1,X2,X3))!=hAPP(hAPP(c_List_Onth(X1),X3),esk446_3(X1,X2,X3))|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_7568]), ['final']). 4.05/4.33 cnf(c_0_13424, 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_8338]), ['final']). 4.05/4.33 cnf(c_0_13425, 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_8339]), ['final']). 4.05/4.33 cnf(c_0_13426, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X2)|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8340]), ['final']). 4.05/4.33 cnf(c_0_13427, 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_8341]), ['final']). 4.05/4.33 cnf(c_0_13428, 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_8342]), ['final']). 4.05/4.33 cnf(c_0_13429, 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_8343]), ['final']). 4.05/4.33 cnf(c_0_13430, plain, (hAPP(c_Fun_Ocomp(X2,X2,X2,hAPP(X3,X4)),hAPP(X3,X4))=hAPP(X3,X4)|~c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8344]), ['final']). 4.05/4.33 cnf(c_0_13431, plain, (hBOOL(hAPP(X1,esk57_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_7560]), ['final']). 4.05/4.33 cnf(c_0_13432, plain, (c_Option_Ooption_ONone(X4)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X4),X3,c_Option_Ooption_ONone(X4),X6),hAPP(X1,X2))|hAPP(X1,X2)!=c_Option_Ooption_ONone(X3)), inference(rw,[status(thm)],[c_0_8345, c_0_7211]), ['final']). 4.05/4.33 cnf(c_0_13433, 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_8346]), ['final']). 4.05/4.33 cnf(c_0_13434, 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_8347]), ['final']). 4.05/4.33 cnf(c_0_13435, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk278_2(X2,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5973]), ['final']). 4.05/4.33 cnf(c_0_13436, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X3,X4)),X1),X2))|hAPP(X1,esk380_4(X2,X1,X3,X4))!=hAPP(X2,esk380_4(X2,X1,X3,X4))|~class_Enum_Oenum(X3)|~class_HOL_Oequal(X4)), inference(split_conjunct,[status(thm)],[c_0_5415]), ['final']). 4.05/4.33 cnf(c_0_13437, plain, (X1=X2|hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X4),c_List_Olist_ONil(X3)))!=hAPP(hAPP(c_List_Oappend(X3),X1),hAPP(hAPP(c_List_Olist_OCons(X3),X5),c_List_Olist_ONil(X3)))), inference(split_conjunct,[status(thm)],[c_0_8348]), ['final']). 4.05/4.33 cnf(c_0_13438, plain, (X1=X2|hAPP(hAPP(c_List_Oappend(X3),X4),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3)))!=hAPP(hAPP(c_List_Oappend(X3),X5),hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_Olist_ONil(X3)))), inference(split_conjunct,[status(thm)],[c_0_8348]), ['final']). 4.05/4.33 cnf(c_0_13439, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)=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_5532]), ['final']). 4.05/4.33 cnf(c_0_13440, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),hAPP(c_COMBK(X1,X2),c_Groups_Oone__class_Oone(X1))),X3)=c_Groups_Oone__class_Oone(X1)|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_8349]), ['final']). 4.05/4.33 cnf(c_0_13441, 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_8350, c_0_5149]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_13442, 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_8351, c_0_5149]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_13443, 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_8352]), ['final']). 4.05/4.33 cnf(c_0_13444, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)=X3|~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_8353]), ['final']). 4.05/4.33 cnf(c_0_13445, 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_8354, c_0_4523]), ['final']). 4.05/4.33 cnf(c_0_13446, 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_8355, c_0_4523]), ['final']). 4.05/4.33 cnf(c_0_13447, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Nat_OSuc,X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8356]), ['final']). 4.05/4.33 cnf(c_0_13448, 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_8357]), ['final']). 4.05/4.33 cnf(c_0_13449, 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_8358]), ['final']). 4.05/4.33 cnf(c_0_13450, 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_8359]), ['final']). 4.05/4.33 cnf(c_0_13451, 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_8360]), ['final']). 4.05/4.33 cnf(c_0_13452, 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_8361]), ['final']). 4.05/4.33 cnf(c_0_13453, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk192_2(X1,X2)),esk193_2(X1,X2)))|c_List_Olinorder__class_Osorted(X2,X1)|~class_Orderings_Olinorder(X2)), inference(split_conjunct,[status(thm)],[c_0_8084]), ['final']). 4.05/4.33 cnf(c_0_13454, 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_8362]), ['final']). 4.05/4.33 cnf(c_0_13455, 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_8363]), ['final']). 4.05/4.33 cnf(c_0_13456, 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_8364]), ['final']). 4.05/4.33 cnf(c_0_13457, 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_8365]), ['final']). 4.05/4.33 cnf(c_0_13458, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk170_2(X1,X2)),esk169_2(X1,X2)))|c_List_Olinorder__class_Osorted(X2,X1)|~class_Orderings_Olinorder(X2)), inference(split_conjunct,[status(thm)],[c_0_7106]), ['final']). 4.05/4.33 cnf(c_0_13459, plain, (X3=X2|~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_8366]), ['final']). 4.05/4.33 cnf(c_0_13460, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X2)),X1))|~hBOOL(hAPP(X1,c_Option_Ooption_ONone(X2)))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X2),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_HOL_Obool,X2),X1),c_Option_Ooption_OSome(X2))))|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_7942]), ['final']). 4.05/4.33 cnf(c_0_13461, 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_8367]), ['final']). 4.05/4.33 cnf(c_0_13462, 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_8368]), ['final']). 4.05/4.33 cnf(c_0_13463, 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_8369, c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_13464, 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_5584]), ['final']). 4.05/4.33 cnf(c_0_13465, plain, (c_Option_Ooption_ONone(X1)=hAPP(X2,X3)|hAPP(X2,X3)=hAPP(c_Option_Ooption_OSome(X1),X4)|hAPP(c_Map_Omap__add(X5,X1,X6,X2),X3)!=hAPP(c_Option_Ooption_OSome(X1),X4)), inference(split_conjunct,[status(thm)],[c_0_8184]), ['final']). 4.05/4.33 cnf(c_0_13466, plain, (hAPP(c_List_Ofilter(X1,X2),esk423_5(X3,X2,X4,X5,X1))=X4|hAPP(c_List_Ofilter(X1,X2),X3)!=hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)), inference(split_conjunct,[status(thm)],[c_0_5138]), ['final']). 4.05/4.33 cnf(c_0_13467, 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_8370, c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_13468, 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_8371, c_0_5149]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_13469, plain, (X1=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)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(rw,[status(thm)],[c_0_8372, c_0_4519]), ['final']). 4.05/4.33 cnf(c_0_13470, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk246_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_8373]), ['final']). 4.05/4.33 cnf(c_0_13471, plain, (hAPP(c_List_Ofilter(X1,X2),esk164_5(X3,X4,X5,X2,X1))=X3|hAPP(c_List_Ofilter(X1,X2),X5)!=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_5107]), ['final']). 4.05/4.33 cnf(c_0_13472, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6))|X4=hAPP(hAPP(X5,X7),X6)|~c_Big__Operators_Ocomm__monoid__big(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_8374]), ['final']). 4.05/4.33 cnf(c_0_13473, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_8375, c_0_4977]), ['final']). 4.05/4.33 cnf(c_0_13474, 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_8376]), ['final']). 4.05/4.33 cnf(c_0_13475, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X1),esk191_2(X2,X1)),X2))), inference(csr,[status(thm)],[c_0_8377, c_0_8378]), ['final']). 4.05/4.33 cnf(c_0_13476, 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_8379]), ['final']). 4.05/4.33 cnf(c_0_13477, 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_8380]), ['final']). 4.05/4.33 cnf(c_0_13478, 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_8381]), ['final']). 4.05/4.33 cnf(c_0_13479, plain, (c_Divides_Odivmod__int(X2,X1)=c_Divides_OnegDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))), inference(split_conjunct,[status(thm)],[c_0_7294]), ['final']). 4.05/4.33 cnf(c_0_13480, 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_8382]), ['final']). 4.05/4.33 cnf(c_0_13481, 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_8383]), ['final']). 4.05/4.33 cnf(c_0_13482, 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_8384]), ['final']). 4.05/4.33 cnf(c_0_13483, plain, (X5=X6|~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X6),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|hAPP(X3,X5)!=hAPP(X3,X6)), inference(split_conjunct,[status(thm)],[c_0_8385]), ['final']). 4.05/4.33 cnf(c_0_13484, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))), inference(rw,[status(thm)],[c_0_8386, c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_13485, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))), inference(rw,[status(thm)],[c_0_8387, c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_13486, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8388, c_0_4427]), c_0_4795]), c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13487, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8389, c_0_4427]), c_0_4795]), c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13488, 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_8390]), ['final']). 4.05/4.33 cnf(c_0_13489, 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),esk420_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_6619]), ['final']). 4.05/4.33 cnf(c_0_13490, plain, (c_List_Olist__all2(X1,X2,X3,X5,X4)|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3),esk249_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_6618]), ['final']). 4.05/4.33 cnf(c_0_13491, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X2),X4)))|~hBOOL(hAPP(X1,esk439_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_7200]), ['final']). 4.05/4.33 cnf(c_0_13492, 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,esk363_3(X2,X3,X1)))|~hBOOL(hAPP(X1,esk361_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5093]), ['final']). 4.05/4.33 cnf(c_0_13493, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))), inference(rw,[status(thm)],[c_0_8391, c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_13494, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8392, c_0_4635]), c_0_4795]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_13495, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))), inference(rw,[status(thm)],[c_0_8393, c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_13496, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))), inference(rw,[status(thm)],[c_0_8394, c_0_4795]), ['final']). 4.05/4.33 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_8395, c_0_5905]), ['final']). 4.05/4.33 cnf(c_0_13498, 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_8126]), ['final']). 4.05/4.33 cnf(c_0_13499, 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_8396]), ['final']). 4.05/4.33 cnf(c_0_13500, 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)),c_List_Olist_ONil(X1)),X2)),c_List_Olistrel(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8397]), ['final']). 4.05/4.33 cnf(c_0_13501, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3)=X2|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Fields_Ofield__inverse__zero(X1)), inference(er,[status(thm)],[c_0_8398]), ['final']). 4.05/4.33 cnf(c_0_13502, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))), inference(rw,[status(thm)],[c_0_8399, c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_13503, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8400, c_0_4427]), c_0_4427]), c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_13504, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8401, c_0_4427]), c_0_4427]), c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_13505, 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_8402]), ['final']). 4.05/4.33 cnf(c_0_13506, plain, (X2=c_List_Olist_ONil(X1)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olistrel(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8403]), ['final']). 4.05/4.33 cnf(c_0_13507, plain, (c_List_Olinorder__class_Osort__key(X2,X1,X3,hAPP(c_List_Ofilter(X2,X4),X5))=hAPP(c_List_Ofilter(X2,X4),c_List_Olinorder__class_Osort__key(X2,X1,X3,X5))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8404]), ['final']). 4.05/4.33 cnf(c_0_13508, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(X2,esk467_4(X2,X3,X4,X1))|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X1),X2),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))|~class_Rings_Ono__zero__divisors(X1)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_8032]), ['final']). 4.05/4.33 cnf(c_0_13509, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),esk217_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_8085]), ['final']). 4.05/4.33 cnf(c_0_13510, 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_8405]), ['final']). 4.05/4.33 cnf(c_0_13511, 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_7519]), ['final']). 4.05/4.33 cnf(c_0_13512, 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_7516]), ['final']). 4.05/4.33 cnf(c_0_13513, 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_8406, c_0_4867]), c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_13514, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk280_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_8065]), ['final']). 4.05/4.33 cnf(c_0_13515, plain, (X3=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(split_conjunct,[status(thm)],[c_0_4605]), ['final']). 4.05/4.33 cnf(c_0_13516, plain, (hAPP(c_Option_Ooption_OSome(X3),esk220_3(X4,X3,X2))=hAPP(X4,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_8407]), ['final']). 4.05/4.33 cnf(c_0_13517, 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_8408, c_0_4867]), c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_13518, plain, (hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,esk436_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_7450]), ['final']). 4.05/4.33 cnf(c_0_13519, 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_8409]), ['final']). 4.05/4.33 cnf(c_0_13520, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),c_Big__Operators_Olattice__class_OSup__fin(X1,X2))=X3|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8410]), ['final']). 4.05/4.33 cnf(c_0_13521, plain, (X3=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(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_8411]), ['final']). 4.05/4.33 cnf(c_0_13522, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X4))), inference(split_conjunct,[status(thm)],[c_0_6800]), ['final']). 4.05/4.33 cnf(c_0_13523, 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_8412]), ['final']). 4.05/4.33 cnf(c_0_13524, 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_8413, c_0_4635]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_13525, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk118_1(X1)))|hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_8414]), ['final']). 4.05/4.33 cnf(c_0_13526, 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_6801]), ['final']). 4.05/4.33 cnf(c_0_13527, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk463_4(X2,X3,X4,X1)),X2))|c_Fun_Oinj__on(X1,X4,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8415]), ['final']). 4.05/4.33 cnf(c_0_13528, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk462_4(X2,X3,X4,X1)),X2))|c_Fun_Oinj__on(X1,X4,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8415]), ['final']). 4.05/4.33 cnf(c_0_13529, plain, (hAPP(X1,esk25_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_8416, c_0_4867]), c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_13530, 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_8417, c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_13531, 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_8418]), ['final']). 4.05/4.33 cnf(c_0_13532, 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_8419]), ['final']). 4.05/4.33 cnf(c_0_13533, plain, (hBOOL(hAPP(hAPP(c_member(X5),X4),c_Map_Odom(X5,X1,X3)))|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8420]), ['final']). 4.05/4.33 cnf(c_0_13534, plain, (hBOOL(hAPP(hAPP(c_member(X3),X4),c_Map_Oran(X5,X3,X1)))|hAPP(X1,X2)!=hAPP(c_Option_Ooption_OSome(X3),X4)), inference(split_conjunct,[status(thm)],[c_0_8421]), ['final']). 4.05/4.33 cnf(c_0_13535, 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_8422]), ['final']). 4.05/4.33 cnf(c_0_13536, 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_8423]), ['final']). 4.05/4.33 cnf(c_0_13537, 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_8424]), ['final']). 4.05/4.33 cnf(c_0_13538, 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_8425]), ['final']). 4.05/4.33 cnf(c_0_13539, 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_8426]), ['final']). 4.05/4.33 cnf(c_0_13540, 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_8427]), ['final']). 4.05/4.33 cnf(c_0_13541, 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_8428]), ['final']). 4.05/4.33 cnf(c_0_13542, plain, (hBOOL(hAPP(X1,esk167_3(X1,X2,X3)))|c_List_Olist__ex1(X2,X1,c_Enum_Oenum__class_Oenum(X2))|~hBOOL(hAPP(X1,X3))|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_8429]), ['final']). 4.05/4.33 cnf(c_0_13543, 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_8430]), ['final']). 4.05/4.33 cnf(c_0_13544, 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_7676]), ['final']). 4.05/4.33 cnf(c_0_13545, 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_8431]), ['final']). 4.05/4.33 cnf(c_0_13546, 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_8432]), ['final']). 4.05/4.33 cnf(c_0_13547, 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_8433]), ['final']). 4.05/4.33 cnf(c_0_13548, 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_8011]), ['final']). 4.05/4.33 cnf(c_0_13549, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X3,X4))))), inference(split_conjunct,[status(thm)],[c_0_8434]), ['final']). 4.05/4.33 cnf(c_0_13550, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_OtakeWhile(X1,X4,X3))))), inference(split_conjunct,[status(thm)],[c_0_8435]), ['final']). 4.05/4.33 cnf(c_0_13551, 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_Int_Onumber__ring(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8016]), ['final']). 4.05/4.33 cnf(c_0_13552, 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,esk513_5(X2,X1,X3,X4,X5)),X2))), inference(split_conjunct,[status(thm)],[c_0_7673]), ['final']). 4.05/4.33 cnf(c_0_13553, plain, (c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk84_4(X3,X4,X2,X1),X3,X4)|~hBOOL(hAPP(X1,X4))|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X4,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8436]), ['final']). 4.05/4.33 cnf(c_0_13554, 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_7886]), ['final']). 4.05/4.33 cnf(c_0_13555, plain, (c_List_Olist_ONil(X1)=X2|hAPP(X3,c_List_Olast(X1,X2))=c_List_Olast(X4,hAPP(hAPP(c_List_Omap(X1,X4),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8437]), ['final']). 4.05/4.33 cnf(c_0_13556, 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_8438]), ['final']). 4.05/4.33 cnf(c_0_13557, 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_8439, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13558, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|c_List_Oremove1(X1,X2,X3)=X3), inference(split_conjunct,[status(thm)],[c_0_8440]), ['final']). 4.05/4.33 cnf(c_0_13559, 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_7893]), ['final']). 4.05/4.33 cnf(c_0_13560, 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_7892]), ['final']). 4.05/4.33 cnf(c_0_13561, 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_7894]), ['final']). 4.05/4.33 cnf(c_0_13562, 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_7887]), ['final']). 4.05/4.33 cnf(c_0_13563, plain, (hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8441, c_0_7804]), c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13564, plain, (hBOOL(hAPP(X1,esk490_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_8242]), ['final']). 4.05/4.33 cnf(c_0_13565, 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_8442]), ['final']). 4.05/4.33 cnf(c_0_13566, plain, (c_List_Oremdups(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=c_List_Oremdups(X1,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7770]), ['final']). 4.05/4.33 cnf(c_0_13567, plain, (esk520_3(X1,X2,X3)=esk521_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_5513]), ['final']). 4.05/4.33 cnf(c_0_13568, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(hAPP(c_member(X2),hAPP(c_List_Ohd(X2),X1)),hAPP(c_List_Oset(X2),X1)))), inference(split_conjunct,[status(thm)],[c_0_8443]), ['final']). 4.05/4.33 cnf(c_0_13569, 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_4648]), ['final']). 4.05/4.33 cnf(c_0_13570, 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_8444]), ['final']). 4.05/4.33 cnf(c_0_13571, 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_8445]), ['final']). 4.05/4.33 cnf(c_0_13572, 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_8446]), ['final']). 4.05/4.33 cnf(c_0_13573, 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)))|hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_5372]), ['final']). 4.05/4.33 cnf(c_0_13574, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),X4)!=c_Option_Ooption_ONone(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))))), inference(rw,[status(thm)],[c_0_8447, c_0_5304]), ['final']). 4.05/4.33 cnf(c_0_13575, 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_8448]), ['final']). 4.05/4.33 cnf(c_0_13576, 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_8449]), ['final']). 4.05/4.33 cnf(c_0_13577, plain, (hAPP(X1,esk128_4(X2,X1,X3,X4))=X4|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Set_Oimage(X3,X5,X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_8015]), ['final']). 4.05/4.33 cnf(c_0_13578, 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_8450]), ['final']). 4.05/4.33 cnf(c_0_13579, plain, (hAPP(X4,X2)=hAPP(c_Map_Omap__add(X1,X3,X5,X4),X2)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_8451]), ['final']). 4.05/4.33 cnf(c_0_13580, 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_8452]), ['final']). 4.05/4.33 cnf(c_0_13581, 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_8453]), ['final']). 4.05/4.33 cnf(c_0_13582, 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_5492]), ['final']). 4.05/4.33 cnf(c_0_13583, 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_8106]), ['final']). 4.05/4.33 cnf(c_0_13584, 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_8107]), ['final']). 4.05/4.33 cnf(c_0_13585, 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_8108]), ['final']). 4.05/4.33 cnf(c_0_13586, plain, (hAPP(X4,X5)=hAPP(X3,X5)|~c_Map_Omap__le(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X5),c_Map_Odom(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_8053]), ['final']). 4.05/4.33 cnf(c_0_13587, 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_8454]), ['final']). 4.05/4.33 cnf(c_0_13588, 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_5968]), ['final']). 4.05/4.33 cnf(c_0_13589, 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_8455]), ['final']). 4.05/4.33 cnf(c_0_13590, 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_8456, c_0_5165]), ['final']). 4.05/4.33 cnf(c_0_13591, 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_8111]), ['final']). 4.05/4.33 cnf(c_0_13592, 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_8113]), ['final']). 4.05/4.33 cnf(c_0_13593, plain, (X2=esk346_3(X4,X1,X3)|~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_7386]), ['final']). 4.05/4.33 cnf(c_0_13594, 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_8457]), ['final']). 4.05/4.33 cnf(c_0_13595, 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_8458, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13596, 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_8459]), ['final']). 4.05/4.33 cnf(c_0_13597, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2))|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8460]), ['final']). 4.05/4.33 cnf(c_0_13598, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk335_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_8461]), ['final']). 4.05/4.33 cnf(c_0_13599, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8462]), ['final']). 4.05/4.33 cnf(c_0_13600, plain, (X2=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_8463]), ['final']). 4.05/4.33 cnf(c_0_13601, plain, (X2=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_8464]), ['final']). 4.05/4.33 cnf(c_0_13602, 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_8465]), ['final']). 4.05/4.33 cnf(c_0_13603, 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_8466]), ['final']). 4.05/4.33 cnf(c_0_13604, 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),esk192_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk193_2(X2,X1))))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8084]), ['final']). 4.05/4.33 cnf(c_0_13605, 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),esk170_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk169_2(X2,X1))))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7106]), ['final']). 4.05/4.33 cnf(c_0_13606, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8467, c_0_4439]), c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_13607, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8468]), ['final']). 4.05/4.33 cnf(c_0_13608, plain, (hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(hAPP(c_member(X1),esk489_3(X2,X3,X1)),esk490_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_8242]), ['final']). 4.05/4.33 cnf(c_0_13609, 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_8469]), ['final']). 4.05/4.33 cnf(c_0_13610, 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_8470]), ['final']). 4.05/4.33 cnf(c_0_13611, 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_8471]), ['final']). 4.05/4.33 cnf(c_0_13612, 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_8472])]), ['final']). 4.05/4.33 cnf(c_0_13613, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8473]), ['final']). 4.05/4.33 cnf(c_0_13614, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),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_8474]), ['final']). 4.05/4.33 cnf(c_0_13615, 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_8475]), ['final']). 4.05/4.33 cnf(c_0_13616, plain, (X1=hAPP(hAPP(c_List_Onth(X2),X3),esk338_3(X3,X1,X2))|~hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_List_Oset(X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_7926]), ['final']). 4.05/4.33 cnf(c_0_13617, 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_8476, c_0_8477]), ['final']). 4.05/4.33 cnf(c_0_13618, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8478]), ['final']). 4.05/4.33 cnf(c_0_13619, 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_8479]), ['final']). 4.05/4.33 cnf(c_0_13620, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),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_8201]), ['final']). 4.05/4.33 cnf(c_0_13621, 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_8480]), ['final']). 4.05/4.33 cnf(c_0_13622, plain, (c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X1,X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8481]), ['final']). 4.05/4.33 cnf(c_0_13623, 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),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8482]), ['final']). 4.05/4.33 cnf(c_0_13624, 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_8483, c_0_5905]), ['final']). 4.05/4.33 cnf(c_0_13625, 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_8484]), ['final']). 4.05/4.33 cnf(c_0_13626, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8485]), ['final']). 4.05/4.33 cnf(c_0_13627, plain, (hAPP(c_Option_Ooption_OSome(X1),esk5_5(X2,X3,X4,X5,X1))=X3|hAPP(c_Option_Ooption_OSome(X5),X2)!=hAPP(hAPP(c_Option_Omap(X1,X5),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_8486]), ['final']). 4.05/4.33 cnf(c_0_13628, 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_8487]), ['final']). 4.05/4.33 cnf(c_0_13629, plain, (hBOOL(hAPP(X1,esk503_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X4),X5),X2))|~hBOOL(hAPP(X1,X5))), inference(split_conjunct,[status(thm)],[c_0_6673]), ['final']). 4.05/4.33 cnf(c_0_13630, 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_8488]), ['final']). 4.05/4.33 cnf(c_0_13631, 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_8489]), ['final']). 4.05/4.33 cnf(c_0_13632, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk444_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_8490]), ['final']). 4.05/4.33 cnf(c_0_13633, plain, (hBOOL(hAPP(X1,esk280_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_8065]), ['final']). 4.05/4.33 cnf(c_0_13634, plain, (hBOOL(hAPP(X1,esk503_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X4),X5),X3))|~hBOOL(hAPP(X1,X5))), inference(split_conjunct,[status(thm)],[c_0_6673]), ['final']). 4.05/4.33 cnf(c_0_13635, 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_8031]), ['final']). 4.05/4.33 cnf(c_0_13636, plain, (hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,esk260_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_7460]), ['final']). 4.05/4.33 cnf(c_0_13637, 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_8491]), ['final']). 4.05/4.33 cnf(c_0_13638, 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_8492]), ['final']). 4.05/4.33 cnf(c_0_13639, 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_8493]), ['final']). 4.05/4.33 cnf(c_0_13640, plain, (X1=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk299_1(X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_8494]), ['final']). 4.05/4.33 cnf(c_0_13641, 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_8495, c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_13642, 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_8496, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13643, plain, (hAPP(X1,esk462_4(X2,X1,X3,X4))=hAPP(X1,esk463_4(X2,X1,X3,X4))|c_Fun_Oinj__on(X4,X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8415]), ['final']). 4.05/4.33 cnf(c_0_13644, plain, (c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X6)|~hBOOL(hAPP(X1,X2))|~c_Natural_Oevaln(X3,X2,X4,X5)|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X5,X4,X6)), inference(split_conjunct,[status(thm)],[c_0_8497]), ['final']). 4.05/4.33 cnf(c_0_13645, 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_8498]), ['final']). 4.05/4.33 cnf(c_0_13646, 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_8499]), ['final']). 4.05/4.33 cnf(c_0_13647, 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),esk103_3(X2,X3,X1)),X3)),X2))|~class_Fields_Olinordered__field__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_8131]), ['final']). 4.05/4.33 cnf(c_0_13648, 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_5253]), ['final']). 4.05/4.33 cnf(c_0_13649, 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_8500]), ['final']). 4.05/4.33 cnf(c_0_13650, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk195_3(X3,X1,X2))))|~c_List_Olist__ex(X2,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_8121]), ['final']). 4.05/4.33 cnf(c_0_13651, plain, (hAPP(hAPP(X3,X4),hAPP(hAPP(X3,X4),X5))=hAPP(hAPP(X3,X4),X5)|~c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8501]), ['final']). 4.05/4.33 cnf(c_0_13652, 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_8502]), ['final']). 4.05/4.33 cnf(c_0_13653, 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_8503]), ['final']). 4.05/4.33 cnf(c_0_13654, 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),esk475_3(X3,X2,X1))))|~class_Fields_Olinordered__field(X1)), inference(split_conjunct,[status(thm)],[c_0_8135]), ['final']). 4.05/4.33 cnf(c_0_13655, 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_8504]), ['final']). 4.05/4.33 cnf(c_0_13656, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2)=c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_List_Oset(X1),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8505]), ['final']). 4.05/4.33 cnf(c_0_13657, 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_8506]), ['final']). 4.05/4.33 cnf(c_0_13658, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))|~class_Groups_Ogroup__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8507]), ['final']). 4.05/4.33 cnf(c_0_13659, 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_8508]), ['final']). 4.05/4.33 cnf(c_0_13660, 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_8509]), ['final']). 4.05/4.33 cnf(c_0_13661, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk291_3(X2,X3,X1)),X2))|hBOOL(hAPP(c_Predicate_OPowp(X1,X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8510]), ['final']). 4.05/4.33 cnf(c_0_13662, 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_8511]), ['final']). 4.05/4.33 cnf(c_0_13663, 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,esk355_3(X2,X3,X1)))|~hBOOL(hAPP(X1,esk353_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_13664, plain, (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(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_8512]), ['final']). 4.05/4.33 cnf(c_0_13665, 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_8513]), ['final']). 4.05/4.33 cnf(c_0_13666, 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_8514]), ['final']). 4.05/4.33 cnf(c_0_13667, 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_8515]), ['final']). 4.05/4.33 cnf(c_0_13668, 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_8516]), ['final']). 4.05/4.33 cnf(c_0_13669, 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_8517]), ['final']). 4.05/4.33 cnf(c_0_13670, 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_8518]), ['final']). 4.05/4.33 cnf(c_0_13671, 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_7516]), ['final']). 4.05/4.33 cnf(c_0_13672, 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_7519]), ['final']). 4.05/4.33 cnf(c_0_13673, 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_8028]), ['final']). 4.05/4.33 cnf(c_0_13674, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))|~class_Groups_Ocomm__monoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8519]), ['final']). 4.05/4.33 cnf(c_0_13675, 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_8520]), ['final']). 4.05/4.33 cnf(c_0_13676, plain, (c_Orderings_Otop__class_Otop(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))))|hAPP(c_Finite__Set_Ocard(X1),X2)!=hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_8521]), ['final']). 4.05/4.33 cnf(c_0_13677, 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_8041]), ['final']). 4.05/4.33 cnf(c_0_13678, 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_8343]), ['final']). 4.05/4.33 cnf(c_0_13679, 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_8342]), ['final']). 4.05/4.33 cnf(c_0_13680, 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,esk171_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_7718]), ['final']). 4.05/4.33 cnf(c_0_13681, 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_8522]), ['final']). 4.05/4.33 cnf(c_0_13682, 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_8523, c_0_5716]), ['final']). 4.05/4.33 cnf(c_0_13683, 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_8524]), ['final']). 4.05/4.33 cnf(c_0_13684, 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,esk146_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_7720]), ['final']). 4.05/4.33 cnf(c_0_13685, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8525]), ['final']). 4.05/4.33 cnf(c_0_13686, 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))), inference(split_conjunct,[status(thm)],[c_0_8526]), ['final']). 4.05/4.33 cnf(c_0_13687, 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_8527]), ['final']). 4.05/4.33 cnf(c_0_13688, 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),esk417_3(X2,X3,X1)),esk416_3(X2,X3,X1))),X2))), inference(split_conjunct,[status(thm)],[c_0_6410]), ['final']). 4.05/4.33 cnf(c_0_13689, plain, (X1=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),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_8528]), ['final']). 4.05/4.33 cnf(c_0_13690, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8529]), ['final']). 4.05/4.33 cnf(c_0_13691, 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),esk416_3(X2,X3,X1)),esk417_3(X2,X3,X1))),X2))), inference(split_conjunct,[status(thm)],[c_0_6410]), ['final']). 4.05/4.33 cnf(c_0_13692, 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_8530, c_0_5716]), ['final']). 4.05/4.33 cnf(c_0_13693, 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_8531]), ['final']). 4.05/4.33 cnf(c_0_13694, 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_8532]), ['final']). 4.05/4.33 cnf(c_0_13695, 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_8050]), ['final']). 4.05/4.33 cnf(c_0_13696, 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_8051]), ['final']). 4.05/4.33 cnf(c_0_13697, 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_8533]), ['final']). 4.05/4.33 cnf(c_0_13698, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))), inference(rw,[status(thm)],[c_0_8534, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13699, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Ozero__class_Ozero(X2)))), inference(rw,[status(thm)],[c_0_8535, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13700, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))), inference(rw,[status(thm)],[c_0_8536, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13701, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)))), inference(rw,[status(thm)],[c_0_8537, c_0_4427]), ['final']). 4.05/4.33 cnf(c_0_13702, plain, (X2=c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8538]), ['final']). 4.05/4.33 cnf(c_0_13703, 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_8539]), ['final']). 4.05/4.33 cnf(c_0_13704, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X3,X2),X4),X5)))|~hBOOL(hAPP(X1,esk13_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_8540]), ['final']). 4.05/4.33 cnf(c_0_13705, 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_8064]), ['final']). 4.05/4.33 cnf(c_0_13706, plain, (X2=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))))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8541]), ['final']). 4.05/4.33 cnf(c_0_13707, plain, (X3=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))), inference(split_conjunct,[status(thm)],[c_0_8542]), ['final']). 4.05/4.33 cnf(c_0_13708, 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_5115]), ['final']). 4.05/4.33 cnf(c_0_13709, 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),esk530_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_7723]), ['final']). 4.05/4.33 cnf(c_0_13710, 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_8543]), ['final']). 4.05/4.33 cnf(c_0_13711, 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_8544]), ['final']). 4.05/4.33 cnf(c_0_13712, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|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_5968]), ['final']). 4.05/4.33 cnf(c_0_13713, 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_8545, c_0_4867]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_13714, 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_8546]), ['final']). 4.05/4.33 cnf(c_0_13715, plain, (X2=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))))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8547]), ['final']). 4.05/4.33 cnf(c_0_13716, plain, (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)=c_Random_Ominus__shift(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_8548]), ['final']). 4.05/4.33 cnf(c_0_13717, plain, (c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X1,X2),X3)=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))|~class_Lazy__Sequence_Osmall__lazy(X1)|~class_Lazy__Sequence_Osmall__lazy(X2)), inference(split_conjunct,[status(thm)],[c_0_8549]), ['final']). 4.05/4.33 cnf(c_0_13718, plain, (X3=X2|~class_Orderings_Olinorder(X1)|~c_List_Olinorder__class_Osorted(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))|~c_List_Olinorder__class_Osorted(X1,X3)|~hBOOL(hAPP(c_List_Odistinct(X1),X3))|hAPP(c_List_Oset(X1),X3)!=hAPP(c_List_Oset(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_8550]), ['final']). 4.05/4.33 cnf(c_0_13719, 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_8551, c_0_6641]), ['final']). 4.05/4.33 cnf(c_0_13720, 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_8552]), ['final']). 4.05/4.33 cnf(c_0_13721, 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_8553]), ['final']). 4.05/4.33 cnf(c_0_13722, 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_8324]), ['final']). 4.05/4.33 cnf(c_0_13723, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_Olinorder__class_Osort__key(X2,X1,X4,X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8554]), ['final']). 4.05/4.33 cnf(c_0_13724, 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_4652]), ['final']). 4.05/4.33 cnf(c_0_13725, 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_8555]), ['final']). 4.05/4.33 cnf(c_0_13726, 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_8555]), ['final']). 4.05/4.33 cnf(c_0_13727, 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_8556]), ['final']). 4.05/4.33 cnf(c_0_13728, plain, (c_Wellfounded_Owf(tc_prod(X3,X1),c_Recdef_Osame__fst(X3,X1,X4,X2))|~c_Wellfounded_Owf(X1,hAPP(X2,esk152_4(X3,X2,X1,X4)))), inference(split_conjunct,[status(thm)],[c_0_8120]), ['final']). 4.05/4.33 cnf(c_0_13729, plain, (c_Big__Operators_Olinorder__class_OMax(X1,X3)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk456_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_7871]), ['final']). 4.05/4.33 cnf(c_0_13730, 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_7433]), ['final']). 4.05/4.33 cnf(c_0_13731, 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_8557]), ['final']). 4.05/4.33 cnf(c_0_13732, 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_8557]), ['final']). 4.05/4.33 cnf(c_0_13733, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk151_2(X2,X1)))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_5991]), ['final']). 4.05/4.33 cnf(c_0_13734, 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_8558]), ['final']). 4.05/4.33 cnf(c_0_13735, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))|hAPP(X1,esk219_4(X1,X2,X3,X4))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_7815]), ['final']). 4.05/4.33 cnf(c_0_13736, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X2),X1)=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|hAPP(X1,esk491_4(X1,X2,X3,X4))!=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_7811]), ['final']). 4.05/4.33 cnf(c_0_13737, plain, (c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X2),X1)|hAPP(X1,esk282_4(X1,X2,X3,X4))!=c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_7818]), ['final']). 4.05/4.33 cnf(c_0_13738, 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,esk196_4(X2,X3,X4,X1))), inference(split_conjunct,[status(thm)],[c_0_7823]), ['final']). 4.05/4.33 cnf(c_0_13739, 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_8559]), ['final']). 4.05/4.33 cnf(c_0_13740, 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_8560]), ['final']). 4.05/4.33 cnf(c_0_13741, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(X1,esk494_3(X2,X3,X1)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))), inference(split_conjunct,[status(thm)],[c_0_5569]), ['final']). 4.05/4.33 cnf(c_0_13742, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),hAPP(c_List_Oset(X4),c_List_Oreplicate(X4,X5,X2))))), inference(split_conjunct,[status(thm)],[c_0_7429]), ['final']). 4.05/4.33 cnf(c_0_13743, 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_7396]), ['final']). 4.05/4.33 cnf(c_0_13744, 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_8181]), ['final']). 4.05/4.33 cnf(c_0_13745, 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_8182]), ['final']). 4.05/4.33 cnf(c_0_13746, 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_8561]), ['final']). 4.05/4.33 cnf(c_0_13747, plain, (X2=c_Big__Operators_Olinorder__class_OMin(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk524_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_7877]), ['final']). 4.05/4.33 cnf(c_0_13748, 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_8183]), ['final']). 4.05/4.33 cnf(c_0_13749, 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_8187]), ['final']). 4.05/4.33 cnf(c_0_13750, 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_8188]), ['final']). 4.05/4.33 cnf(c_0_13751, 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))), inference(split_conjunct,[status(thm)],[c_0_8562]), ['final']). 4.05/4.33 cnf(c_0_13752, 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_8563]), ['final']). 4.05/4.33 cnf(c_0_13753, 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_8564]), ['final']). 4.05/4.33 cnf(c_0_13754, 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),X2),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8565, c_0_4867]), c_0_4867]), c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_13755, 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_8566]), ['final']). 4.05/4.33 cnf(c_0_13756, 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_8567]), ['final']). 4.05/4.33 cnf(c_0_13757, 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_8568]), ['final']). 4.05/4.33 cnf(c_0_13758, 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_8569]), ['final']). 4.05/4.33 cnf(c_0_13759, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk18_2(X2,X1)),esk17_2(X2,X1)))|c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7191]), ['final']). 4.05/4.33 cnf(c_0_13760, 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_8570]), ['final']). 4.05/4.33 cnf(c_0_13761, 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_8571]), ['final']). 4.05/4.33 cnf(c_0_13762, plain, (X2=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))|c_Groups_Oone__class_Oone(X1)=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1)), inference(split_conjunct,[status(thm)],[c_0_5546]), ['final']). 4.05/4.33 cnf(c_0_13763, 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_8572]), ['final']). 4.05/4.33 cnf(c_0_13764, 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)), inference(split_conjunct,[status(thm)],[c_0_8573]), ['final']). 4.05/4.33 cnf(c_0_13765, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk422_5(X3,X4,X5,X6,X1))))|~hBOOL(hAPP(X4,X2))|hAPP(c_List_Ofilter(X1,X4),X3)!=hAPP(hAPP(c_List_Olist_OCons(X1),X6),X5)), inference(split_conjunct,[status(thm)],[c_0_5138]), ['final']). 4.05/4.33 cnf(c_0_13766, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk163_5(X3,X4,X5,X6,X1))))|~hBOOL(hAPP(X6,X2))|hAPP(c_List_Ofilter(X1,X6),X5)!=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_5107]), ['final']). 4.05/4.33 cnf(c_0_13767, plain, (hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk135_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_7422]), ['final']). 4.05/4.33 cnf(c_0_13768, plain, (X1=X2|c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X4),esk179_4(X2,X1,X4,X3),X2)|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X4),X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8574]), ['final']). 4.05/4.33 cnf(c_0_13769, plain, (X1=X2|hAPP(X3,X1)=hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X5),X3),X2),X6),X1)), inference(split_conjunct,[status(thm)],[c_0_8575]), ['final']). 4.05/4.33 cnf(c_0_13770, 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_8576, c_0_6133]), ['final']). 4.05/4.33 cnf(c_0_13771, 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))), inference(split_conjunct,[status(thm)],[c_0_8577]), ['final']). 4.05/4.33 cnf(c_0_13772, 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_8578]), ['final']). 4.05/4.33 cnf(c_0_13773, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=X4|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8579]), ['final']). 4.05/4.33 cnf(c_0_13774, 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),esk359_2(X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2))), inference(split_conjunct,[status(thm)],[c_0_7461]), ['final']). 4.05/4.33 cnf(c_0_13775, 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_Int_Onumber__ring(X1)|~class_Fields_Ofield__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_8580]), ['final']). 4.05/4.33 cnf(c_0_13776, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8581]), ['final']). 4.05/4.33 cnf(c_0_13777, 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_8582]), ['final']). 4.05/4.33 cnf(c_0_13778, plain, (esk396_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_8583]), c_0_8584])]), ['final']). 4.05/4.33 cnf(c_0_13779, 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_8585]), ['final']). 4.05/4.33 cnf(c_0_13780, plain, (c_Natural_Oevaln(X1,X2,X3,esk53_5(X4,X3,X2,X1,X5))|X2=X4|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X5,X1),X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8307]), ['final']). 4.05/4.33 cnf(c_0_13781, 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_8586]), ['final']). 4.05/4.33 cnf(c_0_13782, 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_8587]), ['final']). 4.05/4.33 cnf(c_0_13783, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,esk494_3(X1,X3,X2)))|~hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))), inference(split_conjunct,[status(thm)],[c_0_5569]), ['final']). 4.05/4.33 cnf(c_0_13784, 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_8588]), ['final']). 4.05/4.33 cnf(c_0_13785, plain, (c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3),esk179_4(X4,X2,X3,X1),X4)|~hBOOL(hAPP(X1,X2))|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3),X2,X4)), inference(split_conjunct,[status(thm)],[c_0_8574]), ['final']). 4.05/4.33 cnf(c_0_13786, 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_8589]), ['final']). 4.05/4.33 cnf(c_0_13787, 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_8318]), ['final']). 4.05/4.33 cnf(c_0_13788, 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_8319]), ['final']). 4.05/4.33 cnf(c_0_13789, 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_8590, c_0_5149]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_13790, 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_8591, c_0_5149]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_13791, 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_8320]), ['final']). 4.05/4.33 cnf(c_0_13792, 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_8323]), ['final']). 4.05/4.33 cnf(c_0_13793, 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_8592, c_0_4519]), ['final']). 4.05/4.33 cnf(c_0_13794, plain, (hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X1)=hAPP(c_Finite__Set_Ocard(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_8593]), ['final']). 4.05/4.33 cnf(c_0_13795, 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_8594]), ['final']). 4.05/4.33 cnf(c_0_13796, 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_8595]), ['final']). 4.05/4.33 cnf(c_0_13797, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|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)],[c_0_8596, c_0_4867]), c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_13798, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk50_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_5485]), ['final']). 4.05/4.33 cnf(c_0_13799, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|c_SMT_Oz3mod(X2,X1)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))), inference(split_conjunct,[status(thm)],[c_0_8597]), ['final']). 4.05/4.33 cnf(c_0_13800, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X1)),X2))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1))))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_7471]), ['final']). 4.05/4.33 cnf(c_0_13801, 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_8598]), ['final']). 4.05/4.33 cnf(c_0_13802, 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_8599, c_0_4519]), ['final']). 4.05/4.33 cnf(c_0_13803, plain, (c_Natural_Oevaln(X1,X2,X3,esk53_5(X4,X3,X2,X1,X5))|~hBOOL(hAPP(X5,X2))|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X5,X1),X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8307]), ['final']). 4.05/4.33 cnf(c_0_13804, 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_8289]), ['final']). 4.05/4.33 cnf(c_0_13805, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|~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)), inference(split_conjunct,[status(thm)],[c_0_8290]), ['final']). 4.05/4.33 cnf(c_0_13806, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))|~class_Groups_Ocomm__monoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_8600]), ['final']). 4.05/4.33 cnf(c_0_13807, 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_7725]), ['final']). 4.05/4.33 cnf(c_0_13808, 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_7725]), ['final']). 4.05/4.33 cnf(c_0_13809, 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_8601]), ['final']). 4.05/4.33 cnf(c_0_13810, 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_5346]), ['final']). 4.05/4.33 cnf(c_0_13811, 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_8602]), ['final']). 4.05/4.33 cnf(c_0_13812, 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_8291]), ['final']). 4.05/4.33 cnf(c_0_13813, 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_8294]), ['final']). 4.05/4.33 cnf(c_0_13814, 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_8603, c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_13815, 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_8604]), ['final']). 4.05/4.33 cnf(c_0_13816, 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)), inference(split_conjunct,[status(thm)],[c_0_8605]), ['final']). 4.05/4.33 cnf(c_0_13817, 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_5346]), ['final']). 4.05/4.33 cnf(c_0_13818, 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_8606]), ['final']). 4.05/4.33 cnf(c_0_13819, 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_8121]), ['final']). 4.05/4.33 cnf(c_0_13820, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8607, c_0_4427]), c_0_7916]), ['final']). 4.05/4.33 cnf(c_0_13821, plain, (hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(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_8608]), ['final']). 4.05/4.33 cnf(c_0_13822, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=X1|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_8609, c_0_4867]), c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_13823, 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_8610, c_0_4434]), ['final']). 4.05/4.33 cnf(c_0_13824, 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_8611]), ['final']). 4.05/4.33 cnf(c_0_13825, 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_8612]), ['final']). 4.05/4.33 cnf(c_0_13826, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8613, c_0_4427]), c_0_7918]), c_0_4865]), ['final']). 4.05/4.33 cnf(c_0_13827, 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)), inference(split_conjunct,[status(thm)],[c_0_8614]), ['final']). 4.05/4.33 cnf(c_0_13828, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3)=c_Divides_Odiv__class_Omod(X1,X2,X3)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8615]), ['final']). 4.05/4.33 cnf(c_0_13829, 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_8616]), ['final']). 4.05/4.33 cnf(c_0_13830, 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_8617]), ['final']). 4.05/4.33 cnf(c_0_13831, 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_8618]), ['final']). 4.05/4.33 cnf(c_0_13832, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8619]), ['final']). 4.05/4.33 cnf(c_0_13833, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),esk458_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7232]), ['final']). 4.05/4.33 cnf(c_0_13834, plain, (c_Option_Ooption_ONone(X1)=hAPP(X2,X3)|hBOOL(hAPP(hAPP(c_member(X4),X3),c_Map_Odom(X4,X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_8620]), ['final']). 4.05/4.33 cnf(c_0_13835, 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_8621]), ['final']). 4.05/4.33 cnf(c_0_13836, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),esk360_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7237]), ['final']). 4.05/4.33 cnf(c_0_13837, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),esk300_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7241]), ['final']). 4.05/4.33 cnf(c_0_13838, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(X1,esk267_3(X1,X2,X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7197]), ['final']). 4.05/4.33 cnf(c_0_13839, 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_8622]), ['final']). 4.05/4.33 cnf(c_0_13840, 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_8623]), ['final']). 4.05/4.33 cnf(c_0_13841, 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_8380]), ['final']). 4.05/4.33 cnf(c_0_13842, 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_8382]), ['final']). 4.05/4.33 cnf(c_0_13843, 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_8143]), ['final']). 4.05/4.33 cnf(c_0_13844, 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_8624]), ['final']). 4.05/4.33 cnf(c_0_13845, 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_8625]), ['final']). 4.05/4.33 cnf(c_0_13846, 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_8383]), ['final']). 4.05/4.33 cnf(c_0_13847, 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_8384]), ['final']). 4.05/4.33 cnf(c_0_13848, 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_8626]), ['final']). 4.05/4.33 cnf(c_0_13849, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk254_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_8627, c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_13850, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Oappend(X2),X1),X3))=hAPP(c_List_Ohd(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_8628]), ['final']). 4.05/4.33 cnf(c_0_13851, plain, (X2=X4|~class_Orderings_Olinorder(X1)|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)!=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_8629]), ['final']). 4.05/4.33 cnf(c_0_13852, plain, (X3=X5|~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_8630]), ['final']). 4.05/4.33 cnf(c_0_13853, plain, (~hBOOL(hAPP(hAPP(c_member(X1),esk501_5(X2,X3,X4,X5,X1)),esk502_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_6855]), ['final']). 4.05/4.33 cnf(c_0_13854, 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_8631]), ['final']). 4.05/4.33 cnf(c_0_13855, 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_8632]), ['final']). 4.05/4.33 cnf(c_0_13856, 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_8633]), ['final']). 4.05/4.33 cnf(c_0_13857, plain, (~hBOOL(hAPP(hAPP(c_member(X1),esk130_5(X2,X3,X4,X5,X1)),esk131_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_7240]), ['final']). 4.05/4.33 cnf(c_0_13858, 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_8634]), ['final']). 4.05/4.33 cnf(c_0_13859, 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_8635]), ['final']). 4.05/4.33 cnf(c_0_13860, plain, (X1=hAPP(X2,esk5_5(X1,X3,X2,X4,X5))|hAPP(c_Option_Ooption_OSome(X4),X1)!=hAPP(hAPP(c_Option_Omap(X5,X4),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_8486]), ['final']). 4.05/4.33 cnf(c_0_13861, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|c_Option_Ooption_ONone(X4)=hAPP(c_Map_Orestrict__map(X1,X4,X5,X3),X2)), inference(split_conjunct,[status(thm)],[c_0_8636]), ['final']). 4.05/4.33 cnf(c_0_13862, 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_8637]), ['final']). 4.05/4.33 cnf(c_0_13863, 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_8638]), ['final']). 4.05/4.33 cnf(c_0_13864, 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_8119]), ['final']). 4.05/4.33 cnf(c_0_13865, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk119_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_8414]), ['final']). 4.05/4.33 cnf(c_0_13866, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk417_3(X2,X3,X1)),X3))|c_Relation_Ototal__on(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_6410]), ['final']). 4.05/4.33 cnf(c_0_13867, 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_8639]), ['final']). 4.05/4.33 cnf(c_0_13868, 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_8640]), ['final']). 4.05/4.33 cnf(c_0_13869, plain, (X3=c_Enum_Oenum__the(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_8641, c_0_6300]), ['final']). 4.05/4.33 cnf(c_0_13870, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk416_3(X2,X3,X1)),X3))|c_Relation_Ototal__on(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_6410]), ['final']). 4.05/4.33 cnf(c_0_13871, 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_8642]), ['final']). 4.05/4.33 cnf(c_0_13872, 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))), inference(rw,[status(thm)],[c_0_8643, c_0_4519]), ['final']). 4.05/4.33 cnf(c_0_13873, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),esk194_3(X2,X3,X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_7765]), ['final']). 4.05/4.33 cnf(c_0_13874, 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),esk468_3(X3,X2,X1)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7506]), ['final']). 4.05/4.33 cnf(c_0_13875, 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),esk460_3(X3,X2,X1)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7507]), ['final']). 4.05/4.33 cnf(c_0_13876, 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),esk41_3(X2,X3,X1)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_7505]), ['final']). 4.05/4.33 cnf(c_0_13877, 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_8644]), ['final']). 4.05/4.33 cnf(c_0_13878, 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_8645]), ['final']). 4.05/4.33 cnf(c_0_13879, 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_8646, c_0_4519]), ['final']). 4.05/4.33 cnf(c_0_13880, 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_Olist_OCons(X3),X2),X5)|~hBOOL(hAPP(X1,X2))), inference(rw,[status(thm)],[c_0_8647, c_0_4950]), ['final']). 4.05/4.33 cnf(c_0_13881, 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_8648]), ['final']). 4.05/4.33 cnf(c_0_13882, 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_8649]), ['final']). 4.05/4.33 cnf(c_0_13883, 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_8650]), ['final']). 4.05/4.33 cnf(c_0_13884, 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_8651, c_0_5942]), ['final']). 4.05/4.33 cnf(c_0_13885, 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_8652]), ['final']). 4.05/4.33 cnf(c_0_13886, 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_8650]), ['final']). 4.05/4.33 cnf(c_0_13887, 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_8653]), ['final']). 4.05/4.33 cnf(c_0_13888, 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))), inference(split_conjunct,[status(thm)],[c_0_8654]), ['final']). 4.05/4.33 cnf(c_0_13889, plain, (c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(c_List_Oset(X1),X2))=c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),c_List_Oremdups(X1,X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8655]), ['final']). 4.05/4.33 cnf(c_0_13890, 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_8656]), ['final']). 4.05/4.33 cnf(c_0_13891, 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_8657]), ['final']). 4.05/4.33 cnf(c_0_13892, 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_8657]), ['final']). 4.05/4.33 cnf(c_0_13893, 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_8658]), ['final']). 4.05/4.33 cnf(c_0_13894, 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_8219]), ['final']). 4.05/4.33 cnf(c_0_13895, 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_8659, c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_13896, plain, (c_Groups_Oone__class_Oone(X1)=c_Groups_Osgn__class_Osgn(X1,X2)|c_Groups_Ozero__class_Ozero(X1)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Osgn__if(X1)), inference(split_conjunct,[status(thm)],[c_0_8280]), ['final']). 4.05/4.33 cnf(c_0_13897, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|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_8660]), ['final']). 4.05/4.33 cnf(c_0_13898, 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_8661]), ['final']). 4.05/4.33 cnf(c_0_13899, 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_8662]), ['final']). 4.05/4.33 cnf(c_0_13900, 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_8663]), ['final']). 4.05/4.33 cnf(c_0_13901, 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_8664]), ['final']). 4.05/4.33 cnf(c_0_13902, 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_8665]), ['final']). 4.05/4.33 cnf(c_0_13903, 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_8666]), ['final']). 4.05/4.33 cnf(c_0_13904, 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_8667]), ['final']). 4.05/4.33 cnf(c_0_13905, 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_8668]), ['final']). 4.05/4.33 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_8669]), ['final']). 4.05/4.33 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_8670]), ['final']). 4.05/4.33 cnf(c_0_13908, plain, (hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk14_3(X3,X2,X1)),esk15_3(X3,X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_8540]), ['final']). 4.05/4.33 cnf(c_0_13909, 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_8671]), ['final']). 4.05/4.33 cnf(c_0_13910, 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_7676]), ['final']). 4.05/4.33 cnf(c_0_13911, 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_8672]), ['final']). 4.05/4.33 cnf(c_0_13912, 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_7632]), ['final']). 4.05/4.33 cnf(c_0_13913, 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_8673]), ['final']). 4.05/4.33 cnf(c_0_13914, 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_8674]), ['final']). 4.05/4.33 cnf(c_0_13915, 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),esk320_3(X2,X3,X1)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8062]), ['final']). 4.05/4.33 cnf(c_0_13916, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))|~hBOOL(hAPP(X1,esk355_3(X2,X3,X1)))|~hBOOL(hAPP(X1,esk353_3(X2,X3,X1)))|~hBOOL(hAPP(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_5096]), ['final']). 4.05/4.33 cnf(c_0_13917, 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),esk229_3(X3,X2,X1)))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_8063]), ['final']). 4.05/4.33 cnf(c_0_13918, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,X2))=c_Groups_Ozero__class_Ozero(X1)|~class_Power_Opower(X1)|~class_Rings_Osemiring__0(X1)), inference(split_conjunct,[status(thm)],[c_0_8675]), ['final']). 4.05/4.33 cnf(c_0_13919, 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_8676]), ['final']). 4.05/4.33 cnf(c_0_13920, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8677, c_0_5379]), c_0_7655]), ['final']). 4.05/4.33 cnf(c_0_13921, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oabs__if(X1)), inference(split_conjunct,[status(thm)],[c_0_8517]), ['final']). 4.05/4.33 cnf(c_0_13922, 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_8678]), ['final']). 4.05/4.33 cnf(c_0_13923, 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_8679]), ['final']). 4.05/4.33 cnf(c_0_13924, plain, (hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))=X3|c_Map_Odom(X1,X2,X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5992]), ['final']). 4.05/4.33 cnf(c_0_13925, 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_8548]), ['final']). 4.05/4.33 cnf(c_0_13926, plain, (X2=X3|hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8680]), ['final']). 4.05/4.33 cnf(c_0_13927, 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_7933]), ['final']). 4.05/4.33 cnf(c_0_13928, 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_7933]), ['final']). 4.05/4.33 cnf(c_0_13929, 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_8681]), ['final']). 4.05/4.33 cnf(c_0_13930, 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_7624]), ['final']). 4.05/4.33 cnf(c_0_13931, plain, (hAPP(c_Finite__Set_Ofold1(X1,X2),X4)=hAPP(X3,X4)|~c_Finite__Set_Ofolding__one(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))), inference(split_conjunct,[status(thm)],[c_0_8682]), ['final']). 4.05/4.33 cnf(c_0_13932, 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_8683, c_0_4427]), ['final']). 4.05/4.33 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)),esk334_1(X1)))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_8461]), ['final']). 4.05/4.33 cnf(c_0_13934, 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_8502]), ['final']). 4.05/4.33 cnf(c_0_13935, 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_8503]), ['final']). 4.05/4.33 cnf(c_0_13936, 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_8508]), ['final']). 4.05/4.33 cnf(c_0_13937, 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_8684]), ['final']). 4.05/4.33 cnf(c_0_13938, 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_8685, c_0_4523]), ['final']). 4.05/4.33 cnf(c_0_13939, plain, (c_List_Olist__ex1(X3,X2,X1)|esk347_4(X1,X2,X3,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),X1)))|~hBOOL(hAPP(X2,X4))), inference(split_conjunct,[status(thm)],[c_0_7386]), ['final']). 4.05/4.33 cnf(c_0_13940, 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_8509]), ['final']). 4.05/4.33 cnf(c_0_13941, 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_8686]), ['final']). 4.05/4.33 cnf(c_0_13942, plain, (X2=hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))|hAPP(c_List_Orev(X1),X2)!=hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_5943]), ['final']). 4.05/4.33 cnf(c_0_13943, 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_8687]), ['final']). 4.05/4.33 cnf(c_0_13944, plain, (hBOOL(hAPP(hAPP(X1,esk447_3(X2,X1,X3)),X2))|hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8688]), ['final']). 4.05/4.33 cnf(c_0_13945, plain, (hBOOL(hAPP(hAPP(X1,esk381_3(X2,X1,X3)),X2))|hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8689]), ['final']). 4.05/4.33 cnf(c_0_13946, plain, (hAPP(c_Nat_OSuc,esk246_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_8373]), ['final']). 4.05/4.33 cnf(c_0_13947, 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))), inference(split_conjunct,[status(thm)],[c_0_8690]), ['final']). 4.05/4.33 cnf(c_0_13948, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),esk51_2(X1,X2)),X1))), inference(split_conjunct,[status(thm)],[c_0_8691]), ['final']). 4.05/4.33 cnf(c_0_13949, 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_8430]), ['final']). 4.05/4.33 cnf(c_0_13950, plain, (c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),X4,c_Map_Odom(X1,X2,X4))|~c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),c_Map_Omap__add(X1,X2,X3,X4),c_Map_Odom(X1,X2,X4))), inference(split_conjunct,[status(thm)],[c_0_8262]), ['final']). 4.05/4.33 cnf(c_0_13951, 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_8692]), ['final']). 4.05/4.33 cnf(c_0_13952, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk294_2(X2,X1)),X2))|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_8693]), ['final']). 4.05/4.33 cnf(c_0_13953, plain, (hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2)))|~c_List_Omember(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8694]), ['final']). 4.05/4.33 cnf(c_0_13954, 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_7545]), ['final']). 4.05/4.33 cnf(c_0_13955, plain, (c_Option_Ooption_ONone(X3)=hAPP(c_Map_Omap__add(X5,X3,X4,X1),X2)|hAPP(X1,X2)!=c_Option_Ooption_ONone(X3)|hAPP(X4,X2)!=c_Option_Ooption_ONone(X3)), inference(split_conjunct,[status(thm)],[c_0_8695]), ['final']). 4.05/4.33 cnf(c_0_13956, plain, (c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2),esk374_3(X3,X2,X1),X3)|~hBOOL(hAPP(X1,X3))|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2),X3,X3)), inference(split_conjunct,[status(thm)],[c_0_8696]), ['final']). 4.05/4.33 cnf(c_0_13957, 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)))), inference(split_conjunct,[status(thm)],[c_0_8697]), ['final']). 4.05/4.33 cnf(c_0_13958, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))|~hBOOL(hAPP(X2,esk180_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_5265]), ['final']). 4.05/4.33 cnf(c_0_13959, 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_8698]), ['final']). 4.05/4.33 cnf(c_0_13960, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)=X3|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)))), inference(split_conjunct,[status(thm)],[c_0_8699]), ['final']). 4.05/4.33 cnf(c_0_13961, 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_8700]), ['final']). 4.05/4.33 cnf(c_0_13962, plain, (c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3),X2,X5)|~hBOOL(hAPP(X1,X2))|~c_Natural_Oevalc(X3,X2,X4)|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3),X4,X5)), inference(split_conjunct,[status(thm)],[c_0_8701]), ['final']). 4.05/4.33 cnf(c_0_13963, 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_8179]), ['final']). 4.05/4.33 cnf(c_0_13964, plain, (c_Nitpick_Orefl_H(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk221_2(X2,X1)),esk221_2(X2,X1))),X2))), inference(split_conjunct,[status(thm)],[c_0_8056]), ['final']). 4.05/4.33 cnf(c_0_13965, plain, (c_Natural_Oevaln(X1,X2,X3,esk84_4(X3,X2,X1,X4))|~hBOOL(hAPP(X4,X2))|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X1),X2,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8436]), ['final']). 4.05/4.33 cnf(c_0_13966, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))), inference(split_conjunct,[status(thm)],[c_0_8700]), ['final']). 4.05/4.33 cnf(c_0_13967, plain, (hBOOL(hAPP(X1,esk59_4(X1,X2,X3,X4)))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X3|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_7429]), ['final']). 4.05/4.33 cnf(c_0_13968, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))), inference(split_conjunct,[status(thm)],[c_0_8702]), ['final']). 4.05/4.33 cnf(c_0_13969, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X3|~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_8703]), ['final']). 4.05/4.33 cnf(c_0_13970, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|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_8704]), ['final']). 4.05/4.33 cnf(c_0_13971, 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_Ono__zero__divisors(X1)|~class_Rings_Omult__zero(X1)|~class_Rings_Ozero__neq__one(X1)|~class_Power_Opower(X1)), inference(er,[status(thm)],[c_0_8705]), ['final']). 4.05/4.33 cnf(c_0_13972, 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_8361]), ['final']). 4.05/4.33 cnf(c_0_13973, 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_8425]), ['final']). 4.05/4.33 cnf(c_0_13974, 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_8426]), ['final']). 4.05/4.33 cnf(c_0_13975, 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_8706]), ['final']). 4.05/4.33 cnf(c_0_13976, 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_8707]), ['final']). 4.05/4.33 cnf(c_0_13977, 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_8708]), ['final']). 4.05/4.33 cnf(c_0_13978, 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)), inference(split_conjunct,[status(thm)],[c_0_8709]), ['final']). 4.05/4.33 cnf(c_0_13979, 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_8710]), ['final']). 4.05/4.33 cnf(c_0_13980, 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_8711]), ['final']). 4.05/4.33 cnf(c_0_13981, 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,esk441_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_7965]), ['final']). 4.05/4.33 cnf(c_0_13982, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=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,esk285_3(X1,X2,X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7966]), ['final']). 4.05/4.33 cnf(c_0_13983, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)|~class_Groups_Oab__group__add(X1)), inference(split_conjunct,[status(thm)],[c_0_8712]), ['final']). 4.05/4.33 cnf(c_0_13984, plain, (X2=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8713]), ['final']). 4.05/4.33 cnf(c_0_13985, 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_8714]), ['final']). 4.05/4.33 cnf(c_0_13986, 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_8715]), ['final']). 4.05/4.33 cnf(c_0_13987, 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_8716]), ['final']). 4.05/4.33 cnf(c_0_13988, 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_8717]), ['final']). 4.05/4.33 cnf(c_0_13989, plain, (hBOOL(hAPP(X4,X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(X4,esk405_4(X4,X3,X5,X1)))), inference(split_conjunct,[status(thm)],[c_0_6568]), ['final']). 4.05/4.33 cnf(c_0_13990, plain, (hBOOL(hAPP(X4,X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(X4,esk405_4(X4,X5,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_6568]), ['final']). 4.05/4.33 cnf(c_0_13991, plain, (X5=X4|hAPP(c_Set_Oimage(X1,X2,X3),X4)!=hAPP(c_Set_Oimage(X1,X2,X3),X5)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_8718]), ['final']). 4.05/4.33 cnf(c_0_13992, 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_8719]), ['final']). 4.05/4.33 cnf(c_0_13993, plain, (X1=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Int_OMin=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_8720, c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_13994, 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_8721]), ['final']). 4.05/4.33 cnf(c_0_13995, 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_8722]), ['final']). 4.05/4.33 cnf(c_0_13996, 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_8723]), ['final']). 4.05/4.33 cnf(c_0_13997, 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_8724]), ['final']). 4.05/4.33 cnf(c_0_13998, plain, (c_Orderings_Obot__class_Obot(X1)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_8725]), ['final']). 4.05/4.33 cnf(c_0_13999, 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_8726]), ['final']). 4.05/4.33 cnf(c_0_14000, 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_7795]), ['final']). 4.05/4.33 cnf(c_0_14001, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X3)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8727]), ['final']). 4.05/4.33 cnf(c_0_14002, plain, (hBOOL(hAPP(X1,X2))|hAPP(c_List_Ofilter(X3,X1),c_List_Oreplicate(X3,X4,X2))=c_List_Olist_ONil(X3)), inference(split_conjunct,[status(thm)],[c_0_8728]), ['final']). 4.05/4.33 cnf(c_0_14003, plain, (X1=c_Groups_Oone__class_Oone(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(rw,[status(thm)],[c_0_8729, c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_14004, 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_8730]), ['final']). 4.05/4.33 cnf(c_0_14005, 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_8731]), ['final']). 4.05/4.33 cnf(c_0_14006, plain, (hBOOL(hAPP(hAPP(X3,esk478_2(X4,X3)),X4))|~hBOOL(hAPP(c_Predicate_ORangeP(X1,X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8732]), ['final']). 4.05/4.33 cnf(c_0_14007, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8733]), ['final']). 4.05/4.33 cnf(c_0_14008, 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_8734]), ['final']). 4.05/4.33 cnf(c_0_14009, plain, (X5=X4|hAPP(c_Set_Oimage(X1,X2,X3),X4)!=hAPP(c_Set_Oimage(X1,X2,X3),X5)|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_8735]), ['final']). 4.05/4.33 cnf(c_0_14010, 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_8736]), ['final']). 4.05/4.33 cnf(c_0_14011, 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),esk400_4(hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),X1,X3,X2)))), inference(er,[status(thm)],[c_0_8737]), ['final']). 4.05/4.33 cnf(c_0_14012, plain, (hBOOL(hAPP(hAPP(X3,X4),esk393_2(X4,X3)))|~hBOOL(hAPP(c_Predicate_ODomainP(X1,X2,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8738]), ['final']). 4.05/4.33 cnf(c_0_14013, 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_8083]), ['final']). 4.05/4.33 cnf(c_0_14014, 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_8083]), ['final']). 4.05/4.33 cnf(c_0_14015, 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_8739, c_0_4867]), c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_14016, plain, (X2=X3|~hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_fequal),esk206_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_5447]), ['final']). 4.05/4.33 cnf(c_0_14017, plain, (X1=c_Groups_Oone__class_Oone(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(rw,[status(thm)],[c_0_8740, c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_14018, 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_8088]), ['final']). 4.05/4.33 cnf(c_0_14019, 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_8088]), ['final']). 4.05/4.33 cnf(c_0_14020, 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_8089]), ['final']). 4.05/4.33 cnf(c_0_14021, plain, (hBOOL(hAPP(X5,X2))|c_Natural_Oevaln(c_Com_Ocom_OCond(X5,X6,X1),X2,X3,X4)|~c_Natural_Oevaln(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8741]), ['final']). 4.05/4.33 cnf(c_0_14022, 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_8742]), ['final']). 4.05/4.33 cnf(c_0_14023, 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_8743]), ['final']). 4.05/4.33 cnf(c_0_14024, plain, (X1=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Int_OMin=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)!=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_8744, c_0_4635]), ['final']). 4.05/4.33 cnf(c_0_14025, 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_8089]), ['final']). 4.05/4.33 cnf(c_0_14026, 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_8745]), ['final']). 4.05/4.33 cnf(c_0_14027, 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_8746]), ['final']). 4.05/4.33 cnf(c_0_14028, 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_8728]), ['final']). 4.05/4.33 cnf(c_0_14029, plain, (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),X1),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_8747]), ['final']). 4.05/4.33 cnf(c_0_14030, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1)), inference(er,[status(thm)],[c_0_8748]), ['final']). 4.05/4.33 cnf(c_0_14031, 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_8745]), ['final']). 4.05/4.33 cnf(c_0_14032, 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_8749]), ['final']). 4.05/4.33 cnf(c_0_14033, 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_8750]), ['final']). 4.05/4.33 cnf(c_0_14034, 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_8751]), ['final']). 4.05/4.33 cnf(c_0_14035, plain, (X1=c_List_Olist_ONil(X2)|c_List_Olast(X2,X1)=c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1))), inference(split_conjunct,[status(thm)],[c_0_8752]), ['final']). 4.05/4.33 cnf(c_0_14036, 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_7625]), ['final']). 4.05/4.33 cnf(c_0_14037, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk22_2(X2,X1))=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_6004]), ['final']). 4.05/4.33 cnf(c_0_14038, plain, (X1=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk186_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_6005]), ['final']). 4.05/4.33 cnf(c_0_14039, 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_8753]), ['final']). 4.05/4.33 cnf(c_0_14040, 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_8754]), ['final']). 4.05/4.33 cnf(c_0_14041, plain, (c_List_Olist_ONil(X1)=hAPP(hAPP(c_List_Odrop(X1),X3),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_8755]), ['final']). 4.05/4.33 cnf(c_0_14042, 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_8756, c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_14043, 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_8757, c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_14044, 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_7632]), ['final']). 4.05/4.33 cnf(c_0_14045, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|c_Groups_Osgn__class_Osgn(X1,X2)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8758]), ['final']). 4.05/4.33 cnf(c_0_14046, 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_8759]), ['final']). 4.05/4.33 cnf(c_0_14047, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|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_8490]), ['final']). 4.05/4.33 cnf(c_0_14048, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|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_5986]), ['final']). 4.05/4.33 cnf(c_0_14049, 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_8760]), ['final']). 4.05/4.33 cnf(c_0_14050, 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_8761]), ['final']). 4.05/4.33 cnf(c_0_14051, 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_8762]), ['final']). 4.05/4.33 cnf(c_0_14052, 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_8763]), ['final']). 4.05/4.33 cnf(c_0_14053, plain, (X1=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oone__class_Oone(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)|~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_8763]), ['final']). 4.05/4.33 cnf(c_0_14054, plain, (X2=hAPP(hAPP(c_List_Onth(X1),X5),X4)|hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=hAPP(hAPP(c_List_Odrop(X1),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_8764]), ['final']). 4.05/4.33 cnf(c_0_14055, 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_8765]), ['final']). 4.05/4.33 cnf(c_0_14056, 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_8766]), ['final']). 4.05/4.33 cnf(c_0_14057, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk47_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_8767]), ['final']). 4.05/4.33 cnf(c_0_14058, 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_8768, c_0_5149]), c_0_5149]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_14059, 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_8769]), ['final']). 4.05/4.33 cnf(c_0_14060, plain, (hBOOL(hAPP(X1,esk488_3(X2,X1,X3)))|c_List_OtakeWhile(X3,X1,X2)=hAPP(c_List_Ofilter(X3,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_5184]), ['final']). 4.05/4.33 cnf(c_0_14061, 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_8770]), ['final']). 4.05/4.33 cnf(c_0_14062, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk529_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_8771]), ['final']). 4.05/4.33 cnf(c_0_14063, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),esk133_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_8772]), ['final']). 4.05/4.33 cnf(c_0_14064, 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_8036]), ['final']). 4.05/4.33 cnf(c_0_14065, plain, (c_Map_Omap__le(X1,X2,X3,c_Map_Omap__add(X1,X2,X3,X4))|c_Map_Omap__add(X1,X2,X3,X4)!=c_Map_Omap__add(X1,X2,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_8773]), ['final']). 4.05/4.33 cnf(c_0_14066, 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,esk435_2(X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_8774]), ['final']). 4.05/4.33 cnf(c_0_14067, plain, (c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3,X4)|~c_Natural_Oevaln(c_Com_Ocom_OBODY(X1),X2,hAPP(c_Nat_OSuc,X3),X4)), inference(split_conjunct,[status(thm)],[c_0_8775]), ['final']). 4.05/4.33 cnf(c_0_14068, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk42_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_8776]), ['final']). 4.05/4.33 cnf(c_0_14069, 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_8777]), ['final']). 4.05/4.33 cnf(c_0_14070, 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_8778]), ['final']). 4.05/4.33 cnf(c_0_14071, 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_8581]), ['final']). 4.05/4.33 cnf(c_0_14072, plain, (c_List_Olist_ONil(X1)=X2|hBOOL(hAPP(c_List_Odistinct(X1),c_List_Obutlast(X1,X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8779]), ['final']). 4.05/4.33 cnf(c_0_14073, 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_8780]), ['final']). 4.05/4.33 cnf(c_0_14074, 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_8781]), ['final']). 4.05/4.33 cnf(c_0_14075, 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_8782, c_0_5149]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_14076, 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_8783]), ['final']). 4.05/4.33 cnf(c_0_14077, plain, (hBOOL(hAPP(X1,esk310_2(X1,X2)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7554]), ['final']). 4.05/4.33 cnf(c_0_14078, plain, (hBOOL(hAPP(X1,esk56_2(X1,X2)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7560]), ['final']). 4.05/4.33 cnf(c_0_14079, plain, (c_Natural_Oevaln(c_Com_Ocom_OWhile(X5,X1),X2,X3,X2)|~c_Natural_Oevaln(X1,X2,X3,X4)|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X5,X1),X4,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8436]), ['final']). 4.05/4.33 cnf(c_0_14080, plain, (X3=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_8784]), ['final']). 4.05/4.33 cnf(c_0_14081, 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_4556]), ['final']). 4.05/4.33 cnf(c_0_14082, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|c_Complete__Lattice_OInf__class_OInf(X1,X2)=c_Big__Operators_Olattice__class_OInf__fin(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8785]), ['final']). 4.05/4.33 cnf(c_0_14083, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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_8786]), ['final']). 4.05/4.33 cnf(c_0_14084, 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_8787]), ['final']). 4.05/4.33 cnf(c_0_14085, 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,esk254_2(X1,X2)))), inference(rw,[status(thm)],[c_0_8788, c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_14086, 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_8192]), ['final']). 4.05/4.33 cnf(c_0_14087, 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_8789]), ['final']). 4.05/4.33 cnf(c_0_14088, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk157_1(X1)))|hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5572]), ['final']). 4.05/4.33 cnf(c_0_14089, 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_8444]), ['final']). 4.05/4.33 cnf(c_0_14090, 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_8445]), ['final']). 4.05/4.33 cnf(c_0_14091, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(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_8790]), ['final']). 4.05/4.33 cnf(c_0_14092, plain, (c_Nitpick_Ounknown(tc_HOL_Obool)|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))|~c_Nitpick_Owf_H(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8791]), ['final']). 4.05/4.33 cnf(c_0_14093, 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_8792, c_0_4867]), ['final']). 4.05/4.33 cnf(c_0_14094, 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_8793]), ['final']). 4.05/4.33 cnf(c_0_14095, plain, (c_Natural_Oevaln(X1,esk46_5(X2,X3,X4,X1,X5),X3,X2)|~c_Natural_Oevaln(c_Com_Ocom_OSemi(X5,X1),X4,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8794]), ['final']). 4.05/4.33 cnf(c_0_14096, plain, (c_Natural_Oevaln(X1,X2,X3,esk46_5(X4,X3,X2,X5,X1))|~c_Natural_Oevaln(c_Com_Ocom_OSemi(X1,X5),X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8794]), ['final']). 4.05/4.33 cnf(c_0_14097, plain, (c_Divides_Odivmod__int(X2,X1)=c_Divides_OposDivAlg(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_7294]), ['final']). 4.05/4.33 cnf(c_0_14098, 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_8449]), ['final']). 4.05/4.33 cnf(c_0_14099, 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_8453]), ['final']). 4.05/4.33 cnf(c_0_14100, 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_8795]), ['final']). 4.05/4.33 cnf(c_0_14101, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)!=c_Groups_Ozero__class_Ozero(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))|~class_Int_Oring__char__0(X1)), inference(split_conjunct,[status(thm)],[c_0_5520]), ['final']). 4.05/4.33 cnf(c_0_14102, 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_8796]), ['final']). 4.05/4.33 cnf(c_0_14103, plain, (hAPP(c_List_Oset(X2),X3)=hAPP(c_List_Oset(X2),c_List_Olinorder__class_Osort__key(X2,X1,X4,X3))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8797]), ['final']). 4.05/4.33 cnf(c_0_14104, 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_8454]), ['final']). 4.05/4.33 cnf(c_0_14105, 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_8798, c_0_5165]), ['final']). 4.05/4.33 cnf(c_0_14106, 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_8455]), ['final']). 4.05/4.33 cnf(c_0_14107, 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_8799, c_0_4867]), c_0_5149]), ['final']). 4.05/4.33 cnf(c_0_14108, plain, (c_Natural_Oevaln(c_Com_Ocom_OSemi(X1,X5),X2,X3,X6)|~c_Natural_Oevaln(X1,X2,X3,X4)|~c_Natural_Oevaln(X5,X4,X3,X6)), inference(split_conjunct,[status(thm)],[c_0_8794]), ['final']). 4.05/4.33 cnf(c_0_14109, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Groups_Ozero__class_Ozero(X2)=hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Ozero__class_Ozero(X2)),X1)|~class_Rings_Osemiring__0(X2)|~class_Power_Opower(X2)), inference(split_conjunct,[status(thm)],[c_0_8800]), ['final']). 4.05/4.33 cnf(c_0_14110, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|X1=hAPP(c_Nat_OSuc,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))), inference(split_conjunct,[status(thm)],[c_0_8801]), ['final']). 4.05/4.33 cnf(c_0_14111, 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,esk171_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_7718]), ['final']). 4.05/4.33 cnf(c_0_14112, 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,esk146_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_7720]), ['final']). 4.05/4.33 cnf(c_0_14113, plain, (hAPP(c_Map_Orestrict__map(X1,X4,X5,X3),X2)=hAPP(X5,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8802]), ['final']). 4.05/4.33 cnf(c_0_14114, plain, (c_List_Olist__ex(X1,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X4,X2))), inference(split_conjunct,[status(thm)],[c_0_8312]), ['final']). 4.05/4.33 cnf(c_0_14115, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)=hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8803]), ['final']). 4.05/4.33 cnf(c_0_14116, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,esk180_3(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_5265]), ['final']). 4.05/4.33 cnf(c_0_14117, 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_8050]), ['final']). 4.05/4.33 cnf(c_0_14118, 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_8051]), ['final']). 4.05/4.33 cnf(c_0_14119, 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_8804]), ['final']). 4.05/4.33 cnf(c_0_14120, plain, (~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[c_0_8805, c_0_4795]), ['final']). 4.05/4.33 cnf(c_0_14121, 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_8563]), ['final']). 4.05/4.33 cnf(c_0_14122, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1)))|~hBOOL(hAPP(X2,esk174_3(X1,X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_5288]), ['final']). 4.05/4.33 cnf(c_0_14123, plain, (c_Enum_Oenum__class_Oenum(tc_prod(X1,X2))=c_Enum_Oproduct(X1,X2,c_Enum_Oenum__class_Oenum(X1),c_Enum_Oenum__class_Oenum(X2))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_8806]), ['final']). 4.05/4.33 cnf(c_0_14124, plain, (c_List_Oremdups(X1,c_List_Oremove1(X1,X3,X2))=c_List_Oremove1(X1,X3,c_List_Oremdups(X1,X2))|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8807]), ['final']). 4.05/4.33 cnf(c_0_14125, 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)|esk60_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(er,[status(thm)],[c_0_8808]), ['final']). 4.05/4.33 cnf(c_0_14126, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X1=X3|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_8809]), ['final']). 4.05/4.34 cnf(c_0_14127, 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_8810]), ['final']). 4.05/4.34 cnf(c_0_14128, 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_8811, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_14129, plain, (c_List_Oremdups(X1,X2)=X2|hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)), inference(rw,[status(thm)],[c_0_8812, c_0_8813]), ['final']). 4.05/4.34 cnf(c_0_14130, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk528_2(X1,X2)),X1))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))), inference(split_conjunct,[status(thm)],[c_0_8771]), ['final']). 4.05/4.34 cnf(c_0_14131, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk132_2(X1,X2)),X1))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))), inference(split_conjunct,[status(thm)],[c_0_8772]), ['final']). 4.05/4.34 cnf(c_0_14132, 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_8814, c_0_5379]), c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_14133, 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_8815]), ['final']). 4.05/4.34 cnf(c_0_14134, 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_8816]), ['final']). 4.05/4.34 cnf(c_0_14135, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)|hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))!=X2), inference(split_conjunct,[status(thm)],[c_0_8390]), ['final']). 4.05/4.34 cnf(c_0_14136, 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_8817]), ['final']). 4.05/4.34 cnf(c_0_14137, 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_8818]), ['final']). 4.05/4.34 cnf(c_0_14138, 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_8819, c_0_5379]), c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_14139, 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_8820]), ['final']). 4.05/4.34 cnf(c_0_14140, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(X1,esk292_1(X1)))), inference(rw,[status(thm)],[c_0_8821, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_14141, 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_8822]), ['final']). 4.05/4.34 cnf(c_0_14142, 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_8823]), ['final']). 4.05/4.34 cnf(c_0_14143, 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_5534]), ['final']). 4.05/4.34 cnf(c_0_14144, 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_8824]), ['final']). 4.05/4.34 cnf(c_0_14145, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(X1,esk58_1(X1)))), inference(rw,[status(thm)],[c_0_8825, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_14146, 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_8826, c_0_6133]), ['final']). 4.05/4.34 cnf(c_0_14147, plain, (c_Natural_Oevaln(c_Com_Ocom_OBODY(X1),X2,hAPP(c_Nat_OSuc,X3),X4)|~c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8775]), ['final']). 4.05/4.34 cnf(c_0_14148, plain, (X1=X2|c_Natural_Oevalc(X3,X1,esk179_4(X2,X1,X3,X4))|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X4,X3),X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8574]), ['final']). 4.05/4.34 cnf(c_0_14149, 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_8827]), ['final']). 4.05/4.34 cnf(c_0_14150, 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_4556]), ['final']). 4.05/4.34 cnf(c_0_14151, plain, (~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Int_Onumber__ring(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8828, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), ['final']). 4.05/4.34 cnf(c_0_14152, 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_8829]), ['final']). 4.05/4.34 cnf(c_0_14153, 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_8830]), ['final']). 4.05/4.34 cnf(c_0_14154, plain, (c_Natural_Oevaln(X1,X2,X5,X4)|~c_Natural_Oevaln(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_8831]), ['final']). 4.05/4.34 cnf(c_0_14155, plain, (c_Natural_Oevalc(X3,X2,esk179_4(X4,X2,X3,X1))|~hBOOL(hAPP(X1,X2))|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3),X2,X4)), inference(split_conjunct,[status(thm)],[c_0_8574]), ['final']). 4.05/4.34 cnf(c_0_14156, 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_8832]), ['final']). 4.05/4.34 cnf(c_0_14157, 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_8833]), ['final']). 4.05/4.34 cnf(c_0_14158, 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_8834]), ['final']). 4.05/4.34 cnf(c_0_14159, 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_8428]), ['final']). 4.05/4.34 cnf(c_0_14160, 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_8080]), ['final']). 4.05/4.34 cnf(c_0_14161, 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_8835]), ['final']). 4.05/4.34 cnf(c_0_14162, plain, (hAPP(c_Finite__Set_Ocard(X1),esk49_3(X2,X3,X1))=X2|hAPP(c_Nat_OSuc,X2)!=hAPP(c_Finite__Set_Ocard(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_5466]), ['final']). 4.05/4.34 cnf(c_0_14163, 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_8836]), ['final']). 4.05/4.34 cnf(c_0_14164, 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_8837]), ['final']). 4.05/4.34 cnf(c_0_14165, 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))), inference(split_conjunct,[status(thm)],[c_0_8838]), ['final']). 4.05/4.34 cnf(c_0_14166, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omax(X1)),X2)=c_Big__Operators_Olinorder__class_OMax(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8839]), ['final']). 4.05/4.34 cnf(c_0_14167, 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_8840]), ['final']). 4.05/4.34 cnf(c_0_14168, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,X2)=hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8841]), ['final']). 4.05/4.34 cnf(c_0_14169, plain, (esk49_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_8842]), c_0_4867]), ['final']). 4.05/4.34 cnf(c_0_14170, 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),esk50_2(X2,X3)))|~hBOOL(hAPP(X3,X1))|~hBOOL(hAPP(X3,X2))), inference(split_conjunct,[status(thm)],[c_0_5485]), ['final']). 4.05/4.34 cnf(c_0_14171, plain, (hBOOL(hAPP(X1,esk88_3(X2,X1,X3)))|hAPP(c_List_Ofilter(X3,X1),X2)=c_List_Olist_ONil(X3)), inference(split_conjunct,[status(thm)],[c_0_8080]), ['final']). 4.05/4.34 cnf(c_0_14172, 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_8843]), ['final']). 4.05/4.34 cnf(c_0_14173, 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_7795]), ['final']). 4.05/4.34 cnf(c_0_14174, plain, (c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))=c_Smallcheck_Osmall_H(X3,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_6690]), ['final']). 4.05/4.34 cnf(c_0_14175, plain, (X3=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3)), inference(split_conjunct,[status(thm)],[c_0_8844]), ['final']). 4.05/4.34 cnf(c_0_14176, 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_8845]), ['final']). 4.05/4.34 cnf(c_0_14177, 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_8846]), ['final']). 4.05/4.34 cnf(c_0_14178, plain, (c_Map_Omap__add(X1,X2,X3,X4)=c_Map_Omap__add(X1,X2,X4,X3)|~c_Map_Omap__le(X1,X2,X3,c_Map_Omap__add(X1,X2,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_8773]), ['final']). 4.05/4.34 cnf(c_0_14179, 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_8847]), ['final']). 4.05/4.34 cnf(c_0_14180, 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_8848]), ['final']). 4.05/4.34 cnf(c_0_14181, 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_8849]), ['final']). 4.05/4.34 cnf(c_0_14182, 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_8850, c_0_6133]), ['final']). 4.05/4.34 cnf(c_0_14183, plain, (hBOOL(hAPP(X4,X2))|c_Natural_Oevalc(c_Com_Ocom_OCond(X4,X5,X1),X2,X3)|~c_Natural_Oevalc(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8851]), ['final']). 4.05/4.34 cnf(c_0_14184, 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_8852]), ['final']). 4.05/4.34 cnf(c_0_14185, 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_8853, c_0_4427]), ['final']). 4.05/4.34 cnf(c_0_14186, plain, (X2=hAPP(c_Groups_Oabs__class_Oabs(X1),X2)|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))), inference(split_conjunct,[status(thm)],[c_0_8854]), ['final']). 4.05/4.34 cnf(c_0_14187, 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_8855]), ['final']). 4.05/4.34 cnf(c_0_14188, 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_8856, c_0_4427]), ['final']). 4.05/4.34 cnf(c_0_14189, 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_8857, c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_14190, 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_6029]), ['final']). 4.05/4.34 cnf(c_0_14191, 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_8858]), ['final']). 4.05/4.34 cnf(c_0_14192, plain, (X3=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Groups_Ogroup__add(X1)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)), inference(split_conjunct,[status(thm)],[c_0_8859]), ['final']). 4.05/4.34 cnf(c_0_14193, plain, (X2=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)|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_5552]), ['final']). 4.05/4.34 cnf(c_0_14194, 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_7511]), ['final']). 4.05/4.34 cnf(c_0_14195, 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_8860]), ['final']). 4.05/4.34 cnf(c_0_14196, 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_7511]), ['final']). 4.05/4.34 cnf(c_0_14197, 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_8861]), ['final']). 4.05/4.34 cnf(c_0_14198, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|c_Groups_Ozero__class_Ozero(X3)=c_Nitpick_Osetsum_H(X1,X3,X4,X2)|~class_Groups_Ocomm__monoid__add(X3)), inference(split_conjunct,[status(thm)],[c_0_4937]), ['final']). 4.05/4.34 cnf(c_0_14199, 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_8862]), ['final']). 4.05/4.34 cnf(c_0_14200, plain, (X1=c_Int_OMin|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))!=c_Int_OMin), inference(rw,[status(thm)],[c_0_8863, c_0_4795]), ['final']). 4.05/4.34 cnf(c_0_14201, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Relation_OId__on(X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_8448]), ['final']). 4.05/4.34 cnf(c_0_14202, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk382_3(X3,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7365]), ['final']). 4.05/4.34 cnf(c_0_14203, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk370_3(X3,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_7364]), ['final']). 4.05/4.34 cnf(c_0_14204, 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_8864]), ['final']). 4.05/4.34 cnf(c_0_14205, 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_8865]), ['final']). 4.05/4.34 cnf(c_0_14206, 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_8866]), ['final']). 4.05/4.34 cnf(c_0_14207, 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_8867]), ['final']). 4.05/4.34 cnf(c_0_14208, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_8868]), ['final']). 4.05/4.34 cnf(c_0_14209, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)=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_8869]), ['final']). 4.05/4.34 cnf(c_0_14210, 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_8870]), ['final']). 4.05/4.34 cnf(c_0_14211, 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)), inference(split_conjunct,[status(thm)],[c_0_8871]), ['final']). 4.05/4.34 cnf(c_0_14212, 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_8872]), ['final']). 4.05/4.34 cnf(c_0_14213, 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_8873]), ['final']). 4.05/4.34 cnf(c_0_14214, plain, (c_Natural_Oevaln(c_Com_Ocom_OCond(X5,X1,X6),X2,X3,X4)|~c_Natural_Oevaln(X1,X2,X3,X4)|~hBOOL(hAPP(X5,X2))), inference(split_conjunct,[status(thm)],[c_0_8741]), ['final']). 4.05/4.34 cnf(c_0_14215, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_8874]), ['final']). 4.05/4.34 cnf(c_0_14216, 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_8875]), ['final']). 4.05/4.34 cnf(c_0_14217, 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_8876]), ['final']). 4.05/4.34 cnf(c_0_14218, plain, (X4=c_Divides_Odiv__class_Omod(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_8877]), ['final']). 4.05/4.34 cnf(c_0_14219, 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_8878]), ['final']). 4.05/4.34 cnf(c_0_14220, 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_8878]), ['final']). 4.05/4.34 cnf(c_0_14221, 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_8862]), ['final']). 4.05/4.34 cnf(c_0_14222, 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_8658]), ['final']). 4.05/4.34 cnf(c_0_14223, 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_8663]), ['final']). 4.05/4.34 cnf(c_0_14224, 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_8662]), ['final']). 4.05/4.34 cnf(c_0_14225, 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_8664]), ['final']). 4.05/4.34 cnf(c_0_14226, 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_8879]), ['final']). 4.05/4.34 cnf(c_0_14227, 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_8880]), ['final']). 4.05/4.34 cnf(c_0_14228, 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_8881]), ['final']). 4.05/4.34 cnf(c_0_14229, 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_8882]), ['final']). 4.05/4.34 cnf(c_0_14230, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)|~c_List_Olist__all2(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_8883]), ['final']). 4.05/4.34 cnf(c_0_14231, 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_8884]), ['final']). 4.05/4.34 cnf(c_0_14232, 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_8885]), ['final']). 4.05/4.34 cnf(c_0_14233, 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_8510]), ['final']). 4.05/4.34 cnf(c_0_14234, plain, (hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,esk437_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7450]), ['final']). 4.05/4.34 cnf(c_0_14235, plain, (hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,esk261_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_7460]), ['final']). 4.05/4.34 cnf(c_0_14236, 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_6800]), ['final']). 4.05/4.34 cnf(c_0_14237, 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_6801]), ['final']). 4.05/4.34 cnf(c_0_14238, 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_8886]), ['final']). 4.05/4.34 cnf(c_0_14239, 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_8887]), ['final']). 4.05/4.34 cnf(c_0_14240, 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_8888]), ['final']). 4.05/4.34 cnf(c_0_14241, 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_8889, c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_14242, 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_8890]), ['final']). 4.05/4.34 cnf(c_0_14243, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8891]), ['final']). 4.05/4.34 cnf(c_0_14244, 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_8157]), ['final']). 4.05/4.34 cnf(c_0_14245, 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_8892]), ['final']). 4.05/4.34 cnf(c_0_14246, 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_8156]), ['final']). 4.05/4.34 cnf(c_0_14247, 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_8157]), ['final']). 4.05/4.34 cnf(c_0_14248, 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_8156]), ['final']). 4.05/4.34 cnf(c_0_14249, plain, (X1=c_List_Olist_ONil(X2)|c_List_Olast(X2,hAPP(c_List_Orev(X2),X1))=hAPP(c_List_Ohd(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_8893]), ['final']). 4.05/4.34 cnf(c_0_14250, 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_8894, c_0_4434]), ['final']). 4.05/4.34 cnf(c_0_14251, 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_8895, c_0_5149]), c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_14252, 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_8896, c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_14253, 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,esk156_1(X1)))), inference(rw,[status(thm)],[c_0_8897, c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_14254, 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_8898]), ['final']). 4.05/4.34 cnf(c_0_14255, 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_8042]), ['final']). 4.05/4.34 cnf(c_0_14256, 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_8899]), ['final']). 4.05/4.34 cnf(c_0_14257, 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_8900]), ['final']). 4.05/4.34 cnf(c_0_14258, 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_8901]), ['final']). 4.05/4.34 cnf(c_0_14259, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8902]), ['final']). 4.05/4.34 cnf(c_0_14260, plain, (c_Divides_Odiv__class_Omod(X1,X2,X3)=c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8903]), ['final']). 4.05/4.34 cnf(c_0_14261, 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_8904]), ['final']). 4.05/4.34 cnf(c_0_14262, plain, (hBOOL(hAPP(X1,esk332_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_8905, c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_14263, 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_8906, c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_14264, plain, (X2=X1|hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)!=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)), inference(split_conjunct,[status(thm)],[c_0_8907]), ['final']). 4.05/4.34 cnf(c_0_14265, 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_8908]), ['final']). 4.05/4.34 cnf(c_0_14266, 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_8909]), ['final']). 4.05/4.34 cnf(c_0_14267, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|X2=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))), inference(split_conjunct,[status(thm)],[c_0_8910]), ['final']). 4.05/4.34 cnf(c_0_14268, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk331_1(X1)))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_5573]), ['final']). 4.05/4.34 cnf(c_0_14269, 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_8911]), ['final']). 4.05/4.34 cnf(c_0_14270, 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_8912]), ['final']). 4.05/4.34 cnf(c_0_14271, 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_8913]), ['final']). 4.05/4.34 cnf(c_0_14272, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)=c_SMT_Oz3div(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_8204]), ['final']). 4.05/4.34 cnf(c_0_14273, 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_8914]), ['final']). 4.05/4.34 cnf(c_0_14274, 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_8915]), ['final']). 4.05/4.34 cnf(c_0_14275, plain, (c_Map_Omap__le(X4,X3,X2,X1)|hAPP(X1,esk471_4(X1,X2,X3,X4))!=hAPP(X2,esk471_4(X1,X2,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_8053]), ['final']). 4.05/4.34 cnf(c_0_14276, 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_8916]), ['final']). 4.05/4.34 cnf(c_0_14277, 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_8917]), ['final']). 4.05/4.34 cnf(c_0_14278, 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_8917]), ['final']). 4.05/4.34 cnf(c_0_14279, 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_8313]), ['final']). 4.05/4.34 cnf(c_0_14280, 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_8313]), ['final']). 4.05/4.34 cnf(c_0_14281, plain, (c_Natural_Oevalc(X1,X2,esk374_3(X2,X1,X3))|~hBOOL(hAPP(X3,X2))|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X1),X2,X2)), inference(split_conjunct,[status(thm)],[c_0_8696]), ['final']). 4.05/4.34 cnf(c_0_14282, plain, (c_Natural_Oevalc(c_Com_Ocom_OWhile(X4,X1),X2,X2)|~c_Natural_Oevalc(X1,X2,X3)|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X4,X1),X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8696]), ['final']). 4.05/4.34 cnf(c_0_14283, 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_8918]), ['final']). 4.05/4.34 cnf(c_0_14284, 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_8919]), ['final']). 4.05/4.34 cnf(c_0_14285, 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_8493]), ['final']). 4.05/4.34 cnf(c_0_14286, 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_8920]), ['final']). 4.05/4.34 cnf(c_0_14287, plain, (hBOOL(hAPP(X1,X2))|hAPP(c_List_Ofilter(X3,X1),X4)!=hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5)), inference(split_conjunct,[status(thm)],[c_0_5107]), ['final']). 4.05/4.34 cnf(c_0_14288, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Sum__Type_OPlus(X3,X1,X4,X2)!=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X3,X1),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5931]), ['final']). 4.05/4.34 cnf(c_0_14289, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|c_Sum__Type_OPlus(X2,X3,X1,X4)!=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X2,X3),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5931]), ['final']). 4.05/4.34 cnf(c_0_14290, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)))|~hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,esk174_3(X3,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_5288]), ['final']). 4.05/4.34 cnf(c_0_14291, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X2,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7412]), ['final']). 4.05/4.34 cnf(c_0_14292, 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_7718]), ['final']). 4.05/4.34 cnf(c_0_14293, 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_8921]), ['final']). 4.05/4.34 cnf(c_0_14294, 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_8922]), ['final']). 4.05/4.34 cnf(c_0_14295, 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_8923]), ['final']). 4.05/4.34 cnf(c_0_14296, 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_8924]), ['final']). 4.05/4.34 cnf(c_0_14297, 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_8925]), ['final']). 4.05/4.34 cnf(c_0_14298, 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_8926]), ['final']). 4.05/4.34 cnf(c_0_14299, plain, (c_Natural_Oevaln(X1,X2,X3,X4)|c_Natural_Oevaln(X5,X2,X3,X4)|~c_Natural_Oevaln(c_Com_Ocom_OCond(X6,X5,X1),X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8927]), ['final']). 4.05/4.34 cnf(c_0_14300, plain, (X3=X2|~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_8928]), ['final']). 4.05/4.34 cnf(c_0_14301, 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_8929]), ['final']). 4.05/4.34 cnf(c_0_14302, plain, (X2=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8930]), ['final']). 4.05/4.34 cnf(c_0_14303, 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_8862]), ['final']). 4.05/4.34 cnf(c_0_14304, 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_4652]), ['final']). 4.05/4.34 cnf(c_0_14305, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(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_8931]), ['final']). 4.05/4.34 cnf(c_0_14306, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_8931]), ['final']). 4.05/4.34 cnf(c_0_14307, 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_8932]), ['final']). 4.05/4.34 cnf(c_0_14308, plain, (X3=hAPP(hAPP(c_Orderings_Oord__class_Omax(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_8933]), ['final']). 4.05/4.34 cnf(c_0_14309, 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_8934]), ['final']). 4.05/4.34 cnf(c_0_14310, 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_8935]), ['final']). 4.05/4.34 cnf(c_0_14311, 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_8936]), ['final']). 4.05/4.34 cnf(c_0_14312, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(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_8937]), ['final']). 4.05/4.34 cnf(c_0_14313, 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_8938]), ['final']). 4.05/4.34 cnf(c_0_14314, 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_8304]), ['final']). 4.05/4.34 cnf(c_0_14315, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2)=c_Groups_Oone__class_Oone(X1)|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_8939]), ['final']). 4.05/4.34 cnf(c_0_14316, 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_8940, c_0_5149])]), ['final']). 4.05/4.34 cnf(c_0_14317, 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_8941]), ['final']). 4.05/4.34 cnf(c_0_14318, 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_8942]), ['final']). 4.05/4.34 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_8943]), ['final']). 4.05/4.34 cnf(c_0_14320, 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_8944]), ['final']). 4.05/4.34 cnf(c_0_14321, 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_8945]), ['final']). 4.05/4.34 cnf(c_0_14322, 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_8303]), ['final']). 4.05/4.34 cnf(c_0_14323, 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_8304]), ['final']). 4.05/4.34 cnf(c_0_14324, 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_8303]), ['final']). 4.05/4.34 cnf(c_0_14325, plain, (hAPP(c_List_Oset(X1),esk396_2(X2,X1))=X2|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5537]), ['final']). 4.05/4.34 cnf(c_0_14326, 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)), inference(split_conjunct,[status(thm)],[c_0_8946]), ['final']). 4.05/4.34 cnf(c_0_14327, 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_8947]), ['final']). 4.05/4.34 cnf(c_0_14328, 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_8948]), ['final']). 4.05/4.34 cnf(c_0_14329, 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_8949]), ['final']). 4.05/4.34 cnf(c_0_14330, plain, (X1=X2|c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X2)!=hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))|~class_Orderings_Oorder(X3)), inference(split_conjunct,[status(thm)],[c_0_8950]), ['final']). 4.05/4.34 cnf(c_0_14331, plain, (X1=X2|c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)!=hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))|~class_Orderings_Oorder(X3)), inference(split_conjunct,[status(thm)],[c_0_8950]), ['final']). 4.05/4.34 cnf(c_0_14332, 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_8951]), ['final']). 4.05/4.34 cnf(c_0_14333, 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_5612]), ['final']). 4.05/4.34 cnf(c_0_14334, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))), inference(split_conjunct,[status(thm)],[c_0_8952]), ['final']). 4.05/4.34 cnf(c_0_14335, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8953]), ['final']). 4.05/4.34 cnf(c_0_14336, plain, (X3=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)=X2|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_5574]), ['final']). 4.05/4.34 cnf(c_0_14337, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ono__zero__divisors(X1)|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_8954]), ['final']). 4.05/4.34 cnf(c_0_14338, 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_8466]), ['final']). 4.05/4.34 cnf(c_0_14339, plain, (X3=X4|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4))), inference(split_conjunct,[status(thm)],[c_0_5922]), ['final']). 4.05/4.34 cnf(c_0_14340, 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_8955]), ['final']). 4.05/4.34 cnf(c_0_14341, plain, (hBOOL(hAPP(c_List_Odistinct(X1),esk396_2(X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5537]), ['final']). 4.05/4.34 cnf(c_0_14342, 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_8949]), ['final']). 4.05/4.34 cnf(c_0_14343, 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_8956]), ['final']). 4.05/4.34 cnf(c_0_14344, 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_8435]), ['final']). 4.05/4.34 cnf(c_0_14345, plain, (X3=c_List_Olist_ONil(X1)|c_List_Olist_ONil(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_8957, c_0_5942]), ['final']). 4.05/4.34 cnf(c_0_14346, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Onth(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_List_Ohd(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_8958]), ['final']). 4.05/4.34 cnf(c_0_14347, 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_8959]), ['final']). 4.05/4.34 cnf(c_0_14348, 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_8960]), ['final']). 4.05/4.34 cnf(c_0_14349, plain, (X2=esk168_2(X1,X3)|~hBOOL(hAPP(X1,X2))|~c_List_Olist__ex1(X3,X1,c_Enum_Oenum__class_Oenum(X3))|~class_Enum_Oenum(X3)), inference(split_conjunct,[status(thm)],[c_0_8429]), ['final']). 4.05/4.34 cnf(c_0_14350, plain, (c_Natural_Oevaln(X1,X2,X3,X4)|hBOOL(hAPP(X5,X2))|~c_Natural_Oevaln(c_Com_Ocom_OCond(X5,X6,X1),X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8927]), ['final']). 4.05/4.34 cnf(c_0_14351, plain, (c_List_Olist__ex(X1,X2,X4)|c_List_Olist__ex(X1,X2,X3)|~c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_8878]), ['final']). 4.05/4.34 cnf(c_0_14352, plain, (c_Equiv__Relations_Oequivp(X2,X1)|hAPP(X1,esk98_1(X1))!=hAPP(X1,esk99_1(X1))|~hBOOL(hAPP(hAPP(X1,esk98_1(X1)),esk99_1(X1)))), inference(split_conjunct,[status(thm)],[c_0_8286]), ['final']). 4.05/4.34 cnf(c_0_14353, 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_8961]), ['final']). 4.05/4.34 cnf(c_0_14354, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1))=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Obounded__lattice__bot(X1)), inference(split_conjunct,[status(thm)],[c_0_8962]), ['final']). 4.05/4.34 cnf(c_0_14355, 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_8963]), ['final']). 4.05/4.34 cnf(c_0_14356, 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_8868]), ['final']). 4.05/4.34 cnf(c_0_14357, 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_8870]), ['final']). 4.05/4.34 cnf(c_0_14358, plain, (c_Natural_Oevalc(c_Com_Ocom_OSemi(X4,X1),X5,X3)|~c_Natural_Oevalc(X1,X2,X3)|~c_Natural_Oevalc(X4,X5,X2)), inference(split_conjunct,[status(thm)],[c_0_8964]), ['final']). 4.05/4.34 cnf(c_0_14359, 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_8965]), ['final']). 4.05/4.34 cnf(c_0_14360, 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_8966]), ['final']). 4.05/4.34 cnf(c_0_14361, plain, (X2=hAPP(c_List_Orotate1(X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(split_conjunct,[status(thm)],[c_0_8967]), ['final']). 4.05/4.34 cnf(c_0_14362, plain, (hBOOL(hAPP(c_Predicate_ORangeP(X4,X5,X1),X3))|~hBOOL(hAPP(hAPP(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8968]), ['final']). 4.05/4.34 cnf(c_0_14363, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|X2=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_8969]), ['final']). 4.05/4.34 cnf(c_0_14364, 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_8970]), ['final']). 4.05/4.34 cnf(c_0_14365, 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_8971]), ['final']). 4.05/4.34 cnf(c_0_14366, plain, (hBOOL(hAPP(c_Predicate_ODomainP(X4,X5,X1),X2))|~hBOOL(hAPP(hAPP(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_8972]), ['final']). 4.05/4.34 cnf(c_0_14367, plain, (hAPP(c_Int_ORep__Integ,esk123_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))), inference(split_conjunct,[status(thm)],[c_0_8973]), ['final']). 4.05/4.34 cnf(c_0_14368, plain, (c_List_Olist__ex1(X2,X1,c_Enum_Oenum__class_Oenum(X2))|esk167_3(X1,X2,X3)!=X3|~hBOOL(hAPP(X1,X3))|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_8429]), ['final']). 4.05/4.34 cnf(c_0_14369, plain, (c_Natural_Oevalc(X1,esk466_4(X2,X3,X1,X4),X2)|~c_Natural_Oevalc(c_Com_Ocom_OSemi(X4,X1),X3,X2)), inference(split_conjunct,[status(thm)],[c_0_8964]), ['final']). 4.05/4.34 cnf(c_0_14370, plain, (c_Natural_Oevalc(X1,X2,esk466_4(X3,X2,X4,X1))|~c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4),X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8964]), ['final']). 4.05/4.34 cnf(c_0_14371, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_5530]), ['final']). 4.05/4.34 cnf(c_0_14372, plain, (c_Orderings_Otop__class_Otop(X1)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Orderings_Otop__class_Otop(X1))|~class_Lattices_Obounded__lattice__top(X1)), inference(split_conjunct,[status(thm)],[c_0_8974]), ['final']). 4.05/4.34 cnf(c_0_14373, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_8975]), ['final']). 4.05/4.34 cnf(c_0_14374, 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_8976]), ['final']). 4.05/4.34 cnf(c_0_14375, plain, (hBOOL(hAPP(X1,X2))|c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X2)), inference(split_conjunct,[status(thm)],[c_0_8436]), ['final']). 4.05/4.34 cnf(c_0_14376, plain, (hBOOL(hAPP(X1,esk168_2(X1,X2)))|~c_List_Olist__ex1(X2,X1,c_Enum_Oenum__class_Oenum(X2))|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_8429]), ['final']). 4.05/4.34 cnf(c_0_14377, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Omult__zero(X1)|~class_Rings_Ono__zero__divisors(X1)|~class_Rings_Ozero__neq__one(X1)|~class_Power_Opower(X1)), inference(split_conjunct,[status(thm)],[c_0_5549]), ['final']). 4.05/4.34 cnf(c_0_14378, 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_8977]), ['final']). 4.05/4.34 cnf(c_0_14379, 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),X1))!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)), inference(split_conjunct,[status(thm)],[c_0_8978]), ['final']). 4.05/4.34 cnf(c_0_14380, 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_8978]), ['final']). 4.05/4.34 cnf(c_0_14381, 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_7454]), ['final']). 4.05/4.34 cnf(c_0_14382, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(c_List_Ohd(X2),c_List_Oreplicate(X2,X1,X3))=X3), inference(split_conjunct,[status(thm)],[c_0_8979]), ['final']). 4.05/4.34 cnf(c_0_14383, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Omult__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_8980]), ['final']). 4.05/4.34 cnf(c_0_14384, 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_8981]), ['final']). 4.05/4.34 cnf(c_0_14385, 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_8982]), ['final']). 4.05/4.34 cnf(c_0_14386, plain, (hBOOL(hAPP(X1,X2))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X3|~hBOOL(hAPP(X1,esk356_4(X1,X2,X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_7396]), ['final']). 4.05/4.34 cnf(c_0_14387, plain, (~hBOOL(hAPP(hAPP(c_member(X1),esk48_3(X2,X3,X1)),esk49_3(X2,X3,X1)))|hAPP(c_Nat_OSuc,X2)!=hAPP(c_Finite__Set_Ocard(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_5466]), ['final']). 4.05/4.34 cnf(c_0_14388, 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_8983]), ['final']). 4.05/4.34 cnf(c_0_14389, 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_8984]), ['final']). 4.05/4.34 cnf(c_0_14390, 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_8985]), ['final']). 4.05/4.34 cnf(c_0_14391, plain, (X3=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))|hAPP(c_Relation_ODomain(X1,X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5996]), ['final']). 4.05/4.34 cnf(c_0_14392, 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_5997]), ['final']). 4.05/4.34 cnf(c_0_14393, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X2)=c_Groups_Oone__class_Oone(X1)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_8986]), ['final']). 4.05/4.34 cnf(c_0_14394, 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_6386]), ['final']). 4.05/4.34 cnf(c_0_14395, 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_6386]), ['final']). 4.05/4.34 cnf(c_0_14396, 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__inverse__zero(X1)), inference(split_conjunct,[status(thm)],[c_0_8987]), ['final']). 4.05/4.34 cnf(c_0_14397, 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_8988, c_0_5149]), c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_14398, 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_8815]), ['final']). 4.05/4.34 cnf(c_0_14399, 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_8989, c_0_5379]), c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_14400, plain, (c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5),X2,X4)|~hBOOL(hAPP(X1,X2))|~c_Natural_Oevalc(X3,X2,X4)), inference(split_conjunct,[status(thm)],[c_0_8990]), ['final']). 4.05/4.34 cnf(c_0_14401, 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_8991]), ['final']). 4.05/4.34 cnf(c_0_14402, 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_8992, c_0_8378]), ['final']). 4.05/4.34 cnf(c_0_14403, 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_8993]), ['final']). 4.05/4.34 cnf(c_0_14404, 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_8994]), ['final']). 4.05/4.34 cnf(c_0_14405, 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_8818]), ['final']). 4.05/4.34 cnf(c_0_14406, 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_8820]), ['final']). 4.05/4.34 cnf(c_0_14407, 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_8995, c_0_5379]), c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_14408, 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_8996]), ['final']). 4.05/4.34 cnf(c_0_14409, 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_8997]), ['final']). 4.05/4.34 cnf(c_0_14410, 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_8998]), ['final']). 4.05/4.34 cnf(c_0_14411, 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_8999]), ['final']). 4.05/4.34 cnf(c_0_14412, 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_9000]), ['final']). 4.05/4.34 cnf(c_0_14413, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5969]), ['final']). 4.05/4.34 cnf(c_0_14414, 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_9001]), ['final']). 4.05/4.34 cnf(c_0_14415, plain, (c_Map_Omap__le(X1,X2,X3,X5)|~c_Map_Omap__le(X1,X2,X3,X4)|~c_Map_Omap__le(X1,X2,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_9002]), ['final']). 4.05/4.34 cnf(c_0_14416, 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_9003]), ['final']). 4.05/4.34 cnf(c_0_14417, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|hAPP(X1,X2)!=hAPP(X1,X3)|~c_Equiv__Relations_Oequivp(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_8286]), ['final']). 4.05/4.34 cnf(c_0_14418, 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_9004, c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_14419, 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_8298]), ['final']). 4.05/4.34 cnf(c_0_14420, plain, (c_List_Omember(X1,X3,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))), inference(split_conjunct,[status(thm)],[c_0_8694]), ['final']). 4.05/4.34 cnf(c_0_14421, 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_9005]), ['final']). 4.05/4.34 cnf(c_0_14422, 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_9006]), ['final']). 4.05/4.34 cnf(c_0_14423, 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_9007]), ['final']). 4.05/4.34 cnf(c_0_14424, plain, (X1=X2|hAPP(hAPP(c_List_Olist_OCons(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),X4))), inference(rw,[status(thm)],[c_0_9008, c_0_4519]), ['final']). 4.05/4.34 cnf(c_0_14425, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9009]), ['final']). 4.05/4.34 cnf(c_0_14426, 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_9010, c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_14427, plain, (X2=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),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_9011]), ['final']). 4.05/4.34 cnf(c_0_14428, plain, (X4=X3|~class_Groups_Ocancel__ab__semigroup__add(X1)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)), inference(split_conjunct,[status(thm)],[c_0_9012]), ['final']). 4.05/4.34 cnf(c_0_14429, 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_9013]), ['final']). 4.05/4.34 cnf(c_0_14430, 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_Power_Opower(X1)), inference(split_conjunct,[status(thm)],[c_0_9014]), ['final']). 4.05/4.34 cnf(c_0_14431, 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_9015]), ['final']). 4.05/4.34 cnf(c_0_14432, 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_9016]), ['final']). 4.05/4.34 cnf(c_0_14433, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=X1), inference(split_conjunct,[status(thm)],[c_0_9017]), ['final']). 4.05/4.34 cnf(c_0_14434, 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_7624]), ['final']). 4.05/4.34 cnf(c_0_14435, plain, (hBOOL(hAPP(X1,esk487_3(X2,X1,X3)))|~c_Enum_Oex__n__lists(X3,X1,X2)|~class_Enum_Oenum(X3)), inference(split_conjunct,[status(thm)],[c_0_7338]), ['final']). 4.05/4.34 cnf(c_0_14436, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)=X2|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9018]), ['final']). 4.05/4.34 cnf(c_0_14437, 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_9019]), ['final']). 4.05/4.34 cnf(c_0_14438, 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_9020]), ['final']). 4.05/4.34 cnf(c_0_14439, 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_9021]), ['final']). 4.05/4.34 cnf(c_0_14440, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)!=hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9022]), ['final']). 4.05/4.34 cnf(c_0_14441, plain, (c_List_Olinorder__class_Osorted__list__of__set(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_List_Olist_ONil(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9023]), ['final']). 4.05/4.34 cnf(c_0_14442, 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_9024]), ['final']). 4.05/4.34 cnf(c_0_14443, 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)), inference(split_conjunct,[status(thm)],[c_0_9025]), ['final']). 4.05/4.34 cnf(c_0_14444, plain, (X2=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2)|~class_Lattices_Obounded__lattice__top(X1)), inference(split_conjunct,[status(thm)],[c_0_9026]), ['final']). 4.05/4.34 cnf(c_0_14445, plain, (X2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_9027]), ['final']). 4.05/4.34 cnf(c_0_14446, 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_9028]), ['final']). 4.05/4.34 cnf(c_0_14447, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1))=X2|~class_Lattices_Obounded__lattice__bot(X1)), inference(split_conjunct,[status(thm)],[c_0_9029]), ['final']). 4.05/4.34 cnf(c_0_14448, 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_8963]), ['final']). 4.05/4.34 cnf(c_0_14449, plain, (c_Orderings_Otop__class_Otop(X1)=c_Complete__Lattice_OSup__class_OSup(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_9030]), ['final']). 4.05/4.34 cnf(c_0_14450, plain, (c_Orderings_Otop__class_Otop(X1)=c_Complete__Lattice_OInf__class_OInf(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9031]), ['final']). 4.05/4.34 cnf(c_0_14451, plain, (c_List_Olinorder__class_Osorted(X1,esk401_2(X2,X1))|c_List_Olist_ONil(X1)=X2|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5366]), ['final']). 4.05/4.34 cnf(c_0_14452, 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_9032]), ['final']). 4.05/4.34 cnf(c_0_14453, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Groups_Omonoid__add(X1)), inference(split_conjunct,[status(thm)],[c_0_9033]), ['final']). 4.05/4.34 cnf(c_0_14454, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Rings_Ocomm__semiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9034]), ['final']). 4.05/4.34 cnf(c_0_14455, 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_9035]), ['final']). 4.05/4.34 cnf(c_0_14456, 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_9036]), ['final']). 4.05/4.34 cnf(c_0_14457, 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_9037]), ['final']). 4.05/4.34 cnf(c_0_14458, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Olist_ONil(X1)=X3|hAPP(hAPP(c_List_Otake(X1),X2),X3)!=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_9038]), ['final']). 4.05/4.34 cnf(c_0_14459, plain, (hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,X1)),X3)=c_Orderings_Otop__class_Otop(X1)|~class_Orderings_Otop(X1)), inference(split_conjunct,[status(thm)],[c_0_9039]), ['final']). 4.05/4.34 cnf(c_0_14460, 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_9040]), ['final']). 4.05/4.34 cnf(c_0_14461, 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_9041]), ['final']). 4.05/4.34 cnf(c_0_14462, plain, (X2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))|~class_Groups_Omonoid__mult(X1)), inference(split_conjunct,[status(thm)],[c_0_9042]), ['final']). 4.05/4.34 cnf(c_0_14463, 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_9043]), ['final']). 4.05/4.34 cnf(c_0_14464, plain, (c_Orderings_Obot__class_Obot(X1)=hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3)|~class_Orderings_Obot(X1)), inference(split_conjunct,[status(thm)],[c_0_9044]), ['final']). 4.05/4.34 cnf(c_0_14465, plain, (X4=X5|~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_9045]), ['final']). 4.05/4.34 cnf(c_0_14466, 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_9046]), ['final']). 4.05/4.34 cnf(c_0_14467, plain, (X2=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_9047]), ['final']). 4.05/4.34 cnf(c_0_14468, 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)), inference(split_conjunct,[status(thm)],[c_0_9048]), ['final']). 4.05/4.34 cnf(c_0_14469, 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_9049]), ['final']). 4.05/4.34 cnf(c_0_14470, plain, (X1=X2|hAPP(hAPP(c_Product__Type_OPair(X3,X4),X5),X1)!=hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X2)), inference(split_conjunct,[status(thm)],[c_0_9049]), ['final']). 4.05/4.34 cnf(c_0_14471, 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_8769]), ['final']). 4.05/4.34 cnf(c_0_14472, 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_9050]), ['final']). 4.05/4.34 cnf(c_0_14473, 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_9051]), ['final']). 4.05/4.34 cnf(c_0_14474, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9052]), ['final']). 4.05/4.34 cnf(c_0_14475, plain, (X3=X2|c_Groups_Ozero__class_Ozero(X1)=X3|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Odivision__ring(X1)), inference(split_conjunct,[status(thm)],[c_0_9053]), ['final']). 4.05/4.34 cnf(c_0_14476, 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_9054]), ['final']). 4.05/4.34 cnf(c_0_14477, plain, (X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|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_9055]), ['final']). 4.05/4.34 cnf(c_0_14478, 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_9056, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_14479, 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_8124]), ['final']). 4.05/4.34 cnf(c_0_14480, 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_8031]), ['final']). 4.05/4.34 cnf(c_0_14481, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)=c_SMT_Oz3mod(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_8597]), ['final']). 4.05/4.34 cnf(c_0_14482, plain, (X6=hAPP(X4,hAPP(X3,X6))|~c_Typedef_Otype__definition(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_9057]), ['final']). 4.05/4.34 cnf(c_0_14483, plain, (c_List_Olist__all(X2,X1,X3)|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk36_3(X3,X1,X2))))), inference(split_conjunct,[status(thm)],[c_0_8075]), ['final']). 4.05/4.34 cnf(c_0_14484, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk447_3(X3,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_8688]), ['final']). 4.05/4.34 cnf(c_0_14485, 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_8749]), ['final']). 4.05/4.34 cnf(c_0_14486, 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_8750]), ['final']). 4.05/4.34 cnf(c_0_14487, 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_8751]), ['final']). 4.05/4.34 cnf(c_0_14488, 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_8754]), ['final']). 4.05/4.34 cnf(c_0_14489, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk381_3(X3,X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_8689]), ['final']). 4.05/4.34 cnf(c_0_14490, plain, (c_Natural_Oevaln(X1,X2,esk101_3(X3,X2,X1),X3)|~c_Natural_Oevalc(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9058]), ['final']). 4.05/4.34 cnf(c_0_14491, 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_9059]), ['final']). 4.05/4.34 cnf(c_0_14492, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,esk482_4(X2,X1,hAPP(c_Option_Ooption_OSome(X3),X2),X3)))), inference(er,[status(thm)],[c_0_9060]), ['final']). 4.05/4.34 cnf(c_0_14493, plain, (c_Natural_Oevaln(X1,X2,hAPP(c_Nat_OSuc,X3),X4)|~c_Natural_Oevaln(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_9061]), ['final']). 4.05/4.34 cnf(c_0_14494, 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_9062]), ['final']). 4.05/4.34 cnf(c_0_14495, 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_8123]), ['final']). 4.05/4.34 cnf(c_0_14496, 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_9063]), ['final']). 4.05/4.34 cnf(c_0_14497, 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_9064]), ['final']). 4.05/4.34 cnf(c_0_14498, 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_8924]), ['final']). 4.05/4.34 cnf(c_0_14499, plain, (hBOOL(hAPP(X1,X2))|c_Natural_Oevalc(X3,X2,X4)|~c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X5,X3),X2,X4)), inference(split_conjunct,[status(thm)],[c_0_9065]), ['final']). 4.05/4.34 cnf(c_0_14500, 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_9066]), ['final']). 4.05/4.34 cnf(c_0_14501, plain, (X1=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk42_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_8776]), ['final']). 4.05/4.34 cnf(c_0_14502, plain, (hBOOL(hAPP(X1,X2))|c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3),X2,X2)), inference(split_conjunct,[status(thm)],[c_0_8696]), ['final']). 4.05/4.34 cnf(c_0_14503, 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']). 4.05/4.34 cnf(c_0_14504, 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_9068]), ['final']). 4.05/4.34 cnf(c_0_14505, 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_9069]), ['final']). 4.05/4.34 cnf(c_0_14506, 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_9070]), ['final']). 4.05/4.34 cnf(c_0_14507, 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_9071]), ['final']). 4.05/4.34 cnf(c_0_14508, 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_8766]), ['final']). 4.05/4.34 cnf(c_0_14509, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=c_Random_Oinc__shift(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_6030]), ['final']). 4.05/4.34 cnf(c_0_14510, 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_9072]), ['final']). 4.05/4.34 cnf(c_0_14511, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|c_List_Olist_ONil(tc_Int_Oint)=c_List_Oupto(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7672]), ['final']). 4.05/4.34 cnf(c_0_14512, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_9073]), ['final']). 4.05/4.34 cnf(c_0_14513, plain, (hAPP(X1,X2)=hAPP(X1,X3)|~hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Equiv__Relations_Oequivp(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_8286]), ['final']). 4.05/4.34 cnf(c_0_14514, 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_9074]), ['final']). 4.05/4.34 cnf(c_0_14515, 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_8933]), ['final']). 4.05/4.34 cnf(c_0_14516, 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_9075, c_0_5379]), c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_14517, 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_9076]), ['final']). 4.05/4.34 cnf(c_0_14518, 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_9077]), ['final']). 4.05/4.34 cnf(c_0_14519, 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_9078]), ['final']). 4.05/4.34 cnf(c_0_14520, 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_9079]), ['final']). 4.05/4.34 cnf(c_0_14521, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_9080]), ['final']). 4.05/4.34 cnf(c_0_14522, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_5984]), ['final']). 4.05/4.34 cnf(c_0_14523, plain, (X3=hAPP(c_Option_Ooption_OSome(X1),X2)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Option_Oset(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_9081]), ['final']). 4.05/4.34 cnf(c_0_14524, 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_7416]), ['final']). 4.05/4.34 cnf(c_0_14525, 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_9082]), ['final']). 4.05/4.34 cnf(c_0_14526, 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_9083]), ['final']). 4.05/4.34 cnf(c_0_14527, plain, (X1=X3|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_9084]), ['final']). 4.05/4.34 cnf(c_0_14528, 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_9085]), ['final']). 4.05/4.34 cnf(c_0_14529, 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_9086]), ['final']). 4.05/4.34 cnf(c_0_14530, 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_9087]), ['final']). 4.05/4.34 cnf(c_0_14531, 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_9088]), ['final']). 4.05/4.34 cnf(c_0_14532, 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_9089]), ['final']). 4.05/4.34 cnf(c_0_14533, 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_9090])]), ['final']). 4.05/4.34 cnf(c_0_14534, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9091]), ['final']). 4.05/4.34 cnf(c_0_14535, plain, (c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3)|~c_Natural_Oevalc(c_Com_Ocom_OBODY(X1),X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9092]), ['final']). 4.05/4.34 cnf(c_0_14536, 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_5474]), ['final']). 4.05/4.34 cnf(c_0_14537, 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_9093]), ['final']). 4.05/4.34 cnf(c_0_14538, 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_9094]), ['final']). 4.05/4.34 cnf(c_0_14539, 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_9095]), ['final']). 4.05/4.34 cnf(c_0_14540, 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_9096, c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_14541, plain, (X4=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(c_Set_Oimage(X1,X2,X3),X4)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_5994]), ['final']). 4.05/4.34 cnf(c_0_14542, 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_Ono__zero__divisors(X1)|~class_Rings_Omult__zero(X1)|~class_Rings_Ozero__neq__one(X1)|~class_Power_Opower(X1)), inference(er,[status(thm)],[c_0_9097]), ['final']). 4.05/4.34 cnf(c_0_14543, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)=X3|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9098]), ['final']). 4.05/4.34 cnf(c_0_14544, 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_9099]), ['final']). 4.05/4.34 cnf(c_0_14545, plain, (hAPP(c_Nat_OSuc,esk225_4(X1,X2,X3,X4))=X2|~c_Natural_Oevaln(c_Com_Ocom_OBODY(X4),X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8127]), ['final']). 4.05/4.34 cnf(c_0_14546, 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_9100]), ['final']). 4.05/4.34 cnf(c_0_14547, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk100_1(X1)),X1))|c_Nat__Transfer_Onat__set(X1)), inference(split_conjunct,[status(thm)],[c_0_8595]), ['final']). 4.05/4.34 cnf(c_0_14548, plain, (hBOOL(hAPP(X2,esk506_2(X2,X1)))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X2))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_9101]), ['final']). 4.05/4.34 cnf(c_0_14549, plain, (c_Natural_Oevalc(X1,X2,X3)|c_Natural_Oevalc(X4,X2,X3)|~c_Natural_Oevalc(c_Com_Ocom_OCond(X5,X4,X1),X2,X3)), inference(split_conjunct,[status(thm)],[c_0_8851]), ['final']). 4.05/4.34 cnf(c_0_14550, plain, (hBOOL(hAPP(X1,esk346_3(X2,X1,X3)))|~c_List_Olist__ex1(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7386]), ['final']). 4.05/4.34 cnf(c_0_14551, plain, (hBOOL(hAPP(X1,esk218_3(X2,X1,X3)))|~c_List_Olist__ex(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8312]), ['final']). 4.05/4.34 cnf(c_0_14552, plain, (hBOOL(hAPP(X2,esk386_2(X2,X1)))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X2))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_9102]), ['final']). 4.05/4.34 cnf(c_0_14553, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X2)),X1))|~hBOOL(hAPP(X1,c_Option_Ooption_ONone(X2)))|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_7471]), ['final']). 4.05/4.34 cnf(c_0_14554, 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_9103]), ['final']). 4.05/4.34 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_9104]), ['final']). 4.05/4.34 cnf(c_0_14556, 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_9105]), ['final']). 4.05/4.34 cnf(c_0_14557, 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_8589]), ['final']). 4.05/4.34 cnf(c_0_14558, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))|~class_Orderings_Oorder(X1)), inference(er,[status(thm)],[c_0_9106]), ['final']). 4.05/4.34 cnf(c_0_14559, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9091]), ['final']). 4.05/4.34 cnf(c_0_14560, 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_9107]), ['final']). 4.05/4.34 cnf(c_0_14561, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|X2=X3|c_List_Oreplicate(X4,X5,X2)!=c_List_Oreplicate(X4,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_9108]), ['final']). 4.05/4.34 cnf(c_0_14562, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X1)), inference(split_conjunct,[status(thm)],[c_0_9109]), ['final']). 4.05/4.34 cnf(c_0_14563, 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_9110, c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_14564, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_8975]), ['final']). 4.05/4.34 cnf(c_0_14565, plain, (c_Option_Ooption_ONone(X1)=X2|X2=hAPP(c_Option_Ooption_OSome(X1),esk256_2(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_9111]), ['final']). 4.05/4.34 cnf(c_0_14566, plain, (c_Natural_Oevaln(X3,X2,X4,X5)|~hBOOL(hAPP(X1,X2))|~c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_8927]), ['final']). 4.05/4.34 cnf(c_0_14567, plain, (hAPP(c_Option_Ooption_OSome(X1),esk4_2(X1,X2))=X2|X2=c_Option_Ooption_ONone(X1)), inference(split_conjunct,[status(thm)],[c_0_9112]), ['final']). 4.05/4.34 cnf(c_0_14568, 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_9113]), ['final']). 4.05/4.34 cnf(c_0_14569, plain, (c_List_Olinorder__class_Osort__key(X2,X1,X3,c_List_Olist_ONil(X2))=c_List_Olist_ONil(X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9114]), ['final']). 4.05/4.34 cnf(c_0_14570, 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)), inference(split_conjunct,[status(thm)],[c_0_5372]), ['final']). 4.05/4.34 cnf(c_0_14571, 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_9115]), ['final']). 4.05/4.34 cnf(c_0_14572, 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_9116]), ['final']). 4.05/4.34 cnf(c_0_14573, 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_8984]), ['final']). 4.05/4.34 cnf(c_0_14574, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(X1,esk118_1(X1)))), inference(split_conjunct,[status(thm)],[c_0_8414]), ['final']). 4.05/4.34 cnf(c_0_14575, 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,esk254_2(X2,X1)))), inference(rw,[status(thm)],[c_0_9117, c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_14576, 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_9116]), ['final']). 4.05/4.34 cnf(c_0_14577, plain, (X4=X2|hAPP(hAPP(c_List_Oappend(X1),X2),X3)!=hAPP(hAPP(c_List_Oappend(X1),X4),X3)), inference(split_conjunct,[status(thm)],[c_0_9118]), ['final']). 4.05/4.34 cnf(c_0_14578, plain, (X4=X3|hAPP(hAPP(c_List_Oappend(X1),X2),X3)!=hAPP(hAPP(c_List_Oappend(X1),X2),X4)), inference(split_conjunct,[status(thm)],[c_0_9119]), ['final']). 4.05/4.34 cnf(c_0_14579, 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_6460]), ['final']). 4.05/4.34 cnf(c_0_14580, 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_9120]), ['final']). 4.05/4.34 cnf(c_0_14581, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))|~c_Wellfounded_Oacyclic(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9121]), ['final']). 4.05/4.34 cnf(c_0_14582, 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_9122]), ['final']). 4.05/4.34 cnf(c_0_14583, 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_8912]), ['final']). 4.05/4.34 cnf(c_0_14584, plain, (hAPP(X3,X4)=X5|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5)!=X3), inference(split_conjunct,[status(thm)],[c_0_9123]), ['final']). 4.05/4.34 cnf(c_0_14585, 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_9124]), ['final']). 4.05/4.34 cnf(c_0_14586, plain, (X2=c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9125]), ['final']). 4.05/4.34 cnf(c_0_14587, 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)))), inference(split_conjunct,[status(thm)],[c_0_7282]), ['final']). 4.05/4.34 cnf(c_0_14588, 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_8493]), ['final']). 4.05/4.34 cnf(c_0_14589, 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_7420]), ['final']). 4.05/4.34 cnf(c_0_14590, 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_7420]), ['final']). 4.05/4.34 cnf(c_0_14591, plain, (hAPP(X1,X2)=c_Option_Ooption_ONone(X3)|c_Option_Ooption_ONone(X3)!=hAPP(c_Map_Omap__add(X4,X3,X1,X5),X2)), inference(split_conjunct,[status(thm)],[c_0_8695]), ['final']). 4.05/4.34 cnf(c_0_14592, plain, (hAPP(X1,X2)=c_Option_Ooption_ONone(X3)|c_Option_Ooption_ONone(X3)!=hAPP(c_Map_Omap__add(X4,X3,X5,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_8695]), ['final']). 4.05/4.34 cnf(c_0_14593, plain, (hAPP(hAPP(X2,X4),X4)=X4|~c_Finite__Set_Ofolding__one__idem(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9126]), ['final']). 4.05/4.34 cnf(c_0_14594, 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_9127]), ['final']). 4.05/4.34 cnf(c_0_14595, 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_8124]), ['final']). 4.05/4.34 cnf(c_0_14596, 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_9128]), ['final']). 4.05/4.34 cnf(c_0_14597, plain, (hBOOL(hAPP(X3,X4))|X4=X2|~hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_6019]), ['final']). 4.05/4.34 cnf(c_0_14598, 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_9129]), ['final']). 4.05/4.34 cnf(c_0_14599, plain, (c_Orderings_Otop__class_Otop(X1)=X2|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)!=c_Orderings_Otop__class_Otop(X1)|~class_Lattices_Obounded__lattice__top(X1)), inference(split_conjunct,[status(thm)],[c_0_9129]), ['final']). 4.05/4.34 cnf(c_0_14600, plain, (hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_6019]), ['final']). 4.05/4.34 cnf(c_0_14601, 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_9130]), ['final']). 4.05/4.34 cnf(c_0_14602, 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_9131]), ['final']). 4.05/4.34 cnf(c_0_14603, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk528_2(X1,X2)),X2))), inference(split_conjunct,[status(thm)],[c_0_8771]), ['final']). 4.05/4.34 cnf(c_0_14604, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk132_2(X1,X2)),X2))), inference(split_conjunct,[status(thm)],[c_0_8772]), ['final']). 4.05/4.34 cnf(c_0_14605, plain, (c_Natural_Oevalc(c_Com_Ocom_OBODY(X1),X2,X3)|~c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9132]), ['final']). 4.05/4.34 cnf(c_0_14606, 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_9133]), ['final']). 4.05/4.34 cnf(c_0_14607, 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_9134]), ['final']). 4.05/4.34 cnf(c_0_14608, plain, (c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),esk241_2(X2,X1)),c_Wellfounded_Oacc(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_8929]), ['final']). 4.05/4.34 cnf(c_0_14609, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X2))=c_Groups_Osgn__class_Osgn(X1,X2)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_9135]), ['final']). 4.05/4.34 cnf(c_0_14610, 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_9136, c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_14611, plain, (X3=X2|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|~class_Int_Onumber__ring(X1)|~class_Int_Oring__char__0(X1)), inference(split_conjunct,[status(thm)],[c_0_9137]), ['final']). 4.05/4.34 cnf(c_0_14612, plain, (hBOOL(hAPP(c_Predicate_OPowp(X3,X1),X2))|~hBOOL(hAPP(X1,esk291_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8510]), ['final']). 4.05/4.34 cnf(c_0_14613, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_9138]), ['final']). 4.05/4.34 cnf(c_0_14614, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Oone__class_Oone(X1))|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_9139]), ['final']). 4.05/4.34 cnf(c_0_14615, plain, (hBOOL(hAPP(X1,X2))|X2=X3|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X4),X2,X5,X3)), inference(split_conjunct,[status(thm)],[c_0_8307]), ['final']). 4.05/4.34 cnf(c_0_14616, plain, (hBOOL(hAPP(c_List_Olistsp(X3,X1),X2))|~hBOOL(hAPP(X1,esk67_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8119]), ['final']). 4.05/4.34 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_9140]), ['final']). 4.05/4.34 cnf(c_0_14618, 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_8791]), ['final']). 4.05/4.34 cnf(c_0_14619, plain, (hAPP(c_List_Ofilter(X3,X1),X2)=X2|~hBOOL(hAPP(X1,esk373_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8143]), ['final']). 4.05/4.34 cnf(c_0_14620, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8462]), ['final']). 4.05/4.34 cnf(c_0_14621, 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_9141]), ['final']). 4.05/4.34 cnf(c_0_14622, 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_9142]), ['final']). 4.05/4.34 cnf(c_0_14623, 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_9143, c_0_4867]), ['final']). 4.05/4.34 cnf(c_0_14624, plain, (c_List_Olinorder__class_Osorted(X1,esk396_2(X2,X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_5537]), ['final']). 4.05/4.34 cnf(c_0_14625, 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_8949]), ['final']). 4.05/4.34 cnf(c_0_14626, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~c_Wellfounded_OwfP(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9144]), ['final']). 4.05/4.34 cnf(c_0_14627, plain, (X3=X2|hAPP(X1,X2)!=hAPP(X1,X3)|~c_Typedef_Otype__definition(X4,X5,X1,X6,X7)), inference(split_conjunct,[status(thm)],[c_0_9145]), ['final']). 4.05/4.34 cnf(c_0_14628, plain, (c_Random_Olog(X2,X1)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_7282]), ['final']). 4.05/4.34 cnf(c_0_14629, 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_9146]), ['final']). 4.05/4.34 cnf(c_0_14630, 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_8742]), ['final']). 4.05/4.34 cnf(c_0_14631, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),esk331_1(X1))))|~hBOOL(hAPP(X1,X2))), inference(rw,[status(thm)],[c_0_9147, c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_14632, 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_9148]), ['final']). 4.05/4.34 cnf(c_0_14633, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|~class_Rings_Oring__1__no__zero__divisors(X1)|c_Groups_Ozero__class_Ozero(X1)!=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_9149]), ['final']). 4.05/4.34 cnf(c_0_14634, 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_5576]), ['final']). 4.05/4.34 cnf(c_0_14635, 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_9150, c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_14636, 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_9148]), ['final']). 4.05/4.34 cnf(c_0_14637, plain, (c_Map_Omap__le(X1,X2,X4,X5)|~c_Map_Omap__le(X1,X2,c_Map_Omap__add(X1,X2,X3,X4),X5)), inference(split_conjunct,[status(thm)],[c_0_9151]), ['final']). 4.05/4.34 cnf(c_0_14638, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),esk157_1(X1))))), inference(rw,[status(thm)],[c_0_9152, c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_14639, plain, (c_Natural_Oevalc(X3,X2,X4)|~hBOOL(hAPP(X1,X2))|~c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5),X2,X4)), inference(split_conjunct,[status(thm)],[c_0_8851]), ['final']). 4.05/4.34 cnf(c_0_14640, plain, (X1=X2|hBOOL(hAPP(X3,X1))|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X4),X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8574]), ['final']). 4.05/4.34 cnf(c_0_14641, 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_9153]), ['final']). 4.05/4.34 cnf(c_0_14642, 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_9154]), ['final']). 4.05/4.34 cnf(c_0_14643, 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_9155]), ['final']). 4.05/4.34 cnf(c_0_14644, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))|c_Option_Ooption_ONone(X3)!=hAPP(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_8620]), ['final']). 4.05/4.34 cnf(c_0_14645, 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_9156, c_0_6133]), ['final']). 4.05/4.34 cnf(c_0_14646, 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_4955]), ['final']). 4.05/4.34 cnf(c_0_14647, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2)=X2|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_9157]), ['final']). 4.05/4.34 cnf(c_0_14648, 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_9158]), ['final']). 4.05/4.34 cnf(c_0_14649, 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_9159]), ['final']). 4.05/4.34 cnf(c_0_14650, 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_8770]), ['final']). 4.05/4.34 cnf(c_0_14651, 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_8770]), ['final']). 4.05/4.34 cnf(c_0_14652, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2)=X2|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9160]), ['final']). 4.05/4.34 cnf(c_0_14653, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2)=X2|~class_Lattices_Osemilattice__sup(X1)), inference(split_conjunct,[status(thm)],[c_0_9161]), ['final']). 4.05/4.34 cnf(c_0_14654, 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_8742]), ['final']). 4.05/4.34 cnf(c_0_14655, 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_9162]), ['final']). 4.05/4.34 cnf(c_0_14656, plain, (X2=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2)|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9163]), ['final']). 4.05/4.34 cnf(c_0_14657, 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_8438]), ['final']). 4.05/4.34 cnf(c_0_14658, 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_9164]), ['final']). 4.05/4.34 cnf(c_0_14659, plain, (X3=c_Groups_Ozero__class_Ozero(X1)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)!=X2|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)), inference(split_conjunct,[status(thm)],[c_0_5578]), ['final']). 4.05/4.34 cnf(c_0_14660, 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_9165]), ['final']). 4.05/4.34 cnf(c_0_14661, 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_9166]), ['final']). 4.05/4.34 cnf(c_0_14662, plain, (X2=X3|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_9167]), ['final']). 4.05/4.34 cnf(c_0_14663, plain, (X3=X2|hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)!=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_9168]), ['final']). 4.05/4.34 cnf(c_0_14664, 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_9169]), ['final']). 4.05/4.34 cnf(c_0_14665, 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_9170]), ['final']). 4.05/4.34 cnf(c_0_14666, 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_8827]), ['final']). 4.05/4.34 cnf(c_0_14667, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_8619]), ['final']). 4.05/4.34 cnf(c_0_14668, 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_9171]), ['final']). 4.05/4.34 cnf(c_0_14669, plain, (hBOOL(hAPP(X1,esk334_1(X1)))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))), inference(split_conjunct,[status(thm)],[c_0_8461]), ['final']). 4.05/4.34 cnf(c_0_14670, plain, (hBOOL(hAPP(X1,esk288_2(X2,X1)))|~hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_9172]), ['final']). 4.05/4.34 cnf(c_0_14671, plain, (X1=hAPP(c_Nat_OSuc,esk8_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_9173]), ['final']). 4.05/4.34 cnf(c_0_14672, 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_9174, c_0_4427]), ['final']). 4.05/4.34 cnf(c_0_14673, 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_9175]), ['final']). 4.05/4.34 cnf(c_0_14674, plain, (X2=X1|hAPP(X1,esk448_2(X2,X1))!=hAPP(X2,esk448_2(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_9176]), ['final']). 4.05/4.34 cnf(c_0_14675, plain, (c_Fun_Oinj__on(X4,X3,X2,X1)|esk462_4(X1,X2,X3,X4)!=esk463_4(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8415]), ['final']). 4.05/4.34 cnf(c_0_14676, 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_7274]), ['final']). 4.05/4.34 cnf(c_0_14677, 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_9177]), ['final']). 4.05/4.34 cnf(c_0_14678, 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_9178]), ['final']). 4.05/4.34 cnf(c_0_14679, 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_7274]), ['final']). 4.05/4.34 cnf(c_0_14680, 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_7507]), ['final']). 4.05/4.34 cnf(c_0_14681, plain, (c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X2))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9179]), ['final']). 4.05/4.34 cnf(c_0_14682, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X2),X1))|~hBOOL(hAPP(X1,esk336_2(X1,X2)))|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_9180]), ['final']). 4.05/4.34 cnf(c_0_14683, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X2),X1))|~hBOOL(hAPP(X1,esk52_2(X1,X2)))|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_9181]), ['final']). 4.05/4.34 cnf(c_0_14684, plain, (hBOOL(hAPP(X1,c_Option_Ooption_ONone(X2)))|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X2)),X1))|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_7942]), ['final']). 4.05/4.34 cnf(c_0_14685, plain, (c_Wellfounded_Owf(X1,c_Wellfounded_Omlex__prod(X1,X3,X2))|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9182]), ['final']). 4.05/4.34 cnf(c_0_14686, 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_9183]), ['final']). 4.05/4.34 cnf(c_0_14687, plain, (c_Orderings_Obot__class_Obot(X1)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_9184]), ['final']). 4.05/4.34 cnf(c_0_14688, 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_9185, c_0_4427]), ['final']). 4.05/4.34 cnf(c_0_14689, 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_9186, c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_14690, plain, (c_Enum_Oall__n__lists(X3,X1,X2)|~hBOOL(hAPP(X1,esk21_3(X2,X1,X3)))|~class_Enum_Oenum(X3)), inference(split_conjunct,[status(thm)],[c_0_7220]), ['final']). 4.05/4.34 cnf(c_0_14691, 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_9187]), ['final']). 4.05/4.34 cnf(c_0_14692, 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_9188]), ['final']). 4.05/4.34 cnf(c_0_14693, plain, (c_List_OtakeWhile(X3,X1,X2)=X2|~hBOOL(hAPP(X1,esk397_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8179]), ['final']). 4.05/4.34 cnf(c_0_14694, plain, (c_Option_Ooption_ONone(X1)=X4|hAPP(hAPP(c_Option_Omap(X1,X2),X3),X4)!=c_Option_Ooption_ONone(X2)), inference(split_conjunct,[status(thm)],[c_0_9189]), ['final']). 4.05/4.34 cnf(c_0_14695, 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_9190]), ['final']). 4.05/4.34 cnf(c_0_14696, 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_9191]), ['final']). 4.05/4.34 cnf(c_0_14697, 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_5612]), ['final']). 4.05/4.34 cnf(c_0_14698, plain, (X4=c_List_Olist_ONil(X2)|c_List_Olist_ONil(X1)!=hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)), inference(split_conjunct,[status(thm)],[c_0_9192]), ['final']). 4.05/4.34 cnf(c_0_14699, 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_9193]), ['final']). 4.05/4.34 cnf(c_0_14700, 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_9194]), ['final']). 4.05/4.34 cnf(c_0_14701, 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_9195]), ['final']). 4.05/4.34 cnf(c_0_14702, 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_9196]), ['final']). 4.05/4.34 cnf(c_0_14703, 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_9197]), ['final']). 4.05/4.34 cnf(c_0_14704, 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_9198]), ['final']). 4.05/4.34 cnf(c_0_14705, 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_9199]), ['final']). 4.05/4.34 cnf(c_0_14706, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_9200]), ['final']). 4.05/4.34 cnf(c_0_14707, 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_5591]), ['final']). 4.05/4.34 cnf(c_0_14708, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2)=X2|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9201]), ['final']). 4.05/4.34 cnf(c_0_14709, plain, (X2=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9202]), ['final']). 4.05/4.34 cnf(c_0_14710, 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)), inference(split_conjunct,[status(thm)],[c_0_8660]), ['final']). 4.05/4.34 cnf(c_0_14711, 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_9203]), ['final']). 4.05/4.34 cnf(c_0_14712, 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_5580]), ['final']). 4.05/4.34 cnf(c_0_14713, 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_9204]), ['final']). 4.05/4.34 cnf(c_0_14714, plain, (hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_9205]), ['final']). 4.05/4.34 cnf(c_0_14715, 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_9093]), ['final']). 4.05/4.34 cnf(c_0_14716, 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_9094]), ['final']). 4.05/4.34 cnf(c_0_14717, 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_9006]), ['final']). 4.05/4.34 cnf(c_0_14718, 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_9007]), ['final']). 4.05/4.34 cnf(c_0_14719, plain, (c_Groups_Ozero__class_Ozero(X1)=c_Divides_Odiv__class_Omod(X1,X2,X2)|~class_Divides_Osemiring__div(X1)), inference(split_conjunct,[status(thm)],[c_0_9206]), ['final']). 4.05/4.34 cnf(c_0_14720, 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_9207]), ['final']). 4.05/4.34 cnf(c_0_14721, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X2),X2))|~class_HOL_Oequal(X1)), inference(split_conjunct,[status(thm)],[c_0_9208]), ['final']). 4.05/4.34 cnf(c_0_14722, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))|~class_Orderings_Opreorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9209]), ['final']). 4.05/4.34 cnf(c_0_14723, 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_9102]), ['final']). 4.05/4.34 cnf(c_0_14724, plain, (X1=X2|c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X1)!=c_Nitpick_Opair__box_OPairBox(X3,X4,X6,X2)), inference(split_conjunct,[status(thm)],[c_0_9207]), ['final']). 4.05/4.34 cnf(c_0_14725, 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_9210]), ['final']). 4.05/4.34 cnf(c_0_14726, 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_9210]), ['final']). 4.05/4.34 cnf(c_0_14727, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_9211]), ['final']). 4.05/4.34 cnf(c_0_14728, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_9211]), ['final']). 4.05/4.34 cnf(c_0_14729, 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_9212]), ['final']). 4.05/4.34 cnf(c_0_14730, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Ozero__class_Ozero(X1)!=hAPP(c_Groups_Oabs__class_Oabs(X1),X2)|~class_Groups_Oordered__ab__group__add__abs(X1)), inference(split_conjunct,[status(thm)],[c_0_9213]), ['final']). 4.05/4.34 cnf(c_0_14731, plain, (X3=X4|~c_Map_Omap__le(X1,X2,X3,X4)|~c_Map_Omap__le(X1,X2,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_9214]), ['final']). 4.05/4.34 cnf(c_0_14732, 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_9215]), ['final']). 4.05/4.34 cnf(c_0_14733, 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_9216]), ['final']). 4.05/4.34 cnf(c_0_14734, 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),X2),X1)), inference(split_conjunct,[status(thm)],[c_0_9217]), ['final']). 4.05/4.34 cnf(c_0_14735, 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)),esk100_1(X1)))), inference(split_conjunct,[status(thm)],[c_0_8595]), ['final']). 4.05/4.34 cnf(c_0_14736, plain, (c_Wellfounded_OwfP(X1,X2)|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk129_2(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_9144]), ['final']). 4.05/4.34 cnf(c_0_14737, 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_9218]), ['final']). 4.05/4.34 cnf(c_0_14738, plain, (c_Natural_Oevalc(X1,X2,X4)|~c_Natural_Oevaln(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_9058]), ['final']). 4.05/4.34 cnf(c_0_14739, plain, (X3=X2|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X2),X3))|~class_HOL_Oequal(X1)), inference(split_conjunct,[status(thm)],[c_0_9219]), ['final']). 4.05/4.34 cnf(c_0_14740, 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_8852]), ['final']). 4.05/4.34 cnf(c_0_14741, plain, (c_List_Olist__all(X3,X1,X2)|~hBOOL(hAPP(X1,esk138_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8197]), ['final']). 4.05/4.34 cnf(c_0_14742, plain, (c_List_Olist__all(X3,X1,X2)|~hBOOL(hAPP(X1,esk92_3(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_8200]), ['final']). 4.05/4.34 cnf(c_0_14743, plain, (c_List_Olist__all(X3,X1,X2)|~hBOOL(hAPP(X1,esk66_3(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_8192]), ['final']). 4.05/4.34 cnf(c_0_14744, 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_9220]), ['final']). 4.05/4.34 cnf(c_0_14745, 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_9221]), ['final']). 4.05/4.34 cnf(c_0_14746, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X3,X2,X1)))|~hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,X2))), inference(split_conjunct,[status(thm)],[c_0_9222]), ['final']). 4.05/4.34 cnf(c_0_14747, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~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_9223]), ['final']). 4.05/4.34 cnf(c_0_14748, plain, (hBOOL(hAPP(c_List_Odistinct(X2),X1))|esk54_2(X1,X2)!=esk55_2(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_7772]), ['final']). 4.05/4.34 cnf(c_0_14749, 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_9224]), ['final']). 4.05/4.34 cnf(c_0_14750, 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_9103]), ['final']). 4.05/4.34 cnf(c_0_14751, 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_9104]), ['final']). 4.05/4.34 cnf(c_0_14752, plain, (X4=X3|~c_Natural_Oevalc(X1,X2,X3)|~c_Natural_Oevalc(X1,X2,X4)), inference(split_conjunct,[status(thm)],[c_0_9225]), ['final']). 4.05/4.34 cnf(c_0_14753, plain, (X3=X2|hAPP(c_List_Orev(X1),X2)!=hAPP(c_List_Orev(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_9226]), ['final']). 4.05/4.34 cnf(c_0_14754, plain, (X2=X3|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(c_Option_Ooption_OSome(X1),X3)), inference(split_conjunct,[status(thm)],[c_0_9227]), ['final']). 4.05/4.34 cnf(c_0_14755, plain, (X2=c_List_Olist_ONil(X1)|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_9228]), ['final']). 4.05/4.34 cnf(c_0_14756, plain, (c_Groups_Ozero__class_Ozero(X2)=X1|X1!=hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1)|~class_Groups_Olinordered__ab__group__add(X2)), inference(split_conjunct,[status(thm)],[c_0_5592]), ['final']). 4.05/4.34 cnf(c_0_14757, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Wellfounded_Omax__extp(X1,X3,X2,X4)), inference(split_conjunct,[status(thm)],[c_0_5611]), ['final']). 4.05/4.34 cnf(c_0_14758, 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_9229]), ['final']). 4.05/4.34 cnf(c_0_14759, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X2,X1,X3)))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X1)))), inference(split_conjunct,[status(thm)],[c_0_9230]), ['final']). 4.05/4.34 cnf(c_0_14760, plain, (hBOOL(hAPP(hAPP(X2,X3),X3))|~c_Predicate_Oreflp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9231]), ['final']). 4.05/4.34 cnf(c_0_14761, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Wellfounded_Omax__extp(X1,X3,X4,X2)), inference(split_conjunct,[status(thm)],[c_0_5611]), ['final']). 4.05/4.34 cnf(c_0_14762, plain, (X2=c_List_Olist_ONil(X1)|hAPP(c_List_Oset(X1),X2)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_9232]), ['final']). 4.05/4.34 cnf(c_0_14763, plain, (hBOOL(hAPP(hAPP(X2,X3),X3))|~c_Equiv__Relations_Oequivp(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9233]), ['final']). 4.05/4.34 cnf(c_0_14764, plain, (hBOOL(hAPP(hAPP(c_member(X3),X2),X1))|~hBOOL(hAPP(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_9234]), ['final']). 4.05/4.34 cnf(c_0_14765, plain, (c_List_Olist_ONil(tc_List_Olist(X1))=c_List_Otranspose(X1,X2)|c_List_Olist_ONil(X1)!=esk91_2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_8036]), ['final']). 4.05/4.34 cnf(c_0_14766, 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_9235]), ['final']). 4.05/4.34 cnf(c_0_14767, 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_6018]), ['final']). 4.05/4.34 cnf(c_0_14768, 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_9236]), ['final']). 4.05/4.34 cnf(c_0_14769, 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_9237]), ['final']). 4.05/4.34 cnf(c_0_14770, 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_9238]), ['final']). 4.05/4.34 cnf(c_0_14771, 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_9239]), ['final']). 4.05/4.34 cnf(c_0_14772, 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_9181]), ['final']). 4.05/4.34 cnf(c_0_14773, 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_9240]), ['final']). 4.05/4.34 cnf(c_0_14774, 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_9241]), ['final']). 4.05/4.34 cnf(c_0_14775, plain, (c_Relation_Ototal__on(X3,X2,X1)|esk416_3(X1,X2,X3)!=esk417_3(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_6410]), ['final']). 4.05/4.34 cnf(c_0_14776, plain, (c_Relation_Osingle__valued(X3,X2,X1)|esk79_3(X1,X2,X3)!=esk80_3(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_7181]), ['final']). 4.05/4.34 cnf(c_0_14777, 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_9242]), ['final']). 4.05/4.34 cnf(c_0_14778, plain, (X1=X2|c_Com_Ocom_OLocal(X2,X3,X4)!=c_Com_Ocom_OLocal(X1,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_9243]), ['final']). 4.05/4.34 cnf(c_0_14779, plain, (X1=X2|c_Com_Ocom_OLocal(X3,X1,X4)!=c_Com_Ocom_OLocal(X5,X2,X6)), inference(split_conjunct,[status(thm)],[c_0_9243]), ['final']). 4.05/4.34 cnf(c_0_14780, plain, (X1=X2|c_Com_Ocom_OLocal(X3,X4,X2)!=c_Com_Ocom_OLocal(X5,X6,X1)), inference(split_conjunct,[status(thm)],[c_0_9243]), ['final']). 4.05/4.34 cnf(c_0_14781, plain, (X1=X2|c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X2,X4)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X1,X5)), inference(split_conjunct,[status(thm)],[c_0_9244]), ['final']). 4.05/4.34 cnf(c_0_14782, plain, (c_Orderings_Oord_Omax(X1,c_Orderings_Oord__class_Oless__eq(X1))=c_Orderings_Oord__class_Omax(X1)|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_9245]), ['final']). 4.05/4.34 cnf(c_0_14783, plain, (X3=c_List_Olist_ONil(X1)|hAPP(hAPP(c_List_Oappend(X1),X2),X3)!=X2), inference(split_conjunct,[status(thm)],[c_0_9246]), ['final']). 4.05/4.34 cnf(c_0_14784, plain, (X3=c_List_Olist_ONil(X2)|X1!=hAPP(hAPP(c_List_Oappend(X2),X3),X1)), inference(split_conjunct,[status(thm)],[c_0_9247]), ['final']). 4.05/4.34 cnf(c_0_14785, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2|X1!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9248]), ['final']). 4.05/4.34 cnf(c_0_14786, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_Enum_Oenum__class_Oenum(X1)))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_9249]), ['final']). 4.05/4.34 cnf(c_0_14787, 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_9244]), ['final']). 4.05/4.34 cnf(c_0_14788, plain, (X1=X2|c_List_Oreplicate(X3,X2,X4)!=c_List_Oreplicate(X3,X1,X5)), inference(split_conjunct,[status(thm)],[c_0_9108]), ['final']). 4.05/4.34 cnf(c_0_14789, plain, (X1=X2|c_Com_Ocom_OCall(X2,X3,X4)!=c_Com_Ocom_OCall(X1,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_9250]), ['final']). 4.05/4.34 cnf(c_0_14790, plain, (X1=X2|c_Com_Ocom_OCall(X3,X2,X4)!=c_Com_Ocom_OCall(X5,X1,X6)), inference(split_conjunct,[status(thm)],[c_0_9250]), ['final']). 4.05/4.34 cnf(c_0_14791, plain, (c_Orderings_Oord__class_Omin(X1)=c_Orderings_Oord_Omin(X1,c_Orderings_Oord__class_Oless__eq(X1))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_9251]), ['final']). 4.05/4.34 cnf(c_0_14792, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=esk444_1(X1)), inference(split_conjunct,[status(thm)],[c_0_8490]), ['final']). 4.05/4.34 cnf(c_0_14793, plain, (X1=X2|c_Com_Ocom_OCall(X3,X4,X2)!=c_Com_Ocom_OCall(X5,X6,X1)), inference(split_conjunct,[status(thm)],[c_0_9250]), ['final']). 4.05/4.34 cnf(c_0_14794, plain, (X1=X2|c_Com_Ocom_OCond(X1,X3,X4)!=c_Com_Ocom_OCond(X2,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_9252]), ['final']). 4.05/4.34 cnf(c_0_14795, plain, (X1=X2|c_Com_Ocom_OCond(X3,X2,X4)!=c_Com_Ocom_OCond(X5,X1,X6)), inference(split_conjunct,[status(thm)],[c_0_9252]), ['final']). 4.05/4.34 cnf(c_0_14796, plain, (X1=X2|c_Com_Ocom_OCond(X3,X4,X1)!=c_Com_Ocom_OCond(X5,X6,X2)), inference(split_conjunct,[status(thm)],[c_0_9252]), ['final']). 4.05/4.34 cnf(c_0_14797, plain, (X2=c_List_Oremdups(X1,X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9253]), ['final']). 4.05/4.34 cnf(c_0_14798, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,esk385_2(X2,X1))))), inference(split_conjunct,[status(thm)],[c_0_8245]), ['final']). 4.05/4.34 cnf(c_0_14799, 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_9254]), ['final']). 4.05/4.34 cnf(c_0_14800, plain, (hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk244_1(X1))=hAPP(c_Com_Obody,X1)|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X1)))), inference(split_conjunct,[status(thm)],[c_0_9255]), ['final']). 4.05/4.34 cnf(c_0_14801, plain, (hAPP(c_Com_Obody,X1)=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk94_1(X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X1)))), inference(split_conjunct,[status(thm)],[c_0_9256]), ['final']). 4.05/4.34 cnf(c_0_14802, 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)), inference(split_conjunct,[status(thm)],[c_0_9257]), ['final']). 4.05/4.34 cnf(c_0_14803, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|~class_Rings_Oring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9258]), ['final']). 4.05/4.34 cnf(c_0_14804, 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_9259]), ['final']). 4.05/4.34 cnf(c_0_14805, plain, (c_Groups_Oone__class_Oone(X1)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~class_Rings_Osemiring__1(X1)), inference(split_conjunct,[status(thm)],[c_0_9260]), ['final']). 4.05/4.34 cnf(c_0_14806, plain, (~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2))), inference(er,[status(thm)],[c_0_9261]), ['final']). 4.05/4.34 cnf(c_0_14807, plain, (X2=X3|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3)))), inference(split_conjunct,[status(thm)],[c_0_6020]), ['final']). 4.05/4.34 cnf(c_0_14808, plain, (~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2))), inference(er,[status(thm)],[c_0_9262]), ['final']). 4.05/4.34 cnf(c_0_14809, plain, (class_Smallcheck_Osmall(tc_prod(X2,X1))|~class_Smallcheck_Osmall(X1)|~class_Smallcheck_Osmall(X2)), inference(split_conjunct,[status(thm)],[c_0_9263]), ['final']). 4.05/4.34 cnf(c_0_14810, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X2,X3,X1)))|~hBOOL(hAPP(c_Com_OWT,X1))), inference(split_conjunct,[status(thm)],[c_0_9264]), ['final']). 4.05/4.34 cnf(c_0_14811, 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_9265]), ['final']). 4.05/4.34 cnf(c_0_14812, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|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_9266]), ['final']). 4.05/4.34 cnf(c_0_14813, plain, (class_HOL_Oequal(tc_fun(X2,X1))|~class_HOL_Oequal(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_9267]), ['final']). 4.05/4.34 cnf(c_0_14814, 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_9268]), ['final']). 4.05/4.34 cnf(c_0_14815, 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_9269]), ['final']). 4.05/4.34 cnf(c_0_14816, plain, (class_Finite__Set_Ofinite(tc_fun(X2,X1))|~class_Finite__Set_Ofinite(X1)|~class_Finite__Set_Ofinite(X2)), inference(split_conjunct,[status(thm)],[c_0_9270]), ['final']). 4.05/4.34 cnf(c_0_14817, 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_9271]), ['final']). 4.05/4.34 cnf(c_0_14818, 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_9272]), ['final']). 4.05/4.34 cnf(c_0_14819, plain, (class_Enum_Oenum(tc_sum(X2,X1))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_9273]), ['final']). 4.05/4.34 cnf(c_0_14820, plain, (class_Enum_Oenum(tc_prod(X2,X1))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_9274]), ['final']). 4.05/4.34 cnf(c_0_14821, plain, (class_Enum_Oenum(tc_fun(X2,X1))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)), inference(split_conjunct,[status(thm)],[c_0_9275]), ['final']). 4.05/4.34 cnf(c_0_14822, plain, (~class_Orderings_Olinorder(X1)|c_List_Olist_ONil(X2)!=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_9276]), ['final']). 4.05/4.34 cnf(c_0_14823, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9121]), ['final']). 4.05/4.34 cnf(c_0_14824, 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_9254]), ['final']). 4.05/4.34 cnf(c_0_14825, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Finite__Set_Ofinite(X1)), inference(split_conjunct,[status(thm)],[c_0_9277]), ['final']). 4.05/4.34 cnf(c_0_14826, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X1)))|hAPP(c_Com_Obody,X1)!=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X2)), inference(split_conjunct,[status(thm)],[c_0_9256]), ['final']). 4.05/4.34 cnf(c_0_14827, plain, (X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Olist_ONil(X1)!=c_List_Oreplicate(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9278]), ['final']). 4.05/4.34 cnf(c_0_14828, plain, (X2=c_Groups_Ozero__class_Ozero(X1)|c_Groups_Osgn__class_Osgn(X1,X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1)), inference(split_conjunct,[status(thm)],[c_0_5593]), ['final']). 4.05/4.34 cnf(c_0_14829, plain, (X2=c_Option_Ooption_ONone(X1)|c_Option_Oset(X1,X2)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_9279]), ['final']). 4.05/4.34 cnf(c_0_14830, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|c_List_Oremdups(X1,X2)!=X2), inference(split_conjunct,[status(thm)],[c_0_9280]), ['final']). 4.05/4.34 cnf(c_0_14831, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X2,X1)))|~hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,X2))), inference(split_conjunct,[status(thm)],[c_0_9281]), ['final']). 4.05/4.34 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_9282]), ['final']). 4.05/4.34 cnf(c_0_14833, plain, (c_List_Olist_ONil(X1)=X2|c_List_Olist_ONil(X1)!=hAPP(c_List_Orev(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9283]), ['final']). 4.05/4.34 cnf(c_0_14834, 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_8791]), ['final']). 4.05/4.34 cnf(c_0_14835, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X2)))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_9284]), ['final']). 4.05/4.34 cnf(c_0_14836, 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_9265]), ['final']). 4.05/4.34 cnf(c_0_14837, plain, (hBOOL(hAPP(X3,X2))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9234]), ['final']). 4.05/4.34 cnf(c_0_14838, plain, (c_Wellfounded_Owf(X1,X2)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=esk211_2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_7546]), ['final']). 4.05/4.34 cnf(c_0_14839, plain, (class_Lattices_Obounded__lattice__bot(tc_fun(X2,X1))|~class_Lattices_Obounded__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9285]), ['final']). 4.05/4.34 cnf(c_0_14840, plain, (hBOOL(hAPP(hAPP(c_fconj,X1),X2))|~hBOOL(X1)|~hBOOL(X2)), inference(split_conjunct,[status(thm)],[c_0_9286]), ['final']). 4.05/4.34 cnf(c_0_14841, plain, (class_Orderings_Obot(tc_fun(X2,X1))|~class_Orderings_Obot(X1)), inference(split_conjunct,[status(thm)],[c_0_9287]), ['final']). 4.05/4.34 cnf(c_0_14842, plain, (class_Lattices_Odistrib__lattice(tc_fun(X2,X1))|~class_Lattices_Odistrib__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9288]), ['final']). 4.05/4.34 cnf(c_0_14843, plain, (class_Groups_Ouminus(tc_fun(X2,X1))|~class_Groups_Ouminus(X1)), inference(split_conjunct,[status(thm)],[c_0_9289]), ['final']). 4.05/4.34 cnf(c_0_14844, plain, (class_Lattices_Obounded__lattice__top(tc_fun(X2,X1))|~class_Lattices_Obounded__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9290]), ['final']). 4.05/4.34 cnf(c_0_14845, plain, (class_Lattices_Obounded__lattice(tc_fun(X2,X1))|~class_Lattices_Obounded__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9291]), ['final']). 4.05/4.34 cnf(c_0_14846, plain, (class_Groups_Ominus(tc_fun(X2,X1))|~class_Groups_Ominus(X1)), inference(split_conjunct,[status(thm)],[c_0_9292]), ['final']). 4.05/4.34 cnf(c_0_14847, plain, (class_Lattices_Oboolean__algebra(tc_fun(X2,X1))|~class_Lattices_Oboolean__algebra(X1)), inference(split_conjunct,[status(thm)],[c_0_9293]), ['final']). 4.05/4.34 cnf(c_0_14848, plain, (class_Orderings_Otop(tc_fun(X2,X1))|~class_Orderings_Otop(X1)), inference(split_conjunct,[status(thm)],[c_0_9294]), ['final']). 4.05/4.34 cnf(c_0_14849, plain, (class_Orderings_Opreorder(tc_fun(X2,X1))|~class_Orderings_Opreorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9295]), ['final']). 4.05/4.34 cnf(c_0_14850, plain, (class_Orderings_Oorder(tc_fun(X2,X1))|~class_Orderings_Oorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9296]), ['final']). 4.05/4.34 cnf(c_0_14851, plain, (class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))|~class_Complete__Lattice_Ocomplete__lattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9297]), ['final']). 4.05/4.34 cnf(c_0_14852, plain, (class_Lattices_Osemilattice__inf(tc_fun(X2,X1))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9298]), ['final']). 4.05/4.34 cnf(c_0_14853, 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_9299, c_0_4427]), ['final']). 4.05/4.34 cnf(c_0_14854, plain, (class_Orderings_Oord(tc_fun(X2,X1))|~class_Orderings_Oord(X1)), inference(split_conjunct,[status(thm)],[c_0_9300]), ['final']). 4.05/4.34 cnf(c_0_14855, plain, (class_Lattices_Osemilattice__sup(tc_fun(X2,X1))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9301]), ['final']). 4.05/4.34 cnf(c_0_14856, plain, (class_Lattices_Olattice(tc_fun(X2,X1))|~class_Lattices_Olattice(X1)), inference(split_conjunct,[status(thm)],[c_0_9302]), ['final']). 4.05/4.34 cnf(c_0_14857, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9303]), ['final']). 4.05/4.34 cnf(c_0_14858, plain, (~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2))), inference(split_conjunct,[status(thm)],[c_0_9304]), ['final']). 4.05/4.34 cnf(c_0_14859, plain, (c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Osemiring__1(X1)), inference(er,[status(thm)],[c_0_9305]), ['final']). 4.05/4.34 cnf(c_0_14860, 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_9306]), ['final']). 4.05/4.34 cnf(c_0_14861, plain, (hBOOL(X1)|hBOOL(hAPP(hAPP(c_fimplies,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9307]), ['final']). 4.05/4.34 cnf(c_0_14862, plain, (X1=X2|hAPP(c_Int_ORep__Integ,X1)!=hAPP(c_Int_ORep__Integ,X2)), inference(split_conjunct,[status(thm)],[c_0_9308]), ['final']). 4.05/4.34 cnf(c_0_14863, plain, (X1=X2|c_Com_Ocom_OSemi(X1,X3)!=c_Com_Ocom_OSemi(X2,X4)), inference(split_conjunct,[status(thm)],[c_0_9309]), ['final']). 4.05/4.34 cnf(c_0_14864, plain, (X1=X2|c_Com_Ocom_OSemi(X3,X2)!=c_Com_Ocom_OSemi(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_9309]), ['final']). 4.05/4.34 cnf(c_0_14865, plain, (X1=X2|c_Com_Ocom_OWhile(X1,X3)!=c_Com_Ocom_OWhile(X2,X4)), inference(split_conjunct,[status(thm)],[c_0_9310]), ['final']). 4.05/4.34 cnf(c_0_14866, plain, (X2=X1|hAPP(c_Code__Numeral_Onat__of,X1)!=hAPP(c_Code__Numeral_Onat__of,X2)), inference(split_conjunct,[status(thm)],[c_0_9311]), ['final']). 4.05/4.34 cnf(c_0_14867, 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_9312, c_0_5379]), c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_14868, plain, (X1=X2|c_Com_Ocom_OWhile(X3,X2)!=c_Com_Ocom_OWhile(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_9310]), ['final']). 4.05/4.34 cnf(c_0_14869, plain, (X2=c_List_Olist_ONil(X1)|c_List_Olist_ONil(X1)!=c_List_Oremdups(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9313]), ['final']). 4.05/4.34 cnf(c_0_14870, plain, (X2=X1|hAPP(c_Nat_OSuc,X1)!=hAPP(c_Nat_OSuc,X2)), inference(split_conjunct,[status(thm)],[c_0_9314]), ['final']). 4.05/4.34 cnf(c_0_14871, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X2,X1)))|~hBOOL(hAPP(c_Com_OWT,X1))), inference(split_conjunct,[status(thm)],[c_0_9315]), ['final']). 4.05/4.34 cnf(c_0_14872, plain, (c_Option_Ooption_ONone(tc_Com_Ocom)=hAPP(c_Com_Obody,X1)|hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X1)))), inference(split_conjunct,[status(thm)],[c_0_9316]), ['final']). 4.05/4.34 cnf(c_0_14873, 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_9188]), ['final']). 4.05/4.34 cnf(c_0_14874, plain, (hBOOL(hAPP(hAPP(c_fdisj,X1),X2))|~hBOOL(X1)), inference(split_conjunct,[status(thm)],[c_0_9317]), ['final']). 4.05/4.34 cnf(c_0_14875, plain, (hBOOL(hAPP(hAPP(c_fdisj,X2),X1))|~hBOOL(X1)), inference(split_conjunct,[status(thm)],[c_0_9318]), ['final']). 4.05/4.34 cnf(c_0_14876, plain, (hBOOL(hAPP(hAPP(c_fimplies,X1),X2))|~hBOOL(X2)), inference(split_conjunct,[status(thm)],[c_0_9319]), ['final']). 4.05/4.34 cnf(c_0_14877, 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_5597]), ['final']). 4.05/4.34 cnf(c_0_14878, plain, (X3=X2|~c_List_Olist__all2(X1,X1,c_fequal,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_6024]), ['final']). 4.05/4.34 cnf(c_0_14879, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_9320]), ['final']). 4.05/4.34 cnf(c_0_14880, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_9320]), ['final']). 4.05/4.34 cnf(c_0_14881, plain, (c_Orderings_Oord__class_Omin(X1)=c_Lattices_Osemilattice__inf__class_Oinf(X1)|~class_Orderings_Olinorder(X1)|~class_Lattices_Osemilattice__inf(X1)), inference(split_conjunct,[status(thm)],[c_0_9321]), ['final']). 4.05/4.34 cnf(c_0_14882, plain, (c_Lattices_Osemilattice__sup__class_Osup(X1)=c_Orderings_Oord__class_Omax(X1)|~class_Lattices_Osemilattice__sup(X1)|~class_Orderings_Olinorder(X1)), inference(split_conjunct,[status(thm)],[c_0_9322]), ['final']). 4.05/4.34 cnf(c_0_14883, plain, (hBOOL(hAPP(c_Com_OWT,X3))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X1,X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_9323]), ['final']). 4.05/4.34 cnf(c_0_14884, 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_9324]), ['final']). 4.05/4.34 cnf(c_0_14885, 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_9306]), ['final']). 4.05/4.34 cnf(c_0_14886, plain, (hBOOL(X1)|hBOOL(X2)|~hBOOL(hAPP(hAPP(c_fdisj,X2),X1))), inference(split_conjunct,[status(thm)],[c_0_9325]), ['final']). 4.05/4.34 cnf(c_0_14887, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Wellfounded_Owf(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9326]), ['final']). 4.05/4.34 cnf(c_0_14888, plain, (c_Option_Ooption_ONone(X1)=X2|~c_Option_Ois__none(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9327]), ['final']). 4.05/4.34 cnf(c_0_14889, plain, (class_Finite__Set_Ofinite(tc_Option_Ooption(X1))|~class_Finite__Set_Ofinite(X1)), inference(split_conjunct,[status(thm)],[c_0_9328]), ['final']). 4.05/4.34 cnf(c_0_14890, plain, (hBOOL(hAPP(c_Com_OWT,X1))|hAPP(c_Com_Obody,X2)!=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9329, c_0_7972])]), ['final']). 4.05/4.34 cnf(c_0_14891, plain, (class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X1))|~class_Lazy__Sequence_Osmall__lazy(X1)), inference(split_conjunct,[status(thm)],[c_0_9330]), ['final']). 4.05/4.34 cnf(c_0_14892, plain, (class_Enum_Oenum(tc_Option_Ooption(X1))|~class_Enum_Oenum(X1)), inference(split_conjunct,[status(thm)],[c_0_9331]), ['final']). 4.05/4.34 cnf(c_0_14893, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_fequal,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9332]), ['final']). 4.05/4.34 cnf(c_0_14894, plain, (hBOOL(X1)|~hBOOL(X2)|~hBOOL(hAPP(hAPP(c_fimplies,X2),X1))), inference(split_conjunct,[status(thm)],[c_0_9333]), ['final']). 4.05/4.34 cnf(c_0_14895, plain, (X1=X2|c_Com_Ocom_OBODY(X1)!=c_Com_Ocom_OBODY(X2)), inference(split_conjunct,[status(thm)],[c_0_9334]), ['final']). 4.05/4.34 cnf(c_0_14896, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_9281]), ['final']). 4.05/4.34 cnf(c_0_14897, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Nitpick_Owf_H(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8791]), ['final']). 4.05/4.34 cnf(c_0_14898, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X2,X1)))), inference(split_conjunct,[status(thm)],[c_0_9281]), ['final']). 4.05/4.34 cnf(c_0_14899, plain, (hBOOL(hAPP(c_Com_OWT,X2))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_9335]), ['final']). 4.05/4.34 cnf(c_0_14900, plain, (c_fequal=c_HOL_Oequal__class_Oequal(X1)|~class_HOL_Oequal(X1)), inference(split_conjunct,[status(thm)],[c_0_9336]), ['final']). 4.05/4.34 cnf(c_0_14901, plain, (hBOOL(hAPP(c_fNot,X1))|hBOOL(X1)), inference(split_conjunct,[status(thm)],[c_0_9337]), ['final']). 4.05/4.34 cnf(c_0_14902, plain, (hBOOL(X1)|~hBOOL(hAPP(hAPP(c_fconj,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9338]), ['final']). 4.05/4.34 cnf(c_0_14903, plain, (hBOOL(X2)|~hBOOL(hAPP(hAPP(c_fconj,X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9339]), ['final']). 4.05/4.34 cnf(c_0_14904, plain, (~class_Rings_Osemiring__1(X1)|~c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1))), inference(split_conjunct,[status(thm)],[c_0_9340]), ['final']). 4.05/4.34 cnf(c_0_14905, plain, (~class_Rings_Ozero__neq__one(X1)|c_Groups_Oone__class_Oone(X1)!=c_Groups_Ozero__class_Ozero(X1)), inference(split_conjunct,[status(thm)],[c_0_9341]), ['final']). 4.05/4.34 cnf(c_0_14906, plain, (~hBOOL(hAPP(c_fNot,X1))|~hBOOL(X1)), inference(split_conjunct,[status(thm)],[c_0_9342]), ['final']). 4.05/4.34 cnf(c_0_14907, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9343, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4795]), ['final']). 4.05/4.34 cnf(c_0_14908, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9344, c_0_4795]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), ['final']). 4.05/4.34 cnf(c_0_14909, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))), inference(rw,[status(thm)],[c_0_9345, c_0_5796]), ['final']). 4.05/4.34 cnf(c_0_14910, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))), inference(rw,[status(thm)],[c_0_9346, c_0_5796]), ['final']). 4.05/4.34 cnf(c_0_14911, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))), inference(rw,[status(thm)],[c_0_9347, c_0_5796]), ['final']). 4.05/4.34 cnf(c_0_14912, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)!=c_Int_OMin), inference(rw,[status(thm)],[c_0_9348, c_0_5796]), ['final']). 4.05/4.34 cnf(c_0_14913, 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_9349]), ['final']). 4.05/4.34 cnf(c_0_14914, 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_9350]), ['final']). 4.05/4.34 cnf(c_0_14915, 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_9351]), ['final']). 4.05/4.34 cnf(c_0_14916, 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_9352]), ['final']). 4.05/4.34 cnf(c_0_14917, 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_9353]), ['final']). 4.05/4.34 cnf(c_0_14918, 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_9354]), ['final']). 4.05/4.34 cnf(c_0_14919, 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_9355]), ['final']). 4.05/4.34 cnf(c_0_14920, 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_9356]), ['final']). 4.05/4.34 cnf(c_0_14921, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))), inference(rw,[status(thm)],[c_0_9357, c_0_4795]), ['final']). 4.05/4.34 cnf(c_0_14922, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_9358, c_0_4795]), ['final']). 4.05/4.34 cnf(c_0_14923, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_9359, c_0_4795]), ['final']). 4.05/4.34 cnf(c_0_14924, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5))!=hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))), inference(split_conjunct,[status(thm)],[c_0_9360]), ['final']). 4.05/4.34 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)),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_9361]), ['final']). 4.05/4.34 cnf(c_0_14926, 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_9362]), ['final']). 4.05/4.34 cnf(c_0_14927, 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_9363]), ['final']). 4.05/4.34 cnf(c_0_14928, 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_9364, c_0_5379]), c_0_7655])]), ['final']). 4.05/4.34 cnf(c_0_14929, 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_9365]), ['final']). 4.05/4.34 cnf(c_0_14930, 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_9366]), ['final']). 4.05/4.34 cnf(c_0_14931, 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_9367]), ['final']). 4.05/4.34 cnf(c_0_14932, 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_9368]), ['final']). 4.05/4.34 cnf(c_0_14933, 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_9369, c_0_4523])]), ['final']). 4.05/4.34 cnf(c_0_14934, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2))), inference(er,[status(thm)],[c_0_9370]), ['final']). 4.05/4.34 cnf(c_0_14935, 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_9371]), ['final']). 4.05/4.34 cnf(c_0_14936, 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_9372]), ['final']). 4.05/4.34 cnf(c_0_14937, 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_9373]), ['final']). 4.05/4.34 cnf(c_0_14938, 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_9374]), ['final']). 4.05/4.34 cnf(c_0_14939, 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_9375]), ['final']). 4.05/4.34 cnf(c_0_14940, 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_9376]), ['final']). 4.05/4.34 cnf(c_0_14941, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))!=hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_9377]), ['final']). 4.05/4.34 cnf(c_0_14942, 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_9378]), ['final']). 4.05/4.34 cnf(c_0_14943, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1))), inference(er,[status(thm)],[c_0_9379]), ['final']). 4.05/4.34 cnf(c_0_14944, 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_9380]), ['final']). 4.05/4.34 cnf(c_0_14945, plain, (c_Com_Ocom_OCall(X1,X2,X3)!=c_Com_Ocom_OLocal(X4,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_9381]), ['final']). 4.05/4.34 cnf(c_0_14946, plain, (c_Com_Ocom_OCond(X1,X2,X3)!=c_Com_Ocom_OLocal(X4,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_9382]), ['final']). 4.05/4.34 cnf(c_0_14947, plain, (c_Com_Ocom_OCond(X1,X2,X3)!=c_Com_Ocom_OCall(X4,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_9383]), ['final']). 4.05/4.34 cnf(c_0_14948, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_9384]), ['final']). 4.05/4.34 cnf(c_0_14949, 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_9385, c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_14950, plain, (c_List_Olist_ONil(X1)!=hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_9386]), ['final']). 4.05/4.34 cnf(c_0_14951, 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_9387]), ['final']). 4.05/4.34 cnf(c_0_14952, plain, (c_Com_Ocom_OCond(X1,X2,X3)!=c_Com_Ocom_OWhile(X4,X5)), inference(split_conjunct,[status(thm)],[c_0_9388]), ['final']). 4.05/4.34 cnf(c_0_14953, plain, (c_Com_Ocom_OSemi(X1,X2)!=c_Com_Ocom_OLocal(X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_9389]), ['final']). 4.05/4.34 cnf(c_0_14954, plain, (c_Com_Ocom_OSemi(X1,X2)!=c_Com_Ocom_OCall(X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_9390]), ['final']). 4.05/4.34 cnf(c_0_14955, plain, (c_Com_Ocom_OSemi(X1,X2)!=c_Com_Ocom_OCond(X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_9391]), ['final']). 4.05/4.34 cnf(c_0_14956, plain, (c_Com_Ocom_OWhile(X1,X2)!=c_Com_Ocom_OLocal(X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_9392]), ['final']). 4.05/4.34 cnf(c_0_14957, plain, (c_Com_Ocom_OWhile(X1,X2)!=c_Com_Ocom_OCall(X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_9393]), ['final']). 4.05/4.34 cnf(c_0_14958, plain, (X1!=hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)), inference(split_conjunct,[status(thm)],[c_0_9394]), ['final']). 4.05/4.34 cnf(c_0_14959, plain, (c_Option_Ooption_ONone(X1)!=hAPP(c_Option_Ooption_OSome(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9395]), ['final']). 4.05/4.34 cnf(c_0_14960, plain, (c_Com_Ocom_OBODY(X1)!=c_Com_Ocom_OLocal(X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_9396]), ['final']). 4.05/4.34 cnf(c_0_14961, plain, (c_Com_Ocom_OBODY(X1)!=c_Com_Ocom_OCall(X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_9397]), ['final']). 4.05/4.34 cnf(c_0_14962, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1))), inference(split_conjunct,[status(thm)],[c_0_9398]), ['final']). 4.05/4.34 cnf(c_0_14963, plain, (c_Com_Ocom_OBODY(X1)!=c_Com_Ocom_OCond(X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_9399]), ['final']). 4.05/4.34 cnf(c_0_14964, plain, (c_Com_Ocom_OWhile(X1,X2)!=c_Com_Ocom_OSemi(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_9400]), ['final']). 4.05/4.34 cnf(c_0_14965, plain, (~c_Option_Ois__none(X1,hAPP(c_Option_Ooption_OSome(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_9401]), ['final']). 4.05/4.34 cnf(c_0_14966, 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_9402]), ['final']). 4.05/4.34 cnf(c_0_14967, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(rw,[status(thm)],[c_0_9403, c_0_4427]), ['final']). 4.05/4.34 cnf(c_0_14968, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Int_OMin))), inference(rw,[status(thm)],[c_0_9404, c_0_4427]), ['final']). 4.05/4.34 cnf(c_0_14969, 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_9405]), ['final']). 4.05/4.34 cnf(c_0_14970, plain, (c_Com_Ocom_OSemi(X1,X2)!=c_Com_Ocom_OBODY(X3)), inference(split_conjunct,[status(thm)],[c_0_9406]), ['final']). 4.05/4.34 cnf(c_0_14971, plain, (c_Com_Ocom_OBODY(X1)!=c_Com_Ocom_OWhile(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_9407]), ['final']). 4.05/4.34 cnf(c_0_14972, 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_9408, c_0_4427]), ['final']). 4.05/4.34 cnf(c_0_14973, 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_9409, c_0_4427]), ['final']). 4.05/4.34 cnf(c_0_14974, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_9410]), ['final']). 4.05/4.34 cnf(c_0_14975, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[c_0_9411]), ['final']). 4.05/4.34 cnf(c_0_14976, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,X1)), inference(split_conjunct,[status(thm)],[c_0_9412]), ['final']). 4.05/4.34 cnf(c_0_14977, plain, (~c_List_Olist__ex(X1,X2,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_9413]), ['final']). 4.05/4.34 cnf(c_0_14978, plain, (~c_List_Olist__ex1(X1,X2,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_9414]), ['final']). 4.05/4.34 cnf(c_0_14979, plain, (c_Int_OMin!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)), inference(rw,[status(thm)],[c_0_9415, c_0_4427]), ['final']). 4.05/4.34 cnf(c_0_14980, plain, (X1!=hAPP(c_Nat_OSuc,X1)), inference(split_conjunct,[status(thm)],[c_0_9416]), ['final']). 4.05/4.34 cnf(c_0_14981, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[fact_int__0__neq__1]), ['final']). 4.05/4.34 cnf(c_0_14982, plain, (esk274_1(X1)!=X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9417, c_0_9418])]), ['final']). 4.05/4.34 cnf(c_0_14983, plain, (esk136_0!=esk137_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9419, c_0_9418])]), ['final']). 4.05/4.34 cnf(c_0_14984, plain, (~hBOOL(c_fFalse)), inference(split_conjunct,[status(thm)],[c_0_9420]), ['final']). 4.05/4.34 cnf(c_0_14985, negated_conjecture, (~hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))))), inference(split_conjunct,[status(thm)],[c_0_9421]), ['final']). 4.05/4.34 cnf(c_0_14986, 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9422, c_0_6268]), c_0_6096]), c_0_6096]), c_0_4926]), c_0_4523]), c_0_6268]), ['final']). 4.05/4.34 cnf(c_0_14987, 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_9423, c_0_6096]), c_0_6096]), ['final']). 4.05/4.34 cnf(c_0_14988, plain, (hAPP(c_Set_Oimage(X1,tc_prod(X2,X3),hAPP(hAPP(c_COMBS(X1,X3,tc_prod(X2,X3)),hAPP(hAPP(c_COMBB(X2,tc_fun(X3,tc_prod(X2,X3)),X1),c_Product__Type_OPair(X2,X3)),X4)),X5)),X6)=hAPP(hAPP(c_Product__Type_OSigma(X2,X3),hAPP(c_Set_Oimage(X1,X2,X4),X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),c_Set_Oimage(X1,X3,X5)),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),c_Set_Ovimage(X1,X2,X4)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),c_Set_Oinsert(X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))),X6)))), inference(split_conjunct,[status(thm)],[c_0_9424]), ['final']). 4.05/4.34 cnf(c_0_14989, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9425, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), c_0_6120]), ['final']). 4.05/4.34 cnf(c_0_14990, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9426, c_0_5696]), c_0_5696]), c_0_5696]), ['final']). 4.05/4.34 cnf(c_0_14991, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9427, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), c_0_4635]), c_0_4635]), c_0_4505]), c_0_4795]), c_0_5796]), c_0_4635]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_14992, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X5)),X4))=c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),X1),c_If(tc_Option_Ooption(X2))),X4)),X3)),X5))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9428, c_0_4523]), c_0_5201]), c_0_4523]), c_0_6106]), ['final']). 4.05/4.34 cnf(c_0_14993, 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_9429, c_0_4523]), c_0_5201]), c_0_4523]), c_0_6106]), ['final']). 4.05/4.34 cnf(c_0_14994, 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_9430]), ['final']). 4.05/4.34 cnf(c_0_14995, 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_9431]), ['final']). 4.05/4.34 cnf(c_0_14996, plain, (hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,X4),X5),hAPP(hAPP(c_COMBC(X2,tc_fun(X6,tc_fun(X7,X4)),tc_fun(X3,X4)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X6,X7)),tc_fun(tc_fun(X6,tc_fun(X7,X4)),tc_fun(X3,X4)),X2),c_Product__Type_Oscomp(X3,X6,X7,X4)),X8)),X9))=hAPP(hAPP(c_Product__Type_Oscomp(X1,X6,X7,X4),hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,tc_prod(X6,X7)),X5),X8)),X9)), inference(split_conjunct,[status(thm)],[c_0_9432]), ['final']). 4.05/4.34 cnf(c_0_14997, 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_9433]), ['final']). 4.05/4.34 cnf(c_0_14998, 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_9434]), ['final']). 4.05/4.34 cnf(c_0_14999, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5))), inference(split_conjunct,[status(thm)],[c_0_9435]), ['final']). 4.05/4.34 cnf(c_0_15000, 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_9436]), ['final']). 4.05/4.34 cnf(c_0_15001, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X3))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9437, c_0_4867]), c_0_6120]), ['final']). 4.05/4.34 cnf(c_0_15002, 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_9438, c_0_5130]), c_0_9439]), c_0_5695]), c_0_5696]), c_0_5201]), ['final']). 4.05/4.34 cnf(c_0_15003, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Osublist(X1,X2,X3))=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))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9440, c_0_4915]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15004, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),tc_Option_Ooption(X2),X1,hAPP(c_Option_Omap(X3,X2),X4)),X5)),X6),hAPP(c_Option_Ooption_OSome(X2),hAPP(X4,X7)))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),tc_Option_Ooption(X2),X1,hAPP(c_Option_Omap(X3,X2),X4)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),X5),X6),hAPP(c_Option_Ooption_OSome(X3),X7)))), inference(split_conjunct,[status(thm)],[c_0_9441]), ['final']). 4.05/4.34 cnf(c_0_15005, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9442, c_0_4439]), c_0_4439]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4795]), c_0_4795]), c_0_4814]), c_0_4814]), ['final']). 4.05/4.34 cnf(c_0_15006, plain, (hAPP(c_Set_Oimage(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)))=hAPP(hAPP(c_Product__Type_OSigma(X3,X4),hAPP(c_Set_Oimage(X1,X3,X5),X7)),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),hAPP(c_Set_Oimage(X2,X4,X6),X8)))), inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9443])]), ['final']). 4.05/4.34 cnf(c_0_15007, 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_9444, c_0_4950]), c_0_4950]), ['final']). 4.05/4.34 cnf(c_0_15008, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9445, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.34 cnf(c_0_15009, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9446, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.34 cnf(c_0_15010, 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_9447, c_0_6096]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15011, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),hAPP(X2,X3)),hAPP(hAPP(c_List_Omap(X4,tc_List_Olist(X1)),X2),X5))=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(X4,tc_List_Olist(X1)),X2),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X5)))), inference(rw,[status(thm)],[c_0_9448, c_0_9449]), ['final']). 4.05/4.34 cnf(c_0_15012, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9450, c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), ['final']). 4.05/4.34 cnf(c_0_15013, 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_9451, c_0_7018]), ['final']). 4.05/4.34 cnf(c_0_15014, 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_9452, c_0_4742]), c_0_4742]), ['final']). 4.05/4.34 cnf(c_0_15015, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9453, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_4814]), ['final']). 4.05/4.34 cnf(c_0_15016, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9454, c_0_4795]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4814]), ['final']). 4.05/4.34 cnf(c_0_15017, plain, (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))=hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X2)),hAPP(c_List_Omap(X1,X2),X3)),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9455, c_0_4767]), c_0_4767]), ['final']). 4.05/4.34 cnf(c_0_15018, plain, (c_Map_Orestrict__map(X1,X2,hAPP(c_Fun_Ocomp(X2,tc_Option_Ooption(X2),X1,c_Option_Ooption_OSome(X2)),X3),hAPP(c_List_Oset(X1),X4))=hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Omap(X1,tc_prod(X1,X2)),hAPP(hAPP(c_COMBS(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)),X3)),X4))), inference(split_conjunct,[status(thm)],[c_0_9456]), ['final']). 4.05/4.34 cnf(c_0_15019, 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_9457, c_0_4742]), c_0_4742]), ['final']). 4.05/4.34 cnf(c_0_15020, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9458, c_0_4814]), c_0_9459]), c_0_4814]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_4795]), c_0_4795]), ['final']). 4.05/4.34 cnf(c_0_15021, plain, (hAPP(c_Product__Type_Omap__pair(X3,X3,X1,X2,c_Fun_Oid(X3),X4),hAPP(c_Product__Type_Omap__pair(X5,X3,X1,X1,X6,c_Fun_Oid(X1)),X7))=hAPP(hAPP(c_Product__Type_OPair(X3,X2),hAPP(X6,hAPP(c_Product__Type_Ofst(X5,X1),X7))),hAPP(X4,hAPP(c_Product__Type_Osnd(X5,X1),X7)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9460, c_0_6955]), c_0_4859]), ['final']). 4.05/4.34 cnf(c_0_15022, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),hAPP(c_Product__Type_Omap__pair(X1,X1,X5,X3,c_Fun_Oid(X1),X6),X7))=hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X5),X7))),hAPP(X6,hAPP(c_Product__Type_Osnd(X1,X5),X7)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9461, c_0_6955]), c_0_4859]), ['final']). 4.05/4.34 cnf(c_0_15023, plain, (hAPP(hAPP(c_List_Olist__update(tc_prod(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)),X5),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X7))=hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist__update(X1,X3),X5),X6)),hAPP(hAPP(c_List_Olist__update(X2,X4),X5),X7))), inference(split_conjunct,[status(thm)],[c_0_9462]), ['final']). 4.05/4.34 cnf(c_0_15024, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),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_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9463, c_0_4505]), c_0_4795]), c_0_5796]), ['final']). 4.05/4.34 cnf(c_0_15025, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),hAPP(c_Product__Type_Omap__pair(X1,X1,X5,X3,c_Fun_Oid(X1),X6),X7))=hAPP(c_Product__Type_Omap__pair(X2,X2,X5,X3,c_Fun_Oid(X2),X6),hAPP(c_Product__Type_Omap__pair(X1,X2,X5,X5,X4,c_Fun_Oid(X5)),X7))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9464, c_0_6955]), c_0_6955]), c_0_4859]), c_0_4859]), ['final']). 4.05/4.34 cnf(c_0_15026, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9465, c_0_4814]), c_0_9459]), c_0_4814]), c_0_4795]), c_0_4505]), c_0_4795]), c_0_5796]), ['final']). 4.05/4.34 cnf(c_0_15027, 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_9466]), ['final']). 4.05/4.34 cnf(c_0_15028, 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_9467, c_0_5696]), ['final']). 4.05/4.34 cnf(c_0_15029, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9468, c_0_4439]), c_0_4439]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4795]), c_0_4439]), c_0_4814]), c_0_4814]), ['final']). 4.05/4.34 cnf(c_0_15030, 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_9469, c_0_4859]), c_0_4859]), c_0_4859]), ['final']). 4.05/4.34 cnf(c_0_15031, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),hAPP(c_Product__Type_Omap__pair(X5,X1,X3,X3,X6,c_Fun_Oid(X3)),X7))=hAPP(c_Product__Type_Omap__pair(X5,X2,X3,X3,hAPP(c_Fun_Ocomp(X1,X2,X5,X4),X6),c_Fun_Oid(X3)),X7)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9470, c_0_6955]), c_0_6955]), c_0_6955]), ['final']). 4.05/4.34 cnf(c_0_15032, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5))=hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X3),tc_List_Olist(X3)),X2),c_List_Orotate1(X3)),X5))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9471, c_0_5942]), c_0_5942]), ['final']). 4.05/4.34 cnf(c_0_15033, 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_9472]), ['final']). 4.05/4.34 cnf(c_0_15034, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X1,X4),X5)),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),X3),X6),X4))), inference(split_conjunct,[status(thm)],[c_0_9473]), ['final']). 4.05/4.34 cnf(c_0_15035, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X3))), inference(split_conjunct,[status(thm)],[c_0_9474]), ['final']). 4.05/4.34 cnf(c_0_15036, plain, (c_Map_Odom(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),c_Option_Ooption_ONone(X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))), inference(er,[status(thm)],[c_0_9475]), ['final']). 4.05/4.34 cnf(c_0_15037, 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_9476]), ['final']). 4.05/4.34 cnf(c_0_15038, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6))=hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X5)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X6))), inference(split_conjunct,[status(thm)],[c_0_9477]), ['final']). 4.05/4.34 cnf(c_0_15039, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6),hAPP(X4,X7))=hAPP(c_Fun_Ocomp(X3,X2,X1,X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X3),X5),X6),X7))), inference(split_conjunct,[status(thm)],[c_0_9478]), ['final']). 4.05/4.34 cnf(c_0_15040, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X3))), inference(split_conjunct,[status(thm)],[c_0_9479]), ['final']). 4.05/4.34 cnf(c_0_15041, 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_9480]), ['final']). 4.05/4.34 cnf(c_0_15042, 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_9481]), ['final']). 4.05/4.34 cnf(c_0_15043, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(X5,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9482]), ['final']). 4.05/4.34 cnf(c_0_15044, 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_9483]), ['final']). 4.05/4.34 cnf(c_0_15045, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,hAPP(c_Fun_Ocomp(X2,tc_HOL_Obool,X1,X3),X4)),X5))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),hAPP(c_List_Ofilter(X2,X3),hAPP(hAPP(c_List_Omap(X1,X2),X4),X5)))), inference(split_conjunct,[status(thm)],[c_0_9484]), ['final']). 4.05/4.34 cnf(c_0_15046, 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_9485]), ['final']). 4.05/4.34 cnf(c_0_15047, plain, (hAPP(c_Fun_Ocomp(tc_prod(X1,X2),X2,tc_prod(X3,X4),c_Product__Type_Osnd(X1,X2)),c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6))=hAPP(c_Fun_Ocomp(X4,X2,tc_prod(X3,X4),X6),c_Product__Type_Osnd(X3,X4))), inference(split_conjunct,[status(thm)],[c_0_9486]), ['final']). 4.05/4.34 cnf(c_0_15048, plain, (c_Map_Orestrict__map(X1,X2,X3,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),c_Option_Ooption_ONone(X2))), inference(split_conjunct,[status(thm)],[c_0_9487]), ['final']). 4.05/4.34 cnf(c_0_15049, 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_9488]), ['final']). 4.05/4.34 cnf(c_0_15050, 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_9489]), ['final']). 4.05/4.34 cnf(c_0_15051, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2))=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2))), inference(rw,[status(thm)],[c_0_9490, c_0_4767]), ['final']). 4.05/4.34 cnf(c_0_15052, 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_9491]), ['final']). 4.05/4.34 cnf(c_0_15053, plain, (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))=hAPP(c_Relation_ODomain(X1,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3))), inference(split_conjunct,[status(thm)],[c_0_9492]), ['final']). 4.05/4.34 cnf(c_0_15054, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),c_Relation_ORange(X1,X2))=hAPP(c_Relation_ORange(X1,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3))), inference(split_conjunct,[status(thm)],[c_0_9493]), ['final']). 4.05/4.34 cnf(c_0_15055, 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_9494, c_0_4867]), c_0_5668]), c_0_5669]), ['final']). 4.05/4.34 cnf(c_0_15056, 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_9495, c_0_4867]), c_0_5668]), c_0_5669]), ['final']). 4.05/4.34 cnf(c_0_15057, 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_9496, c_0_4523]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15058, plain, (hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)),X5),hAPP(X3,X6))=hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(hAPP(c_List_Olist__update(X2,X4),X5),X6))), inference(split_conjunct,[status(thm)],[c_0_9497]), ['final']). 4.05/4.34 cnf(c_0_15059, 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_9498]), ['final']). 4.05/4.34 cnf(c_0_15060, 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_9499]), ['final']). 4.05/4.34 cnf(c_0_15061, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(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))), inference(split_conjunct,[status(thm)],[c_0_9500]), ['final']). 4.05/4.34 cnf(c_0_15062, plain, (hAPP(hAPP(c_Option_Omap(X1,X2),X3),hAPP(hAPP(c_Option_Omap(X4,X1),X5),X6))=hAPP(hAPP(c_Option_Omap(X4,X2),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6)), inference(split_conjunct,[status(thm)],[c_0_9501]), ['final']). 4.05/4.34 cnf(c_0_15063, 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_9502, c_0_7550]), ['final']). 4.05/4.34 cnf(c_0_15064, 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_9503]), ['final']). 4.05/4.34 cnf(c_0_15065, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X1,X2))=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X3,X1,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9504, c_0_4867]), c_0_5668]), c_0_5669]), c_0_5670]), c_0_9505]), ['final']). 4.05/4.34 cnf(c_0_15066, 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_9506, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15067, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),hAPP(X2,X3)),hAPP(hAPP(c_List_Omap(X4,X1),X2),X5))=hAPP(hAPP(c_List_Omap(X4,X1),X2),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9507]), ['final']). 4.05/4.34 cnf(c_0_15068, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(c_Fun_Ocomp(X4,X1,X2,X5),X6))=hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,X2),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X4),X3),X5)),X6)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9508, c_0_4902]), c_0_4902]), c_0_4902]), ['final']). 4.05/4.34 cnf(c_0_15069, plain, (hAPP(c_Set_Oimage(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6)=hAPP(c_Set_Oimage(X3,X2,X4),hAPP(c_Set_Oimage(X1,X3,X5),X6))), inference(split_conjunct,[status(thm)],[c_0_9509]), ['final']). 4.05/4.34 cnf(c_0_15070, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X5))=hAPP(hAPP(c_Set_Oinsert(X2),hAPP(X3,X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9510]), ['final']). 4.05/4.34 cnf(c_0_15071, 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_9511]), ['final']). 4.05/4.34 cnf(c_0_15072, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),X4)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),X4))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9512, c_0_4902]), c_0_4902]), ['final']). 4.05/4.34 cnf(c_0_15073, 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_9513]), ['final']). 4.05/4.34 cnf(c_0_15074, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Otake(X1),X4),X5))=hAPP(hAPP(c_List_Otake(X2),X4),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9514]), ['final']). 4.05/4.34 cnf(c_0_15075, 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_Enum_Oenum__the(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))), inference(rw,[status(thm)],[c_0_9515, c_0_6300]), ['final']). 4.05/4.34 cnf(c_0_15076, plain, (hAPP(hAPP(c_Relation_Oinv__image(X1,X2),hAPP(c_Relation_Oconverse(X1,X1),X3)),X4)=hAPP(c_Relation_Oconverse(X2,X2),hAPP(hAPP(c_Relation_Oinv__image(X1,X2),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9516]), ['final']). 4.05/4.34 cnf(c_0_15077, plain, (hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),hAPP(c_Nat_OSuc,X5))=hAPP(hAPP(X3,X4),hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9517]), ['final']). 4.05/4.34 cnf(c_0_15078, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X2))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X3,X1,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9518, c_0_4867]), c_0_5668]), c_0_5669]), c_0_5670]), c_0_9519]), ['final']). 4.05/4.34 cnf(c_0_15079, plain, (c_List_Olist_Olist__size(X1,hAPP(c_Fun_Ocomp(X2,tc_Nat_Onat,X1,X3),X4),X5)=c_List_Olist_Olist__size(X2,X3,hAPP(hAPP(c_List_Omap(X1,X2),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9520]), ['final']). 4.05/4.34 cnf(c_0_15080, 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_9521, c_0_4902]), ['final']). 4.05/4.34 cnf(c_0_15081, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X1,hAPP(X2,X3),c_Option_Ooption_OSome(X1)),hAPP(X4,X3))=hAPP(c_Map_Omap__add(X5,X1,X2,X4),X3)), inference(split_conjunct,[status(thm)],[c_0_9522]), ['final']). 4.05/4.34 cnf(c_0_15082, plain, (hAPP(hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)),hAPP(c_Product__Type_Osnd(X2,X3),X4))=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X5),X1),X4)), inference(split_conjunct,[status(thm)],[c_0_9523]), ['final']). 4.05/4.34 cnf(c_0_15083, 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_9524]), ['final']). 4.05/4.34 cnf(c_0_15084, 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_9525]), ['final']). 4.05/4.34 cnf(c_0_15085, plain, (hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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_9526, c_0_5716]), ['final']). 4.05/4.34 cnf(c_0_15086, 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_9527]), ['final']). 4.05/4.34 cnf(c_0_15087, 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_9528]), ['final']). 4.05/4.34 cnf(c_0_15088, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))=hAPP(c_List_Orotate1(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_9529]), ['final']). 4.05/4.34 cnf(c_0_15089, 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_9530]), ['final']). 4.05/4.34 cnf(c_0_15090, 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_9531]), ['final']). 4.05/4.34 cnf(c_0_15091, plain, (hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_List_Oset(X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9532]), ['final']). 4.05/4.34 cnf(c_0_15092, 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_9533]), ['final']). 4.05/4.34 cnf(c_0_15093, 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_9534]), ['final']). 4.05/4.34 cnf(c_0_15094, plain, (hAPP(hAPP(X1,X2),hAPP(c_Nat_Onat_Onat__rec(X3,X4,X1),X2))=hAPP(c_Nat_Onat_Onat__rec(X3,X4,X1),hAPP(c_Nat_OSuc,X2))), inference(split_conjunct,[status(thm)],[c_0_9535]), ['final']). 4.05/4.34 cnf(c_0_15095, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_9536]), ['final']). 4.05/4.34 cnf(c_0_15096, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(X1))=c_List_Opartition(X1,X2,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_9537]), ['final']). 4.05/4.34 cnf(c_0_15097, plain, (hAPP(hAPP(X1,X2),hAPP(X3,X2))=hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),X1),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_9538]), ['final']). 4.05/4.34 cnf(c_0_15098, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))), inference(split_conjunct,[status(thm)],[c_0_9539]), ['final']). 4.05/4.34 cnf(c_0_15099, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Orev(X1),X3))=hAPP(c_List_Orev(X1),hAPP(c_List_Ofilter(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9540]), ['final']). 4.05/4.34 cnf(c_0_15100, plain, (c_Fun_Oid(tc_prod(X1,X2))=hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_9541]), ['final']). 4.05/4.34 cnf(c_0_15101, 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_9542]), ['final']). 4.05/4.34 cnf(c_0_15102, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool))=hAPP(c_List_Olexn(X1,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_9543]), ['final']). 4.05/4.34 cnf(c_0_15103, 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_9544]), ['final']). 4.05/4.34 cnf(c_0_15104, 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_9545]), ['final']). 4.05/4.34 cnf(c_0_15105, plain, (c_Enum_Osublists(X1,c_List_Olist_ONil(X1))=hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(tc_List_Olist(X1)))), inference(split_conjunct,[status(thm)],[c_0_9546]), ['final']). 4.05/4.34 cnf(c_0_15106, 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_9547, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15107, 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_9548, c_0_4915]), c_0_4915]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15108, 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_9549]), ['final']). 4.05/4.34 cnf(c_0_15109, 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_9550, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15110, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))=c_Divides_Oadjust(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9551, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_15111, 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_9552]), ['final']). 4.05/4.34 cnf(c_0_15112, 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_9553]), ['final']). 4.05/4.34 cnf(c_0_15113, 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_9554, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15114, 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_9555, c_0_4926]), c_0_6123]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15115, 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_9556, c_0_5011]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15116, plain, (c_Map_Omap__upds(X1,X2,X3,X4,X5)=hAPP(c_List_Ofoldl(tc_fun(X1,tc_Option_Ooption(X2)),tc_prod(X1,X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_prod(X1,X2),tc_fun(X1,tc_Option_Ooption(X2))),tc_fun(X1,tc_Option_Ooption(X2))),c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(X1,tc_Option_Ooption(X2))),c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(X1,tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(X1,tc_Option_Ooption(X2))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2)))),X1),c_COMBB(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)),X2))),c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2))))),c_Option_Ooption_OSome(X2))),X3),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9557]), ['final']). 4.05/4.34 cnf(c_0_15117, 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_9558]), ['final']). 4.05/4.34 cnf(c_0_15118, plain, (hAPP(c_List_Ofoldl(tc_fun(X1,tc_Option_Ooption(X2)),tc_prod(X1,X2),hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),X1),c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))),X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),X1),c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),X1,tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)))))),c_Option_Ooption_OSome(X2)))),X4),hAPP(c_List_Orev(tc_prod(X1,X2)),X3))=c_Map_Omap__add(X1,X2,X4,hAPP(c_Map_Omap__of(X1,X2),X3))), inference(rw,[status(thm)],[c_0_9559, c_0_4742]), ['final']). 4.05/4.34 cnf(c_0_15119, 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_9560, c_0_5205]), c_0_5205]), c_0_5205]), ['final']). 4.05/4.34 cnf(c_0_15120, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3)),X1)))=hAPP(c_Divides_Oadjust(X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9561, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), c_0_4795]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_15121, 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_9562, c_0_6340]), c_0_6340]), c_0_6340]), c_0_6340]), c_0_6340]), c_0_6340]), ['final']). 4.05/4.34 cnf(c_0_15122, 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_9563, c_0_4915]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15123, 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_9564, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15124, 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)],[c_0_9565, c_0_9566]), c_0_9567]), ['final']). 4.05/4.34 cnf(c_0_15125, plain, (c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBC(X1,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),X1),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X1),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),X1),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)=hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),X3)), inference(rw,[status(thm)],[c_0_9568, c_0_9569]), ['final']). 4.05/4.34 cnf(c_0_15126, 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))), inference(split_conjunct,[status(thm)],[c_0_9570]), ['final']). 4.05/4.34 cnf(c_0_15127, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,tc_fun(X2,tc_HOL_Obool)),X7),X8)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X3,X6),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X3,X6),X4),hAPP(c_COMBK(tc_fun(X6,tc_HOL_Obool),X3),X7))),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X6,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3,tc_fun(X6,tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),tc_fun(X6,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),tc_fun(tc_fun(X6,tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),tc_fun(X6,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X3),c_COMBB(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),c_Product__Type_OSigma(X1,X2)),X5))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X6),c_COMBK(tc_fun(X2,tc_HOL_Obool),X1)),X8))))), inference(split_conjunct,[status(thm)],[c_0_9571]), ['final']). 4.05/4.34 cnf(c_0_15128, 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_9572, c_0_5130]), c_0_5130]), c_0_4867]), c_0_5695]), c_0_5696]), c_0_5201]), c_0_5130]), c_0_5130]), c_0_9439]), ['final']). 4.05/4.34 cnf(c_0_15129, 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_9573, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15130, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)),X5)=hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X1,X2)),X2,c_List_Olist_ONil(tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2)))),X2),c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(X2))),hAPP(hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),X2),c_List_Olist_OCons(tc_prod(X1,X2))),hAPP(c_Product__Type_OPair(X1,X2),X3)))),hAPP(c_List_Ozip(X1,X2),X4))),X5)), inference(split_conjunct,[status(thm)],[c_0_9574]), ['final']). 4.05/4.34 cnf(c_0_15131, 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_9575]), ['final']). 4.05/4.34 cnf(c_0_15132, 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_9576]), ['final']). 4.05/4.34 cnf(c_0_15133, 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_9577, c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_15134, 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_9578, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15135, 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_9579, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15136, 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_9580, c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_15137, 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_9581, c_0_4915]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15138, 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_9582]), ['final']). 4.05/4.34 cnf(c_0_15139, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Nitpick_OFrac), inference(split_conjunct,[status(thm)],[fact_Nitpick_OFrac__def]), ['final']). 4.05/4.34 cnf(c_0_15140, 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_9583, c_0_9584]), ['final']). 4.05/4.34 cnf(c_0_15141, 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_9585, c_0_6100]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15142, 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_9586, c_0_9587]), ['final']). 4.05/4.34 cnf(c_0_15143, 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_9588, c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_15144, 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_9589, c_0_6113]), ['final']). 4.05/4.34 cnf(c_0_15145, 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_9590, c_0_5696]), c_0_5696]), c_0_5696]), ['final']). 4.05/4.34 cnf(c_0_15146, 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_9591, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15147, 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_9592, c_0_5696]), c_0_6396]), ['final']). 4.05/4.34 cnf(c_0_15148, 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_9593, c_0_4635]), c_0_5130]), c_0_5130]), ['final']). 4.05/4.34 cnf(c_0_15149, 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_9594, c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_15150, 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_9595, c_0_4635]), c_0_5011]), c_0_5011]), ['final']). 4.05/4.34 cnf(c_0_15151, 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_9596, c_0_5696]), c_0_6396]), ['final']). 4.05/4.34 cnf(c_0_15152, 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_9597, c_0_4767]), ['final']). 4.05/4.34 cnf(c_0_15153, 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_9598, c_0_6340]), c_0_6340]), c_0_6340]), c_0_6340]), ['final']). 4.05/4.34 cnf(c_0_15154, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Map_Odom(X1,X3,X4))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X3,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),c_Map_Odom(X1,X3,X4))))=c_Map_Odom(X1,X3,c_Fun_Ooverride__on(X1,tc_Option_Ooption(X3),X5,X4,X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9599, c_0_4915]), c_0_4523]), c_0_4915]), c_0_4523]), c_0_6396]), ['final']). 4.05/4.34 cnf(c_0_15155, plain, (hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Omap(tc_prod(X1,X3),tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X3,tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,X2),tc_fun(X3,tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(tc_fun(X3,X2),tc_fun(X3,tc_prod(X1,X2))),X1),c_COMBB(X2,tc_prod(X1,X2),X3)),c_Product__Type_OPair(X1,X2))),X4))),X5))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),tc_Option_Ooption(X2),X1,hAPP(c_Option_Omap(X3,X2),X4)),hAPP(c_Map_Omap__of(X1,X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9600]), ['final']). 4.05/4.34 cnf(c_0_15156, 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_9601]), ['final']). 4.05/4.34 cnf(c_0_15157, 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_9602, c_0_9584]), ['final']). 4.05/4.34 cnf(c_0_15158, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9603, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.34 cnf(c_0_15159, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9604, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.34 cnf(c_0_15160, 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_9605, c_0_4635]), c_0_5130]), c_0_5130]), ['final']). 4.05/4.34 cnf(c_0_15161, 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_9606, c_0_4635]), c_0_5011]), c_0_5011]), ['final']). 4.05/4.34 cnf(c_0_15162, 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_9607, c_0_9608]), ['final']). 4.05/4.34 cnf(c_0_15163, 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_9609, c_0_6096]), ['final']). 4.05/4.34 cnf(c_0_15164, 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_9610]), ['final']). 4.05/4.34 cnf(c_0_15165, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9611, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_15166, 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_9612]), ['final']). 4.05/4.34 cnf(c_0_15167, 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_9613]), ['final']). 4.05/4.34 cnf(c_0_15168, 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_9614, c_0_4926]), ['final']). 4.05/4.34 cnf(c_0_15169, plain, (c_Enum_Oenum__the(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_9615, c_0_4926]), ['final']). 4.05/4.34 cnf(c_0_15170, plain, (c_New__Random__Sequence_Oneg__decr__bind(X1,X2,X3,X4,X5,X6,X7)=c_New__DSequence_Oneg__decr__bind(X1,X2,hAPP(hAPP(hAPP(X3,X5),X6),X7),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))))),X4),X5)),X6)),X7))), inference(split_conjunct,[status(thm)],[c_0_9616]), ['final']). 4.05/4.34 cnf(c_0_15171, 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_9617]), ['final']). 4.05/4.34 cnf(c_0_15172, plain, (hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X1,X2,X3,X4),X5),X6),X7)=c_New__DSequence_Opos__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_9618]), ['final']). 4.05/4.34 cnf(c_0_15173, 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_9619]), ['final']). 4.05/4.34 cnf(c_0_15174, 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_9620, c_0_9621]), ['final']). 4.05/4.34 cnf(c_0_15175, 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_9622]), ['final']). 4.05/4.34 cnf(c_0_15176, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X5,X3),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2,X5),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X5,X3),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X1),c_Relation_Orel__comp(X2,X5,X3)),X6)),X7))=hAPP(hAPP(c_Relation_Orel__comp(X2,X5,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X5),tc_HOL_Obool)),X4),X6)),X7)), inference(split_conjunct,[status(thm)],[c_0_9623]), ['final']). 4.05/4.34 cnf(c_0_15177, 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_9624, c_0_6096]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15178, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofilter(X1,X4),X5))=c_List_Omap__filter(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),X1),c_If(tc_Option_Ooption(X2))),X4)),hAPP(hAPP(c_COMBB(X2,tc_Option_Ooption(X2),X1),c_Option_Ooption_OSome(X2)),X3))),c_Option_Ooption_ONone(X2)),X5)), inference(split_conjunct,[status(thm)],[c_0_9625]), ['final']). 4.05/4.34 cnf(c_0_15179, 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_9626]), ['final']). 4.05/4.34 cnf(c_0_15180, 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_9627, c_0_4915]), c_0_4915]), c_0_4915]), c_0_4915]), ['final']). 4.05/4.34 cnf(c_0_15181, 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)))), inference(split_conjunct,[status(thm)],[c_0_9628]), ['final']). 4.05/4.34 cnf(c_0_15182, 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_9629, c_0_6395]), c_0_9630]), ['final']). 4.05/4.34 cnf(c_0_15183, 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_9631]), ['final']). 4.05/4.34 cnf(c_0_15184, 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_9632]), ['final']). 4.05/4.34 cnf(c_0_15185, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9633, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_6266]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_15186, 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_9634, c_0_9635]), ['final']). 4.05/4.34 cnf(c_0_15187, 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_9636]), ['final']). 4.05/4.34 cnf(c_0_15188, 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_9637, c_0_6096]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15189, 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_9638, c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_15190, plain, (c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),X1),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)=hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X2)), inference(rw,[status(thm)],[c_0_9639, c_0_9569]), ['final']). 4.05/4.34 cnf(c_0_15191, 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_9640]), ['final']). 4.05/4.34 cnf(c_0_15192, 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_9641, c_0_5696]), c_0_5696]), ['final']). 4.05/4.34 cnf(c_0_15193, 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_9642, c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_15194, 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_9643, c_0_5205]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15195, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9644, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4814]), ['final']). 4.05/4.34 cnf(c_0_15196, plain, (c_Enum_Oenum__the(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_9645, c_0_4915]), c_0_5205]), ['final']). 4.05/4.34 cnf(c_0_15197, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9646, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), c_0_4814]), c_0_9647]), c_0_4795]), ['final']). 4.05/4.34 cnf(c_0_15198, 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_9648]), ['final']). 4.05/4.34 cnf(c_0_15199, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5)), inference(split_conjunct,[status(thm)],[c_0_9649]), ['final']). 4.05/4.34 cnf(c_0_15200, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5)), inference(split_conjunct,[status(thm)],[c_0_9650]), ['final']). 4.05/4.34 cnf(c_0_15201, 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_9651, c_0_4902]), c_0_4902]), c_0_4902]), ['final']). 4.05/4.34 cnf(c_0_15202, plain, (hAPP(hAPP(c_List_Omap(X1,X2),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2)),X3)),hAPP(c_List_Ofilter(X1,c_Map_Odom(X1,X2,X3)),X4))=c_List_Omap__filter(X1,X2,X3,X4)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9652, c_0_5201]), c_0_9653]), ['final']). 4.05/4.34 cnf(c_0_15203, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9654, c_0_4814]), c_0_9647]), c_0_5753]), c_0_4814]), c_0_4505]), c_0_4795]), c_0_5796]), c_0_4795]), ['final']). 4.05/4.34 cnf(c_0_15204, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9655, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.34 cnf(c_0_15205, 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_9656]), ['final']). 4.05/4.34 cnf(c_0_15206, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),tc_prod(X2,X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X2,X1)),hAPP(c_COMBC(X2,X1,tc_prod(X2,X1)),c_Product__Type_OPair(X2,X1)))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))=hAPP(hAPP(c_Product__Type_OSigma(X2,X1),X4),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9657]), ['final']). 4.05/4.34 cnf(c_0_15207, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9658, c_0_4505]), c_0_4795]), c_0_5796]), c_0_4635]), c_0_4795]), c_0_4814]), c_0_4814]), c_0_5753]), c_0_4635]), c_0_4635]), c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_15208, 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_9659]), ['final']). 4.05/4.34 cnf(c_0_15209, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),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)), inference(rw,[status(thm)],[c_0_9660, c_0_9661]), ['final']). 4.05/4.34 cnf(c_0_15210, plain, (hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3))),c_Option_Ooption_OSome(X2)))=c_Map_Oran(X1,X2,X3)), inference(rw,[status(thm)],[c_0_9662, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15211, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5)),X6)=hAPP(hAPP(c_List_Omap(tc_prod(X3,X2),tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(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))),hAPP(hAPP(c_List_Ozip(X3,X2),X5),X6))), inference(split_conjunct,[status(thm)],[c_0_9663]), ['final']). 4.05/4.34 cnf(c_0_15212, 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_9664, c_0_4767]), ['final']). 4.05/4.34 cnf(c_0_15213, 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_9665, c_0_5696]), c_0_5696]), ['final']). 4.05/4.34 cnf(c_0_15214, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9666, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.34 cnf(c_0_15215, plain, (hAPP(c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Oappend(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1)))),X2)=hAPP(c_List_Orotate1(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9667]), ['final']). 4.05/4.34 cnf(c_0_15216, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9668, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_15217, 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_9669]), ['final']). 4.05/4.34 cnf(c_0_15218, 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_9670]), ['final']). 4.05/4.34 cnf(c_0_15219, plain, (c_Lazy__Sequence_Ohb__not__seq(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),X2)))=hAPP(c_New__DSequence_Opos__not__seq(X1),X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9671, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), ['final']). 4.05/4.34 cnf(c_0_15220, 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9672, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_6049]), ['final']). 4.05/4.34 cnf(c_0_15221, 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_9673]), ['final']). 4.05/4.34 cnf(c_0_15222, 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))), inference(split_conjunct,[status(thm)],[c_0_9674]), ['final']). 4.05/4.34 cnf(c_0_15223, 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_9675]), ['final']). 4.05/4.34 cnf(c_0_15224, 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_9676]), ['final']). 4.05/4.34 cnf(c_0_15225, 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))), inference(split_conjunct,[status(thm)],[c_0_9677]), ['final']). 4.05/4.34 cnf(c_0_15226, plain, (c_Map_Orestrict__map(X1,X2,X3,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=c_Map_Orestrict__map(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_9678]), ['final']). 4.05/4.34 cnf(c_0_15227, 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_9679, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15228, 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_9680, c_0_6340]), c_0_6340]), ['final']). 4.05/4.34 cnf(c_0_15229, 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_9681]), ['final']). 4.05/4.34 cnf(c_0_15230, plain, (c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak))), inference(split_conjunct,[status(thm)],[fact_max__rpair__set]), ['final']). 4.05/4.34 cnf(c_0_15231, plain, (c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak))), inference(split_conjunct,[status(thm)],[fact_min__rpair__set]), ['final']). 4.05/4.34 cnf(c_0_15232, 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)), inference(split_conjunct,[status(thm)],[c_0_9682]), ['final']). 4.05/4.34 cnf(c_0_15233, 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_9683]), ['final']). 4.05/4.34 cnf(c_0_15234, 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_9684, c_0_4814]), ['final']). 4.05/4.34 cnf(c_0_15235, 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_9685, c_0_5668]), ['final']). 4.05/4.34 cnf(c_0_15236, 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_9686, c_0_5942]), c_0_5942]), ['final']). 4.05/4.34 cnf(c_0_15237, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool))),X4))), inference(split_conjunct,[status(thm)],[c_0_9687]), ['final']). 4.05/4.34 cnf(c_0_15238, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),c_Int_OMin)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9688, c_0_4814]), c_0_4814]), c_0_4814]), c_0_4795]), c_0_4795]), ['final']). 4.05/4.34 cnf(c_0_15239, 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_9689, c_0_5695]), c_0_5201]), c_0_6118]), c_0_4523]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15240, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9690, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_15241, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9691, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4866]), c_0_4865]), c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_15242, 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_9692, c_0_5205]), c_0_4523]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15243, 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_9693]), ['final']). 4.05/4.34 cnf(c_0_15244, 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_9694]), ['final']). 4.05/4.34 cnf(c_0_15245, 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_9695]), ['final']). 4.05/4.34 cnf(c_0_15246, 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_9696, c_0_4915]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15247, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool),X1),c_Relation_Oconverse(X3,X2)),X5))=hAPP(c_Relation_Oconverse(X3,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_prod(X3,X2),tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9697]), ['final']). 4.05/4.34 cnf(c_0_15248, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool),X1),c_Relation_Oconverse(X3,X2)),X5))=hAPP(c_Relation_Oconverse(X3,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X3,X2),tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9698]), ['final']). 4.05/4.34 cnf(c_0_15249, 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_9699]), ['final']). 4.05/4.34 cnf(c_0_15250, 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_9700]), ['final']). 4.05/4.34 cnf(c_0_15251, 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_9701]), ['final']). 4.05/4.34 cnf(c_0_15252, 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_9702, c_0_6268]), ['final']). 4.05/4.34 cnf(c_0_15253, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)=hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3)),hAPP(hAPP(c_List_Otake(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3))), inference(rw,[status(thm)],[c_0_9703, c_0_5942]), ['final']). 4.05/4.34 cnf(c_0_15254, 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)), inference(split_conjunct,[status(thm)],[c_0_9704]), ['final']). 4.05/4.34 cnf(c_0_15255, 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))), inference(split_conjunct,[status(thm)],[c_0_9705]), ['final']). 4.05/4.34 cnf(c_0_15256, 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_9706]), ['final']). 4.05/4.34 cnf(c_0_15257, 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),esk293_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_9707]), ['final']). 4.05/4.34 cnf(c_0_15258, 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_9708]), ['final']). 4.05/4.34 cnf(c_0_15259, 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_9709]), ['final']). 4.05/4.34 cnf(c_0_15260, 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_9710]), ['final']). 4.05/4.34 cnf(c_0_15261, 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_9711]), ['final']). 4.05/4.34 cnf(c_0_15262, 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_9712]), ['final']). 4.05/4.34 cnf(c_0_15263, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9713, c_0_4427]), c_0_4427]), c_0_4814]), c_0_4814]), c_0_4814]), c_0_4795]), c_0_9714]), c_0_4427]), c_0_4505]), c_0_4795]), c_0_5796]), ['final']). 4.05/4.34 cnf(c_0_15264, 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_9715]), ['final']). 4.05/4.34 cnf(c_0_15265, 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_9716]), ['final']). 4.05/4.34 cnf(c_0_15266, 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_9717, c_0_5696]), c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_15267, 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_9718]), ['final']). 4.05/4.34 cnf(c_0_15268, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9719]), ['final']). 4.05/4.34 cnf(c_0_15269, 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))), inference(split_conjunct,[status(thm)],[c_0_9720]), ['final']). 4.05/4.34 cnf(c_0_15270, plain, (c_Enum_Oenum__the(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_Enum_Oenum__the(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9721, c_0_4980]), c_0_4980]), ['final']). 4.05/4.34 cnf(c_0_15271, 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_9722]), ['final']). 4.05/4.34 cnf(c_0_15272, 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_9723]), ['final']). 4.05/4.34 cnf(c_0_15273, 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_9724, c_0_4523]), c_0_5205]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15274, 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_9725]), ['final']). 4.05/4.34 cnf(c_0_15275, 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_9726, c_0_5696]), ['final']). 4.05/4.34 cnf(c_0_15276, 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_9727]), ['final']). 4.05/4.34 cnf(c_0_15277, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9728, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), c_0_4814]), c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_15278, 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_9729, c_0_5149]), c_0_5149]), c_0_9730]), c_0_5149]), c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_15279, 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_9731]), ['final']). 4.05/4.34 cnf(c_0_15280, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9732, c_0_4795]), c_0_4977]), c_0_4795]), c_0_4977]), c_0_4814]), c_0_5795]), c_0_9733]), c_0_4795]), ['final']). 4.05/4.34 cnf(c_0_15281, 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_9734]), ['final']). 4.05/4.34 cnf(c_0_15282, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9735, c_0_4814]), c_0_5795]), c_0_9733]), c_0_4795]), c_0_4795]), ['final']). 4.05/4.34 cnf(c_0_15283, 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_9736, c_0_5696]), ['final']). 4.05/4.34 cnf(c_0_15284, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X5),X4))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X5)),X4)), inference(split_conjunct,[status(thm)],[c_0_9737]), ['final']). 4.05/4.34 cnf(c_0_15285, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9738]), ['final']). 4.05/4.34 cnf(c_0_15286, 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_9739, c_0_9740]), ['final']). 4.05/4.34 cnf(c_0_15287, 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_9741, c_0_6962]), c_0_6962]), c_0_6963]), ['final']). 4.05/4.34 cnf(c_0_15288, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9742, c_0_4977]), c_0_4977]), c_0_4795]), c_0_4505]), c_0_4795]), c_0_5796]), ['final']). 4.05/4.34 cnf(c_0_15289, 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_9743]), ['final']). 4.05/4.34 cnf(c_0_15290, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3))),X3))), inference(split_conjunct,[status(thm)],[c_0_9744]), ['final']). 4.05/4.34 cnf(c_0_15291, 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_9745]), ['final']). 4.05/4.34 cnf(c_0_15292, 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),esk114_1(X1)),esk115_1(X1)))))=X1), inference(rw,[status(thm)],[c_0_9746, c_0_5696]), ['final']). 4.05/4.34 cnf(c_0_15293, plain, (c_List_Omap__filter(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))=hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(X2),X2,c_List_Omap__filter(X1,X2,X3,X5),hAPP(hAPP(c_COMBC(X2,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olist_OCons(X2)),c_List_Omap__filter(X1,X2,X3,X5))),hAPP(X3,X4))), inference(split_conjunct,[status(thm)],[c_0_9747]), ['final']). 4.05/4.34 cnf(c_0_15294, 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_9748, c_0_5942]), c_0_5942]), c_0_5942]), ['final']). 4.05/4.34 cnf(c_0_15295, 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_9749]), ['final']). 4.05/4.34 cnf(c_0_15296, 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_9750]), ['final']). 4.05/4.34 cnf(c_0_15297, 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_9751]), ['final']). 4.05/4.34 cnf(c_0_15298, plain, (c_Product__Type_Omap__pair(X1,X2,X3,X4,hAPP(c_Fun_Ocomp(X5,X2,X1,X6),X7),hAPP(c_Fun_Ocomp(X8,X4,X3,X9),X10))=hAPP(c_Fun_Ocomp(tc_prod(X5,X8),tc_prod(X2,X4),tc_prod(X1,X3),c_Product__Type_Omap__pair(X5,X2,X8,X4,X6,X9)),c_Product__Type_Omap__pair(X1,X5,X3,X8,X7,X10))), inference(split_conjunct,[status(thm)],[c_0_9752]), ['final']). 4.05/4.34 cnf(c_0_15299, plain, (c_Random_Oselect__weight(X1,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X2))=c_Random_Oselect__weight(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_9753]), ['final']). 4.05/4.34 cnf(c_0_15300, 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_9754]), ['final']). 4.05/4.34 cnf(c_0_15301, 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_9755]), ['final']). 4.05/4.34 cnf(c_0_15302, plain, (c_Enum_Oenum__the(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(rw,[status(thm)],[c_0_9756, c_0_4980]), ['final']). 4.05/4.34 cnf(c_0_15303, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_Set_Oinsert(X1),X2)),X5))), inference(split_conjunct,[status(thm)],[c_0_9757]), ['final']). 4.05/4.34 cnf(c_0_15304, plain, (hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),X3),X4))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_Map_Omap__of(X1,X2),X4)),hAPP(c_Product__Type_Ofst(X1,X2),X3)),hAPP(c_Option_Ooption_OSome(X2),hAPP(c_Product__Type_Osnd(X1,X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_9758]), ['final']). 4.05/4.34 cnf(c_0_15305, 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9759, c_0_6268]), c_0_9760]), c_0_6268]), c_0_6268]), ['final']). 4.05/4.34 cnf(c_0_15306, 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_9761, c_0_5201]), c_0_9762]), ['final']). 4.05/4.34 cnf(c_0_15307, 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_9763, c_0_5205]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15308, 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_9764, c_0_4902]), ['final']). 4.05/4.34 cnf(c_0_15309, 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_9765, c_0_9766]), ['final']). 4.05/4.34 cnf(c_0_15310, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Relation_OImage(X4,X2,X5)),X6))=hAPP(c_Relation_OImage(X4,X2,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6))), inference(split_conjunct,[status(thm)],[c_0_9767]), ['final']). 4.05/4.34 cnf(c_0_15311, 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_9768]), ['final']). 4.05/4.34 cnf(c_0_15312, 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_9769, c_0_4902]), ['final']). 4.05/4.34 cnf(c_0_15313, 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_5814, c_0_9766]), ['final']). 4.05/4.34 cnf(c_0_15314, 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_9770]), ['final']). 4.05/4.34 cnf(c_0_15315, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3)), inference(split_conjunct,[status(thm)],[c_0_9771]), ['final']). 4.05/4.34 cnf(c_0_15316, 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_9772]), ['final']). 4.05/4.34 cnf(c_0_15317, 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_9773]), ['final']). 4.05/4.34 cnf(c_0_15318, 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_9774, c_0_4822]), ['final']). 4.05/4.34 cnf(c_0_15319, 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_9775]), ['final']). 4.05/4.34 cnf(c_0_15320, plain, (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))=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))), inference(split_conjunct,[status(thm)],[c_0_9776]), ['final']). 4.05/4.34 cnf(c_0_15321, 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_9777]), ['final']). 4.05/4.34 cnf(c_0_15322, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9778]), ['final']). 4.05/4.34 cnf(c_0_15323, plain, (c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X3),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBB(tc_fun(X3,X2),tc_fun(tc_Option_Ooption(X3),tc_Option_Ooption(X2)),X1),c_Option_Omap(X3,X2)),X4)),X5))=c_Map_Odom(X1,X3,X5)), inference(split_conjunct,[status(thm)],[c_0_9779]), ['final']). 4.05/4.34 cnf(c_0_15324, 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_9780]), ['final']). 4.05/4.34 cnf(c_0_15325, 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_9781]), ['final']). 4.05/4.34 cnf(c_0_15326, 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_9782, c_0_4767]), c_0_4767]), ['final']). 4.05/4.34 cnf(c_0_15327, 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_9783]), ['final']). 4.05/4.34 cnf(c_0_15328, 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_9784]), ['final']). 4.05/4.34 cnf(c_0_15329, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9785]), ['final']). 4.05/4.34 cnf(c_0_15330, 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_9786]), ['final']). 4.05/4.34 cnf(c_0_15331, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Transitive__Closure_Ortrancl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool))))=c_FunDef_Opair__leq), inference(rw,[status(thm)],[c_0_9787, c_0_5716]), ['final']). 4.05/4.34 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)),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_9788, c_0_5696]), ['final']). 4.05/4.34 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)),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_9789, c_0_5696]), ['final']). 4.05/4.34 cnf(c_0_15334, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4))=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))), inference(split_conjunct,[status(thm)],[c_0_9790]), ['final']). 4.05/4.34 cnf(c_0_15335, 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_9791]), ['final']). 4.05/4.34 cnf(c_0_15336, 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_9792]), ['final']). 4.05/4.34 cnf(c_0_15337, 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_9793]), ['final']). 4.05/4.34 cnf(c_0_15338, 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_9794]), ['final']). 4.05/4.34 cnf(c_0_15339, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4))),c_Map_Odom(X1,X2,X5))=c_Map_Odom(X1,X2,c_Map_Omap__upds(X1,X2,X5,X4,X3))), inference(split_conjunct,[status(thm)],[c_0_9795]), ['final']). 4.05/4.34 cnf(c_0_15340, 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_9796, c_0_6268]), ['final']). 4.05/4.34 cnf(c_0_15341, 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_9797, c_0_4867]), c_0_5668]), c_0_5669]), c_0_5670]), ['final']). 4.05/4.34 cnf(c_0_15342, 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)), inference(split_conjunct,[status(thm)],[c_0_9798]), ['final']). 4.05/4.34 cnf(c_0_15343, 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_9799, c_0_5205]), ['final']). 4.05/4.34 cnf(c_0_15344, plain, (c_Lazy__Sequence_Oappend(tc_Option_Ooption(X1),hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)),tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)),c_Lazy__Sequence_Ohit__bound(X1),c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)))),X2),c_Lazy__Sequence_Ohb__flat(X1,X3))=c_Lazy__Sequence_Ohb__flat(X1,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1))),X2,X3))), inference(split_conjunct,[status(thm)],[c_0_9800]), ['final']). 4.05/4.34 cnf(c_0_15345, 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_9801, c_0_5201]), c_0_5201])]), ['final']). 4.05/4.34 cnf(c_0_15346, 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_9802]), ['final']). 4.05/4.34 cnf(c_0_15347, 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_9803]), ['final']). 4.05/4.34 cnf(c_0_15348, 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_9804]), ['final']). 4.05/4.34 cnf(c_0_15349, 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_9805, c_0_9806]), ['final']). 4.05/4.34 cnf(c_0_15350, 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_9807]), ['final']). 4.05/4.34 cnf(c_0_15351, 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_9808, c_0_9809]), ['final']). 4.05/4.34 cnf(c_0_15352, 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_9810, c_0_5696]), c_0_5696]), ['final']). 4.05/4.34 cnf(c_0_15353, 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_9811, c_0_9812]), ['final']). 4.05/4.34 cnf(c_0_15354, 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_9813]), ['final']). 4.05/4.34 cnf(c_0_15355, 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_9814, c_0_5131]), ['final']). 4.05/4.34 cnf(c_0_15356, 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))), inference(split_conjunct,[status(thm)],[c_0_9815]), ['final']). 4.05/4.34 cnf(c_0_15357, 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_9816]), ['final']). 4.05/4.34 cnf(c_0_15358, 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_9817]), ['final']). 4.05/4.34 cnf(c_0_15359, 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)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9818, c_0_5942]), c_0_5942]), ['final']). 4.05/4.34 cnf(c_0_15360, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2)=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)))), inference(split_conjunct,[status(thm)],[c_0_9819]), ['final']). 4.05/4.34 cnf(c_0_15361, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__add(X1,X2,X3,X4)),X5),hAPP(c_Option_Ooption_OSome(X2),X6))=c_Map_Omap__add(X1,X2,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X4),X5),hAPP(c_Option_Ooption_OSome(X2),X6)))), inference(split_conjunct,[status(thm)],[c_0_9820]), ['final']). 4.05/4.34 cnf(c_0_15362, 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_9821, c_0_5130]), c_0_5130]), ['final']). 4.05/4.34 cnf(c_0_15363, 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_9822, c_0_9823]), ['final']). 4.05/4.34 cnf(c_0_15364, 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_9824, c_0_9825]), ['final']). 4.05/4.34 cnf(c_0_15365, 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_9826, c_0_6106]), ['final']). 4.05/4.34 cnf(c_0_15366, 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_9827]), ['final']). 4.05/4.34 cnf(c_0_15367, 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_9828, c_0_4902]), c_0_4902]), c_0_4902]), ['final']). 4.05/4.34 cnf(c_0_15368, 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_9829, c_0_4902]), c_0_4902]), c_0_4902]), ['final']). 4.05/4.34 cnf(c_0_15369, 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_9830]), ['final']). 4.05/4.34 cnf(c_0_15370, 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_9831, c_0_4902]), c_0_4902]), c_0_4902]), ['final']). 4.05/4.34 cnf(c_0_15371, 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_9832, c_0_5011]), c_0_5011]), ['final']). 4.05/4.34 cnf(c_0_15372, 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_9833, c_0_9834]), ['final']). 4.05/4.34 cnf(c_0_15373, 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)), inference(split_conjunct,[status(thm)],[c_0_9835]), ['final']). 4.05/4.34 cnf(c_0_15374, 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_9836]), ['final']). 4.05/4.34 cnf(c_0_15375, 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_9837, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15376, plain, (c_Map_Odom(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X3),hAPP(c_Option_Ooption_OSome(X2),X4)))=hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(er,[status(thm)],[c_0_9838]), ['final']). 4.05/4.34 cnf(c_0_15377, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),X3)),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X4),X3))=hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)),X3)), inference(split_conjunct,[status(thm)],[c_0_9839]), ['final']). 4.05/4.34 cnf(c_0_15378, plain, (hAPP(c_List_Oset(tc_prod(X1,X2)),c_Enum_Oproduct(X1,X2,X3,X4))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_List_Oset(X1),X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_List_Oset(X2),X4)))), inference(split_conjunct,[status(thm)],[c_0_9840]), ['final']). 4.05/4.34 cnf(c_0_15379, 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_9841]), ['final']). 4.05/4.34 cnf(c_0_15380, plain, (c_Lazy__Sequence_Ohb__flat(X2,c_Lazy__Sequence_Ohb__map(X1,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))),X5),X4),hAPP(X3,X4)))=hAPP(c_New__DSequence_Oneg__bind(X1,X2,X3,X5),X4)), inference(rw,[status(thm)],[c_0_9842, c_0_6587]), ['final']). 4.05/4.34 cnf(c_0_15381, plain, (hAPP(c_Finite__Set_Ocard(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X2),X4))), inference(split_conjunct,[status(thm)],[c_0_9843]), ['final']). 4.05/4.34 cnf(c_0_15382, 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_9844])]), c_0_9845]), c_0_9845])]), ['final']). 4.05/4.34 cnf(c_0_15383, 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_9846]), ['final']). 4.05/4.34 cnf(c_0_15384, plain, (hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),tc_Option_Ooption(X2),tc_Option_Ooption(X3),hAPP(c_Option_Omap(X1,X2),X4)),hAPP(c_Option_Omap(X3,X1),X5))=hAPP(c_Option_Omap(X3,X2),hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9847]), ['final']). 4.05/4.34 cnf(c_0_15385, 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))), inference(split_conjunct,[status(thm)],[c_0_9848]), ['final']). 4.05/4.34 cnf(c_0_15386, 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_9849]), ['final']). 4.05/4.34 cnf(c_0_15387, 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_9850, c_0_5716]), ['final']). 4.05/4.34 cnf(c_0_15388, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4))=hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9851]), ['final']). 4.05/4.34 cnf(c_0_15389, 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_9852]), ['final']). 4.05/4.34 cnf(c_0_15390, 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))), inference(split_conjunct,[status(thm)],[c_0_9853]), ['final']). 4.05/4.34 cnf(c_0_15391, 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_9854, c_0_4902]), ['final']). 4.05/4.34 cnf(c_0_15392, plain, (hAPP(hAPP(c_List_Odrop(tc_prod(X1,X2)),X3),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))=hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Odrop(X1),X3),X4)),hAPP(hAPP(c_List_Odrop(X2),X3),X5))), inference(split_conjunct,[status(thm)],[c_0_9855]), ['final']). 4.05/4.34 cnf(c_0_15393, 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_9856, c_0_5011]), ['final']). 4.05/4.34 cnf(c_0_15394, plain, (c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))=c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_9857]), ['final']). 4.05/4.34 cnf(c_0_15395, 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_9858]), ['final']). 4.05/4.34 cnf(c_0_15396, 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))), inference(split_conjunct,[status(thm)],[c_0_9859]), ['final']). 4.05/4.34 cnf(c_0_15397, 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_9860]), ['final']). 4.05/4.34 cnf(c_0_15398, 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_9861, c_0_4523]), c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15399, 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_9862, c_0_4767]), ['final']). 4.05/4.34 cnf(c_0_15400, 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_9863]), ['final']). 4.05/4.34 cnf(c_0_15401, 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_9864, c_0_6606]), ['final']). 4.05/4.34 cnf(c_0_15402, plain, (c_Map_Omap__add(X1,X2,X3,hAPP(c_Map_Omap__of(X1,X2),hAPP(c_List_Orev(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))))=c_Map_Omap__upds(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_9865]), ['final']). 4.05/4.34 cnf(c_0_15403, 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_9866]), ['final']). 4.05/4.34 cnf(c_0_15404, 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))), inference(split_conjunct,[status(thm)],[c_0_9867]), ['final']). 4.05/4.34 cnf(c_0_15405, 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_9868]), ['final']). 4.05/4.34 cnf(c_0_15406, plain, (hAPP(c_Relation_ORange(X1,X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))=hAPP(hAPP(c_Set_Oinsert(X2),X4),hAPP(c_Relation_ORange(X1,X2),X5))), inference(split_conjunct,[status(thm)],[c_0_9869]), ['final']). 4.05/4.34 cnf(c_0_15407, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))=hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X5))), inference(split_conjunct,[status(thm)],[c_0_9870]), ['final']). 4.05/4.34 cnf(c_0_15408, 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_9871, c_0_5696]), ['final']). 4.05/4.34 cnf(c_0_15409, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(c_Nat_OSuc,X2)),c_List_Orotate1(X1)),X3)=hAPP(c_List_Orotate1(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9872, c_0_5942]), c_0_5942]), ['final']). 4.05/4.34 cnf(c_0_15410, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))))), inference(rw,[status(thm)],[c_0_9873, c_0_7243]), ['final']). 4.05/4.34 cnf(c_0_15411, 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_9874]), ['final']). 4.05/4.34 cnf(c_0_15412, 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_9875]), ['final']). 4.05/4.34 cnf(c_0_15413, 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_9876]), ['final']). 4.05/4.34 cnf(c_0_15414, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)),X3)=hAPP(c_Option_Ooption_OSome(X2),X4)), inference(er,[status(thm)],[c_0_9877]), ['final']). 4.05/4.34 cnf(c_0_15415, 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_9878, c_0_5696]), ['final']). 4.05/4.34 cnf(c_0_15416, plain, (hAPP(c_Relation_Oconverse(X1,X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5))=hAPP(hAPP(c_Relation_Orel__comp(X2,X3,X1),hAPP(c_Relation_Oconverse(X3,X2),X5)),hAPP(c_Relation_Oconverse(X1,X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9879]), ['final']). 4.05/4.34 cnf(c_0_15417, plain, (hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_OPow(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_9880]), ['final']). 4.05/4.34 cnf(c_0_15418, 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_9881]), ['final']). 4.05/4.34 cnf(c_0_15419, 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_9882, c_0_5011]), ['final']). 4.05/4.34 cnf(c_0_15420, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))), inference(rw,[status(thm)],[c_0_9883, c_0_5716]), ['final']). 4.05/4.34 cnf(c_0_15421, 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_9884]), ['final']). 4.05/4.34 cnf(c_0_15422, 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))), inference(split_conjunct,[status(thm)],[c_0_9885]), ['final']). 4.05/4.34 cnf(c_0_15423, 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_9886]), ['final']). 4.05/4.34 cnf(c_0_15424, 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_9887, c_0_5716]), ['final']). 4.05/4.34 cnf(c_0_15425, 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_9888]), ['final']). 4.05/4.34 cnf(c_0_15426, plain, (hAPP(hAPP(c_List_Onth(X1),X2),X3)=hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Oappend(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)),X3))), inference(split_conjunct,[status(thm)],[c_0_9889]), ['final']). 4.05/4.34 cnf(c_0_15427, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(X1)),c_Option_Ooption_ONone(X1)),hAPP(c_Set_Oimage(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_9890]), ['final']). 4.05/4.34 cnf(c_0_15428, 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_9891, c_0_5696]), c_0_9892]), ['final']). 4.05/4.34 cnf(c_0_15429, 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_9893]), ['final']). 4.05/4.34 cnf(c_0_15430, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OField(X1),X2)),hAPP(c_Relation_OField(X1),X3))=hAPP(c_Relation_OField(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9894]), ['final']). 4.05/4.34 cnf(c_0_15431, 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_9895, c_0_4902])]), ['final']). 4.05/4.34 cnf(c_0_15432, plain, (c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),X5))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X5)),X4),hAPP(X3,X4))), inference(split_conjunct,[status(thm)],[c_0_9896]), ['final']). 4.05/4.34 cnf(c_0_15433, 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_9897]), ['final']). 4.05/4.34 cnf(c_0_15434, 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_9898, c_0_5130]), c_0_5130]), ['final']). 4.05/4.34 cnf(c_0_15435, 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_9899, c_0_4950]), ['final']). 4.05/4.34 cnf(c_0_15436, plain, (X1=hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X2),hAPP(c_List_Onth(X2),X1)),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(X2)),X1))))), inference(rw,[status(thm)],[c_0_9900, c_0_4519]), ['final']). 4.05/4.34 cnf(c_0_15437, plain, (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),hAPP(c_COMBK(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_9901]), ['final']). 4.05/4.34 cnf(c_0_15438, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X6)),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_9902]), ['final']). 4.05/4.34 cnf(c_0_15439, 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_9903]), ['final']). 4.05/4.34 cnf(c_0_15440, 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_9904]), ['final']). 4.05/4.34 cnf(c_0_15441, 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_9905, c_0_5011]), c_0_5011]), ['final']). 4.05/4.34 cnf(c_0_15442, 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_9906]), ['final']). 4.05/4.34 cnf(c_0_15443, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9907]), ['final']). 4.05/4.34 cnf(c_0_15444, 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_9908]), ['final']). 4.05/4.34 cnf(c_0_15445, 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_9909]), ['final']). 4.05/4.34 cnf(c_0_15446, 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_9910]), ['final']). 4.05/4.34 cnf(c_0_15447, 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))), inference(split_conjunct,[status(thm)],[c_0_9911]), ['final']). 4.05/4.34 cnf(c_0_15448, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9912]), ['final']). 4.05/4.34 cnf(c_0_15449, 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_9913]), ['final']). 4.05/4.34 cnf(c_0_15450, 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))), inference(split_conjunct,[status(thm)],[c_0_9914]), ['final']). 4.05/4.34 cnf(c_0_15451, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_9915]), ['final']). 4.05/4.34 cnf(c_0_15452, 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))), inference(split_conjunct,[status(thm)],[c_0_9916]), ['final']). 4.05/4.34 cnf(c_0_15453, 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))), inference(split_conjunct,[status(thm)],[c_0_9917]), ['final']). 4.05/4.34 cnf(c_0_15454, 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_9918]), ['final']). 4.05/4.34 cnf(c_0_15455, 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_9919, c_0_5011]), c_0_5011]), ['final']). 4.05/4.34 cnf(c_0_15456, 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_9920, c_0_4867]), c_0_5669]), ['final']). 4.05/4.34 cnf(c_0_15457, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X3)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9921]), ['final']). 4.05/4.34 cnf(c_0_15458, 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),X2),X3))=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)), inference(split_conjunct,[status(thm)],[c_0_9922]), ['final']). 4.05/4.34 cnf(c_0_15459, 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_9923, c_0_5131]), ['final']). 4.05/4.34 cnf(c_0_15460, 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_9924]), ['final']). 4.05/4.34 cnf(c_0_15461, 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_9925, c_0_4519]), ['final']). 4.05/4.34 cnf(c_0_15462, 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_9926, c_0_5716]), ['final']). 4.05/4.34 cnf(c_0_15463, plain, (hAPP(c_New__DSequence_Opos__bind(X1,X2,X3,X4),X5)=hAPP(c_Lazy__Sequence_Obind(X1,X2,hAPP(X3,X5)),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_9927]), ['final']). 4.05/4.34 cnf(c_0_15464, 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_9928]), ['final']). 4.05/4.34 cnf(c_0_15465, 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_9929]), ['final']). 4.05/4.34 cnf(c_0_15466, 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_9930, c_0_4867]), c_0_5668]), c_0_5669]), ['final']). 4.05/4.34 cnf(c_0_15467, 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_9931]), ['final']). 4.05/4.34 cnf(c_0_15468, plain, (c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olistsp(X1,X2)),c_List_Olistsp(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_9932]), ['final']). 4.05/4.34 cnf(c_0_15469, 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_9933]), ['final']). 4.05/4.34 cnf(c_0_15470, 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_9934]), ['final']). 4.05/4.34 cnf(c_0_15471, 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_9935, c_0_6561]), c_0_6561]), ['final']). 4.05/4.34 cnf(c_0_15472, plain, (c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X1),hAPP(hAPP(c_Option_Omap(X2,X1),X3),X4),c_Lazy__Sequence_Ohb__map(X2,X1,X3,X5))=c_Lazy__Sequence_Ohb__map(X2,X1,X3,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X2),X4,X5))), inference(split_conjunct,[status(thm)],[c_0_9936]), ['final']). 4.05/4.34 cnf(c_0_15473, 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_9937]), ['final']). 4.05/4.34 cnf(c_0_15474, plain, (hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X3),c_Option_Ooption_ONone(X2)),X4)=c_Option_Ooption_ONone(X2)), inference(split_conjunct,[status(thm)],[c_0_9938]), ['final']). 4.05/4.34 cnf(c_0_15475, 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_9939, c_0_5905]), ['final']). 4.05/4.34 cnf(c_0_15476, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X3)), inference(split_conjunct,[status(thm)],[c_0_9940]), ['final']). 4.05/4.34 cnf(c_0_15477, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_9941]), ['final']). 4.05/4.34 cnf(c_0_15478, 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_9942]), ['final']). 4.05/4.34 cnf(c_0_15479, plain, (c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X2,c_Option_Ooption_ONone(X1),hAPP(hAPP(c_COMBB(X1,tc_Option_Ooption(X1),X2),c_Option_Ooption_OSome(X1)),X3))=hAPP(c_Option_Omap(X2,X1),X3)), inference(split_conjunct,[status(thm)],[c_0_9943]), ['final']). 4.05/4.34 cnf(c_0_15480, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9944]), ['final']). 4.05/4.34 cnf(c_0_15481, 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)), inference(split_conjunct,[status(thm)],[c_0_9945]), ['final']). 4.05/4.34 cnf(c_0_15482, plain, (hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),X3),X4))=c_Map_Omap__add(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X4),hAPP(c_Map_Omap__of(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_9946]), ['final']). 4.05/4.34 cnf(c_0_15483, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Ofilter(X1,X2),X3)),hAPP(c_List_Ofilter(X1,X2),X4))=hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4))), inference(split_conjunct,[status(thm)],[c_0_9947]), ['final']). 4.05/4.34 cnf(c_0_15484, 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_9948, c_0_4902]), ['final']). 4.05/4.34 cnf(c_0_15485, 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_9949, c_0_9762]), ['final']). 4.05/4.34 cnf(c_0_15486, 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_9950, c_0_4902]), ['final']). 4.05/4.34 cnf(c_0_15487, 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_9951, c_0_4902]), ['final']). 4.05/4.34 cnf(c_0_15488, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1))=X2), inference(rw,[status(thm)],[c_0_9952, c_0_4902]), ['final']). 4.05/4.34 cnf(c_0_15489, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_COMBI(X1))=X2), inference(rw,[status(thm)],[c_0_9953, c_0_4902]), ['final']). 4.05/4.34 cnf(c_0_15490, plain, (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),X1),X2)),X3))=hAPP(hAPP(c_List_Odrop(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)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9954, c_0_4519]), c_0_4519]), ['final']). 4.05/4.34 cnf(c_0_15491, 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_9955]), ['final']). 4.05/4.34 cnf(c_0_15492, 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_9956])])]), c_0_9957]), c_0_4867]), c_0_9958]), ['final']). 4.05/4.34 cnf(c_0_15493, 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_9959]), ['final']). 4.05/4.34 cnf(c_0_15494, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),hAPP(c_Map_Omap__of(X2,X1),X3)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))), inference(split_conjunct,[status(thm)],[c_0_9960]), ['final']). 4.05/4.34 cnf(c_0_15495, plain, (hAPP(c_List_Ofoldl(X1,X2,X3,X4),hAPP(hAPP(c_List_Oappend(X2),X5),X6))=hAPP(c_List_Ofoldl(X1,X2,X3,hAPP(c_List_Ofoldl(X1,X2,X3,X4),X5)),X6)), inference(split_conjunct,[status(thm)],[c_0_9961]), ['final']). 4.05/4.34 cnf(c_0_15496, plain, (c_Fun_Oinj__on(X1,tc_prod(X2,X1),esk293_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_9707]), ['final']). 4.05/4.34 cnf(c_0_15497, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X3)=c_Divides_Odiv__class_Omod(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_9962]), ['final']). 4.05/4.34 cnf(c_0_15498, 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_9963]), ['final']). 4.05/4.34 cnf(c_0_15499, 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)), inference(split_conjunct,[status(thm)],[c_0_9964]), ['final']). 4.05/4.34 cnf(c_0_15500, 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_9965]), ['final']). 4.05/4.34 cnf(c_0_15501, 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_9966]), ['final']). 4.05/4.34 cnf(c_0_15502, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)), inference(rw,[status(thm)],[c_0_9967, c_0_5942]), ['final']). 4.05/4.34 cnf(c_0_15503, plain, (c_Map_Odom(X1,X2,c_Map_Omap__add(X1,X2,X3,X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X4)),c_Map_Odom(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_9968]), ['final']). 4.05/4.34 cnf(c_0_15504, 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_9969]), ['final']). 4.05/4.34 cnf(c_0_15505, 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_9970]), ['final']). 4.05/4.34 cnf(c_0_15506, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X2),X1,c_Option_Ooption_ONone(X2),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),hAPP(X4,X5))=c_Option_Ooption_ONone(X2)), inference(rw,[status(thm)],[c_0_9971, c_0_7211]), ['final']). 4.05/4.34 cnf(c_0_15507, 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_9972, c_0_4767]), ['final']). 4.05/4.34 cnf(c_0_15508, plain, (hAPP(c_Option_Ooption_OSome(tc_prod(X1,tc_Lazy__Sequence_Olazy__sequence(X1))),hAPP(hAPP(c_Product__Type_OPair(X1,tc_Lazy__Sequence_Olazy__sequence(X1)),X2),X3))=hAPP(c_Lazy__Sequence_Oyield(X1),c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_9973]), ['final']). 4.05/4.34 cnf(c_0_15509, 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_9974, c_0_4795]), ['final']). 4.05/4.34 cnf(c_0_15510, 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_9975, c_0_4635]), c_0_5149]), c_0_4867]), ['final']). 4.05/4.34 cnf(c_0_15511, 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_9976]), ['final']). 4.05/4.34 cnf(c_0_15512, 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_9977]), ['final']). 4.05/4.34 cnf(c_0_15513, plain, (hAPP(c_Product__Type_Osnd(X1,X2),X3)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X2),hAPP(c_COMBK(tc_fun(X2,X2),X1),c_COMBI(X2))),X3)), inference(split_conjunct,[status(thm)],[c_0_9978]), ['final']). 4.05/4.34 cnf(c_0_15514, 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_9979]), ['final']). 4.05/4.34 cnf(c_0_15515, 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_9980]), ['final']). 4.05/4.34 cnf(c_0_15516, 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_9981]), ['final']). 4.05/4.34 cnf(c_0_15517, 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_9982]), ['final']). 4.05/4.34 cnf(c_0_15518, 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_9983]), ['final']). 4.05/4.34 cnf(c_0_15519, 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)), inference(split_conjunct,[status(thm)],[c_0_9984]), ['final']). 4.05/4.34 cnf(c_0_15520, 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)), inference(split_conjunct,[status(thm)],[c_0_9985]), ['final']). 4.05/4.34 cnf(c_0_15521, 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_9986]), ['final']). 4.05/4.34 cnf(c_0_15522, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X1),X2)),hAPP(c_Relation_ORange(X1,X1),X2))=hAPP(c_Relation_OField(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_9987]), ['final']). 4.05/4.34 cnf(c_0_15523, 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_9988, c_0_6120]), c_0_9989]), c_0_4867]), c_0_6120]), c_0_5905]), ['final']). 4.05/4.34 cnf(c_0_15524, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBI(tc_fun(X1,tc_HOL_Obool)))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)), inference(split_conjunct,[status(thm)],[c_0_9990]), ['final']). 4.05/4.34 cnf(c_0_15525, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBI(tc_fun(X1,tc_HOL_Obool)))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)), inference(split_conjunct,[status(thm)],[c_0_9991]), ['final']). 4.05/4.34 cnf(c_0_15526, 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)), inference(split_conjunct,[status(thm)],[c_0_9992]), ['final']). 4.05/4.34 cnf(c_0_15527, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))), inference(split_conjunct,[status(thm)],[c_0_9993]), ['final']). 4.05/4.34 cnf(c_0_15528, 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_9994]), c_0_9995]), c_0_9995]), ['final']). 4.05/4.34 cnf(c_0_15529, 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_9996, c_0_5149]), c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_15530, 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)), inference(split_conjunct,[status(thm)],[c_0_9997]), ['final']). 4.05/4.34 cnf(c_0_15531, 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)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9998, c_0_5716]), c_0_5716]), ['final']). 4.05/4.34 cnf(c_0_15532, 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_9999]), ['final']). 4.05/4.34 cnf(c_0_15533, 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_10000]), ['final']). 4.05/4.34 cnf(c_0_15534, 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_10001]), ['final']). 4.05/4.34 cnf(c_0_15535, 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_10002]), ['final']). 4.05/4.34 cnf(c_0_15536, 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_10003]), ['final']). 4.05/4.34 cnf(c_0_15537, 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_10004]), ['final']). 4.05/4.34 cnf(c_0_15538, 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_10005]), ['final']). 4.05/4.34 cnf(c_0_15539, 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_10006]), ['final']). 4.05/4.34 cnf(c_0_15540, 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_10007, c_0_4867]), ['final']). 4.05/4.34 cnf(c_0_15541, 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_10008, c_0_10009]), ['final']). 4.05/4.34 cnf(c_0_15542, 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_10010, c_0_6492]), ['final']). 4.05/4.34 cnf(c_0_15543, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10011]), ['final']). 4.05/4.34 cnf(c_0_15544, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)=c_List_Obutlast(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_10012]), ['final']). 4.05/4.34 cnf(c_0_15545, 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)), inference(rw,[status(thm)],[c_0_10013, c_0_6268]), ['final']). 4.05/4.34 cnf(c_0_15546, 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)), inference(rw,[status(thm)],[c_0_10014, c_0_6268]), ['final']). 4.05/4.34 cnf(c_0_15547, 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)), inference(rw,[status(thm)],[c_0_10015, c_0_5942]), ['final']). 4.05/4.34 cnf(c_0_15548, plain, (c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))), inference(split_conjunct,[status(thm)],[c_0_10016]), ['final']). 4.05/4.34 cnf(c_0_15549, 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_10017]), ['final']). 4.05/4.34 cnf(c_0_15550, 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_10018]), ['final']). 4.05/4.34 cnf(c_0_15551, plain, (c_Code__Numeral_Odiv__mod__code__numeral(X1,X2)=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))), inference(split_conjunct,[status(thm)],[c_0_10019]), ['final']). 4.05/4.34 cnf(c_0_15552, 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_10020]), ['final']). 4.05/4.34 cnf(c_0_15553, 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_10021]), ['final']). 4.05/4.34 cnf(c_0_15554, 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_10022]), ['final']). 4.05/4.34 cnf(c_0_15555, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4))=hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4)), inference(split_conjunct,[status(thm)],[c_0_10023]), ['final']). 4.05/4.34 cnf(c_0_15556, 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_10024, c_0_5011]), ['final']). 4.05/4.34 cnf(c_0_15557, 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)), inference(split_conjunct,[status(thm)],[c_0_10025]), ['final']). 4.05/4.34 cnf(c_0_15558, 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_10026]), ['final']). 4.05/4.34 cnf(c_0_15559, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_10027]), ['final']). 4.05/4.34 cnf(c_0_15560, 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_10028]), ['final']). 4.05/4.34 cnf(c_0_15561, 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_10029]), ['final']). 4.05/4.34 cnf(c_0_15562, 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_10030]), ['final']). 4.05/4.34 cnf(c_0_15563, 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_10031]), ['final']). 4.05/4.34 cnf(c_0_15564, plain, (hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4))=hAPP(c_Product__Type_Ofst(X5,X6),hAPP(c_Product__Type_Omap__pair(X2,X5,X3,X6,X1,X7),X4))), inference(split_conjunct,[status(thm)],[c_0_10032]), ['final']). 4.05/4.34 cnf(c_0_15565, 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_10033]), ['final']). 4.05/4.34 cnf(c_0_15566, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2))=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))), inference(split_conjunct,[status(thm)],[c_0_10034]), ['final']). 4.05/4.34 cnf(c_0_15567, 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_10035]), ['final']). 4.05/4.34 cnf(c_0_15568, plain, (c_Enum_Oenum__the(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_10036, c_0_5695]), ['final']). 4.05/4.34 cnf(c_0_15569, 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_10037, c_0_5695]), ['final']). 4.05/4.34 cnf(c_0_15570, 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_10038]), ['final']). 4.05/4.34 cnf(c_0_15571, 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_10039]), ['final']). 4.05/4.34 cnf(c_0_15572, 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_10040, c_0_4867]), c_0_5669]), ['final']). 4.05/4.34 cnf(c_0_15573, 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_10041, c_0_5696]), ['final']). 4.05/4.34 cnf(c_0_15574, 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_10042]), ['final']). 4.05/4.34 cnf(c_0_15575, 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_10043, c_0_5696]), ['final']). 4.05/4.34 cnf(c_0_15576, plain, (X1=hAPP(hAPP(c_Relation_Orel__comp(X2,X2,X3),c_Transitive__Closure_Ortrancl(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),X1)), inference(rw,[status(thm)],[c_0_10044, c_0_5716]), ['final']). 4.05/4.34 cnf(c_0_15577, 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_10045, c_0_5716]), ['final']). 4.05/4.34 cnf(c_0_15578, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10046]), ['final']). 4.05/4.34 cnf(c_0_15579, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBB(X2,tc_Option_Ooption(X2),X1),c_Option_Ooption_OSome(X2)),X3))), inference(split_conjunct,[status(thm)],[c_0_10047]), ['final']). 4.05/4.34 cnf(c_0_15580, 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_10048, c_0_4523])]), ['final']). 4.05/4.34 cnf(c_0_15581, 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_10049]), ['final']). 4.05/4.34 cnf(c_0_15582, plain, (hAPP(hAPP(X1,X2),X3)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X5,X6),X1),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_10050]), ['final']). 4.05/4.34 cnf(c_0_15583, 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']). 4.05/4.34 cnf(c_0_15584, plain, (c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[fact_UN__lessThan__UNIV]), ['final']). 4.05/4.34 cnf(c_0_15585, 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']). 4.05/4.34 cnf(c_0_15586, plain, (c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[fact_UN__atLeast__UNIV]), ['final']). 4.05/4.34 cnf(c_0_15587, 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_10051]), ['final']). 4.05/4.34 cnf(c_0_15588, 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_10052, c_0_5379]), c_0_4867]), c_0_5669]), ['final']). 4.05/4.34 cnf(c_0_15589, plain, (c_Predicate_Opred__comp(X1,X2,X3,c_Predicate_Oconversep(X2,X1,X4),c_Predicate_Oconversep(X3,X2,X5))=c_Predicate_Oconversep(X3,X1,c_Predicate_Opred__comp(X3,X2,X1,X5,X4))), inference(split_conjunct,[status(thm)],[c_0_10053]), ['final']). 4.05/4.34 cnf(c_0_15590, 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_10054]), ['final']). 4.05/4.34 cnf(c_0_15591, plain, (c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool))=c_Sum__Type_OPlus(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10055]), ['final']). 4.05/4.34 cnf(c_0_15592, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)=hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)), inference(split_conjunct,[status(thm)],[c_0_10056]), ['final']). 4.05/4.34 cnf(c_0_15593, 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_10057, c_0_7018]), ['final']). 4.05/4.34 cnf(c_0_15594, 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_10058])]), ['final']). 4.05/4.34 cnf(c_0_15595, 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_10059]), ['final']). 4.05/4.34 cnf(c_0_15596, 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_10060]), ['final']). 4.05/4.34 cnf(c_0_15597, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))), inference(rw,[status(thm)],[c_0_10061, c_0_10062]), ['final']). 4.05/4.34 cnf(c_0_15598, 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_10063]), ['final']). 4.05/4.34 cnf(c_0_15599, 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_10064]), ['final']). 4.05/4.34 cnf(c_0_15600, plain, (c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))=c_Transitive__Closure_Ortrancl(X1,X2)), inference(rw,[status(thm)],[c_0_10065, c_0_6268]), ['final']). 4.05/4.34 cnf(c_0_15601, 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_10066, c_0_6268]), ['final']). 4.05/4.34 cnf(c_0_15602, 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_10067]), ['final']). 4.05/4.34 cnf(c_0_15603, 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_10068]), ['final']). 4.05/4.34 cnf(c_0_15604, 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_10069]), c_0_10070]), ['final']). 4.05/4.34 cnf(c_0_15605, plain, (hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X2)),X3))=hAPP(hAPP(c_List_Otake(X1),X2),hAPP(c_List_Otl(X1),X3))), inference(split_conjunct,[status(thm)],[c_0_10071]), ['final']). 4.05/4.34 cnf(c_0_15606, 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_10072]), ['final']). 4.05/4.34 cnf(c_0_15607, 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_10073, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15608, 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_10074, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15609, 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_10075]), ['final']). 4.05/4.34 cnf(c_0_15610, 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_10076]), ['final']). 4.05/4.34 cnf(c_0_15611, 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_10077]), ['final']). 4.05/4.34 cnf(c_0_15612, 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_10078]), ['final']). 4.05/4.34 cnf(c_0_15613, 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_10079]), ['final']). 4.05/4.34 cnf(c_0_15614, plain, (c_Map_Orestrict__map(X1,X2,c_Map_Orestrict__map(X1,X2,X3,X4),X5)=c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5))), inference(split_conjunct,[status(thm)],[c_0_10080]), ['final']). 4.05/4.34 cnf(c_0_15615, plain, (c_Map_Omap__le(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),c_Option_Ooption_ONone(X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_10081]), ['final']). 4.05/4.34 cnf(c_0_15616, 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_10082]), ['final']). 4.05/4.34 cnf(c_0_15617, 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_10083, c_0_4427]), c_0_4865]), c_0_4427]), c_0_4865]), ['final']). 4.05/4.34 cnf(c_0_15618, 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_10084]), ['final']). 4.05/4.34 cnf(c_0_15619, 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_10085]), ['final']). 4.05/4.34 cnf(c_0_15620, 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)), inference(split_conjunct,[status(thm)],[c_0_10086]), ['final']). 4.05/4.34 cnf(c_0_15621, 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_10087]), ['final']). 4.05/4.34 cnf(c_0_15622, 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_10088]), ['final']). 4.05/4.34 cnf(c_0_15623, 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_Enum_Oenum__the(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)))), inference(rw,[status(thm)],[c_0_10089, c_0_6300]), ['final']). 4.05/4.34 cnf(c_0_15624, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Odrop(X1),X2),X3))=X3), inference(split_conjunct,[status(thm)],[c_0_10090]), ['final']). 4.05/4.34 cnf(c_0_15625, plain, (X1=hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(c_Product__Type_Ofst(X2,X3),X1)),hAPP(c_Product__Type_Osnd(X2,X3),X1))), inference(split_conjunct,[status(thm)],[c_0_10091]), ['final']). 4.05/4.34 cnf(c_0_15626, 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))), inference(split_conjunct,[status(thm)],[c_0_10092]), ['final']). 4.05/4.34 cnf(c_0_15627, 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_10093]), ['final']). 4.05/4.34 cnf(c_0_15628, plain, (hAPP(hAPP(X1,X2),X3)=c_Product__Type_Oprod_Oprod__rec(X4,X5,X6,X1,hAPP(hAPP(c_Product__Type_OPair(X4,X5),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_10094]), ['final']). 4.05/4.34 cnf(c_0_15629, 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_10095, c_0_5165]), c_0_7540]), ['final']). 4.05/4.34 cnf(c_0_15630, plain, (hAPP(c_Map_Orestrict__map(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),X3),X4)=c_Option_Ooption_ONone(X2)), inference(split_conjunct,[status(thm)],[c_0_10096]), ['final']). 4.05/4.34 cnf(c_0_15631, 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_10097, c_0_4523]), ['final']). 4.05/4.34 cnf(c_0_15632, 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_10098]), ['final']). 4.05/4.34 cnf(c_0_15633, plain, (hAPP(c_List_Oset(X1),c_List_Oreplicate(X1,hAPP(c_Nat_OSuc,X2),X3))=hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10099]), ['final']). 4.05/4.34 cnf(c_0_15634, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_10100]), ['final']). 4.05/4.34 cnf(c_0_15635, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Otl(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_10101]), ['final']). 4.05/4.34 cnf(c_0_15636, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)), inference(rw,[status(thm)],[c_0_10102, c_0_4519]), ['final']). 4.05/4.34 cnf(c_0_15637, 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))), inference(split_conjunct,[status(thm)],[c_0_10103]), ['final']). 4.05/4.34 cnf(c_0_15638, 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_10104]), ['final']). 4.05/4.34 cnf(c_0_15639, 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_10105, c_0_5011]), ['final']). 4.05/4.34 cnf(c_0_15640, 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_10106]), ['final']). 4.05/4.34 cnf(c_0_15641, 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_10107]), ['final']). 4.05/4.34 cnf(c_0_15642, 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_10108]), ['final']). 4.05/4.34 cnf(c_0_15643, 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_10109, c_0_5716]), ['final']). 4.05/4.34 cnf(c_0_15644, 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_10110]), ['final']). 4.05/4.34 cnf(c_0_15645, plain, (c_Map_Omap__upds(X1,X2,c_Map_Omap__add(X1,X2,X3,X4),X5,X6)=c_Map_Omap__add(X1,X2,X3,c_Map_Omap__upds(X1,X2,X4,X5,X6))), inference(split_conjunct,[status(thm)],[c_0_10111]), ['final']). 4.05/4.34 cnf(c_0_15646, 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_10112, c_0_5905]), ['final']). 4.05/4.34 cnf(c_0_15647, 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_10113]), ['final']). 4.05/4.34 cnf(c_0_15648, plain, (c_SetInterval_Oord__class_OatLeastAtMost(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),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10114]), ['final']). 4.05/4.34 cnf(c_0_15649, plain, (hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Enum_Oenum__the(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_10115, c_0_6300]), ['final']). 4.05/4.34 cnf(c_0_15650, 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_10116]), ['final']). 4.05/4.34 cnf(c_0_15651, 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_10117]), ['final']). 4.05/4.34 cnf(c_0_15652, 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_10118]), ['final']). 4.05/4.34 cnf(c_0_15653, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10119]), ['final']). 4.05/4.34 cnf(c_0_15654, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)), inference(split_conjunct,[status(thm)],[c_0_10120]), ['final']). 4.05/4.34 cnf(c_0_15655, 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_10121]), ['final']). 4.05/4.34 cnf(c_0_15656, 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)), inference(split_conjunct,[status(thm)],[c_0_10122]), ['final']). 4.05/4.34 cnf(c_0_15657, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Obutlast(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10123]), ['final']). 4.05/4.34 cnf(c_0_15658, plain, (hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),X1),X2)=c_Smallcheck_Osmall_H(X1,hAPP(c_Code__Numeral_Oint__of,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X2)))), inference(split_conjunct,[status(thm)],[c_0_10124]), ['final']). 4.05/4.34 cnf(c_0_15659, plain, (X1=hAPP(hAPP(c_Product__Type_Oscomp(X2,X3,X4,tc_prod(X3,X4)),X1),c_Product__Type_OPair(X3,X4))), inference(split_conjunct,[status(thm)],[c_0_10125]), ['final']). 4.05/4.34 cnf(c_0_15660, plain, (c_Int_OInteg=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)), inference(split_conjunct,[status(thm)],[fact_Integ__def]), ['final']). 4.05/4.34 cnf(c_0_15661, 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))), inference(split_conjunct,[status(thm)],[c_0_10126]), ['final']). 4.05/4.34 cnf(c_0_15662, plain, (c_Map_Odom(X1,X2,c_Map_Orestrict__map(X1,X2,X3,X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),X4)), inference(split_conjunct,[status(thm)],[c_0_10127]), ['final']). 4.05/4.34 cnf(c_0_15663, 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))), inference(split_conjunct,[status(thm)],[c_0_10128]), ['final']). 4.05/4.34 cnf(c_0_15664, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2)), inference(split_conjunct,[status(thm)],[c_0_10129]), ['final']). 4.05/4.34 cnf(c_0_15665, 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_10130]), ['final']). 4.05/4.34 cnf(c_0_15666, 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_10131]), ['final']). 4.05/4.34 cnf(c_0_15667, 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),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10132]), ['final']). 4.05/4.34 cnf(c_0_15668, 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_10133]), ['final']). 4.05/4.34 cnf(c_0_15669, 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_10134]), ['final']). 4.05/4.34 cnf(c_0_15670, 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_10135]), ['final']). 4.05/4.34 cnf(c_0_15671, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=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)))), inference(split_conjunct,[status(thm)],[c_0_10136]), ['final']). 4.05/4.34 cnf(c_0_15672, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Enum_Oenum__the(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), inference(rw,[status(thm)],[c_0_10137, c_0_6300]), ['final']). 4.05/4.34 cnf(c_0_15673, 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_10138]), ['final']). 4.05/4.34 cnf(c_0_15674, plain, (c_Option_Ooption_Ooption__size(X1,X2,hAPP(c_Option_Ooption_OSome(X1),X3))=hAPP(c_Nat_OSuc,hAPP(X2,X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10139, c_0_4867]), c_0_5669]), ['final']). 4.05/4.34 cnf(c_0_15675, 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_10140]), ['final']). 4.05/4.34 cnf(c_0_15676, 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_10141, c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_15677, 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_10142, c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_15678, 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_10143, c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_15679, 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_10144, c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_15680, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_10145]), ['final']). 4.05/4.34 cnf(c_0_15681, 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_10146]), ['final']). 4.05/4.34 cnf(c_0_15682, 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_10147]), ['final']). 4.05/4.34 cnf(c_0_15683, 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_10148]), ['final']). 4.05/4.34 cnf(c_0_15684, 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_10149, c_0_10150]), ['final']). 4.05/4.34 cnf(c_0_15685, plain, (c_List_Oreplicate(X1,X2,hAPP(X3,X4))=hAPP(hAPP(c_List_Omap(X5,X1),X3),c_List_Oreplicate(X5,X2,X4))), inference(split_conjunct,[status(thm)],[c_0_10151]), ['final']). 4.05/4.34 cnf(c_0_15686, 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_10152]), ['final']). 4.05/4.34 cnf(c_0_15687, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X1,X2,X3))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10153, c_0_4867]), c_0_5669]), ['final']). 4.05/4.34 cnf(c_0_15688, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X1)=hAPP(c_fequal,X1)), inference(rw,[status(thm)],[c_0_10154, c_0_5696]), ['final']). 4.05/4.34 cnf(c_0_15689, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_10155]), ['final']). 4.05/4.34 cnf(c_0_15690, 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_10156, c_0_7018]), c_0_7018]), ['final']). 4.05/4.34 cnf(c_0_15691, 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_10157]), ['final']). 4.05/4.34 cnf(c_0_15692, 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_10158]), ['final']). 4.05/4.34 cnf(c_0_15693, 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_10159, c_0_5011]), c_0_5011]), ['final']). 4.05/4.34 cnf(c_0_15694, 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_10160]), ['final']). 4.05/4.34 cnf(c_0_15695, 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)), inference(split_conjunct,[status(thm)],[c_0_10161]), ['final']). 4.05/4.34 cnf(c_0_15696, 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_10162, c_0_5379]), c_0_5379]), c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_15697, 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_10163, c_0_5130]), c_0_5130]), ['final']). 4.05/4.34 cnf(c_0_15698, 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_10164, c_0_5379]), c_0_5379]), c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_15699, 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_10165, c_0_5379]), c_0_4867]), c_0_5669]), ['final']). 4.05/4.34 cnf(c_0_15700, plain, (c_Map_Omap__add(X1,X2,X3,c_Map_Omap__add(X1,X2,X4,X5))=c_Map_Omap__add(X1,X2,c_Map_Omap__add(X1,X2,X3,X4),X5)), inference(split_conjunct,[status(thm)],[c_0_10166]), ['final']). 4.05/4.34 cnf(c_0_15701, 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_10167]), ['final']). 4.05/4.34 cnf(c_0_15702, plain, (c_Smallcheck_Ofull__small_H(X1,hAPP(c_Code__Numeral_Oint__of,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X2)))=c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_10168]), ['final']). 4.05/4.34 cnf(c_0_15703, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=c_Map_Oran(X2,X1,hAPP(c_COMBK(tc_Option_Ooption(X1),X2),c_Option_Ooption_ONone(X1)))), inference(split_conjunct,[status(thm)],[c_0_10169]), ['final']). 4.05/4.34 cnf(c_0_15704, 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_10170]), ['final']). 4.05/4.34 cnf(c_0_15705, 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_10171]), ['final']). 4.05/4.34 cnf(c_0_15706, 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_10172]), ['final']). 4.05/4.34 cnf(c_0_15707, 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_10173]), ['final']). 4.05/4.34 cnf(c_0_15708, 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_10174]), ['final']). 4.05/4.34 cnf(c_0_15709, plain, (hAPP(c_Option_Ooption_OSome(X1),hAPP(X2,X3))=hAPP(hAPP(c_Option_Omap(X4,X1),X2),hAPP(c_Option_Ooption_OSome(X4),X3))), inference(split_conjunct,[status(thm)],[c_0_10175]), ['final']). 4.05/4.34 cnf(c_0_15710, 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))), inference(split_conjunct,[status(thm)],[c_0_10176]), ['final']). 4.05/4.34 cnf(c_0_15711, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))))), inference(er,[status(thm)],[c_0_10177]), ['final']). 4.05/4.34 cnf(c_0_15712, 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_10178]), ['final']). 4.05/4.34 cnf(c_0_15713, plain, (c_List_Oreplicate(X1,hAPP(c_Nat_OSuc,X2),X3)=hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Oreplicate(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_10179]), ['final']). 4.05/4.34 cnf(c_0_15714, plain, (c_Lazy__Sequence_Oappend(tc_Option_Ooption(X1),hAPP(X2,X3),hAPP(X4,X3))=hAPP(c_New__DSequence_Oneg__union(X1,X2,X4),X3)), inference(split_conjunct,[status(thm)],[c_0_10180]), ['final']). 4.05/4.34 cnf(c_0_15715, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Obutlast(X1,X3))=c_List_Obutlast(X1,hAPP(hAPP(c_List_Odrop(X1),X2),X3))), inference(split_conjunct,[status(thm)],[c_0_10181]), ['final']). 4.05/4.34 cnf(c_0_15716, 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_10182]), ['final']). 4.05/4.34 cnf(c_0_15717, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4))), inference(split_conjunct,[status(thm)],[c_0_10183]), ['final']). 4.05/4.34 cnf(c_0_15718, 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_10184]), ['final']). 4.05/4.34 cnf(c_0_15719, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),c_Enum_Oenum__the(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))))), inference(rw,[status(thm)],[c_0_10185, c_0_6300]), ['final']). 4.05/4.34 cnf(c_0_15720, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X1)=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))), inference(split_conjunct,[status(thm)],[c_0_10186]), ['final']). 4.05/4.34 cnf(c_0_15721, plain, (hAPP(hAPP(X1,X2),X3)=c_Nitpick_Opair__box_Opair__box__rec(X4,X5,X6,X1,c_Nitpick_Opair__box_OPairBox(X4,X5,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_10187]), ['final']). 4.05/4.34 cnf(c_0_15722, 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_10188]), ['final']). 4.05/4.34 cnf(c_0_15723, plain, (c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel)), inference(split_conjunct,[status(thm)],[fact_equiv__intrel]), ['final']). 4.05/4.34 cnf(c_0_15724, 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_10189, c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_15725, plain, (hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6)=hAPP(X4,hAPP(X5,X6))), inference(split_conjunct,[status(thm)],[c_0_10190]), ['final']). 4.05/4.34 cnf(c_0_15726, plain, (hAPP(hAPP(X1,X2),X3)=hAPP(hAPP(hAPP(c_COMBC(X4,X5,X6),X1),X3),X2)), inference(split_conjunct,[status(thm)],[c_0_10191]), ['final']). 4.05/4.34 cnf(c_0_15727, 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_10192, c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_15728, 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_10193]), ['final']). 4.05/4.34 cnf(c_0_15729, plain, (c_Map_Omap__add(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),X3)=X3), inference(split_conjunct,[status(thm)],[c_0_10194]), ['final']). 4.05/4.34 cnf(c_0_15730, 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_10195, c_0_4635]), c_0_4635])])]), c_0_10196]), ['final']). 4.05/4.34 cnf(c_0_15731, plain, (c_Map_Omap__add(X1,X2,X3,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)))=X3), inference(split_conjunct,[status(thm)],[c_0_10197]), ['final']). 4.05/4.34 cnf(c_0_15732, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),X5)=c_Enum_Oenum__the(X2,c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5))), inference(rw,[status(thm)],[c_0_10198, c_0_4980]), ['final']). 4.05/4.34 cnf(c_0_15733, 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_10199, c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_15734, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X1,X2))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10200, c_0_4867]), c_0_5669]), ['final']). 4.05/4.34 cnf(c_0_15735, 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_10201, c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_15736, 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_10202]), ['final']). 4.05/4.34 cnf(c_0_15737, plain, (hAPP(c_Relation_OImage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10203]), ['final']). 4.05/4.34 cnf(c_0_15738, 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_10204]), ['final']). 4.05/4.34 cnf(c_0_15739, 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))), inference(split_conjunct,[status(thm)],[c_0_10205]), ['final']). 4.05/4.34 cnf(c_0_15740, plain, (c_Predicate_Opred__comp(X1,X1,X1,c_fequal,c_Predicate_Opred__comp(X1,X1,X1,X2,c_fequal))=X2), inference(split_conjunct,[status(thm)],[c_0_10206]), ['final']). 4.05/4.34 cnf(c_0_15741, 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_10207]), ['final']). 4.05/4.34 cnf(c_0_15742, 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_10208, c_0_10209]), c_0_5379]), c_0_5379]), c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_15743, plain, (c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2))=c_List_Otranspose(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_10210]), ['final']). 4.05/4.34 cnf(c_0_15744, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3))=hAPP(c_Relation_ORange(X2,X1),X3)), inference(split_conjunct,[status(thm)],[c_0_10211]), ['final']). 4.05/4.34 cnf(c_0_15745, plain, (hAPP(c_Relation_ODomain(X1,X2),X3)=hAPP(c_Relation_ORange(X2,X1),hAPP(c_Relation_Oconverse(X1,X2),X3))), inference(split_conjunct,[status(thm)],[c_0_10212]), ['final']). 4.05/4.34 cnf(c_0_15746, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk449_1(X1)),c_Int_OInteg))), inference(split_conjunct,[status(thm)],[c_0_10213]), ['final']). 4.05/4.34 cnf(c_0_15747, plain, (hAPP(c_Map_Orestrict__map(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4)=c_Option_Ooption_ONone(X2)), inference(split_conjunct,[status(thm)],[c_0_10214]), ['final']). 4.05/4.34 cnf(c_0_15748, 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_10215, c_0_10216]), ['final']). 4.05/4.34 cnf(c_0_15749, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X1,X2)),c_Nitpick_Opair__box_OPairBox(X1,X2,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_10217]), ['final']). 4.05/4.34 cnf(c_0_15750, 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_10218, c_0_5716]), ['final']). 4.05/4.34 cnf(c_0_15751, 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_10219]), ['final']). 4.05/4.34 cnf(c_0_15752, 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_10220]), ['final']). 4.05/4.34 cnf(c_0_15753, 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_10221]), ['final']). 4.05/4.34 cnf(c_0_15754, 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_10222]), ['final']). 4.05/4.34 cnf(c_0_15755, 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_10223]), ['final']). 4.05/4.34 cnf(c_0_15756, 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_10224]), ['final']). 4.05/4.34 cnf(c_0_15757, 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_10225, c_0_4977]), ['final']). 4.05/4.34 cnf(c_0_15758, 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_10226]), ['final']). 4.05/4.34 cnf(c_0_15759, 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_10227]), ['final']). 4.05/4.34 cnf(c_0_15760, 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_10228, c_0_6120]), c_0_6120]), c_0_5905]), ['final']). 4.05/4.34 cnf(c_0_15761, plain, (c_Product__Type_Omap__pair(X1,X1,X2,X2,c_COMBI(X1),c_COMBI(X2))=c_Fun_Oid(tc_prod(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10229]), ['final']). 4.05/4.34 cnf(c_0_15762, 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(rw,[status(thm)],[c_0_10230, c_0_6955]), ['final']). 4.05/4.34 cnf(c_0_15763, 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_10231, c_0_4867]), c_0_5669]), ['final']). 4.05/4.34 cnf(c_0_15764, plain, (c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X1,X2,X3,X4,c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X5,X6))=hAPP(hAPP(X4,X5),X6)), inference(split_conjunct,[status(thm)],[c_0_10232]), ['final']). 4.05/4.34 cnf(c_0_15765, plain, (hAPP(c_Option_Ooption_Ooption__case(X1,X2,X3,X4),hAPP(c_Option_Ooption_OSome(X2),X5))=hAPP(X4,X5)), inference(split_conjunct,[status(thm)],[c_0_10233]), ['final']). 4.05/4.34 cnf(c_0_15766, plain, (X1=hAPP(hAPP(c_Finite__Set_Ofold(X2,X3,X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10234]), ['final']). 4.05/4.34 cnf(c_0_15767, 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_10235]), ['final']). 4.05/4.34 cnf(c_0_15768, 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_10236]), ['final']). 4.05/4.34 cnf(c_0_15769, plain, (X1=c_Set_Othe__elem(X2,hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))), inference(split_conjunct,[status(thm)],[c_0_10237]), ['final']). 4.05/4.34 cnf(c_0_15770, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X1,X2,X3))=hAPP(c_Nat_OSuc,c_Com_Ocom_Ocom__size(X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10238, c_0_4867]), c_0_5669]), ['final']). 4.05/4.34 cnf(c_0_15771, 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), inference(split_conjunct,[status(thm)],[c_0_10239]), ['final']). 4.05/4.34 cnf(c_0_15772, plain, (c_Map_Omap__le(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_10240]), ['final']). 4.05/4.34 cnf(c_0_15773, 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_10241]), ['final']). 4.05/4.34 cnf(c_0_15774, 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_10242]), ['final']). 4.05/4.34 cnf(c_0_15775, 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_10243]), ['final']). 4.05/4.34 cnf(c_0_15776, 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_10244]), ['final']). 4.05/4.34 cnf(c_0_15777, plain, (c_List_Oremdups(X1,hAPP(c_List_Ofilter(X1,X2),X3))=hAPP(c_List_Ofilter(X1,X2),c_List_Oremdups(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_10245]), ['final']). 4.05/4.34 cnf(c_0_15778, plain, (c_Map_Odom(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(er,[status(thm)],[c_0_10246]), ['final']). 4.05/4.34 cnf(c_0_15779, plain, (X1=hAPP(hAPP(c_List_Olist__update(X2,X1),X3),hAPP(hAPP(c_List_Onth(X2),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_10247]), ['final']). 4.05/4.34 cnf(c_0_15780, 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_10248]), ['final']). 4.05/4.34 cnf(c_0_15781, 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_10249]), ['final']). 4.05/4.34 cnf(c_0_15782, plain, (hAPP(c_Set_OPow(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10250]), ['final']). 4.05/4.34 cnf(c_0_15783, plain, (c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg)), inference(split_conjunct,[status(thm)],[fact_type__definition__Integ]), ['final']). 4.05/4.34 cnf(c_0_15784, 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_10251]), ['final']). 4.05/4.34 cnf(c_0_15785, plain, (c_Option_Ooption_ONone(X1)=hAPP(hAPP(c_Map_Omap__of(X2,X1),c_List_Olist_ONil(tc_prod(X2,X1))),X3)), inference(split_conjunct,[status(thm)],[c_0_10252]), ['final']). 4.05/4.34 cnf(c_0_15786, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))), inference(split_conjunct,[status(thm)],[c_0_10253]), ['final']). 4.05/4.34 cnf(c_0_15787, 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_10254]), ['final']). 4.05/4.34 cnf(c_0_15788, 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_10255]), ['final']). 4.05/4.34 cnf(c_0_15789, 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_10256]), ['final']). 4.05/4.34 cnf(c_0_15790, 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_10257]), ['final']). 4.05/4.34 cnf(c_0_15791, plain, (c_Option_Ooption_Ooption__rec(X1,X2,X3,X4,hAPP(c_Option_Ooption_OSome(X2),X5))=hAPP(X4,X5)), inference(split_conjunct,[status(thm)],[c_0_10258]), ['final']). 4.05/4.34 cnf(c_0_15792, 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_10259]), ['final']). 4.05/4.34 cnf(c_0_15793, 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_10260]), ['final']). 4.05/4.34 cnf(c_0_15794, plain, (hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[fact_greaterThan__0]), ['final']). 4.05/4.34 cnf(c_0_15795, 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_10261]), ['final']). 4.05/4.34 cnf(c_0_15796, plain, (c_New__DSequence_Opos__single(X1,X2)=hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X1),X2),X3),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_10262]), ['final']). 4.05/4.34 cnf(c_0_15797, 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_10263]), ['final']). 4.05/4.34 cnf(c_0_15798, plain, (c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X3), inference(er,[status(thm)],[c_0_10264]), ['final']). 4.05/4.34 cnf(c_0_15799, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))=c_Relation_OId__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10265]), ['final']). 4.05/4.34 cnf(c_0_15800, 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)), inference(split_conjunct,[status(thm)],[c_0_10266]), ['final']). 4.05/4.34 cnf(c_0_15801, 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_Orotate1(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_10267]), ['final']). 4.05/4.34 cnf(c_0_15802, 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_10268]), ['final']). 4.05/4.34 cnf(c_0_15803, 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_10269, c_0_4519]), ['final']). 4.05/4.34 cnf(c_0_15804, 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_10270, c_0_10271]), ['final']). 4.05/4.34 cnf(c_0_15805, 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_10272]), ['final']). 4.05/4.34 cnf(c_0_15806, 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_10273, c_0_6120]), ['final']). 4.05/4.34 cnf(c_0_15807, 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(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10274, c_0_4867]), c_0_4867]), ['final']). 4.05/4.34 cnf(c_0_15808, 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_Odivmod__int(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10275]), ['final']). 4.05/4.34 cnf(c_0_15809, 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_10276, c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_15810, 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_10277, c_0_4859]), ['final']). 4.05/4.34 cnf(c_0_15811, plain, (X1=c_Fun_Ooverride__on(X2,X3,X1,X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10278]), ['final']). 4.05/4.34 cnf(c_0_15812, plain, (X1=hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X2,X3),X4),X5),X1),X5)), inference(split_conjunct,[status(thm)],[c_0_10279]), ['final']). 4.05/4.34 cnf(c_0_15813, 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_10280]), ['final']). 4.05/4.34 cnf(c_0_15814, 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_10281]), ['final']). 4.05/4.34 cnf(c_0_15815, 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_10282]), ['final']). 4.05/4.34 cnf(c_0_15816, 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_10283]), ['final']). 4.05/4.34 cnf(c_0_15817, plain, (X1=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X2,X3),X1),X4),hAPP(X1,X4))), inference(split_conjunct,[status(thm)],[c_0_10284]), ['final']). 4.05/4.34 cnf(c_0_15818, 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_10285]), ['final']). 4.05/4.34 cnf(c_0_15819, plain, (X1=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_10286]), ['final']). 4.05/4.34 cnf(c_0_15820, 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),X2)), inference(split_conjunct,[status(thm)],[c_0_10287]), ['final']). 4.05/4.34 cnf(c_0_15821, plain, (c_List_Olist_ONil(tc_prod(X1,X2))=hAPP(hAPP(c_List_Ozip(X1,X2),c_List_Olist_ONil(X1)),X3)), inference(split_conjunct,[status(thm)],[c_0_10288]), ['final']). 4.05/4.34 cnf(c_0_15822, plain, (c_List_Olist_ONil(tc_prod(X1,X2))=hAPP(hAPP(c_List_Ozip(X1,X2),X3),c_List_Olist_ONil(X2))), inference(split_conjunct,[status(thm)],[c_0_10289]), ['final']). 4.05/4.34 cnf(c_0_15823, 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_10290, c_0_4867])]), ['final']). 4.05/4.34 cnf(c_0_15824, 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_10291]), ['final']). 4.05/4.34 cnf(c_0_15825, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X1,X2))=hAPP(c_Nat_OSuc,c_Com_Ocom_Ocom__size(X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10292, c_0_4867]), c_0_5669]), ['final']). 4.05/4.34 cnf(c_0_15826, 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_10293]), ['final']). 4.05/4.34 cnf(c_0_15827, 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_10294]), ['final']). 4.05/4.34 cnf(c_0_15828, 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_10295]), ['final']). 4.05/4.34 cnf(c_0_15829, 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_10296]), ['final']). 4.05/4.34 cnf(c_0_15830, 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_10297, c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_15831, plain, (c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[fact_inj__int]), ['final']). 4.05/4.34 cnf(c_0_15832, 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_10298]), ['final']). 4.05/4.34 cnf(c_0_15833, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))), inference(split_conjunct,[status(thm)],[c_0_10299]), ['final']). 4.05/4.34 cnf(c_0_15834, 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_10300]), ['final']). 4.05/4.34 cnf(c_0_15835, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))), inference(split_conjunct,[status(thm)],[c_0_10301]), ['final']). 4.05/4.34 cnf(c_0_15836, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2)), inference(split_conjunct,[status(thm)],[c_0_10302]), ['final']). 4.05/4.34 cnf(c_0_15837, 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_10303]), ['final']). 4.05/4.34 cnf(c_0_15838, 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_10304]), ['final']). 4.05/4.34 cnf(c_0_15839, 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_10305]), ['final']). 4.05/4.34 cnf(c_0_15840, plain, (c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))=c_List_Olists(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[c_0_10306]), ['final']). 4.05/4.34 cnf(c_0_15841, 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_10307]), ['final']). 4.05/4.34 cnf(c_0_15842, 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_10308]), ['final']). 4.05/4.34 cnf(c_0_15843, 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_10309]), ['final']). 4.05/4.34 cnf(c_0_15844, 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_10310]), ['final']). 4.05/4.34 cnf(c_0_15845, 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_10311]), ['final']). 4.05/4.34 cnf(c_0_15846, 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_10312]), ['final']). 4.05/4.34 cnf(c_0_15847, 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_10313]), ['final']). 4.05/4.34 cnf(c_0_15848, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10314]), ['final']). 4.05/4.34 cnf(c_0_15849, 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_10315]), ['final']). 4.05/4.34 cnf(c_0_15850, 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_10316]), ['final']). 4.05/4.34 cnf(c_0_15851, plain, (c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[fact_transfer__morphism__nat__int]), ['final']). 4.05/4.34 cnf(c_0_15852, 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_10317]), ['final']). 4.05/4.34 cnf(c_0_15853, 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_10318, c_0_4519]), ['final']). 4.05/4.34 cnf(c_0_15854, 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_10319, c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_15855, 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_10320]), ['final']). 4.05/4.34 cnf(c_0_15856, plain, (c_Enum_Oenum__the(X1,c_Finite__Set_Ofold1Set(X1,X2,X3))=hAPP(c_Finite__Set_Ofold1(X1,X2),X3)), inference(rw,[status(thm)],[c_0_10321, c_0_4980]), ['final']). 4.05/4.34 cnf(c_0_15857, plain, (hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3))=X3), inference(split_conjunct,[status(thm)],[c_0_10322]), ['final']). 4.05/4.34 cnf(c_0_15858, plain, (c_Relation_OId__on(X1,X2)=hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId__on(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10323]), ['final']). 4.05/4.34 cnf(c_0_15859, 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_10324, c_0_7022]), ['final']). 4.05/4.34 cnf(c_0_15860, plain, (c_List_Olist_ONil(X1)=hAPP(hAPP(c_List_Olist__update(X1,c_List_Olist_ONil(X1)),X2),X3)), inference(split_conjunct,[status(thm)],[c_0_10325]), ['final']). 4.05/4.34 cnf(c_0_15861, plain, (c_List_Osublist(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_10326]), ['final']). 4.05/4.34 cnf(c_0_15862, 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_10327]), ['final']). 4.05/4.34 cnf(c_0_15863, plain, (c_Option_Ooption_ONone(X1)=hAPP(hAPP(c_Option_Omap(X2,X1),X3),c_Option_Ooption_ONone(X2))), inference(split_conjunct,[status(thm)],[c_0_10328]), ['final']). 4.05/4.34 cnf(c_0_15864, 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_10329]), ['final']). 4.05/4.34 cnf(c_0_15865, 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_10330]), ['final']). 4.05/4.34 cnf(c_0_15866, 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_10331]), ['final']). 4.05/4.34 cnf(c_0_15867, 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_10332]), ['final']). 4.05/4.34 cnf(c_0_15868, plain, (hAPP(c_List_Oset(X1),X2)=hAPP(c_List_Oset(X1),hAPP(c_List_Orotate1(X1),X2))), inference(split_conjunct,[status(thm)],[c_0_10333]), ['final']). 4.05/4.34 cnf(c_0_15869, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X1)),hAPP(c_Option_Ooption_OSome(X1),X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_10334]), ['final']). 4.05/4.34 cnf(c_0_15870, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)=hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))), inference(split_conjunct,[status(thm)],[c_0_10335]), ['final']). 4.05/4.34 cnf(c_0_15871, 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_10336]), ['final']). 4.05/4.34 cnf(c_0_15872, plain, (hAPP(c_Fun_Ocomp(X1,X1,X2,c_Fun_Oid(X1)),X3)=X3), inference(split_conjunct,[status(thm)],[c_0_10337]), ['final']). 4.05/4.34 cnf(c_0_15873, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[fact_code__numeral__zero__minus__one]), ['final']). 4.05/4.34 cnf(c_0_15874, plain, (hAPP(c_List_Olist_Olist__case(X1,X2,X3,X4),c_List_Olist_ONil(X2))=X3), inference(split_conjunct,[status(thm)],[c_0_10338]), ['final']). 4.05/4.34 cnf(c_0_15875, plain, (hAPP(c_List_Ofoldl(X1,X2,X3,X4),c_List_Olist_ONil(X2))=X4), inference(split_conjunct,[status(thm)],[c_0_10339]), ['final']). 4.05/4.34 cnf(c_0_15876, plain, (hAPP(c_Fun_Ocomp(X1,X2,X1,X3),c_Fun_Oid(X1))=X3), inference(split_conjunct,[status(thm)],[c_0_10340]), ['final']). 4.05/4.34 cnf(c_0_15877, plain, (X1=hAPP(c_Option_Ooption_Ooption__case(X2,X3,X1,X4),c_Option_Ooption_ONone(X3))), inference(split_conjunct,[status(thm)],[c_0_10341]), ['final']). 4.05/4.34 cnf(c_0_15878, 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_10342]), ['final']). 4.05/4.34 cnf(c_0_15879, 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']). 4.05/4.34 cnf(c_0_15880, plain, (hAPP(X1,X2)=c_Nat_Onat_Onat__case(X3,X4,X1,hAPP(c_Nat_OSuc,X2))), inference(split_conjunct,[status(thm)],[c_0_10343]), ['final']). 4.05/4.34 cnf(c_0_15881, 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_10344]), ['final']). 4.05/4.34 cnf(c_0_15882, plain, (c_Map_Omap__le(X1,X2,X3,c_Map_Omap__add(X1,X2,X4,X3))), inference(split_conjunct,[status(thm)],[c_0_10345]), ['final']). 4.05/4.34 cnf(c_0_15883, plain, (X1=hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X3))), inference(split_conjunct,[status(thm)],[c_0_10346]), ['final']). 4.05/4.34 cnf(c_0_15884, plain, (X1=hAPP(c_List_Otl(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1))), inference(split_conjunct,[status(thm)],[c_0_10347]), ['final']). 4.05/4.34 cnf(c_0_15885, 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_10348]), ['final']). 4.05/4.34 cnf(c_0_15886, 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_10349]), ['final']). 4.05/4.34 cnf(c_0_15887, 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_10350]), ['final']). 4.05/4.34 cnf(c_0_15888, 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_10351, c_0_4867]), ['final']). 4.05/4.34 cnf(c_0_15889, 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_10352]), ['final']). 4.05/4.34 cnf(c_0_15890, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X2)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)), inference(split_conjunct,[status(thm)],[c_0_10353]), ['final']). 4.05/4.34 cnf(c_0_15891, 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_10354, c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_15892, 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_10355]), ['final']). 4.05/4.34 cnf(c_0_15893, 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_10356, c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_15894, 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_10357, c_0_4867]), ['final']). 4.05/4.34 cnf(c_0_15895, plain, (hAPP(c_List_Oset(X1),c_List_Oremdups(X1,X2))=hAPP(c_List_Oset(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10358]), ['final']). 4.05/4.34 cnf(c_0_15896, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[fact_card__UNIV__unit]), ['final']). 4.05/4.34 cnf(c_0_15897, 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_10359]), ['final']). 4.05/4.34 cnf(c_0_15898, plain, (X1=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X1),X1)), inference(split_conjunct,[status(thm)],[c_0_10360]), ['final']). 4.05/4.34 cnf(c_0_15899, plain, (c_List_Olist__all2(X1,X2,X3,c_List_Olist_ONil(X1),c_List_Olist_ONil(X2))), inference(er,[status(thm)],[c_0_10361]), ['final']). 4.05/4.34 cnf(c_0_15900, 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_10362]), ['final']). 4.05/4.34 cnf(c_0_15901, 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_10363]), ['final']). 4.05/4.34 cnf(c_0_15902, 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_10364]), ['final']). 4.05/4.34 cnf(c_0_15903, 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_10365]), ['final']). 4.05/4.34 cnf(c_0_15904, plain, (c_Map_Omap__upds(X1,X2,X3,c_List_Olist_ONil(X1),X4)=X3), inference(split_conjunct,[status(thm)],[c_0_10366]), ['final']). 4.05/4.34 cnf(c_0_15905, plain, (c_Map_Omap__upds(X1,X2,X3,X4,c_List_Olist_ONil(X2))=X3), inference(split_conjunct,[status(thm)],[c_0_10367]), ['final']). 4.05/4.34 cnf(c_0_15906, plain, (X1=c_Option_Ooption_Ooption__rec(X2,X3,X1,X4,c_Option_Ooption_ONone(X3))), inference(split_conjunct,[status(thm)],[c_0_10368]), ['final']). 4.05/4.34 cnf(c_0_15907, 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_10369]), ['final']). 4.05/4.34 cnf(c_0_15908, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[fact_int__0__less__1]), ['final']). 4.05/4.34 cnf(c_0_15909, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]), ['final']). 4.05/4.34 cnf(c_0_15910, 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_10370]), ['final']). 4.05/4.34 cnf(c_0_15911, plain, (c_Predicate_Oconversep(X1,X2,c_Predicate_Oconversep(X2,X1,X3))=X3), inference(split_conjunct,[status(thm)],[c_0_10371]), ['final']). 4.05/4.34 cnf(c_0_15912, plain, (hAPP(c_Option_Omap(X1,X1),c_Fun_Oid(X1))=c_Fun_Oid(tc_Option_Ooption(X1))), inference(split_conjunct,[status(thm)],[c_0_10372]), ['final']). 4.05/4.34 cnf(c_0_15913, plain, (c_Fun_Oid(tc_Option_Ooption(X1))=hAPP(c_Option_Omap(X1,X1),c_COMBI(X1))), inference(split_conjunct,[status(thm)],[c_0_10373]), ['final']). 4.05/4.34 cnf(c_0_15914, plain, (c_Fun_Oid(tc_List_Olist(X1))=hAPP(c_List_Omap(X1,X1),c_COMBI(X1))), inference(split_conjunct,[status(thm)],[c_0_10374]), ['final']). 4.05/4.34 cnf(c_0_15915, plain, (hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2))), inference(er,[status(thm)],[c_0_10375]), ['final']). 4.05/4.34 cnf(c_0_15916, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2)))), inference(er,[status(thm)],[c_0_10376]), ['final']). 4.05/4.34 cnf(c_0_15917, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_10377]), ['final']). 4.05/4.34 cnf(c_0_15918, plain, (c_List_Omap__filter(X1,X2,X3,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X2)), inference(split_conjunct,[status(thm)],[c_0_10378]), ['final']). 4.05/4.34 cnf(c_0_15919, plain, (hAPP(hAPP(c_List_Otake(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_10379]), ['final']). 4.05/4.34 cnf(c_0_15920, 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_10380]), ['final']). 4.05/4.34 cnf(c_0_15921, 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_10381]), ['final']). 4.05/4.34 cnf(c_0_15922, 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_10382]), ['final']). 4.05/4.34 cnf(c_0_15923, 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_10383]), ['final']). 4.05/4.34 cnf(c_0_15924, 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_10384]), ['final']). 4.05/4.34 cnf(c_0_15925, 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_10385]), ['final']). 4.05/4.34 cnf(c_0_15926, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)), inference(split_conjunct,[status(thm)],[c_0_10386]), ['final']). 4.05/4.34 cnf(c_0_15927, 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_10387, c_0_5011]), ['final']). 4.05/4.34 cnf(c_0_15928, 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_10388]), ['final']). 4.05/4.34 cnf(c_0_15929, 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_10389]), ['final']). 4.05/4.34 cnf(c_0_15930, 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_10390, c_0_5011]), ['final']). 4.05/4.34 cnf(c_0_15931, 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_10391, c_0_5149]), ['final']). 4.05/4.34 cnf(c_0_15932, 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_10392]), ['final']). 4.05/4.34 cnf(c_0_15933, 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_10393]), ['final']). 4.05/4.34 cnf(c_0_15934, plain, (hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_10394]), ['final']). 4.05/4.34 cnf(c_0_15935, plain, (c_Fun_Oinj__on(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10395]), ['final']). 4.05/4.34 cnf(c_0_15936, plain, (c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10396]), ['final']). 4.05/4.34 cnf(c_0_15937, plain, (X1=hAPP(c_Set_Oimage(X2,X2,c_Fun_Oid(X2)),X1)), inference(split_conjunct,[status(thm)],[c_0_10397]), ['final']). 4.05/4.34 cnf(c_0_15938, 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_10398]), ['final']). 4.05/4.34 cnf(c_0_15939, plain, (hAPP(c_Relation_ODomain(X1,X1),c_Relation_OId__on(X1,X2))=X2), inference(split_conjunct,[status(thm)],[c_0_10399]), ['final']). 4.05/4.34 cnf(c_0_15940, plain, (X1=hAPP(c_Relation_ORange(X2,X2),c_Relation_OId__on(X2,X1))), inference(split_conjunct,[status(thm)],[c_0_10400]), ['final']). 4.05/4.34 cnf(c_0_15941, plain, (hAPP(c_List_Oset(X1),c_List_Olist_ONil(X1))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10401]), ['final']). 4.05/4.34 cnf(c_0_15942, 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))), inference(split_conjunct,[status(thm)],[fact_atLeast__0]), ['final']). 4.05/4.34 cnf(c_0_15943, 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_10402]), ['final']). 4.05/4.34 cnf(c_0_15944, plain, (c_List_Oremdups(X1,X2)=c_List_Oremdups(X1,c_List_Oremdups(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10403]), ['final']). 4.05/4.34 cnf(c_0_15945, 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_10404]), ['final']). 4.05/4.34 cnf(c_0_15946, plain, (hAPP(c_Lazy__Sequence_Osingle(X1),X2)=hAPP(c_New__DSequence_Opos__single(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_10405]), ['final']). 4.05/4.34 cnf(c_0_15947, plain, (c_List_Olist_ONil(X1)=hAPP(c_List_Ofilter(X1,X2),c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10406]), ['final']). 4.05/4.34 cnf(c_0_15948, 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_10407]), ['final']). 4.05/4.34 cnf(c_0_15949, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X1)),c_Option_Ooption_ONone(X1))), inference(split_conjunct,[status(thm)],[c_0_10408]), ['final']). 4.05/4.34 cnf(c_0_15950, 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_10409]), ['final']). 4.05/4.34 cnf(c_0_15951, plain, (X1=c_Nat_Onat_Onat__case(X2,X1,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_10410]), ['final']). 4.05/4.34 cnf(c_0_15952, plain, (X1=hAPP(hAPP(c_COMBK(X2,X3),X1),X4)), inference(split_conjunct,[status(thm)],[c_0_10411]), ['final']). 4.05/4.34 cnf(c_0_15953, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_10412]), ['final']). 4.05/4.34 cnf(c_0_15954, plain, (c_List_Olist__all2(X1,X1,c_fequal,X2,X2)), inference(er,[status(thm)],[c_0_10413]), ['final']). 4.05/4.34 cnf(c_0_15955, plain, (X1=hAPP(hAPP(c_List_Odrop(X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)), inference(split_conjunct,[status(thm)],[c_0_10414]), ['final']). 4.05/4.34 cnf(c_0_15956, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1))=X2), inference(split_conjunct,[status(thm)],[c_0_10415]), ['final']). 4.05/4.34 cnf(c_0_15957, 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_10416]), ['final']). 4.05/4.34 cnf(c_0_15958, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=X1), inference(split_conjunct,[status(thm)],[c_0_10417]), ['final']). 4.05/4.34 cnf(c_0_15959, 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_10418]), ['final']). 4.05/4.34 cnf(c_0_15960, 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_10419, c_0_5130]), ['final']). 4.05/4.34 cnf(c_0_15961, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1), inference(split_conjunct,[status(thm)],[c_0_10420]), ['final']). 4.05/4.34 cnf(c_0_15962, 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_10421]), ['final']). 4.05/4.34 cnf(c_0_15963, plain, (X1=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[c_0_10422]), ['final']). 4.05/4.34 cnf(c_0_15964, 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_10423, c_0_5130]), ['final']). 4.05/4.34 cnf(c_0_15965, 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_10424]), ['final']). 4.05/4.34 cnf(c_0_15966, 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_10425]), ['final']). 4.05/4.34 cnf(c_0_15967, plain, (c_Option_Oset(X1,c_Option_Ooption_ONone(X1))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))), inference(split_conjunct,[status(thm)],[c_0_10426]), ['final']). 4.05/4.34 cnf(c_0_15968, plain, (c_Lazy__Sequence_Ohb__single(X1,X2)=hAPP(c_New__DSequence_Oneg__single(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_10427]), ['final']). 4.05/4.34 cnf(c_0_15969, plain, (c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10428]), ['final']). 4.05/4.34 cnf(c_0_15970, plain, (c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10429]), ['final']). 4.05/4.34 cnf(c_0_15971, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(X1,X2,X3))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_10430]), ['final']). 4.05/4.34 cnf(c_0_15972, plain, (c_Relation_Orefl__on(X1,X2,c_Relation_OId__on(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10431]), ['final']). 4.05/4.34 cnf(c_0_15973, plain, (hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2))), inference(split_conjunct,[status(thm)],[c_0_10432]), ['final']). 4.05/4.34 cnf(c_0_15974, plain, (c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10433]), ['final']). 4.05/4.34 cnf(c_0_15975, plain, (c_List_OtakeWhile(X1,X2,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_10434]), ['final']). 4.05/4.34 cnf(c_0_15976, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1)))), inference(split_conjunct,[status(thm)],[c_0_10435]), ['final']). 4.05/4.34 cnf(c_0_15977, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_10436]), ['final']). 4.05/4.34 cnf(c_0_15978, plain, (hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_10437]), ['final']). 4.05/4.34 cnf(c_0_15979, plain, (c_List_Olist_ONil(X1)=c_List_Osublist(X1,c_List_Olist_ONil(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_10438]), ['final']). 4.05/4.34 cnf(c_0_15980, plain, (c_List_Olist_ONil(X1)=c_List_Oremove1(X1,X2,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10439]), ['final']). 4.05/4.34 cnf(c_0_15981, 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_10440]), ['final']). 4.05/4.34 cnf(c_0_15982, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Option_Ooption_Ooption__size(X1,X2,c_Option_Ooption_ONone(X1))), inference(split_conjunct,[status(thm)],[c_0_10441]), ['final']). 4.05/4.34 cnf(c_0_15983, 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_10442]), ['final']). 4.05/4.34 cnf(c_0_15984, 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_10443]), ['final']). 4.05/4.34 cnf(c_0_15985, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X1)), inference(split_conjunct,[status(thm)],[c_0_10444]), ['final']). 4.05/4.34 cnf(c_0_15986, plain, (c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X1))), inference(split_conjunct,[status(thm)],[c_0_10445]), ['final']). 4.05/4.34 cnf(c_0_15987, plain, (hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_10446]), ['final']). 4.05/4.34 cnf(c_0_15988, plain, (c_List_Olist_ONil(X1)=hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_9529]), ['final']). 4.05/4.34 cnf(c_0_15989, plain, (c_List_Olist_ONil(X1)=hAPP(c_List_Otl(X1),c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10447]), ['final']). 4.05/4.34 cnf(c_0_15990, plain, (c_FunDef_Opair__less=c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than)), inference(split_conjunct,[status(thm)],[fact_pair__less__def]), ['final']). 4.05/4.34 cnf(c_0_15991, plain, (c_List_Osplice(X1,c_List_Olist_ONil(X1),X2)=X2), inference(split_conjunct,[status(thm)],[c_0_10448]), ['final']). 4.05/4.34 cnf(c_0_15992, 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']). 4.05/4.34 cnf(c_0_15993, plain, (hAPP(c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),X2))=X2), inference(split_conjunct,[status(thm)],[c_0_10449]), ['final']). 4.05/4.34 cnf(c_0_15994, plain, (X1=c_List_Osplice(X2,X1,c_List_Olist_ONil(X2))), inference(split_conjunct,[status(thm)],[c_0_10450]), ['final']). 4.05/4.34 cnf(c_0_15995, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X1), inference(split_conjunct,[status(thm)],[c_0_10392]), ['final']). 4.05/4.34 cnf(c_0_15996, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), inference(split_conjunct,[status(thm)],[fact_code__numeral_Osize_I3_J]), ['final']). 4.05/4.34 cnf(c_0_15997, 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_10451, c_0_4427]), ['final']). 4.05/4.34 cnf(c_0_15998, 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_10452, c_0_4427]), c_0_4427]), ['final']). 4.05/4.34 cnf(c_0_15999, hypothesis, (hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))), inference(split_conjunct,[status(thm)],[conj_3]), ['final']). 4.05/4.34 cnf(c_0_16000, 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']). 4.05/4.34 cnf(c_0_16001, plain, (c_FunDef_Omax__strict=c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)), inference(split_conjunct,[status(thm)],[fact_max__strict__def]), ['final']). 4.05/4.34 cnf(c_0_16002, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))), inference(split_conjunct,[status(thm)],[fact_int__1]), ['final']). 4.05/4.34 cnf(c_0_16003, plain, (c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1)), inference(split_conjunct,[status(thm)],[c_0_10453]), ['final']). 4.05/4.34 cnf(c_0_16004, 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_10454]), ['final']). 4.05/4.34 cnf(c_0_16005, 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_10455]), ['final']). 4.05/4.34 cnf(c_0_16006, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))), inference(split_conjunct,[status(thm)],[fact_finite__dom__body]), ['final']). 4.05/4.34 cnf(c_0_16007, plain, (c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J]), ['final']). 4.05/4.34 cnf(c_0_16008, plain, (c_List_Olist__all(X1,X2,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10456]), ['final']). 4.05/4.34 cnf(c_0_16009, plain, (c_Wellfounded_Owf(X1,c_List_Omeasures(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10457]), ['final']). 4.05/4.34 cnf(c_0_16010, plain, (c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10458]), ['final']). 4.05/4.34 cnf(c_0_16011, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X1))), inference(split_conjunct,[status(thm)],[c_0_10459]), ['final']). 4.05/4.34 cnf(c_0_16012, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X1))), inference(split_conjunct,[status(thm)],[c_0_10460]), ['final']). 4.05/4.34 cnf(c_0_16013, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1))), inference(split_conjunct,[status(thm)],[c_0_10461]), ['final']). 4.05/4.34 cnf(c_0_16014, plain, (c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)), inference(split_conjunct,[status(thm)],[fact_wf__pair__less]), ['final']). 4.05/4.34 cnf(c_0_16015, 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_10462]), ['final']). 4.05/4.34 cnf(c_0_16016, 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_10463, c_0_4427]), ['final']). 4.05/4.34 cnf(c_0_16017, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OBODY(X1))), inference(split_conjunct,[status(thm)],[c_0_10464]), ['final']). 4.05/4.34 cnf(c_0_16018, plain, (c_Nitpick_Onat__gcd(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1), inference(er,[status(thm)],[c_0_10465]), ['final']). 4.05/4.34 cnf(c_0_16019, 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_10466, c_0_4427]), ['final']). 4.05/4.34 cnf(c_0_16020, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))), inference(rw,[status(thm)],[c_0_10467, c_0_4635]), ['final']). 4.05/4.34 cnf(c_0_16021, plain, (c_List_Obutlast(X1,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1)), inference(split_conjunct,[status(thm)],[c_0_10468]), ['final']). 4.05/4.34 cnf(c_0_16022, plain, (c_Random_Oinc__shift(X1,X1)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), inference(er,[status(thm)],[c_0_10469]), ['final']). 4.05/4.34 cnf(c_0_16023, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olist_ONil(X1)))), inference(split_conjunct,[status(thm)],[c_0_10470]), ['final']). 4.05/4.34 cnf(c_0_16024, plain, (hBOOL(hAPP(hAPP(c_fequal,X1),X1))), inference(er,[status(thm)],[c_0_10471]), ['final']). 4.05/4.34 cnf(c_0_16025, plain, (c_List_Olist_ONil(X1)=c_List_Oremdups(X1,c_List_Olist_ONil(X1))), inference(split_conjunct,[status(thm)],[c_0_10472]), ['final']). 4.05/4.34 cnf(c_0_16026, plain, (c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X2))=X2), inference(split_conjunct,[status(thm)],[c_0_10473]), ['final']). 4.05/4.34 cnf(c_0_16027, plain, (c_Enum_Oenum__the(X1,hAPP(c_fequal,X2))=X2), inference(rw,[status(thm)],[c_0_10474, c_0_4980]), ['final']). 4.05/4.34 cnf(c_0_16028, 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_10475]), ['final']). 4.05/4.34 cnf(c_0_16029, plain, (hAPP(c_New__DSequence_Opos__empty(X1),X2)=c_Lazy__Sequence_Oempty(X1)), inference(split_conjunct,[status(thm)],[c_0_10476]), ['final']). 4.05/4.34 cnf(c_0_16030, plain, (hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_bool_Osize_I4_J]), ['final']). 4.05/4.34 cnf(c_0_16031, plain, (hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_bool_Osize_I3_J]), ['final']). 4.05/4.34 cnf(c_0_16032, plain, (c_Map_Omap__le(X1,X2,X3,X3)), inference(split_conjunct,[status(thm)],[c_0_10477]), ['final']). 4.05/4.34 cnf(c_0_16033, 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_10478, c_0_4427]), ['final']). 4.05/4.34 cnf(c_0_16034, plain, (c_fequal=c_Predicate_Oconversep(X1,X1,c_fequal)), inference(split_conjunct,[status(thm)],[c_0_10479]), ['final']). 4.05/4.34 cnf(c_0_16035, plain, (X1=hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X1))), inference(split_conjunct,[status(thm)],[c_0_10480]), ['final']). 4.05/4.34 cnf(c_0_16036, 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_10481, c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_16037, 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_10482, c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_16038, 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_10483, c_0_5379]), ['final']). 4.05/4.34 cnf(c_0_16039, plain, (class_HOL_Oequal(tc_Nitpick_Opair__box(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10484]), ['final']). 4.05/4.34 cnf(c_0_16040, plain, (class_HOL_Oequal(tc_sum(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10485]), ['final']). 4.05/4.34 cnf(c_0_16041, plain, (class_HOL_Oequal(tc_prod(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10486]), ['final']). 4.05/4.34 cnf(c_0_16042, plain, (class_Nat_Osize(tc_Nitpick_Opair__box(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10487]), ['final']). 4.05/4.34 cnf(c_0_16043, plain, (class_Nat_Osize(tc_sum(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10488]), ['final']). 4.05/4.34 cnf(c_0_16044, plain, (class_Nat_Osize(tc_prod(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_10489]), ['final']). 4.05/4.34 cnf(c_0_16045, plain, (c_Option_Ois__none(X1,c_Option_Ooption_ONone(X1))), inference(split_conjunct,[status(thm)],[c_0_10490]), ['final']). 4.05/4.34 cnf(c_0_16046, plain, (c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X1))), inference(split_conjunct,[status(thm)],[c_0_10491]), ['final']). 4.05/4.34 cnf(c_0_16047, plain, (c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X1))), inference(split_conjunct,[status(thm)],[c_0_10492]), ['final']). 4.05/4.34 cnf(c_0_16048, plain, (X1=hAPP(c_COMBI(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_10493]), ['final']). 4.05/4.34 cnf(c_0_16049, plain, (X1=hAPP(c_Fun_Oid(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_10494]), ['final']). 4.05/4.34 cnf(c_0_16050, plain, (hAPP(c_Int_OAbs__Integ,esk449_1(X1))=X1), inference(split_conjunct,[status(thm)],[c_0_10213]), ['final']). 4.05/4.34 cnf(c_0_16051, plain, (c_Com_Obody=hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies)), inference(split_conjunct,[status(thm)],[fact_body__def]), ['final']). 4.05/4.34 cnf(c_0_16052, plain, (X1=hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X1)), inference(split_conjunct,[status(thm)],[c_0_10495]), ['final']). 4.05/4.34 cnf(c_0_16053, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OBODY(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[c_0_10496]), ['final']). 4.05/4.34 cnf(c_0_16054, plain, (c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than)), inference(split_conjunct,[status(thm)],[fact_wf__less__than]), ['final']). 4.05/4.34 cnf(c_0_16055, plain, (c_Equiv__Relations_Oequivp(X1,c_fequal)), inference(split_conjunct,[status(thm)],[c_0_10497]), ['final']). 4.05/4.34 cnf(c_0_16056, plain, (c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat)), inference(split_conjunct,[status(thm)],[fact_wf__pred__nat]), ['final']). 4.05/4.34 cnf(c_0_16057, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_code__numeral_Osize_I1_J]), ['final']). 4.05/4.34 cnf(c_0_16058, plain, (class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X1))), inference(split_conjunct,[status(thm)],[c_0_10498]), ['final']). 4.05/4.34 cnf(c_0_16059, plain, (class_HOL_Oequal(tc_Option_Ooption(X1))), inference(split_conjunct,[status(thm)],[c_0_10499]), ['final']). 4.05/4.34 cnf(c_0_16060, plain, (class_HOL_Oequal(tc_List_Olist(X1))), inference(split_conjunct,[status(thm)],[c_0_10500]), ['final']). 4.05/4.34 cnf(c_0_16061, plain, (class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X1))), inference(split_conjunct,[status(thm)],[c_0_10501]), ['final']). 4.05/4.34 cnf(c_0_16062, plain, (class_Nat_Osize(tc_Option_Ooption(X1))), inference(split_conjunct,[status(thm)],[c_0_10502]), ['final']). 4.05/4.34 cnf(c_0_16063, plain, (c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_nat_Osize_I1_J]), ['final']). 4.05/4.34 cnf(c_0_16064, plain, (class_Nat_Osize(tc_List_Olist(X1))), inference(split_conjunct,[status(thm)],[c_0_10503]), ['final']). 4.05/4.34 cnf(c_0_16065, plain, (c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J]), ['final']). 4.05/4.34 cnf(c_0_16066, plain, (c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint))), inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J]), ['final']). 4.05/4.34 cnf(c_0_16067, plain, (c_HOL_Obool_Obool__size(c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_bool_Osize_I2_J]), ['final']). 4.05/4.34 cnf(c_0_16068, plain, (c_HOL_Obool_Obool__size(c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[fact_bool_Osize_I1_J]), ['final']). 4.05/4.34 cnf(c_0_16069, plain, (c_Fun_Oid(tc_Int_Oint)=c_Int_Oring__1__class_Oof__int(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[fact_of__int__eq__id]), ['final']). 4.05/4.34 cnf(c_0_16070, 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']). 4.05/4.34 cnf(c_0_16071, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]), ['final']). 4.05/4.34 cnf(c_0_16072, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict]), ['final']). 4.05/4.34 cnf(c_0_16073, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]), ['final']). 4.05/4.34 cnf(c_0_16074, plain, (class_Groups_Oabs__if(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]), ['final']). 4.05/4.34 cnf(c_0_16075, plain, (class_Lattices_Obounded__lattice__bot(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__bot]), ['final']). 4.05/4.34 cnf(c_0_16076, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16077, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16078, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16079, plain, (class_Groups_Oab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16080, plain, (class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16081, plain, (class_Groups_Oab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16082, plain, (class_Rings_Olinordered__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]), ['final']). 4.05/4.34 cnf(c_0_16083, plain, (class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring]), ['final']). 4.05/4.34 cnf(c_0_16084, plain, (class_Rings_Olinordered__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]), ['final']). 4.05/4.34 cnf(c_0_16085, plain, (class_Rings_Oring__no__zero__divisors(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]), ['final']). 4.05/4.34 cnf(c_0_16086, plain, (class_Orderings_Owellorder(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Owellorder]), ['final']). 4.05/4.34 cnf(c_0_16087, plain, (class_Rings_Ocomm__ring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]), ['final']). 4.05/4.34 cnf(c_0_16088, plain, (class_Groups_Osgn__if(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]), ['final']). 4.05/4.34 cnf(c_0_16089, plain, (class_Rings_Oidom(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]), ['final']). 4.05/4.34 cnf(c_0_16090, plain, (class_Smallcheck_Osmall(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Smallcheck_Osmall]), ['final']). 4.05/4.34 cnf(c_0_16091, plain, (class_Smallcheck_Osmall(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Smallcheck_Osmall]), ['final']). 4.05/4.34 cnf(c_0_16092, plain, (class_Int_Oring__char__0(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]), ['final']). 4.05/4.34 cnf(c_0_16093, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le]), ['final']). 4.05/4.34 cnf(c_0_16094, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le]), ['final']). 4.05/4.34 cnf(c_0_16095, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le]), ['final']). 4.05/4.34 cnf(c_0_16096, plain, (class_Rings_Ocomm__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]), ['final']). 4.05/4.34 cnf(c_0_16097, plain, (class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring]), ['final']). 4.05/4.34 cnf(c_0_16098, plain, (class_Rings_Ocomm__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]), ['final']). 4.05/4.34 cnf(c_0_16099, plain, (class_Orderings_Obot(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]), ['final']). 4.05/4.34 cnf(c_0_16100, plain, (class_Orderings_Obot(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Obot]), ['final']). 4.05/4.34 cnf(c_0_16101, plain, (class_Lattices_Odistrib__lattice(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Odistrib__lattice]), ['final']). 4.05/4.34 cnf(c_0_16102, plain, (class_Lattices_Odistrib__lattice(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Odistrib__lattice]), ['final']). 4.05/4.34 cnf(c_0_16103, plain, (class_Lattices_Odistrib__lattice(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Odistrib__lattice]), ['final']). 4.05/4.34 cnf(c_0_16104, plain, (class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16105, plain, (class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16106, plain, (class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16107, plain, (class_Groups_Osemigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osemigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16108, plain, (class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16109, plain, (class_Groups_Osemigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Osemigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16110, plain, (class_Rings_Olinordered__ring__strict(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]), ['final']). 4.05/4.34 cnf(c_0_16111, plain, (class_Groups_Ouminus(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ouminus]), ['final']). 4.05/4.34 cnf(c_0_16112, plain, (class_Groups_Ouminus(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]), ['final']). 4.05/4.34 cnf(c_0_16113, plain, (class_Rings_Ono__zero__divisors(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]), ['final']). 4.05/4.34 cnf(c_0_16114, plain, (class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors]), ['final']). 4.05/4.34 cnf(c_0_16115, plain, (class_Rings_Ono__zero__divisors(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]), ['final']). 4.05/4.34 cnf(c_0_16116, plain, (class_Lattices_Obounded__lattice__top(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__top]), ['final']). 4.05/4.34 cnf(c_0_16117, plain, (class_Rings_Oordered__ring__abs(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]), ['final']). 4.05/4.34 cnf(c_0_16118, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16119, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16120, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16121, plain, (class_Groups_Oab__semigroup__mult(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]), ['final']). 4.05/4.34 cnf(c_0_16122, plain, (class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult]), ['final']). 4.05/4.34 cnf(c_0_16123, plain, (class_Groups_Oab__semigroup__mult(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]), ['final']). 4.05/4.34 cnf(c_0_16124, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]), ['final']). 4.05/4.34 cnf(c_0_16125, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]), ['final']). 4.05/4.34 cnf(c_0_16126, plain, (class_Rings_Oordered__comm__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]), ['final']). 4.05/4.34 cnf(c_0_16127, plain, (class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring]), ['final']). 4.05/4.34 cnf(c_0_16128, plain, (class_Rings_Oordered__comm__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]), ['final']). 4.05/4.34 cnf(c_0_16129, plain, (class_Groups_Omonoid__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]), ['final']). 4.05/4.34 cnf(c_0_16130, plain, (class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add]), ['final']). 4.05/4.34 cnf(c_0_16131, plain, (class_Groups_Omonoid__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]), ['final']). 4.05/4.34 cnf(c_0_16132, plain, (class_Rings_Oordered__cancel__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]), ['final']). 4.05/4.34 cnf(c_0_16133, plain, (class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring]), ['final']). 4.05/4.34 cnf(c_0_16134, plain, (class_Rings_Oordered__cancel__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]), ['final']). 4.05/4.34 cnf(c_0_16135, plain, (class_Groups_Omonoid__mult(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]), ['final']). 4.05/4.34 cnf(c_0_16136, plain, (class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult]), ['final']). 4.05/4.34 cnf(c_0_16137, plain, (class_Groups_Omonoid__mult(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]), ['final']). 4.05/4.34 cnf(c_0_16138, plain, (class_Groups_Oone(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]), ['final']). 4.05/4.34 cnf(c_0_16139, plain, (class_Groups_Oone(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oone]), ['final']). 4.05/4.34 cnf(c_0_16140, plain, (class_Groups_Oone(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]), ['final']). 4.05/4.34 cnf(c_0_16141, plain, (class_HOL_Oequal(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__HOL_Oequal]), ['final']). 4.05/4.34 cnf(c_0_16142, plain, (class_HOL_Oequal(tc_Code__Evaluation_Oterm)), inference(split_conjunct,[status(thm)],[arity_Code____Evaluation__Oterm__HOL_Oequal]), ['final']). 4.05/4.34 cnf(c_0_16143, plain, (class_HOL_Oequal(tc_Com_Ostate)), inference(split_conjunct,[status(thm)],[arity_Com__Ostate__HOL_Oequal]), ['final']). 4.05/4.34 cnf(c_0_16144, plain, (class_HOL_Oequal(tc_Com_Ovname)), inference(split_conjunct,[status(thm)],[arity_Com__Ovname__HOL_Oequal]), ['final']). 4.05/4.34 cnf(c_0_16145, plain, (class_HOL_Oequal(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__HOL_Oequal]), ['final']). 4.05/4.34 cnf(c_0_16146, plain, (class_HOL_Oequal(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__HOL_Oequal]), ['final']). 4.05/4.34 cnf(c_0_16147, plain, (class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__HOL_Oequal]), ['final']). 4.05/4.34 cnf(c_0_16148, plain, (class_HOL_Oequal(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__HOL_Oequal]), ['final']). 4.05/4.34 cnf(c_0_16149, plain, (class_Lattices_Obounded__lattice(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice]), ['final']). 4.05/4.34 cnf(c_0_16150, plain, (class_Nat_Osemiring__char__0(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Nat_Osemiring__char__0]), ['final']). 4.05/4.34 cnf(c_0_16151, plain, (class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0]), ['final']). 4.05/4.34 cnf(c_0_16152, plain, (class_Nat_Osemiring__char__0(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Nat_Osemiring__char__0]), ['final']). 4.05/4.34 cnf(c_0_16153, plain, (class_Groups_Ominus(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ominus]), ['final']). 4.05/4.34 cnf(c_0_16154, plain, (class_Groups_Ominus(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ominus]), ['final']). 4.05/4.34 cnf(c_0_16155, plain, (class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ominus]), ['final']). 4.05/4.34 cnf(c_0_16156, plain, (class_Groups_Ominus(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ominus]), ['final']). 4.05/4.34 cnf(c_0_16157, plain, (class_Rings_Oordered__ring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]), ['final']). 4.05/4.34 cnf(c_0_16158, plain, (class_Groups_Oordered__comm__monoid__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]), ['final']). 4.05/4.34 cnf(c_0_16159, plain, (class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add]), ['final']). 4.05/4.34 cnf(c_0_16160, plain, (class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]), ['final']). 4.05/4.34 cnf(c_0_16161, plain, (class_Rings_Oordered__semiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]), ['final']). 4.05/4.34 cnf(c_0_16162, plain, (class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring]), ['final']). 4.05/4.34 cnf(c_0_16163, plain, (class_Rings_Oordered__semiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]), ['final']). 4.05/4.34 cnf(c_0_16164, plain, (class_Rings_Olinordered__ring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]), ['final']). 4.05/4.34 cnf(c_0_16165, plain, (class_Rings_Omult__zero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]), ['final']). 4.05/4.34 cnf(c_0_16166, plain, (class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero]), ['final']). 4.05/4.34 cnf(c_0_16167, plain, (class_Rings_Omult__zero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]), ['final']). 4.05/4.34 cnf(c_0_16168, plain, (class_Lattices_Oboolean__algebra(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]), ['final']). 4.05/4.34 cnf(c_0_16169, plain, (class_Rings_Ozero__neq__one(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]), ['final']). 4.05/4.34 cnf(c_0_16170, plain, (class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one]), ['final']). 4.05/4.34 cnf(c_0_16171, plain, (class_Rings_Ozero__neq__one(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]), ['final']). 4.05/4.34 cnf(c_0_16172, plain, (class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1__no__zero__divisors]), ['final']). 4.05/4.34 cnf(c_0_16173, plain, (class_Finite__Set_Ofinite(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite]), ['final']). 4.05/4.34 cnf(c_0_16174, plain, (class_Finite__Set_Ofinite(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]), ['final']). 4.05/4.34 cnf(c_0_16175, plain, (class_Rings_Oring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]), ['final']). 4.05/4.34 cnf(c_0_16176, plain, (class_Orderings_Otop(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]), ['final']). 4.05/4.34 cnf(c_0_16177, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16178, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16179, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16180, plain, (class_Rings_Osemiring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]), ['final']). 4.05/4.34 cnf(c_0_16181, plain, (class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring]), ['final']). 4.05/4.34 cnf(c_0_16182, plain, (class_Rings_Osemiring(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]), ['final']). 4.05/4.34 cnf(c_0_16183, plain, (class_Groups_Olinordered__ab__group__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]), ['final']). 4.05/4.34 cnf(c_0_16184, plain, (class_Groups_Ocancel__semigroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16185, plain, (class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16186, plain, (class_Groups_Ocancel__semigroup__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]), ['final']). 4.05/4.34 cnf(c_0_16187, plain, (class_Orderings_Opreorder(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]), ['final']). 4.05/4.34 cnf(c_0_16188, plain, (class_Orderings_Opreorder(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]), ['final']). 4.05/4.34 cnf(c_0_16189, plain, (class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder]), ['final']). 4.05/4.34 cnf(c_0_16190, plain, (class_Orderings_Opreorder(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]), ['final']). 4.05/4.34 cnf(c_0_16191, plain, (class_Nat_Osize(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Nat_Osize]), ['final']). 4.05/4.34 cnf(c_0_16192, plain, (class_Nat_Osize(tc_Code__Evaluation_Oterm)), inference(split_conjunct,[status(thm)],[arity_Code____Evaluation__Oterm__Nat_Osize]), ['final']). 4.05/4.34 cnf(c_0_16193, plain, (class_Nat_Osize(tc_Com_Ostate)), inference(split_conjunct,[status(thm)],[arity_Com__Ostate__Nat_Osize]), ['final']). 4.05/4.34 cnf(c_0_16194, plain, (class_Nat_Osize(tc_Com_Ovname)), inference(split_conjunct,[status(thm)],[arity_Com__Ovname__Nat_Osize]), ['final']). 4.05/4.34 cnf(c_0_16195, plain, (class_Nat_Osize(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Nat_Osize]), ['final']). 4.05/4.34 cnf(c_0_16196, plain, (class_Nat_Osize(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Nat_Osize]), ['final']). 4.05/4.34 cnf(c_0_16197, plain, (class_Nat_Osize(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Nat_Osize]), ['final']). 4.05/4.34 cnf(c_0_16198, plain, (class_Divides_Oring__div(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Oring__div]), ['final']). 4.05/4.34 cnf(c_0_16199, plain, (class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]), ['final']). 4.05/4.34 cnf(c_0_16200, plain, (class_Rings_Olinordered__semidom(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]), ['final']). 4.05/4.34 cnf(c_0_16201, plain, (class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom]), ['final']). 4.05/4.34 cnf(c_0_16202, plain, (class_Rings_Olinordered__semidom(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]), ['final']). 4.05/4.34 cnf(c_0_16203, plain, (class_Groups_Ozero(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]), ['final']). 4.05/4.34 cnf(c_0_16204, plain, (class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ozero]), ['final']). 4.05/4.34 cnf(c_0_16205, plain, (class_Groups_Ozero(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]), ['final']). 4.05/4.34 cnf(c_0_16206, plain, (class_Rings_Olinordered__semiring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]), ['final']). 4.05/4.34 cnf(c_0_16207, plain, (class_Rings_Osemiring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]), ['final']). 4.05/4.34 cnf(c_0_16208, plain, (class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1]), ['final']). 4.05/4.34 cnf(c_0_16209, plain, (class_Rings_Osemiring__1(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]), ['final']). 4.05/4.34 cnf(c_0_16210, plain, (class_Rings_Osemiring__0(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]), ['final']). 4.05/4.34 cnf(c_0_16211, plain, (class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0]), ['final']). 4.05/4.34 cnf(c_0_16212, plain, (class_Rings_Osemiring__0(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]), ['final']). 4.05/4.34 cnf(c_0_16213, plain, (class_Rings_Olinordered__idom(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]), ['final']). 4.05/4.34 cnf(c_0_16214, plain, (class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy]), ['final']). 4.05/4.34 cnf(c_0_16215, plain, (class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lazy__Sequence_Osmall__lazy]), ['final']). 4.05/4.34 cnf(c_0_16216, plain, (class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add__abs]), ['final']). 4.05/4.34 cnf(c_0_16217, plain, (class_Enum_Oenum(tc_Product__Type_Ounit)), inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Enum_Oenum]), ['final']). 4.05/4.34 cnf(c_0_16218, plain, (class_Enum_Oenum(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Enum_Oenum]), ['final']). 4.05/4.34 cnf(c_0_16219, plain, (class_Rings_Oring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]), ['final']). 4.05/4.34 cnf(c_0_16220, plain, (class_Int_Onumber__ring(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]), ['final']). 4.05/4.34 cnf(c_0_16221, plain, (class_Orderings_Oorder(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]), ['final']). 4.05/4.34 cnf(c_0_16222, plain, (class_Orderings_Oorder(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]), ['final']). 4.05/4.34 cnf(c_0_16223, plain, (class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oorder]), ['final']). 4.05/4.34 cnf(c_0_16224, plain, (class_Orderings_Oorder(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]), ['final']). 4.05/4.34 cnf(c_0_16225, plain, (class_Groups_Ocomm__monoid__mult(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]), ['final']). 4.05/4.35 cnf(c_0_16226, plain, (class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult]), ['final']). 4.05/4.35 cnf(c_0_16227, plain, (class_Groups_Ocomm__monoid__mult(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]), ['final']). 4.05/4.35 cnf(c_0_16228, plain, (class_Rings_Olinordered__semiring__strict(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]), ['final']). 4.05/4.35 cnf(c_0_16229, plain, (class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict]), ['final']). 4.05/4.35 cnf(c_0_16230, plain, (class_Rings_Olinordered__semiring__strict(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]), ['final']). 4.05/4.35 cnf(c_0_16231, plain, (class_Groups_Oordered__ab__group__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]), ['final']). 4.05/4.35 cnf(c_0_16232, plain, (class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice]), ['final']). 4.05/4.35 cnf(c_0_16233, plain, (class_Groups_Ogroup__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]), ['final']). 4.05/4.35 cnf(c_0_16234, plain, (class_Lattices_Osemilattice__inf(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__inf]), ['final']). 4.05/4.35 cnf(c_0_16235, plain, (class_Lattices_Osemilattice__inf(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]), ['final']). 4.05/4.35 cnf(c_0_16236, plain, (class_Lattices_Osemilattice__inf(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]), ['final']). 4.05/4.35 cnf(c_0_16237, plain, (class_Orderings_Oord(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]), ['final']). 4.05/4.35 cnf(c_0_16238, plain, (class_Orderings_Oord(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]), ['final']). 4.05/4.35 cnf(c_0_16239, plain, (class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oord]), ['final']). 4.05/4.35 cnf(c_0_16240, plain, (class_Orderings_Oord(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]), ['final']). 4.05/4.35 cnf(c_0_16241, plain, (class_Lattices_Osemilattice__sup(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__sup]), ['final']). 4.05/4.35 cnf(c_0_16242, plain, (class_Lattices_Osemilattice__sup(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__sup]), ['final']). 4.05/4.35 cnf(c_0_16243, plain, (class_Lattices_Osemilattice__sup(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__sup]), ['final']). 4.05/4.35 cnf(c_0_16244, plain, (class_Int_Onumber(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber]), ['final']). 4.05/4.35 cnf(c_0_16245, plain, (class_Int_Onumber(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Int_Onumber]), ['final']). 4.05/4.35 cnf(c_0_16246, plain, (class_Int_Onumber(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Int_Onumber]), ['final']). 4.05/4.35 cnf(c_0_16247, plain, (class_Groups_Ocomm__monoid__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]), ['final']). 4.05/4.35 cnf(c_0_16248, plain, (class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add]), ['final']). 4.05/4.35 cnf(c_0_16249, plain, (class_Groups_Ocomm__monoid__add(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]), ['final']). 4.05/4.35 cnf(c_0_16250, plain, (class_Rings_Ocomm__semiring__1(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]), ['final']). 4.05/4.35 cnf(c_0_16251, plain, (class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1]), ['final']). 4.05/4.35 cnf(c_0_16252, plain, (class_Rings_Ocomm__semiring__1(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]), ['final']). 4.05/4.35 cnf(c_0_16253, plain, (class_Orderings_Olinorder(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]), ['final']). 4.05/4.35 cnf(c_0_16254, plain, (class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder]), ['final']). 4.05/4.35 cnf(c_0_16255, plain, (class_Orderings_Olinorder(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]), ['final']). 4.05/4.35 cnf(c_0_16256, plain, (class_Power_Opower(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]), ['final']). 4.05/4.35 cnf(c_0_16257, plain, (class_Power_Opower(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Power_Opower]), ['final']). 4.05/4.35 cnf(c_0_16258, plain, (class_Power_Opower(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]), ['final']). 4.05/4.35 cnf(c_0_16259, plain, (class_Groups_Oab__group__add(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]), ['final']). 4.05/4.35 cnf(c_0_16260, plain, (class_Lattices_Olattice(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Olattice]), ['final']). 4.05/4.35 cnf(c_0_16261, plain, (class_Lattices_Olattice(tc_HOL_Obool)), inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]), ['final']). 4.05/4.35 cnf(c_0_16262, plain, (class_Lattices_Olattice(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]), ['final']). 4.05/4.35 cnf(c_0_16263, plain, (class_Divides_Osemiring__div(tc_Int_Oint)), inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]), ['final']). 4.05/4.35 cnf(c_0_16264, plain, (class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral)), inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div]), ['final']). 4.05/4.35 cnf(c_0_16265, plain, (class_Divides_Osemiring__div(tc_Nat_Onat)), inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]), ['final']). 4.05/4.35 cnf(c_0_16266, hypothesis, (hBOOL(hAPP(c_Com_OWT,v_c))), inference(split_conjunct,[status(thm)],[conj_2]), ['final']). 4.05/4.35 cnf(c_0_16267, plain, (class_HOL_Oequal(tc_Com_Ocom)), inference(split_conjunct,[status(thm)],[arity_Com__Ocom__HOL_Oequal]), ['final']). 4.05/4.35 cnf(c_0_16268, plain, (class_Nat_Osize(tc_Com_Ocom)), inference(split_conjunct,[status(thm)],[arity_Com__Ocom__Nat_Osize]), ['final']). 4.05/4.35 cnf(c_0_16269, plain, (hBOOL(c_fTrue)), inference(split_conjunct,[status(thm)],[help_c__fTrue__1]), ['final']). 4.05/4.35 4.05/4.35 # End clausification derivation 4.05/4.35 # Begin listing active clauses obtained from FOF to CNF conversion 4.05/4.35 cnf(i_0_6845, hypothesis, (c_Hoare__Mirabelle_Ostate__not__singleton)). 4.05/4.35 cnf(i_0_3991, hypothesis, (c_Com_OWT__bodies)). 4.05/4.35 cnf(i_0_6834, plain, (hBOOL(c_fTrue))). 4.05/4.35 cnf(i_0_452, plain, (class_Nat_Osize(tc_Com_Ocom))). 4.05/4.35 cnf(i_0_1824, plain, (class_HOL_Oequal(tc_Com_Ocom))). 4.05/4.35 cnf(i_0_6020, hypothesis, (hBOOL(hAPP(c_Com_OWT,v_c)))). 4.05/4.35 cnf(i_0_2477, plain, (c_Int_OPls=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.05/4.35 cnf(i_0_5981, plain, (c_Code__Numeral_Osubtract__code__numeral=c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_1078, plain, (class_Divides_Osemiring__div(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_6596, plain, (c_Code__Numeral_Oof__nat=c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_5730, plain, (class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_1745, plain, (class_Divides_Osemiring__div(tc_Int_Oint))). 4.05/4.35 cnf(i_0_6126, plain, (class_Lattices_Olattice(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_4603, plain, (class_Lattices_Olattice(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_2126, plain, (class_Lattices_Olattice(tc_Int_Oint))). 4.05/4.35 cnf(i_0_3354, plain, (class_Groups_Oab__group__add(tc_Int_Oint))). 4.05/4.35 cnf(i_0_2046, plain, (class_Power_Opower(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_767, plain, (class_Power_Opower(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_10, plain, (class_Power_Opower(tc_Int_Oint))). 4.05/4.35 cnf(i_0_54, plain, (class_Orderings_Olinorder(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_2595, plain, (class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_6742, plain, (class_Orderings_Olinorder(tc_Int_Oint))). 4.05/4.35 cnf(i_0_5627, plain, (class_Rings_Ocomm__semiring__1(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_3995, plain, (class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_2979, plain, (class_Rings_Ocomm__semiring__1(tc_Int_Oint))). 4.05/4.35 cnf(i_0_341, plain, (class_Groups_Ocomm__monoid__add(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_6575, plain, (class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_4702, plain, (class_Groups_Ocomm__monoid__add(tc_Int_Oint))). 4.05/4.35 cnf(i_0_1587, plain, (class_Int_Onumber(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_5843, plain, (class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_1432, plain, (class_Int_Onumber(tc_Int_Oint))). 4.05/4.35 cnf(i_0_4815, plain, (class_Lattices_Osemilattice__sup(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_6989, plain, (class_Lattices_Osemilattice__sup(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_981, plain, (class_Lattices_Osemilattice__sup(tc_Int_Oint))). 4.05/4.35 cnf(i_0_6285, plain, (class_Orderings_Oord(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_7095, plain, (class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_5100, plain, (class_Orderings_Oord(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_6980, plain, (class_Orderings_Oord(tc_Int_Oint))). 4.05/4.35 cnf(i_0_2082, plain, (class_Lattices_Osemilattice__inf(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_3534, plain, (class_Lattices_Osemilattice__inf(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_894, plain, (class_Lattices_Osemilattice__inf(tc_Int_Oint))). 4.05/4.35 cnf(i_0_6941, plain, (class_Groups_Ogroup__add(tc_Int_Oint))). 4.05/4.35 cnf(i_0_7447, plain, (class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_6214, plain, (class_Groups_Oordered__ab__group__add(tc_Int_Oint))). 4.05/4.35 cnf(i_0_1538, plain, (class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_89, plain, (class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_1391, plain, (class_Rings_Olinordered__semiring__strict(tc_Int_Oint))). 4.05/4.35 cnf(i_0_4970, plain, (class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_3691, plain, (class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_3573, plain, (class_Groups_Ocomm__monoid__mult(tc_Int_Oint))). 4.05/4.35 cnf(i_0_5162, plain, (class_Orderings_Oorder(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_7557, plain, (class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_3871, plain, (class_Orderings_Oorder(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_4437, plain, (class_Orderings_Oorder(tc_Int_Oint))). 4.05/4.35 cnf(i_0_2292, plain, (class_Int_Onumber__ring(tc_Int_Oint))). 4.05/4.35 cnf(i_0_1604, plain, (class_Rings_Oring__1(tc_Int_Oint))). 4.05/4.35 cnf(i_0_5597, plain, (class_Enum_Oenum(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_2806, plain, (class_Enum_Oenum(tc_Product__Type_Ounit))). 4.05/4.35 cnf(i_0_3054, plain, (class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))). 4.05/4.35 cnf(i_0_172, plain, (class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))). 4.05/4.35 cnf(i_0_6540, plain, (class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))). 4.05/4.35 cnf(i_0_804, plain, (class_Rings_Olinordered__idom(tc_Int_Oint))). 4.05/4.35 cnf(i_0_842, plain, (class_Rings_Osemiring__0(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_4242, plain, (class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_5535, plain, (class_Rings_Osemiring__0(tc_Int_Oint))). 4.05/4.35 cnf(i_0_1738, plain, (class_Rings_Osemiring__1(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_5709, plain, (class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_5711, plain, (class_Rings_Osemiring__1(tc_Int_Oint))). 4.05/4.35 cnf(i_0_203, plain, (class_Rings_Olinordered__semiring__1(tc_Int_Oint))). 4.05/4.35 cnf(i_0_221, plain, (class_Groups_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_5890, plain, (class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_4577, plain, (class_Groups_Ozero(tc_Int_Oint))). 4.05/4.35 cnf(i_0_4741, plain, (class_Rings_Olinordered__semidom(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_4781, plain, (class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_1055, plain, (class_Rings_Olinordered__semidom(tc_Int_Oint))). 4.05/4.35 cnf(i_0_4782, plain, (class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))). 4.05/4.35 cnf(i_0_6567, plain, (class_Divides_Oring__div(tc_Int_Oint))). 4.05/4.35 cnf(i_0_1328, plain, (class_Nat_Osize(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_6042, plain, (class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_1695, plain, (class_Nat_Osize(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_337, plain, (class_Nat_Osize(tc_Com_Ovname))). 4.05/4.35 cnf(i_0_914, plain, (class_Nat_Osize(tc_Com_Ostate))). 4.05/4.35 cnf(i_0_4327, plain, (class_Nat_Osize(tc_Code__Evaluation_Oterm))). 4.05/4.35 cnf(i_0_3184, plain, (class_Nat_Osize(tc_Product__Type_Ounit))). 4.05/4.35 cnf(i_0_1207, plain, (class_Orderings_Opreorder(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_1583, plain, (class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_338, plain, (class_Orderings_Opreorder(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_4129, plain, (class_Orderings_Opreorder(tc_Int_Oint))). 4.05/4.35 cnf(i_0_5529, plain, (class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_4487, plain, (class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_6578, plain, (class_Groups_Ocancel__semigroup__add(tc_Int_Oint))). 4.05/4.35 cnf(i_0_5034, plain, (class_Groups_Olinordered__ab__group__add(tc_Int_Oint))). 4.05/4.35 cnf(i_0_7379, plain, (class_Rings_Osemiring(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_4945, plain, (class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_2351, plain, (class_Rings_Osemiring(tc_Int_Oint))). 4.05/4.35 cnf(i_0_1846, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_7526, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_3039, plain, (class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))). 4.05/4.35 cnf(i_0_4413, plain, (class_Orderings_Otop(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_3700, plain, (class_Rings_Oring(tc_Int_Oint))). 4.05/4.35 cnf(i_0_4149, plain, (class_Finite__Set_Ofinite(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_7187, plain, (class_Finite__Set_Ofinite(tc_Product__Type_Ounit))). 4.05/4.35 cnf(i_0_4922, plain, (class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))). 4.05/4.35 cnf(i_0_1865, plain, (class_Rings_Ozero__neq__one(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_3906, plain, (class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_2892, plain, (class_Rings_Ozero__neq__one(tc_Int_Oint))). 4.05/4.35 cnf(i_0_1512, plain, (class_Lattices_Oboolean__algebra(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_2578, plain, (class_Rings_Omult__zero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_680, plain, (class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_1794, plain, (class_Rings_Omult__zero(tc_Int_Oint))). 4.05/4.35 cnf(i_0_2310, plain, (class_Rings_Olinordered__ring(tc_Int_Oint))). 4.05/4.35 cnf(i_0_3015, plain, (class_Rings_Oordered__semiring(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_2980, plain, (class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_6690, plain, (class_Rings_Oordered__semiring(tc_Int_Oint))). 4.05/4.35 cnf(i_0_1754, plain, (class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_899, plain, (class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_4629, plain, (class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))). 4.05/4.35 cnf(i_0_6365, plain, (class_Rings_Oordered__ring(tc_Int_Oint))). 4.05/4.35 cnf(i_0_7288, plain, (class_Groups_Ominus(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_6752, plain, (class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_1638, plain, (class_Groups_Ominus(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_3423, plain, (class_Groups_Ominus(tc_Int_Oint))). 4.05/4.35 cnf(i_0_4383, plain, (class_Nat_Osemiring__char__0(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_2344, plain, (class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_789, plain, (class_Nat_Osemiring__char__0(tc_Int_Oint))). 4.05/4.35 cnf(i_0_813, plain, (class_Lattices_Obounded__lattice(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_817, plain, (class_HOL_Oequal(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_1213, plain, (class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_2252, plain, (class_HOL_Oequal(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_7172, plain, (class_HOL_Oequal(tc_Int_Oint))). 4.05/4.35 cnf(i_0_1390, plain, (class_HOL_Oequal(tc_Com_Ovname))). 4.05/4.35 cnf(i_0_4013, plain, (class_HOL_Oequal(tc_Com_Ostate))). 4.05/4.35 cnf(i_0_5956, plain, (class_HOL_Oequal(tc_Code__Evaluation_Oterm))). 4.05/4.35 cnf(i_0_2127, plain, (class_HOL_Oequal(tc_Product__Type_Ounit))). 4.05/4.35 cnf(i_0_5647, plain, (class_Groups_Oone(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_1804, plain, (class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_6964, plain, (class_Groups_Oone(tc_Int_Oint))). 4.05/4.35 cnf(i_0_2577, plain, (class_Groups_Omonoid__mult(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_1809, plain, (class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_2135, plain, (class_Groups_Omonoid__mult(tc_Int_Oint))). 4.05/4.35 cnf(i_0_2083, plain, (class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_4904, plain, (class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_1590, plain, (class_Rings_Oordered__cancel__semiring(tc_Int_Oint))). 4.05/4.35 cnf(i_0_5126, plain, (class_Groups_Omonoid__add(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_3295, plain, (class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_6647, plain, (class_Groups_Omonoid__add(tc_Int_Oint))). 4.05/4.35 cnf(i_0_3990, plain, (class_Rings_Oordered__comm__semiring(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_6191, plain, (class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_969, plain, (class_Rings_Oordered__comm__semiring(tc_Int_Oint))). 4.05/4.35 cnf(i_0_7479, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_971, plain, (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))). 4.05/4.35 cnf(i_0_5462, plain, (class_Groups_Oab__semigroup__mult(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_4540, plain, (class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_4964, plain, (class_Groups_Oab__semigroup__mult(tc_Int_Oint))). 4.05/4.35 cnf(i_0_1050, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_2915, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_2514, plain, (class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))). 4.05/4.35 cnf(i_0_7076, plain, (class_Rings_Oordered__ring__abs(tc_Int_Oint))). 4.05/4.35 cnf(i_0_1633, plain, (class_Lattices_Obounded__lattice__top(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_5076, plain, (class_Rings_Ono__zero__divisors(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_1877, plain, (class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_3182, plain, (class_Rings_Ono__zero__divisors(tc_Int_Oint))). 4.05/4.35 cnf(i_0_1372, plain, (class_Groups_Ouminus(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_4195, plain, (class_Groups_Ouminus(tc_Int_Oint))). 4.05/4.35 cnf(i_0_4644, plain, (class_Rings_Olinordered__ring__strict(tc_Int_Oint))). 4.05/4.35 cnf(i_0_5336, plain, (class_Groups_Osemigroup__add(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_3321, plain, (class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_1486, plain, (class_Groups_Osemigroup__add(tc_Int_Oint))). 4.05/4.35 cnf(i_0_1491, plain, (class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_3708, plain, (class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_4438, plain, (class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))). 4.05/4.35 cnf(i_0_2727, plain, (class_Lattices_Odistrib__lattice(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_3019, plain, (class_Lattices_Odistrib__lattice(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_5833, plain, (class_Lattices_Odistrib__lattice(tc_Int_Oint))). 4.05/4.35 cnf(i_0_3199, plain, (class_Orderings_Obot(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_3438, plain, (class_Orderings_Obot(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_4532, plain, (class_Rings_Ocomm__semiring(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_3414, plain, (class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_5305, plain, (class_Rings_Ocomm__semiring(tc_Int_Oint))). 4.05/4.35 cnf(i_0_6771, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_7077, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_5857, plain, (class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))). 4.05/4.35 cnf(i_0_6131, plain, (class_Int_Oring__char__0(tc_Int_Oint))). 4.05/4.35 cnf(i_0_2114, plain, (class_Smallcheck_Osmall(tc_Int_Oint))). 4.05/4.35 cnf(i_0_5591, plain, (class_Smallcheck_Osmall(tc_Product__Type_Ounit))). 4.05/4.35 cnf(i_0_2272, plain, (class_Rings_Oidom(tc_Int_Oint))). 4.05/4.35 cnf(i_0_7162, plain, (class_Groups_Osgn__if(tc_Int_Oint))). 4.05/4.35 cnf(i_0_4651, plain, (class_Rings_Ocomm__ring__1(tc_Int_Oint))). 4.05/4.35 cnf(i_0_2401, plain, (class_Orderings_Owellorder(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_4757, plain, (class_Rings_Oring__no__zero__divisors(tc_Int_Oint))). 4.05/4.35 cnf(i_0_5668, plain, (class_Rings_Olinordered__semiring(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_3311, plain, (class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_2809, plain, (class_Rings_Olinordered__semiring(tc_Int_Oint))). 4.05/4.35 cnf(i_0_6459, plain, (class_Groups_Oab__semigroup__add(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_6426, plain, (class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_4155, plain, (class_Groups_Oab__semigroup__add(tc_Int_Oint))). 4.05/4.35 cnf(i_0_5917, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_6333, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_3682, plain, (class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))). 4.05/4.35 cnf(i_0_4685, plain, (class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))). 4.05/4.35 cnf(i_0_5460, plain, (class_Groups_Oabs__if(tc_Int_Oint))). 4.05/4.35 cnf(i_0_6319, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_4452, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_5434, plain, (class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))). 4.05/4.35 cnf(i_0_3, plain, (c_Orderings_Oord__class_Omax(tc_Nat_Onat)=c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_2887, plain, (c_Orderings_Obot__class_Obot(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_6768, plain, (c_Orderings_Oord__class_Omin(tc_Nat_Onat)=c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_4059, plain, (c_Int_Oring__1__class_Oof__int(tc_Int_Oint)=c_Fun_Oid(tc_Int_Oint))). 4.05/4.35 cnf(i_0_2239, plain, (c_HOL_Obool_Obool__size(c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_7218, plain, (c_HOL_Obool_Obool__size(c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_7407, plain, (c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))). 4.05/4.35 cnf(i_0_3161, plain, (c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 4.05/4.35 cnf(i_0_7345, plain, (class_Nat_Osize(tc_List_Olist(X1)))). 4.05/4.35 cnf(i_0_6809, plain, (c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_7057, plain, (class_Nat_Osize(tc_Option_Ooption(X1)))). 4.05/4.35 cnf(i_0_950, plain, (class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)))). 4.05/4.35 cnf(i_0_5700, plain, (class_HOL_Oequal(tc_List_Olist(X1)))). 4.05/4.35 cnf(i_0_2459, plain, (class_HOL_Oequal(tc_Option_Ooption(X1)))). 4.05/4.35 cnf(i_0_4716, plain, (class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X1)))). 4.05/4.35 cnf(i_0_5934, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_4704, plain, (c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat))). 4.05/4.35 cnf(i_0_2347, plain, (c_Equiv__Relations_Oequivp(X1,c_fequal))). 4.05/4.35 cnf(i_0_4190, plain, (c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than))). 4.05/4.35 cnf(i_0_6287, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OBODY(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_4518, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.05/4.35 cnf(i_0_1148, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X1)=X1)). 4.05/4.35 cnf(i_0_7347, plain, (hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies)=c_Com_Obody)). 4.05/4.35 cnf(i_0_2521, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)=X1)). 4.05/4.35 cnf(i_0_6401, plain, (hAPP(c_Int_OAbs__Integ,esk449_1(X1))=X1)). 4.05/4.35 cnf(i_0_111, plain, (hAPP(c_Fun_Oid(X1),X2)=X2)). 4.05/4.35 cnf(i_0_4817, plain, (hAPP(c_COMBI(X1),X2)=X2)). 4.05/4.35 cnf(i_0_7277, plain, (hAPP(c_Set_OCollect(X1),X2)=X2)). 4.05/4.35 cnf(i_0_1531, plain, (c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X1)))). 4.05/4.35 cnf(i_0_6664, plain, (c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X1)))). 4.05/4.35 cnf(i_0_1151, plain, (c_Option_Ois__none(X1,c_Option_Ooption_ONone(X1)))). 4.05/4.35 cnf(i_0_4236, plain, (class_Nat_Osize(tc_prod(X1,X2)))). 4.05/4.35 cnf(i_0_206, plain, (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_5342, plain, (class_Nat_Osize(tc_sum(X1,X2)))). 4.05/4.35 cnf(i_0_3681, plain, (class_Nat_Osize(tc_Nitpick_Opair__box(X1,X2)))). 4.05/4.35 cnf(i_0_6954, plain, (class_HOL_Oequal(tc_prod(X1,X2)))). 4.05/4.35 cnf(i_0_3160, plain, (class_HOL_Oequal(tc_sum(X1,X2)))). 4.05/4.35 cnf(i_0_7171, plain, (class_HOL_Oequal(tc_Nitpick_Opair__box(X1,X2)))). 4.05/4.35 cnf(i_0_5508, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Onat__of,X1))=X1)). 4.05/4.35 cnf(i_0_3639, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_2557, plain, (hAPP(c_Code__Numeral_Onat__of,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1))=X1)). 4.05/4.35 cnf(i_0_1164, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X1))=X1)). 4.05/4.35 cnf(i_0_1233, plain, (c_Predicate_Oconversep(X1,X1,c_fequal)=c_fequal)). 4.05/4.35 cnf(i_0_6043, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_2609, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_2504, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_6031, plain, (c_Map_Omap__le(X1,X2,X3,X3))). 4.05/4.35 cnf(i_0_154, plain, (hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_5477, plain, (hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_4910, plain, (hAPP(c_New__DSequence_Opos__empty(X1),X2)=c_Lazy__Sequence_Oempty(X1))). 4.05/4.35 cnf(i_0_1235, plain, (c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))). 4.05/4.35 cnf(i_0_142, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Int_OMin)). 4.05/4.35 cnf(i_0_3291, plain, (c_Enum_Oenum__the(X1,hAPP(c_fequal,X2))=X2)). 4.05/4.35 cnf(i_0_1299, plain, (c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X2))=X2)). 4.05/4.35 cnf(i_0_3194, plain, (c_List_Oremdups(X1,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.05/4.35 cnf(i_0_2463, plain, (hBOOL(hAPP(hAPP(c_fequal,X1),X1)))). 4.05/4.35 cnf(i_0_5479, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olist_ONil(X1))))). 4.05/4.35 cnf(i_0_7131, plain, (c_Random_Oinc__shift(X1,X1)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_3185, plain, (c_List_Obutlast(X1,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.05/4.35 cnf(i_0_818, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)))). 4.05/4.35 cnf(i_0_5039, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.05/4.35 cnf(i_0_6180, plain, (c_Nitpick_Onat__gcd(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1)). 4.05/4.35 cnf(i_0_5687, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OBODY(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_6607, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.05/4.35 cnf(i_0_4428, plain, (hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.05/4.35 cnf(i_0_2721, plain, (c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less))). 4.05/4.35 cnf(i_0_6714, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)))). 4.05/4.35 cnf(i_0_2543, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X1)))). 4.05/4.35 cnf(i_0_1184, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X1)))). 4.05/4.35 cnf(i_0_7256, plain, (c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X2)))). 4.05/4.35 cnf(i_0_7299, plain, (c_Wellfounded_Owf(X1,c_List_Omeasures(X1,X2)))). 4.05/4.35 cnf(i_0_1980, plain, (c_List_Olist__all(X1,X2,c_List_Olist_ONil(X1)))). 4.05/4.35 cnf(i_0_3549, plain, (c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))))). 4.05/4.35 cnf(i_0_3143, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))))). 4.05/4.35 cnf(i_0_1915, plain, (c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.05/4.35 cnf(i_0_3328, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.05/4.35 cnf(i_0_6312, plain, (c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1))). 4.05/4.35 cnf(i_0_7249, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Int_Oint))). 4.05/4.35 cnf(i_0_5611, plain, (c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)=c_FunDef_Omax__strict)). 4.05/4.35 cnf(i_0_7399, plain, (c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)=c_FunDef_Omin__strict)). 4.05/4.35 cnf(i_0_3079, hypothesis, (hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))))). 4.05/4.35 cnf(i_0_2988, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.05/4.35 cnf(i_0_3908, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)=X1)). 4.05/4.35 cnf(i_0_2400, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X1)). 4.05/4.35 cnf(i_0_7100, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X1)). 4.05/4.35 cnf(i_0_643, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_675, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=X1)). 4.05/4.35 cnf(i_0_3350, plain, (c_List_Osplice(X1,X2,c_List_Olist_ONil(X1))=X2)). 4.05/4.35 cnf(i_0_4559, plain, (hAPP(c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),X2))=X2)). 4.05/4.35 cnf(i_0_3701, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.05/4.35 cnf(i_0_2798, plain, (c_List_Osplice(X1,c_List_Olist_ONil(X1),X2)=X2)). 4.05/4.35 cnf(i_0_6848, plain, (c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than)=c_FunDef_Opair__less)). 4.05/4.35 cnf(i_0_6233, plain, (hAPP(c_List_Otl(X1),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.05/4.35 cnf(i_0_5446, plain, (hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.05/4.35 cnf(i_0_1400, plain, (hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.05/4.35 cnf(i_0_3801, plain, (c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X1)))). 4.05/4.35 cnf(i_0_5325, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_2250, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.05/4.35 cnf(i_0_2392, plain, (c_List_Oreplicate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)=c_List_Olist_ONil(X1))). 4.05/4.35 cnf(i_0_3976, plain, (c_Option_Ooption_Ooption__size(X1,X2,c_Option_Ooption_ONone(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_6286, plain, (c_List_Olist_Olist__size(X1,X2,c_List_Olist_ONil(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_1982, plain, (c_List_Oremove1(X1,X2,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.05/4.35 cnf(i_0_5995, plain, (c_List_Osublist(X1,c_List_Olist_ONil(X1),X2)=c_List_Olist_ONil(X1))). 4.05/4.35 cnf(i_0_2559, plain, (hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X2))))). 4.05/4.35 cnf(i_0_2997, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X2))))). 4.05/4.35 cnf(i_0_1347, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))))). 4.05/4.35 cnf(i_0_5106, plain, (c_List_OtakeWhile(X1,X2,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.05/4.35 cnf(i_0_7178, plain, (c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X2)))). 4.05/4.35 cnf(i_0_1018, plain, (hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)))). 4.05/4.35 cnf(i_0_7427, plain, (c_Relation_Orefl__on(X1,X2,c_Relation_OId__on(X1,X2)))). 4.05/4.35 cnf(i_0_5239, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(X1,X2,X3))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_811, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.05/4.35 cnf(i_0_1401, plain, (c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X2))). 4.05/4.35 cnf(i_0_7524, plain, (c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2))). 4.05/4.35 cnf(i_0_1815, plain, (hAPP(c_New__DSequence_Oneg__single(X1,X2),X3)=c_Lazy__Sequence_Ohb__single(X1,X2))). 4.05/4.35 cnf(i_0_4049, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X2))))). 4.05/4.35 cnf(i_0_778, plain, (c_Option_Oset(X1,c_Option_Ooption_ONone(X1))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.05/4.35 cnf(i_0_210, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))=X1)). 4.05/4.35 cnf(i_0_4025, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1)). 4.05/4.35 cnf(i_0_2117, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))))). 4.05/4.35 cnf(i_0_4658, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1)). 4.05/4.35 cnf(i_0_784, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1)). 4.05/4.35 cnf(i_0_3823, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))=X1)). 4.05/4.35 cnf(i_0_2600, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X1)). 4.05/4.35 cnf(i_0_450, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=X1)). 4.05/4.35 cnf(i_0_7558, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)=X1)). 4.05/4.35 cnf(i_0_1457, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=X1)). 4.05/4.35 cnf(i_0_2815, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)=X1)). 4.05/4.35 cnf(i_0_5891, plain, (hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2))=X2)). 4.05/4.35 cnf(i_0_2854, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1))=X2)). 4.05/4.35 cnf(i_0_5436, plain, (hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=X2)). 4.05/4.35 cnf(i_0_3883, plain, (c_List_Olist__all2(X1,X1,c_fequal,X2,X2))). 4.05/4.35 cnf(i_0_5295, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)=X2)). 4.05/4.35 cnf(i_0_3889, plain, (hAPP(hAPP(c_COMBK(X1,X2),X3),X4)=X3)). 4.05/4.35 cnf(i_0_5911, plain, (c_Nat_Onat_Onat__case(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2)). 4.05/4.35 cnf(i_0_7411, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=X2)). 4.05/4.35 cnf(i_0_3193, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X1)),c_Option_Ooption_ONone(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_1083, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Olist_ONil(X1))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_1904, plain, (hAPP(c_List_Ofilter(X1,X2),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.05/4.35 cnf(i_0_6630, plain, (hAPP(c_New__DSequence_Opos__single(X1,X2),X3)=hAPP(c_Lazy__Sequence_Osingle(X1),X2))). 4.05/4.35 cnf(i_0_5148, plain, (hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X1)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 4.05/4.35 cnf(i_0_7548, plain, (c_List_Otranspose(X1,c_List_Olist_ONil(tc_List_Olist(X1)))=c_List_Olist_ONil(tc_List_Olist(X1)))). 4.05/4.35 cnf(i_0_234, plain, (c_List_Oremdups(X1,c_List_Oremdups(X1,X2))=c_List_Oremdups(X1,X2))). 4.05/4.35 cnf(i_0_6290, plain, (c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X2))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.05/4.35 cnf(i_0_733, plain, (hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))). 4.05/4.35 cnf(i_0_1682, plain, (hAPP(c_List_Oset(X1),c_List_Olist_ONil(X1))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.05/4.35 cnf(i_0_2197, plain, (hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X1)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))). 4.05/4.35 cnf(i_0_874, plain, (hAPP(c_Relation_ORange(X1,X1),c_Relation_OId__on(X1,X2))=X2)). 4.05/4.35 cnf(i_0_1426, plain, (hAPP(c_Relation_ODomain(X1,X1),c_Relation_OId__on(X1,X2))=X2)). 4.05/4.35 cnf(i_0_859, plain, (hAPP(c_Nat_Onat_Onat__rec(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2)). 4.05/4.35 cnf(i_0_5649, plain, (hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X2)=X2)). 4.05/4.35 cnf(i_0_775, plain, (c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)))). 4.05/4.35 cnf(i_0_7403, plain, (c_Fun_Oinj__on(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1),X2))). 4.05/4.35 cnf(i_0_4610, plain, (hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X2)=X2)). 4.05/4.35 cnf(i_0_3289, plain, (hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))=hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1))). 4.05/4.35 cnf(i_0_3803, plain, (hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1))=hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X1))). 4.05/4.35 cnf(i_0_287, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X1)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))). 4.05/4.35 cnf(i_0_4508, plain, (hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X1))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))). 4.05/4.35 cnf(i_0_676, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.05/4.35 cnf(i_0_7159, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_3597, plain, (hAPP(c_Int_Onat,X1)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))). 4.05/4.35 cnf(i_0_1364, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_4076, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))=X1)). 4.05/4.35 cnf(i_0_6668, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_352, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))). 4.05/4.35 cnf(i_0_599, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))))). 4.05/4.35 cnf(i_0_1749, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_5343, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.05/4.35 cnf(i_0_5612, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))))). 4.05/4.35 cnf(i_0_1989, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_3584, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_7092, plain, (hAPP(hAPP(c_List_Otake(X1),X2),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.05/4.35 cnf(i_0_3162, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1)))). 4.05/4.35 cnf(i_0_4388, plain, (c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2))). 4.05/4.35 cnf(i_0_3551, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.05/4.35 cnf(i_0_2329, plain, (hAPP(hAPP(c_List_Otake(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=c_List_Olist_ONil(X1))). 4.05/4.35 cnf(i_0_1186, plain, (c_List_Omap__filter(X1,X2,X3,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X2))). 4.05/4.35 cnf(i_0_3716, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(X1,X2,X3))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_5281, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))))). 4.05/4.35 cnf(i_0_1972, plain, (hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)))). 4.05/4.35 cnf(i_0_7026, plain, (hAPP(c_List_Omap(X1,X1),c_COMBI(X1))=c_Fun_Oid(tc_List_Olist(X1)))). 4.05/4.35 cnf(i_0_3057, plain, (hAPP(c_Option_Omap(X1,X1),c_COMBI(X1))=c_Fun_Oid(tc_Option_Ooption(X1)))). 4.05/4.35 cnf(i_0_3726, plain, (hAPP(c_Option_Omap(X1,X1),c_Fun_Oid(X1))=c_Fun_Oid(tc_Option_Ooption(X1)))). 4.05/4.35 cnf(i_0_3636, plain, (c_Predicate_Oconversep(X1,X2,c_Predicate_Oconversep(X2,X1,X3))=X3)). 4.05/4.35 cnf(i_0_4547, plain, (hAPP(c_List_Omap(X1,X1),c_Fun_Oid(X1))=c_Fun_Oid(tc_List_Olist(X1)))). 4.05/4.35 cnf(i_0_4326, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.05/4.35 cnf(i_0_4474, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.05/4.35 cnf(i_0_3959, plain, (c_Lazy__Sequence_Osmall__lazy_H(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))=c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X1))). 4.05/4.35 cnf(i_0_4355, plain, (c_Option_Ooption_Ooption__rec(X1,X2,X3,X4,c_Option_Ooption_ONone(X2))=X3)). 4.05/4.35 cnf(i_0_367, plain, (c_Map_Omap__upds(X1,X2,X3,X4,c_List_Olist_ONil(X2))=X3)). 4.05/4.35 cnf(i_0_7232, plain, (c_Map_Omap__upds(X1,X2,X3,c_List_Olist_ONil(X1),X4)=X3)). 4.05/4.35 cnf(i_0_3649, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))))). 4.05/4.35 cnf(i_0_6981, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2))))). 4.05/4.35 cnf(i_0_3164, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)))). 4.05/4.35 cnf(i_0_2015, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_OSuc,X1))). 4.05/4.35 cnf(i_0_839, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)=hAPP(c_Nat_OSuc,X1))). 4.05/4.35 cnf(i_0_6289, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X2)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2))). 4.05/4.35 cnf(i_0_2334, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))))). 4.05/4.35 cnf(i_0_6890, plain, (c_List_Olist__all2(X1,X2,X3,c_List_Olist_ONil(X1),c_List_Olist_ONil(X2)))). 4.05/4.35 cnf(i_0_5137, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X2)=X2)). 4.05/4.35 cnf(i_0_1156, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X2)=X2)). 4.05/4.35 cnf(i_0_5946, plain, (hAPP(c_Product__Type_Osnd(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4))=X4)). 4.05/4.35 cnf(i_0_7184, plain, (hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_858, plain, (hAPP(c_Product__Type_Ofst(X1,X2),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4))=X3)). 4.05/4.35 cnf(i_0_940, plain, (hAPP(c_List_Oset(X1),c_List_Oremdups(X1,X2))=hAPP(c_List_Oset(X1),X2))). 4.05/4.35 cnf(i_0_6409, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_67, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_2285, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_OMin)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.05/4.35 cnf(i_0_4734, plain, (c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)))). 4.05/4.35 cnf(i_0_1097, plain, (hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral)),c_Int_Onat)=c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_6949, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X2)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))). 4.05/4.35 cnf(i_0_4902, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))). 4.05/4.35 cnf(i_0_6311, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_OPow(X1),X2))=X2)). 4.05/4.35 cnf(i_0_1194, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1)). 4.05/4.35 cnf(i_0_615, plain, (hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))). 4.05/4.35 cnf(i_0_6583, plain, (c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X2))). 4.05/4.35 cnf(i_0_4593, plain, (c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.05/4.35 cnf(i_0_4136, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X1)). 4.05/4.35 cnf(i_0_5656, plain, (hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X3)). 4.05/4.35 cnf(i_0_2033, plain, (hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X2)). 4.05/4.35 cnf(i_0_1945, plain, (c_Map_Omap__le(X1,X2,X3,c_Map_Omap__add(X1,X2,X4,X3)))). 4.05/4.35 cnf(i_0_2362, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oreplicate(X1,X2,X3))=X2)). 4.05/4.35 cnf(i_0_6064, plain, (c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4))=hAPP(X3,X4))). 4.05/4.35 cnf(i_0_7007, plain, (hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of)=c_Code__Numeral_Oint__of)). 4.05/4.35 cnf(i_0_7105, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_6624, plain, (hAPP(c_Option_Ooption_Ooption__case(X1,X2,X3,X4),c_Option_Ooption_ONone(X2))=X3)). 4.05/4.35 cnf(i_0_3820, plain, (hAPP(c_Fun_Ocomp(X1,X2,X1,X3),c_Fun_Oid(X1))=X3)). 4.05/4.35 cnf(i_0_220, plain, (hAPP(c_List_Ofoldl(X1,X2,X3,X4),c_List_Olist_ONil(X2))=X4)). 4.05/4.35 cnf(i_0_455, plain, (hAPP(c_List_Olist_Olist__case(X1,X2,X3,X4),c_List_Olist_ONil(X2))=X3)). 4.05/4.35 cnf(i_0_961, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 4.05/4.35 cnf(i_0_1369, plain, (hAPP(c_Fun_Ocomp(X1,X1,X2,c_Fun_Oid(X1)),X3)=X3)). 4.05/4.35 cnf(i_0_4606, plain, (c_Enum_Oproduct(X1,X2,c_List_Olist_ONil(X1),X3)=c_List_Olist_ONil(tc_prod(X1,X2)))). 4.05/4.35 cnf(i_0_597, plain, (hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))). 4.05/4.35 cnf(i_0_1680, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X1)),hAPP(c_Option_Ooption_OSome(X1),X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.05/4.35 cnf(i_0_1071, plain, (hAPP(c_List_Oset(X1),hAPP(c_List_Orotate1(X1),X2))=hAPP(c_List_Oset(X1),X2))). 4.05/4.35 cnf(i_0_3762, plain, (hAPP(c_List_Oset(X1),hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Oset(X1),X2))). 4.05/4.35 cnf(i_0_7483, plain, (c_Nitpick_OAbs__Frac(X1,c_Nitpick_Onorm__frac(X2,X3))=hAPP(hAPP(c_Nitpick_Ofrac(X1),X2),X3))). 4.06/4.35 cnf(i_0_1101, plain, (c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X2))=c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2)))). 4.06/4.35 cnf(i_0_5448, plain, (c_Wellfounded_Owf(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_1806, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X2))). 4.06/4.35 cnf(i_0_6606, plain, (hAPP(hAPP(c_Option_Omap(X1,X2),X3),c_Option_Ooption_ONone(X1))=c_Option_Ooption_ONone(X2))). 4.06/4.35 cnf(i_0_7341, plain, (hAPP(hAPP(c_Nat_Ocompow(X1,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=c_Fun_Oid(X1))). 4.06/4.35 cnf(i_0_6608, plain, (c_List_Osublist(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_List_Olist_ONil(X1))). 4.06/4.35 cnf(i_0_3686, plain, (hAPP(hAPP(c_List_Olist__update(X1,c_List_Olist_ONil(X1)),X2),X3)=c_List_Olist_ONil(X1))). 4.06/4.35 cnf(i_0_6428, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than),X2)))). 4.06/4.35 cnf(i_0_4335, plain, (hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId__on(X1,X2))=c_Relation_OId__on(X1,X2))). 4.06/4.35 cnf(i_0_6050, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))). 4.06/4.35 cnf(i_0_190, plain, (hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3))=X3)). 4.06/4.35 cnf(i_0_1332, plain, (c_Enum_Oenum__the(X1,c_Finite__Set_Ofold1Set(X1,X2,X3))=hAPP(c_Finite__Set_Ofold1(X1,X2),X3))). 4.06/4.35 cnf(i_0_1269, plain, (hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2)). 4.06/4.35 cnf(i_0_1770, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_List_Olist_ONil(tc_Nat_Onat))). 4.06/4.35 cnf(i_0_3845, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.35 cnf(i_0_3167, plain, (c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))))). 4.06/4.35 cnf(i_0_3358, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 4.06/4.35 cnf(i_0_6416, plain, (c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.35 cnf(i_0_7489, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X1)))). 4.06/4.35 cnf(i_0_5094, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))). 4.06/4.35 cnf(i_0_6156, plain, (c_List_Oinsert(X1,X2,c_List_Olist_ONil(X1))=hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))). 4.06/4.35 cnf(i_0_1428, plain, (hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_937, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))),X1)=X1)). 4.06/4.35 cnf(i_0_1212, plain, (hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_1410, plain, (c_List_Oinsert(X1,X2,c_List_Oremdups(X1,X3))=c_List_Oremdups(X1,c_List_Oinsert(X1,X2,X3)))). 4.06/4.35 cnf(i_0_5933, plain, (hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X1,X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))). 4.06/4.35 cnf(i_0_1352, plain, (hAPP(c_List_Orev(X1),c_List_Oreplicate(X1,X2,X3))=c_List_Oreplicate(X1,X2,X3))). 4.06/4.35 cnf(i_0_4347, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))). 4.06/4.35 cnf(i_0_3758, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))). 4.06/4.35 cnf(i_0_1487, plain, (c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)))). 4.06/4.35 cnf(i_0_6999, plain, (c_List_Olists(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_1136, plain, (c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 4.06/4.35 cnf(i_0_3378, plain, (hAPP(c_Relation_OField(X1),hAPP(c_Relation_Oconverse(X1,X1),X2))=hAPP(c_Relation_OField(X1),X2))). 4.06/4.35 cnf(i_0_1290, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))))). 4.06/4.35 cnf(i_0_2631, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.06/4.35 cnf(i_0_2711, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))))). 4.06/4.35 cnf(i_0_958, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1))))). 4.06/4.35 cnf(i_0_1663, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))))). 4.06/4.35 cnf(i_0_5234, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1))))))). 4.06/4.35 cnf(i_0_2874, plain, (c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_6689, plain, (c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_1885, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),X1)))). 4.06/4.35 cnf(i_0_5122, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X1)))). 4.06/4.35 cnf(i_0_6344, plain, (hAPP(c_New__DSequence_Oneg__decr__bind(X1,X2,X3,X4),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Lazy__Sequence_Ohit__bound(X2))). 4.06/4.35 cnf(i_0_7032, plain, (hAPP(c_New__DSequence_Opos__decr__bind(X1,X2,X3,X4),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))=c_Lazy__Sequence_Oempty(X2))). 4.06/4.35 cnf(i_0_7304, plain, (hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue)=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_2107, plain, (hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_422, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X1,X2))=hAPP(c_Nat_OSuc,c_Com_Ocom_Ocom__size(X2)))). 4.06/4.35 cnf(i_0_6934, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))=X2)). 4.06/4.35 cnf(i_0_3495, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 4.06/4.35 cnf(i_0_5882, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),X3),c_List_Olist_ONil(X2))=c_List_Olist_ONil(tc_prod(X1,X2)))). 4.06/4.35 cnf(i_0_5771, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),c_List_Olist_ONil(X1)),X3)=c_List_Olist_ONil(tc_prod(X1,X2)))). 4.06/4.35 cnf(i_0_3503, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_527, plain, (hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)=X2)). 4.06/4.35 cnf(i_0_2291, plain, (c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X4))). 4.06/4.35 cnf(i_0_7129, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),hAPP(X3,X4))=X3)). 4.06/4.35 cnf(i_0_4283, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)=X2)). 4.06/4.35 cnf(i_0_2890, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)=X1)). 4.06/4.35 cnf(i_0_2533, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.35 cnf(i_0_278, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.06/4.35 cnf(i_0_7514, plain, (hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5),X4)=X5)). 4.06/4.35 cnf(i_0_266, plain, (c_Fun_Ooverride__on(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=X3)). 4.06/4.35 cnf(i_0_2427, plain, (c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))=c_Divides_OnegateSnd)). 4.06/4.35 cnf(i_0_5084, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),c_Int_OMin)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))). 4.06/4.35 cnf(i_0_3460, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X1,X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))). 4.06/4.35 cnf(i_0_3782, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.06/4.35 cnf(i_0_5053, plain, (c_List_Osublist(X1,X2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))=hAPP(hAPP(c_List_Otake(X1),X3),X2))). 4.06/4.35 cnf(i_0_2017, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))))). 4.06/4.35 cnf(i_0_3482, plain, (c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_6072, plain, (hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))))). 4.06/4.35 cnf(i_0_5742, plain, (c_Divides_Odivmod__int(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). 4.06/4.35 cnf(i_0_5428, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.06/4.35 cnf(i_0_7541, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orotate1(X1),X2))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))). 4.06/4.35 cnf(i_0_393, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orev(X1),X2))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))). 4.06/4.35 cnf(i_0_1723, plain, (c_Relation_OId__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_6460, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X2)=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))). 4.06/4.35 cnf(i_0_7408, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))=X1)). 4.06/4.35 cnf(i_0_4637, plain, (c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X3)). 4.06/4.35 cnf(i_0_3258, plain, (c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3),X4)=c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,c_Lazy__Sequence_Oappend(X1,X3,X4)))). 4.06/4.35 cnf(i_0_6148, plain, (hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X1),X2),X3),X4),X5)=c_New__DSequence_Opos__single(X1,X2))). 4.06/4.35 cnf(i_0_6456, plain, (hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X1),X2),X3),X4),X5)=c_New__DSequence_Oneg__single(X1,X2))). 4.06/4.35 cnf(i_0_6397, plain, (hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_6396, plain, (hAPP(c_Relation_ORange(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_2315, plain, (hAPP(c_Relation_ODomain(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_1802, plain, (c_Option_Ooption_Ooption__rec(X1,X2,X3,X4,hAPP(c_Option_Ooption_OSome(X2),X5))=hAPP(X4,X5))). 4.06/4.35 cnf(i_0_5421, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))=c_List_Olist_ONil(X1))). 4.06/4.35 cnf(i_0_6910, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X2))))). 4.06/4.35 cnf(i_0_835, plain, (hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_5776, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))). 4.06/4.35 cnf(i_0_2736, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.35 cnf(i_0_7078, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),c_List_Olist_ONil(tc_prod(X1,X2))),X3)=c_Option_Ooption_ONone(X2))). 4.06/4.35 cnf(i_0_6406, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X2)=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))). 4.06/4.35 cnf(i_0_4897, plain, (c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg))). 4.06/4.35 cnf(i_0_6847, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremdups(X1,X2))=hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2)))). 4.06/4.35 cnf(i_0_7177, plain, (hAPP(c_Set_OPow(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_2005, plain, (hAPP(c_Random_Oiterate(X1,X2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),X3),X4)=hAPP(c_Product__Type_OPair(X1,X2),X4))). 4.06/4.35 cnf(i_0_2686, plain, (hAPP(hAPP(c_List_Odrop(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=X3)). 4.06/4.35 cnf(i_0_1461, plain, (hAPP(hAPP(c_List_Olist__update(X1,X2),X3),hAPP(hAPP(c_List_Onth(X1),X2),X3))=X2)). 4.06/4.35 cnf(i_0_998, plain, (c_Map_Odom(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_2738, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=X2)). 4.06/4.35 cnf(i_0_5257, plain, (c_List_Oremdups(X1,hAPP(c_List_Ofilter(X1,X2),X3))=hAPP(c_List_Ofilter(X1,X2),c_List_Oremdups(X1,X3)))). 4.06/4.35 cnf(i_0_1905, plain, (c_Transitive__Closure_Ortrancl(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))=hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)))). 4.06/4.35 cnf(i_0_2690, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))=X2)). 4.06/4.35 cnf(i_0_2009, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))))). 4.06/4.35 cnf(i_0_6224, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=X2)). 4.06/4.35 cnf(i_0_4002, plain, (c_Map_Omap__le(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),X3))). 4.06/4.35 cnf(i_0_1963, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=X2)). 4.06/4.35 cnf(i_0_7500, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X1,X2,X3))=hAPP(c_Nat_OSuc,c_Com_Ocom_Ocom__size(X3)))). 4.06/4.35 cnf(i_0_6832, plain, (c_Set_Othe__elem(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2)). 4.06/4.35 cnf(i_0_5932, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2)=X2)). 4.06/4.35 cnf(i_0_1120, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)=X2)). 4.06/4.35 cnf(i_0_4887, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=X2)). 4.06/4.35 cnf(i_0_1552, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=X4)). 4.06/4.35 cnf(i_0_1689, plain, (hAPP(c_Option_Ooption_Ooption__case(X1,X2,X3,X4),hAPP(c_Option_Ooption_OSome(X2),X5))=hAPP(X4,X5))). 4.06/4.35 cnf(i_0_3992, plain, (hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6)=hAPP(X4,hAPP(X5,X6)))). 4.06/4.35 cnf(i_0_2556, plain, (c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X1,X2,X3,X4,c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X5,X6))=hAPP(hAPP(X4,X5),X6))). 4.06/4.35 cnf(i_0_4707, plain, (c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X1))=hAPP(c_Nat_OSuc,c_Nat_Onat_Onat__size(X1)))). 4.06/4.35 cnf(i_0_3434, plain, (c_Product__Type_Omap__pair(X1,X1,X2,X2,c_Fun_Oid(X1),c_Fun_Oid(X2))=c_Fun_Oid(tc_prod(X1,X2)))). 4.06/4.35 cnf(i_0_5604, plain, (c_Product__Type_Omap__pair(X1,X1,X2,X2,c_COMBI(X1),c_COMBI(X2))=c_Fun_Oid(tc_prod(X1,X2)))). 4.06/4.35 cnf(i_0_1252, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 4.06/4.35 cnf(i_0_3352, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))))). 4.06/4.35 cnf(i_0_1967, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))). 4.06/4.35 cnf(i_0_5221, plain, (c_Divides_Opdivmod(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)))). 4.06/4.35 cnf(i_0_6063, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X1)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.06/4.35 cnf(i_0_6537, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(c_Nat_OSuc,X1))))). 4.06/4.35 cnf(i_0_866, plain, (c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X2))=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_2045, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))). 4.06/4.35 cnf(i_0_3721, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1))). 4.06/4.35 cnf(i_0_5615, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))))=X3)). 4.06/4.35 cnf(i_0_5835, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 4.06/4.35 cnf(i_0_1336, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.06/4.35 cnf(i_0_5614, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))))=X2)). 4.06/4.35 cnf(i_0_263, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)))). 4.06/4.35 cnf(i_0_6441, plain, (c_Relation_Osingle__valued(X1,X1,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))). 4.06/4.35 cnf(i_0_3509, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X1,X2)),c_Nitpick_Opair__box_OPairBox(X1,X2,X3,X4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.35 cnf(i_0_1488, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))). 4.06/4.35 cnf(i_0_3198, plain, (hAPP(c_Map_Orestrict__map(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4)=c_Option_Ooption_ONone(X2))). 4.06/4.35 cnf(i_0_6400, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk449_1(X1)),c_Int_OInteg)))). 4.06/4.35 cnf(i_0_1688, plain, (hAPP(c_Relation_ORange(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3))=hAPP(c_Relation_ODomain(X2,X1),X3))). 4.06/4.35 cnf(i_0_480, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3))=hAPP(c_Relation_ORange(X2,X1),X3))). 4.06/4.35 cnf(i_0_3956, plain, (c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2))=c_List_Otranspose(X1,X2))). 4.06/4.35 cnf(i_0_2777, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))). 4.06/4.35 cnf(i_0_826, plain, (c_List_Oset__Cons(X1,X2,c_List_Olistset(X1,X3))=c_List_Olistset(X1,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.06/4.35 cnf(i_0_1414, plain, (c_Predicate_Opred__comp(X1,X1,X1,c_fequal,c_Predicate_Opred__comp(X1,X1,X1,X2,c_fequal))=X2)). 4.06/4.35 cnf(i_0_7562, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_7431, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_6034, plain, (hAPP(c_Relation_OImage(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_1435, plain, (hAPP(c_Relation_OField(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_2982, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=X1)). 4.06/4.35 cnf(i_0_3683, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X1,X2))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)))). 4.06/4.35 cnf(i_0_6665, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X1),hAPP(c_Code__Numeral_Onat__of,X2)))=c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,X2))). 4.06/4.35 cnf(i_0_7220, plain, (c_Enum_Oenum__the(X1,c_Finite__Set_Ofold__graph(X2,X1,X3,X4,X5))=hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,X3),X4),X5))). 4.06/4.35 cnf(i_0_2765, plain, (c_Map_Omap__add(X1,X2,X3,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)))=X3)). 4.06/4.35 cnf(i_0_5331, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)=c_Groups_Oone__class_Oone(tc_Int_Oint))). 4.06/4.35 cnf(i_0_3783, plain, (c_Map_Omap__add(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),X3)=X3)). 4.06/4.35 cnf(i_0_3679, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))))). 4.06/4.35 cnf(i_0_1747, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X1,X2,X3,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X4))))=hAPP(X3,X4))). 4.06/4.35 cnf(i_0_4477, plain, (hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6)=hAPP(hAPP(X4,X6),X5))). 4.06/4.35 cnf(i_0_5975, plain, (hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6)=hAPP(X4,hAPP(X5,X6)))). 4.06/4.35 cnf(i_0_3556, plain, (hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)))). 4.06/4.35 cnf(i_0_5502, plain, (c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel))). 4.06/4.35 cnf(i_0_1924, plain, (c_Nitpick_Opair__box_Opair__box__case(X1,X2,X3,X4,c_Nitpick_Opair__box_OPairBox(X1,X2,X5,X6))=hAPP(hAPP(X4,X5),X6))). 4.06/4.35 cnf(i_0_2139, plain, (c_Nitpick_Opair__box_Opair__box__rec(X1,X2,X3,X4,c_Nitpick_Opair__box_OPairBox(X1,X2,X5,X6))=hAPP(hAPP(X4,X5),X6))). 4.06/4.35 cnf(i_0_1518, plain, (hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X1))). 4.06/4.35 cnf(i_0_6047, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),c_Enum_Oenum__the(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)))))). 4.06/4.35 cnf(i_0_3811, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X1)),c_Int_OInteg)))). 4.06/4.35 cnf(i_0_475, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4)))). 4.06/4.35 cnf(i_0_1187, plain, (hAPP(c_List_Oset(X1),c_List_Oinsert(X1,X2,X3))=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))). 4.06/4.35 cnf(i_0_282, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Odrop(X1),X2),X3))=hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Obutlast(X1,X3)))). 4.06/4.35 cnf(i_0_6293, plain, (c_Lazy__Sequence_Oappend(tc_Option_Ooption(X1),hAPP(X2,X3),hAPP(X4,X3))=hAPP(c_New__DSequence_Oneg__union(X1,X2,X4),X3))). 4.06/4.35 cnf(i_0_876, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Oreplicate(X1,X3,X2))=c_List_Oreplicate(X1,hAPP(c_Nat_OSuc,X3),X2))). 4.06/4.35 cnf(i_0_3566, plain, (hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_5458, plain, (c_List_Oremove1(X1,X2,hAPP(c_List_Ofilter(X1,X3),X4))=hAPP(c_List_Ofilter(X1,X3),c_List_Oremove1(X1,X2,X4)))). 4.06/4.35 cnf(i_0_3359, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))))). 4.06/4.35 cnf(i_0_128, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)))). 4.06/4.35 cnf(i_0_1591, plain, (hAPP(hAPP(c_Option_Omap(X1,X2),X3),hAPP(c_Option_Ooption_OSome(X1),X4))=hAPP(c_Option_Ooption_OSome(X2),hAPP(X3,X4)))). 4.06/4.35 cnf(i_0_5965, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(c_List_Otl(X1),X3))=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X2)),X3))). 4.06/4.35 cnf(i_0_703, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.35 cnf(i_0_7192, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))))). 4.06/4.35 cnf(i_0_4767, plain, (hAPP(c_Relation_OImage(X1,X1,c_Relation_OId__on(X1,X2)),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.06/4.35 cnf(i_0_4282, plain, (hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))). 4.06/4.35 cnf(i_0_3053, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X1),c_COMBK(X1,X2)),X3)=hAPP(c_Product__Type_Ofst(X1,X2),X3))). 4.06/4.35 cnf(i_0_5163, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))). 4.06/4.35 cnf(i_0_1502, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),X2,c_Product__Type_Osnd(X1,X2)),X3)=hAPP(c_Relation_ORange(X1,X2),X3))). 4.06/4.35 cnf(i_0_7075, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),X1,c_Product__Type_Ofst(X1,X2)),X3)=hAPP(c_Relation_ODomain(X1,X2),X3))). 4.06/4.35 cnf(i_0_5541, plain, (c_Map_Oran(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_1183, plain, (c_Smallcheck_Ofull__small_H(X1,hAPP(c_Code__Numeral_Oint__of,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X2)))=c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,X1,X2))). 4.06/4.35 cnf(i_0_1805, plain, (hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X3)). 4.06/4.35 cnf(i_0_5298, plain, (c_Map_Omap__add(X1,X2,c_Map_Omap__add(X1,X2,X3,X4),X5)=c_Map_Omap__add(X1,X2,X3,c_Map_Omap__add(X1,X2,X4,X5)))). 4.06/4.35 cnf(i_0_7132, plain, (c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1))))=hAPP(c_Nat_OSuc,c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1)))). 4.06/4.35 cnf(i_0_321, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))). 4.06/4.35 cnf(i_0_3232, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X1),X2)))). 4.06/4.35 cnf(i_0_6380, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))). 4.06/4.35 cnf(i_0_1646, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X2)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2))). 4.06/4.35 cnf(i_0_4207, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3),X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))=X5)). 4.06/4.35 cnf(i_0_4210, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X1),X2)))). 4.06/4.35 cnf(i_0_7512, plain, (c_Relation_Orefl__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_7033, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X2))))))). 4.06/4.35 cnf(i_0_2489, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)))). 4.06/4.35 cnf(i_0_1526, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))). 4.06/4.35 cnf(i_0_5736, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X1)=hAPP(c_fequal,X1))). 4.06/4.35 cnf(i_0_7121, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X1,X2,X3))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3)))). 4.06/4.35 cnf(i_0_3402, plain, (hAPP(c_Product__Type_Ofst(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Opartition(X1,X2,X3))=hAPP(c_List_Ofilter(X1,X2),X3))). 4.06/4.35 cnf(i_0_4514, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Oreplicate(X1,X4,X5))=c_List_Oreplicate(X2,X4,hAPP(X3,X5)))). 4.06/4.35 cnf(i_0_1291, plain, (c_Wellfounded_OwfP(X1,hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))). 4.06/4.35 cnf(i_0_6284, plain, (c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),X2))). 4.06/4.35 cnf(i_0_6024, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))). 4.06/4.35 cnf(i_0_80, plain, (hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))). 4.06/4.35 cnf(i_0_2545, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)))). 4.06/4.35 cnf(i_0_6529, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2))). 4.06/4.35 cnf(i_0_3858, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X1),X2))). 4.06/4.35 cnf(i_0_5329, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X1),X2))). 4.06/4.35 cnf(i_0_4, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),X2))). 4.06/4.35 cnf(i_0_1092, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),X2))). 4.06/4.35 cnf(i_0_2474, plain, (hAPP(c_Relation_Oconverse(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel1(X1,X2))=c_List_Olistrel1(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)))). 4.06/4.35 cnf(i_0_3931, plain, (c_Option_Ooption_Ooption__size(X1,X2,hAPP(c_Option_Ooption_OSome(X1),X3))=hAPP(c_Nat_OSuc,hAPP(X2,X3)))). 4.06/4.35 cnf(i_0_2613, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))). 4.06/4.35 cnf(i_0_3910, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))). 4.06/4.35 cnf(i_0_2113, plain, (c_Enum_Oenum__the(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))). 4.06/4.35 cnf(i_0_7241, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_3499, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_6066, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_3483, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_3851, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_6795, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_4022, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_5199, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2)=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_846, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_6212, plain, (c_Map_Odom(X1,X2,c_Map_Orestrict__map(X1,X2,X3,X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),X4))). 4.06/4.35 cnf(i_0_5177, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_5794, plain, (hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel)=c_Int_OInteg)). 4.06/4.35 cnf(i_0_283, plain, (hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,tc_prod(X2,X3)),X4),c_Product__Type_OPair(X2,X3))=X4)). 4.06/4.35 cnf(i_0_4664, plain, (c_Smallcheck_Osmall_H(X1,hAPP(c_Code__Numeral_Oint__of,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,X2)))=hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),X1),X2))). 4.06/4.35 cnf(i_0_3987, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Obutlast(X1,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 4.06/4.35 cnf(i_0_7102, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)=hAPP(c_Finite__Set_Ocard(X1),X2))). 4.06/4.35 cnf(i_0_3255, plain, (c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))). 4.06/4.35 cnf(i_0_3651, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_1366, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X2))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.06/4.35 cnf(i_0_5112, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),X2))))). 4.06/4.35 cnf(i_0_3332, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))). 4.06/4.35 cnf(i_0_2896, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.35 cnf(i_0_3068, plain, (hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Enum_Oenum__the(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))). 4.06/4.35 cnf(i_0_369, plain, (hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X2))=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))). 4.06/4.35 cnf(i_0_6263, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2)))). 4.06/4.35 cnf(i_0_1838, plain, (c_Nat_Onat_Onat__case(X1,X2,hAPP(c_List_Onth(X1),X3),X4)=hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4))). 4.06/4.35 cnf(i_0_5116, plain, (hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))). 4.06/4.35 cnf(i_0_6976, plain, (c_Map_Omap__upds(X1,X2,c_Map_Omap__add(X1,X2,X3,X4),X5,X6)=c_Map_Omap__add(X1,X2,X3,c_Map_Omap__upds(X1,X2,X4,X5,X6)))). 4.06/4.35 cnf(i_0_3929, plain, (hAPP(c_List_Olist_Olist__case(X1,X2,X3,X4),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X6))=hAPP(hAPP(X4,X5),X6))). 4.06/4.35 cnf(i_0_582, plain, (hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)=X2)). 4.06/4.35 cnf(i_0_4254, plain, (hAPP(c_Relation_OImage(X1,X1,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),X2)=X2)). 4.06/4.35 cnf(i_0_1898, plain, (hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X1,X3),hAPP(c_Product__Type_OPair(X2,X1),X4)),X5)=hAPP(X5,X4))). 4.06/4.35 cnf(i_0_7242, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1)))))). 4.06/4.35 cnf(i_0_693, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)))). 4.06/4.35 cnf(i_0_1292, plain, (hAPP(hAPP(c_List_Otake(X1),X2),c_List_Oreplicate(X1,X3,X4))=c_List_Oreplicate(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X2),X3),X4))). 4.06/4.35 cnf(i_0_5206, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),c_List_Oreplicate(X1,X3,X4))=c_List_Oreplicate(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2),X4))). 4.06/4.35 cnf(i_0_5926, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))). 4.06/4.35 cnf(i_0_6222, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))). 4.06/4.35 cnf(i_0_2410, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Otl(X1),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 4.06/4.35 cnf(i_0_4527, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))). 4.06/4.35 cnf(i_0_4250, plain, (hAPP(c_List_Oset(X1),c_List_Oreplicate(X1,hAPP(c_Nat_OSuc,X2),X3))=hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_5735, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_Set_OPow(X1),X2))))). 4.06/4.35 cnf(i_0_6181, plain, (c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat))))). 4.06/4.35 cnf(i_0_4099, plain, (hAPP(c_Map_Orestrict__map(X1,X2,hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)),X3),X4)=c_Option_Ooption_ONone(X2))). 4.06/4.35 cnf(i_0_6734, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2))). 4.06/4.35 cnf(i_0_3689, plain, (c_Product__Type_Oprod_Oprod__rec(X1,X2,X3,X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6))=hAPP(hAPP(X4,X5),X6))). 4.06/4.35 cnf(i_0_1438, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))). 4.06/4.35 cnf(i_0_951, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_996, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(c_Product__Type_Ofst(X1,X2),X3)),hAPP(c_Product__Type_Osnd(X1,X2),X3))=X3)). 4.06/4.35 cnf(i_0_5201, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Odrop(X1),X2),X3))=X3)). 4.06/4.35 cnf(i_0_1082, plain, (hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Enum_Oenum__the(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2))). 4.06/4.35 cnf(i_0_726, plain, (hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))=hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))). 4.06/4.35 cnf(i_0_3050, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Odrop(X1),X2),X4))). 4.06/4.35 cnf(i_0_4395, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(c_Nat_OSuc,X4))=hAPP(hAPP(c_List_Onth(X1),X3),X4))). 4.06/4.35 cnf(i_0_2538, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1))). 4.06/4.35 cnf(i_0_1603, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2))). 4.06/4.35 cnf(i_0_4454, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))). 4.06/4.35 cnf(i_0_546, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(hAPP(c_List_Oappend(X1),X2),X3))=X2)). 4.06/4.35 cnf(i_0_7252, plain, (c_Map_Omap__le(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),c_Option_Ooption_ONone(X2)),X3))). 4.06/4.35 cnf(i_0_3752, plain, (c_Map_Orestrict__map(X1,X2,c_Map_Orestrict__map(X1,X2,X3,X4),X5)=c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)))). 4.06/4.35 cnf(i_0_1601, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2))))). 4.06/4.35 cnf(i_0_201, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))))). 4.06/4.35 cnf(i_0_1956, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X3)))). 4.06/4.35 cnf(i_0_3351, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X2)))). 4.06/4.35 cnf(i_0_6065, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X2)))). 4.06/4.35 cnf(i_0_2221, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),X1))))). 4.06/4.35 cnf(i_0_881, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X1))))). 4.06/4.35 cnf(i_0_479, plain, (hAPP(hAPP(c_List_Otake(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))). 4.06/4.35 cnf(i_0_1333, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X2),X1))). 4.06/4.35 cnf(i_0_5552, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2))). 4.06/4.35 cnf(i_0_6073, plain, (hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X2)),X3))=hAPP(hAPP(c_List_Otake(X1),X2),hAPP(c_List_Otl(X1),X3)))). 4.06/4.35 cnf(i_0_4304, plain, (c_Nitpick_Onorm__frac(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))). 4.06/4.35 cnf(i_0_1282, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_1868, plain, (hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3))=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X2)),X3))). 4.06/4.35 cnf(i_0_4156, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Odrop(X1),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2))). 4.06/4.35 cnf(i_0_3684, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Otake(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2))). 4.06/4.35 cnf(i_0_3849, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2)=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))). 4.06/4.35 cnf(i_0_3975, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_Enum_On__lists(X1,X2,X3))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2))). 4.06/4.35 cnf(i_0_4695, plain, (hAPP(hAPP(c_Relation_Orel__comp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Wellfounded_Opred__nat),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))=c_Wellfounded_Oless__than)). 4.06/4.35 cnf(i_0_2529, plain, (c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.06/4.35 cnf(i_0_2652, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.06/4.35 cnf(i_0_3888, plain, (hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1))))). 4.06/4.35 cnf(i_0_6259, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)=c_List_OtakeWhile(X1,X2,X3))). 4.06/4.35 cnf(i_0_6465, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)))). 4.06/4.35 cnf(i_0_545, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(hAPP(c_List_Oappend(X1),X2),X3))=X3)). 4.06/4.35 cnf(i_0_4476, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))). 4.06/4.35 cnf(i_0_6915, plain, (c_Sum__Type_OPlus(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X1,X2),tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_6425, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 4.06/4.35 cnf(i_0_3159, plain, (hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4)=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))). 4.06/4.35 cnf(i_0_5310, plain, (c_Sum__Type_OPlus(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_5146, plain, (c_Divides_OnegDivAlg(c_Int_OMin,X1)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)))). 4.06/4.35 cnf(i_0_7096, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))=c_List_Obutlast(X1,X2))). 4.06/4.35 cnf(i_0_1216, plain, (c_Predicate_Opred__comp(X1,X2,X3,c_Predicate_Oconversep(X2,X1,X4),c_Predicate_Oconversep(X3,X2,X5))=c_Predicate_Oconversep(X3,X1,c_Predicate_Opred__comp(X3,X2,X1,X5,X4)))). 4.06/4.35 cnf(i_0_4445, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1))))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X1)))). 4.06/4.35 cnf(i_0_5183, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))). 4.06/4.35 cnf(i_0_6626, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat))=c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_3537, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat))=c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_2030, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat))=c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_3589, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_4090, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6))=hAPP(hAPP(X4,X5),X6))). 4.06/4.35 cnf(i_0_3559, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))))))). 4.06/4.35 cnf(i_0_1930, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(tc_Nat_Onat,X1,X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X3)))))). 4.06/4.35 cnf(i_0_4184, plain, (c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBB(X2,tc_Option_Ooption(X2),X1),c_Option_Ooption_OSome(X2)),X3))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_1353, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3),X2)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2))). 4.06/4.35 cnf(i_0_7107, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X2),X3),c_Transitive__Closure_Ortrancl(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_HOL_Obool))))=X3)). 4.06/4.35 cnf(i_0_2503, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),X3)=X3)). 4.06/4.35 cnf(i_0_3861, plain, (c_List_Olistset(X1,c_List_Olist_ONil(tc_fun(X1,tc_HOL_Obool)))=hAPP(c_fequal,c_List_Olist_ONil(X1)))). 4.06/4.35 cnf(i_0_4397, plain, (hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)))). 4.06/4.35 cnf(i_0_2996, plain, (c_List_Olists(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=hAPP(c_fequal,c_List_Olist_ONil(X1)))). 4.06/4.35 cnf(i_0_3705, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X3)))). 4.06/4.35 cnf(i_0_434, plain, (c_List_Oremdups(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Oremdups(X2,X4)))=c_List_Oremdups(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)))). 4.06/4.35 cnf(i_0_6481, plain, (hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))). 4.06/4.35 cnf(i_0_4597, plain, (c_Finite__Set_Ofold(X1,X2,hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X1),X3),X4))=hAPP(c_Finite__Set_Ofold__image(X2,X1,X3),X4))). 4.06/4.35 cnf(i_0_2062, plain, (hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,X4),X5),X6),X7)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X4),X6),hAPP(X5,X7)))). 4.06/4.35 cnf(i_0_1370, plain, (hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2)=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_1579, plain, (c_Hilbert__Choice_OEps(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2)). 4.06/4.35 cnf(i_0_534, plain, (c_Enum_Oenum__the(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2)). 4.06/4.35 cnf(i_0_2911, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))))). 4.06/4.35 cnf(i_0_5712, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Ortrancl(X1,X3))))). 4.06/4.35 cnf(i_0_6211, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)))). 4.06/4.35 cnf(i_0_2199, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))). 4.06/4.35 cnf(i_0_1921, plain, (hAPP(c_Product__Type_Ofst(X1,X2),hAPP(c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6),X7))=hAPP(X5,hAPP(c_Product__Type_Ofst(X3,X4),X7)))). 4.06/4.35 cnf(i_0_4513, plain, (hAPP(c_Product__Type_Osnd(X1,X2),hAPP(c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6),X7))=hAPP(X6,hAPP(c_Product__Type_Osnd(X3,X4),X7)))). 4.06/4.35 cnf(i_0_1408, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))). 4.06/4.35 cnf(i_0_918, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))). 4.06/4.35 cnf(i_0_4394, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))). 4.06/4.35 cnf(i_0_3580, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)))). 4.06/4.35 cnf(i_0_5961, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)))). 4.06/4.35 cnf(i_0_1170, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))). 4.06/4.35 cnf(i_0_904, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))). 4.06/4.35 cnf(i_0_4015, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))). 4.06/4.35 cnf(i_0_4166, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))). 4.06/4.35 cnf(i_0_2737, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Odrop(X1),X3),X4))=hAPP(hAPP(c_List_Odrop(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X4))). 4.06/4.35 cnf(i_0_5364, plain, (hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Otake(X1),X3),X4))=hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X2),X3)),X4))). 4.06/4.35 cnf(i_0_6958, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4)=hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)))). 4.06/4.35 cnf(i_0_4888, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),X4)=hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)))). 4.06/4.35 cnf(i_0_5945, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),X3),hAPP(X3,X4))=hAPP(X3,hAPP(hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),X3),X4)))). 4.06/4.35 cnf(i_0_6136, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Orev(X1),X2)),hAPP(c_List_Orev(X1),X3))=hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Oappend(X1),X3),X2)))). 4.06/4.35 cnf(i_0_6833, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),X2)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,X2))=c_Code__Numeral_Odiv__mod__code__numeral(X1,X2))). 4.06/4.35 cnf(i_0_5673, plain, (hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)),X3),X5)=hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X5))). 4.06/4.35 cnf(i_0_6650, plain, (hAPP(c_Product__Type_Osnd(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Opartition(X1,X2,X3))=hAPP(c_List_Ofilter(X1,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X1,c_fNot),X2)),X3))). 4.06/4.35 cnf(i_0_3985, plain, (c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))). 4.06/4.35 cnf(i_0_4504, plain, (hAPP(c_List_Oset(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3))=hAPP(c_List_Oset(X1),X3))). 4.06/4.35 cnf(i_0_7194, plain, (hAPP(c_Relation_ODomain(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))=hAPP(c_Relation_ODomain(X1,X1),X2))). 4.06/4.35 cnf(i_0_4660, plain, (hAPP(c_Relation_ORange(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))=hAPP(c_Relation_ORange(X1,X1),X2))). 4.06/4.35 cnf(i_0_6612, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)=c_List_Obutlast(X1,X2))). 4.06/4.35 cnf(i_0_7060, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_5548, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))). 4.06/4.35 cnf(i_0_7480, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))). 4.06/4.35 cnf(i_0_3388, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_Enum_Osublists(X1,X2))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))). 4.06/4.35 cnf(i_0_440, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Oreplicate(X1,X2,X3)),c_List_Oreplicate(X1,X4,X3))=c_List_Oreplicate(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4),X3))). 4.06/4.35 cnf(i_0_2433, plain, (c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),c_List_Otranspose(X1,X2)))))). 4.06/4.35 cnf(i_0_690, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.06/4.35 cnf(i_0_1434, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3))),hAPP(c_List_Oset(X1),X2))))). 4.06/4.35 cnf(i_0_5546, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X2,X3))),hAPP(c_List_Oset(X1),X3))))). 4.06/4.35 cnf(i_0_2044, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_6360, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X4)=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_2552, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X2)))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X2)))). 4.06/4.35 cnf(i_0_6963, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))). 4.06/4.35 cnf(i_0_6418, plain, (hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))=c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_4948, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.06/4.35 cnf(i_0_15, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.06/4.35 cnf(i_0_4698, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))))=hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X2))). 4.06/4.35 cnf(i_0_4671, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.35 cnf(i_0_678, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))). 4.06/4.35 cnf(i_0_2858, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3))). 4.06/4.35 cnf(i_0_6712, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBI(tc_fun(X1,tc_HOL_Obool)))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))). 4.06/4.35 cnf(i_0_4048, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBI(tc_fun(X1,tc_HOL_Obool)))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2))). 4.06/4.35 cnf(i_0_7328, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1))). 4.06/4.35 cnf(i_0_3614, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X1),X2)),hAPP(c_Relation_ORange(X1,X1),X2))=hAPP(c_Relation_OField(X1),X2))). 4.06/4.35 cnf(i_0_492, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),X3))). 4.06/4.35 cnf(i_0_5972, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X3))). 4.06/4.35 cnf(i_0_443, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X3),X2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X3),X2))). 4.06/4.35 cnf(i_0_6744, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X3),X2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3),X2))). 4.06/4.35 cnf(i_0_6463, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))))). 4.06/4.35 cnf(i_0_819, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.06/4.35 cnf(i_0_4253, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Olist_OCons(X1),X3),hAPP(hAPP(c_List_Otake(X1),X2),X4)))). 4.06/4.35 cnf(i_0_1778, plain, (c_List_Oreplicate(X1,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,hAPP(c_fequal,X2)),X3)),X2)=hAPP(c_List_Ofilter(X1,hAPP(c_fequal,X2)),X3))). 4.06/4.35 cnf(i_0_667, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X2),hAPP(c_COMBK(tc_fun(X2,X2),X1),c_COMBI(X2))),X3)=hAPP(c_Product__Type_Osnd(X1,X2),X3))). 4.06/4.35 cnf(i_0_7517, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,X2),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X3),X2))=hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(c_Nat_OSuc,X3)),X2))). 4.06/4.35 cnf(i_0_4384, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oimage(X2,tc_fun(X1,tc_HOL_Obool),X3),X4))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X4),X3))). 4.06/4.35 cnf(i_0_629, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oimage(X2,tc_fun(X1,tc_HOL_Obool),X3),X4))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X4),X3))). 4.06/4.35 cnf(i_0_461, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))). 4.06/4.35 cnf(i_0_3609, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))=X1)). 4.06/4.35 cnf(i_0_5705, plain, (hAPP(c_Option_Ooption_OSome(tc_prod(X1,tc_Lazy__Sequence_Olazy__sequence(X1))),hAPP(hAPP(c_Product__Type_OPair(X1,tc_Lazy__Sequence_Olazy__sequence(X1)),X2),X3))=hAPP(c_Lazy__Sequence_Oyield(X1),c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3)))). 4.06/4.35 cnf(i_0_1422, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),c_List_Oreplicate(tc_List_Olist(X1),X2,c_List_Olist_ONil(X1)))=c_List_Olist_ONil(X1))). 4.06/4.35 cnf(i_0_1047, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X2,c_Option_Ooption_ONone(X1),hAPP(c_COMBK(tc_Option_Ooption(X1),X2),c_Option_Ooption_ONone(X1))),hAPP(X3,X4))=c_Option_Ooption_ONone(X1))). 4.06/4.35 cnf(i_0_377, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3))),hAPP(c_List_Oset(X1),X3))))). 4.06/4.35 cnf(i_0_6190, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3))),hAPP(c_List_Oset(X1),X3))))). 4.06/4.35 cnf(i_0_1618, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),c_Map_Odom(X1,X2,X4))=c_Map_Odom(X1,X2,c_Map_Omap__add(X1,X2,X4,X3)))). 4.06/4.35 cnf(i_0_1407, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3))=hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)))). 4.06/4.35 cnf(i_0_5250, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))). 4.06/4.35 cnf(i_0_1130, plain, (c_Random_Oselect__weight(X1,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X1)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X1),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X2)),X3))=c_Random_Oselect__weight(X1,X3))). 4.06/4.35 cnf(i_0_6896, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))=X3)). 4.06/4.35 cnf(i_0_6436, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),X2)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3),X2))). 4.06/4.35 cnf(i_0_6322, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)))). 4.06/4.35 cnf(i_0_4662, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X3)),X2))). 4.06/4.35 cnf(i_0_4035, plain, (c_Fun_Oinj__on(X1,tc_prod(X2,X1),esk293_4(X3,X4,X2,X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X4),X3)))). 4.06/4.35 cnf(i_0_1001, plain, (hAPP(c_List_Ofoldl(X1,X2,X3,hAPP(c_List_Ofoldl(X1,X2,X3,X4),X5)),X6)=hAPP(c_List_Ofoldl(X1,X2,X3,X4),hAPP(hAPP(c_List_Oappend(X2),X5),X6)))). 4.06/4.35 cnf(i_0_2665, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))). 4.06/4.35 cnf(i_0_5086, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),hAPP(c_Map_Omap__of(X2,X1),X3)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))))). 4.06/4.35 cnf(i_0_4266, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)))))). 4.06/4.35 cnf(i_0_551, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.06/4.35 cnf(i_0_7000, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Orev(X1),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))=hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)))). 4.06/4.35 cnf(i_0_4108, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X1),X3))=hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)))). 4.06/4.35 cnf(i_0_5757, plain, (hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X1),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3)))=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)),X3)))). 4.06/4.35 cnf(i_0_1176, plain, (hAPP(c_Set_Ovimage(X1,X2,X3),X4)=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3))). 4.06/4.35 cnf(i_0_6564, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_COMBI(X1))=X2)). 4.06/4.35 cnf(i_0_2745, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1))=X2)). 4.06/4.35 cnf(i_0_3613, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_7525, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X3)=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_3643, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)))). 4.06/4.35 cnf(i_0_3355, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Osplice(X1,X2,X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)))). 4.06/4.35 cnf(i_0_7052, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X4),X3))),X4)))). 4.06/4.35 cnf(i_0_4011, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Ofilter(X1,X2),X3)),hAPP(c_List_Ofilter(X1,X2),X4))=hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)))). 4.06/4.35 cnf(i_0_994, plain, (c_Map_Omap__add(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3),hAPP(c_Map_Omap__of(X1,X2),X4))=hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),X4),X3)))). 4.06/4.35 cnf(i_0_7402, plain, (hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X3),X4))=hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X4))). 4.06/4.35 cnf(i_0_5914, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.06/4.35 cnf(i_0_5501, plain, (c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X2,c_Option_Ooption_ONone(X1),hAPP(hAPP(c_COMBB(X1,tc_Option_Ooption(X1),X2),c_Option_Ooption_OSome(X1)),X3))=hAPP(c_Option_Omap(X2,X1),X3))). 4.06/4.35 cnf(i_0_5170, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.06/4.35 cnf(i_0_6021, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.06/4.35 cnf(i_0_528, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.06/4.35 cnf(i_0_6629, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)))). 4.06/4.35 cnf(i_0_908, plain, (hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X3),c_Option_Ooption_ONone(X2)),X4)=c_Option_Ooption_ONone(X2))). 4.06/4.35 cnf(i_0_6526, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_6580, plain, (c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X1),hAPP(hAPP(c_Option_Omap(X2,X1),X3),X4),c_Lazy__Sequence_Ohb__map(X2,X1,X3,X5))=c_Lazy__Sequence_Ohb__map(X2,X1,X3,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(X2),X4,X5)))). 4.06/4.35 cnf(i_0_4552, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X3)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))). 4.06/4.35 cnf(i_0_1307, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4))=X2)). 4.06/4.35 cnf(i_0_2927, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4))=X2)). 4.06/4.35 cnf(i_0_446, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olistsp(X1,X2)),c_List_Olistsp(X1,X3))=c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.06/4.35 cnf(i_0_1495, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X3)),X4)=X4)). 4.06/4.35 cnf(i_0_2384, plain, (c_Nitpick_Opair__box_Opair__box__size(X1,X2,X3,X4,c_Nitpick_Opair__box_OPairBox(X1,X2,X5,X6))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X3,X5)),hAPP(c_Nat_OSuc,hAPP(X4,X6))))). 4.06/4.35 cnf(i_0_4453, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)))=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X1,X2)))). 4.06/4.35 cnf(i_0_3038, plain, (hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(c_Nat_OSuc,X4)),X5)=hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist__update(X1,X3),X4),X5)))). 4.06/4.35 cnf(i_0_5756, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.06/4.35 cnf(i_0_170, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.06/4.35 cnf(i_0_516, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.06/4.35 cnf(i_0_202, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),X1,hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1)),X2)=hAPP(c_List_Orev(X1),X2))). 4.06/4.35 cnf(i_0_6100, plain, (hAPP(c_Lazy__Sequence_Obind(X1,X2,hAPP(X3,X4)),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)),X5),X4))=hAPP(c_New__DSequence_Opos__bind(X1,X2,X3,X5),X4))). 4.06/4.35 cnf(i_0_323, plain, (c_Relation_Oirrefl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))))). 4.06/4.35 cnf(i_0_6483, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_COMBK(X1,tc_Nat_Onat),X2)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))=c_List_Oreplicate(X1,X3,X2))). 4.06/4.35 cnf(i_0_6183, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X4,X5,X6),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X7),X8))=hAPP(hAPP(c_Product__Type_OPair(X2,X4),hAPP(X5,X7)),hAPP(X6,X8)))). 4.06/4.35 cnf(i_0_4538, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X1,tc_Nat_Onat),X3),X2)))=c_List_Olist_Olist__size(X1,X3,X2))). 4.06/4.35 cnf(i_0_3631, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X3)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)))). 4.06/4.35 cnf(i_0_7134, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X3)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3)))). 4.06/4.35 cnf(i_0_6090, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))). 4.06/4.35 cnf(i_0_497, plain, (c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X1)),X2)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))). 4.06/4.35 cnf(i_0_6539, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel(X1,X2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2)))))). 4.06/4.35 cnf(i_0_4569, plain, (hAPP(c_Set_Oimage(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),c_List_Oset(X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_Osublists(X1,X2)))=hAPP(c_Set_OPow(X1),hAPP(c_List_Oset(X1),X2)))). 4.06/4.35 cnf(i_0_6125, plain, (hAPP(hAPP(c_Nat_Ocompow(tc_fun(X1,X2),tc_fun(X1,X2)),X3),c_Fun_Ocomp(X2,X2,X1,X4))=c_Fun_Ocomp(X2,X2,X1,hAPP(hAPP(c_Nat_Ocompow(X2,X2),X3),X4)))). 4.06/4.35 cnf(i_0_1375, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))). 4.06/4.35 cnf(i_0_3622, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)))). 4.06/4.35 cnf(i_0_6060, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))). 4.06/4.35 cnf(i_0_6574, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))). 4.06/4.35 cnf(i_0_2375, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))). 4.06/4.35 cnf(i_0_7185, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)),hAPP(hAPP(c_List_Odrop(X1),X3),X4))=hAPP(hAPP(c_List_Odrop(X1),X3),hAPP(hAPP(c_List_Otake(X1),X2),X4)))). 4.06/4.35 cnf(i_0_1926, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))))). 4.06/4.35 cnf(i_0_5074, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X3))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_1125, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2))). 4.06/4.35 cnf(i_0_6994, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),X2))). 4.06/4.35 cnf(i_0_2499, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)),X2))). 4.06/4.35 cnf(i_0_2143, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X3)),X2))). 4.06/4.35 cnf(i_0_336, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X1),X3)),X2))). 4.06/4.35 cnf(i_0_3363, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)),X4))=hAPP(hAPP(c_List_Otake(X1),X3),hAPP(hAPP(c_List_Odrop(X1),X2),X4)))). 4.06/4.35 cnf(i_0_751, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X1,X2))=c_List_Olex(X1,X2))). 4.06/4.35 cnf(i_0_4354, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5)),X4),X6)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X6))). 4.06/4.35 cnf(i_0_1541, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_5507, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_List_Onth(X1),X2)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))=X2)). 4.06/4.35 cnf(i_0_7549, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),X3)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.06/4.35 cnf(i_0_3757, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3))=X3)). 4.06/4.35 cnf(i_0_2808, plain, (c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X1)),X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))). 4.06/4.35 cnf(i_0_6051, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_OtakeWhile(X1,hAPP(c_Fun_Ocomp(X2,tc_HOL_Obool,X1,X4),X3),X5))=c_List_OtakeWhile(X2,X4,hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)))). 4.06/4.35 cnf(i_0_4157, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X4)),X5),hAPP(X3,X5))=c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)))). 4.06/4.35 cnf(i_0_4341, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_COMBB(X3,tc_HOL_Obool,X1),hAPP(hAPP(c_Set_Oinsert(X3),hAPP(X4,X2)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X4))))). 4.06/4.35 cnf(i_0_483, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OField(X1),X2)),hAPP(c_Relation_OField(X1),X3))=hAPP(c_Relation_OField(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.06/4.35 cnf(i_0_4070, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))=X2)). 4.06/4.35 cnf(i_0_1889, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X1)),hAPP(c_fequal,X1))=hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X1))). 4.06/4.35 cnf(i_0_7344, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(X1)),c_Option_Ooption_ONone(X1)),hAPP(c_Set_Oimage(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_2751, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X4))=hAPP(hAPP(c_List_Onth(X1),X3),X4))). 4.06/4.35 cnf(i_0_537, plain, (c_List_Osplice(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))=hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X4),c_List_Osplice(X1,X3,X5))))). 4.06/4.35 cnf(i_0_5367, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.06/4.35 cnf(i_0_6905, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Odrop(X1),X3),X2)))). 4.06/4.35 cnf(i_0_6774, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Otake(X1),X3),X2)))). 4.06/4.35 cnf(i_0_742, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Oreplicate(X1,X2,X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Olist_OCons(X1),X3),hAPP(hAPP(c_List_Oappend(X1),c_List_Oreplicate(X1,X2,X3)),X4)))). 4.06/4.35 cnf(i_0_6703, plain, (c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.06/4.35 cnf(i_0_4029, plain, (c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.06/4.35 cnf(i_0_1589, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),c_List_Oreplicate(X1,X3,X4)),c_List_Oreplicate(X2,X5,X6))=c_List_Oreplicate(tc_prod(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X3),X5),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X6)))). 4.06/4.35 cnf(i_0_6654, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4))=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_4691, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_OPow(X1),X3))=hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.06/4.35 cnf(i_0_661, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X3)),X3)=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X2)),X3))). 4.06/4.35 cnf(i_0_5765, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),hAPP(c_Relation_Oconverse(X2,X1),X4)),hAPP(c_Relation_Oconverse(X3,X2),X5))=hAPP(c_Relation_Oconverse(X3,X1),hAPP(hAPP(c_Relation_Orel__comp(X3,X2,X1),X5),X4)))). 4.06/4.35 cnf(i_0_7566, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X3))=hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),X2),X3))). 4.06/4.35 cnf(i_0_642, plain, (hAPP(c_Option_Ooption_Ooption__case(X1,tc_prod(X2,tc_Lazy__Sequence_Olazy__sequence(X2)),X3,hAPP(c_Product__Type_Oprod_Oprod__case(X2,tc_Lazy__Sequence_Olazy__sequence(X2),X1),X4)),hAPP(c_Lazy__Sequence_Oyield(X2),X5))=c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X1,X2,X3,X4,X5))). 4.06/4.35 cnf(i_0_361, plain, (hAPP(c_Set_OPow(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=hAPP(c_fequal,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_7423, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)),X3)=hAPP(c_Option_Ooption_OSome(X2),X4))). 4.06/4.35 cnf(i_0_3105, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel1(X1,c_Transitive__Closure_Ortrancl(X1,X2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2)))))). 4.06/4.35 cnf(i_0_7290, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))))). 4.06/4.35 cnf(i_0_4275, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(X1))),c_List_Olistrel(X1,X2))))). 4.06/4.35 cnf(i_0_650, plain, (c_Map_Odom(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3))=hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)))). 4.06/4.35 cnf(i_0_5717, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)))))). 4.06/4.35 cnf(i_0_1365, plain, (hAPP(c_List_Orotate1(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3))=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(c_Nat_OSuc,X2)),c_List_Orotate1(X1)),X3))). 4.06/4.35 cnf(i_0_6198, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X1)),hAPP(c_fequal,hAPP(c_Nat_OSuc,X1)))=hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)))). 4.06/4.35 cnf(i_0_4361, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))=hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X5)))). 4.06/4.35 cnf(i_0_6408, plain, (hAPP(c_Relation_ORange(X1,X2),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))=hAPP(hAPP(c_Set_Oinsert(X2),X4),hAPP(c_Relation_ORange(X1,X2),X5)))). 4.06/4.35 cnf(i_0_3083, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))). 4.06/4.35 cnf(i_0_5707, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(c_List_Ofilter(X1,hAPP(c_Fun_Ocomp(X2,tc_HOL_Obool,X1,X4),X3)),X5))=hAPP(c_List_Ofilter(X2,X4),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)))). 4.06/4.35 cnf(i_0_4675, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))=c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_6297, plain, (c_Map_Omap__add(X1,X2,X3,hAPP(c_Map_Omap__of(X1,X2),hAPP(c_List_Orev(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))))=c_Map_Omap__upds(X1,X2,X3,X4,X5))). 4.06/4.35 cnf(i_0_3805, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),c_Int_Onat),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X1)=X1)). 4.06/4.35 cnf(i_0_5178, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))=hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(hAPP(c_List_Oappend(X2),X4),X5)))). 4.06/4.35 cnf(i_0_4612, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),X3))). 4.06/4.35 cnf(i_0_5450, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.06/4.35 cnf(i_0_5534, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.06/4.35 cnf(i_0_4189, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.06/4.35 cnf(i_0_3298, plain, (hAPP(c_List_Oset(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)),c_List_Oset(X1)))). 4.06/4.35 cnf(i_0_5230, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3))=hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),X3))). 4.06/4.35 cnf(i_0_6933, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))),hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(c_List_Oset(X1),X2)))))). 4.06/4.35 cnf(i_0_7452, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),c_Predicate_Oconversep(X2,X1,X3)),c_Predicate_Oconversep(X2,X1,X4))=c_Predicate_Oconversep(X2,X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_fun(X1,tc_HOL_Obool))),X3),X4)))). 4.06/4.35 cnf(i_0_1823, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),c_Predicate_Oconversep(X2,X1,X3)),c_Predicate_Oconversep(X2,X1,X4))=c_Predicate_Oconversep(X2,X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_fun(X1,tc_HOL_Obool))),X3),X4)))). 4.06/4.35 cnf(i_0_5889, plain, (c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3)))=c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.06/4.35 cnf(i_0_3146, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X1,X2))),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)))). 4.06/4.35 cnf(i_0_6594, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Otake(X1),X3),X4)),hAPP(hAPP(c_List_Otake(X2),X3),X5))=hAPP(hAPP(c_List_Otake(tc_prod(X1,X2)),X3),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5)))). 4.06/4.35 cnf(i_0_217, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Odrop(X1),X3),X4)),hAPP(hAPP(c_List_Odrop(X2),X3),X5))=hAPP(hAPP(c_List_Odrop(tc_prod(X1,X2)),X3),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5)))). 4.06/4.35 cnf(i_0_4963, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),c_Set_Ovimage(X2,X1,X4))=hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4))). 4.06/4.35 cnf(i_0_2338, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.06/4.35 cnf(i_0_3720, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),X3)),hAPP(c_Relation_ORange(X2,X1),X4))=hAPP(c_Relation_ORange(X2,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4)))). 4.06/4.35 cnf(i_0_542, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4))=hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))). 4.06/4.35 cnf(i_0_2972, plain, (c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))))). 4.06/4.35 cnf(i_0_3110, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Relation_OId__on(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))))). 4.06/4.35 cnf(i_0_3186, plain, (hAPP(c_Fun_Ocomp(tc_List_Olist(X1),tc_List_Olist(X2),tc_List_Olist(X3),hAPP(c_List_Omap(X1,X2),X4)),hAPP(c_List_Omap(X3,X1),X5))=hAPP(c_List_Omap(X3,X2),hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5)))). 4.06/4.35 cnf(i_0_1504, plain, (hAPP(c_Fun_Ocomp(tc_Option_Ooption(X1),tc_Option_Ooption(X2),tc_Option_Ooption(X3),hAPP(c_Option_Omap(X1,X2),X4)),hAPP(c_Option_Omap(X3,X1),X5))=hAPP(c_Option_Omap(X3,X2),hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5)))). 4.06/4.35 cnf(i_0_2540, plain, (c_Fun_Oinj__on(tc_prod(X1,X2),tc_prod(X2,X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X2,X1)),hAPP(c_COMBC(X2,X1,tc_prod(X2,X1)),c_Product__Type_OPair(X2,X1))),X3))). 4.06/4.35 cnf(i_0_849, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3)),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X2),c_Product__Type_Osnd(X1,X2)),X3))=X3)). 4.06/4.35 cnf(i_0_2466, plain, (hAPP(c_Finite__Set_Ocard(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X2),X4)))). 4.06/4.35 cnf(i_0_5716, plain, (c_Lazy__Sequence_Ohb__flat(X1,c_Lazy__Sequence_Ohb__map(X2,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)),hAPP(hAPP(c_COMBC(X2,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1))),X3),X4),hAPP(X5,X4)))=hAPP(c_New__DSequence_Oneg__bind(X2,X1,X5,X3),X4))). 4.06/4.35 cnf(i_0_1981, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2)). 4.06/4.35 cnf(i_0_5161, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_List_Oset(X1),X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_List_Oset(X2),X4)))=hAPP(c_List_Oset(tc_prod(X1,X2)),c_Enum_Oproduct(X1,X2,X3,X4)))). 4.06/4.35 cnf(i_0_1627, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),X3)),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X4),X3))=hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)),X3))). 4.06/4.35 cnf(i_0_494, plain, (c_Map_Odom(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X3),hAPP(c_Option_Ooption_OSome(X2),X4)))=hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_6027, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))=c_Wellfounded_Opred__nat)). 4.06/4.35 cnf(i_0_3397, plain, (hAPP(c_Set_Oimage(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3)),hAPP(c_Set_OPow(X1),X4))=hAPP(c_Set_OPow(X2),hAPP(c_Set_Oimage(X1,X2,X3),X4)))). 4.06/4.35 cnf(i_0_2160, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3)),hAPP(c_List_Ofilter(X1,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X1,c_fNot),X2)),X3))=c_List_Opartition(X1,X2,X3))). 4.06/4.35 cnf(i_0_6864, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2))=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2))). 4.06/4.35 cnf(i_0_6387, plain, (c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat)),X1)),X2)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1)))). 4.06/4.35 cnf(i_0_1076, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X5),X4))=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),X5)),X4))). 4.06/4.35 cnf(i_0_2035, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5))=hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5)))). 4.06/4.35 cnf(i_0_4818, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X3),X5))=hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5)))). 4.06/4.35 cnf(i_0_7534, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X5),X4))=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X5)),X4))). 4.06/4.35 cnf(i_0_1496, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X5),X4))=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X5)),X4))). 4.06/4.35 cnf(i_0_2274, plain, (hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X5)=hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)))). 4.06/4.35 cnf(i_0_3919, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),X3))). 4.06/4.35 cnf(i_0_1100, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)),X3))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)))). 4.06/4.35 cnf(i_0_6299, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),X3))=c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)))). 4.06/4.35 cnf(i_0_5648, plain, (c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)),X1)),X2)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1)))). 4.06/4.35 cnf(i_0_1763, plain, (c_Map_Omap__add(X1,X2,X3,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X4),X5),hAPP(c_Option_Ooption_OSome(X2),X6)))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__add(X1,X2,X3,X4)),X5),hAPP(c_Option_Ooption_OSome(X2),X6)))). 4.06/4.35 cnf(i_0_2138, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2))). 4.06/4.35 cnf(i_0_1000, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),c_List_Orotate1(X1)),X3)=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3))). 4.06/4.35 cnf(i_0_6028, plain, (c_Map_Omap__upds(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)),X6,X7)=c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X6),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X7)))). 4.06/4.35 cnf(i_0_7406, plain, (c_Fun_Oinj__on(X1,tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_1048, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X2,X1),X3)),hAPP(c_Relation_Oconverse(X2,X1),X4))=hAPP(c_Relation_Oconverse(X2,X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4)))). 4.06/4.35 cnf(i_0_832, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X2,X1),X3)),hAPP(c_Relation_Oconverse(X2,X1),X4))=hAPP(c_Relation_Oconverse(X2,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4)))). 4.06/4.35 cnf(i_0_7287, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2),X3)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))). 4.06/4.35 cnf(i_0_6155, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X5),X4))=hAPP(c_Relation_OImage(X2,X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X5)),X4))). 4.06/4.35 cnf(i_0_1549, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),hAPP(c_COMBC(X1,X2,X1),X3)),X4),X5)=hAPP(c_List_Ofoldl(X1,X2,X3,X4),X5))). 4.06/4.35 cnf(i_0_2078, plain, (hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(c_fequal,c_List_Olist_ONil(X1)))=hAPP(c_fequal,c_List_Olist_ONil(X1)))). 4.06/4.35 cnf(i_0_4919, plain, (c_Divides_Odivmod__int(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2))=c_Divides_Opdivmod(X1,X2))). 4.06/4.35 cnf(i_0_6240, plain, (c_Nat_Onat_Onat__case(tc_List_Olist(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Odrop(X1)),X3),X4)=hAPP(hAPP(c_List_Odrop(X1),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))). 4.06/4.35 cnf(i_0_223, plain, (hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X1),X2)))=hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X1),X2))). 4.06/4.35 cnf(i_0_350, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))),c_List_Olexord(X1,X4))))). 4.06/4.35 cnf(i_0_189, plain, (c_List_OtakeWhile(tc_prod(X1,X2),hAPP(c_Fun_Ocomp(X2,tc_HOL_Obool,tc_prod(X1,X2),X3),c_Product__Type_Osnd(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))=hAPP(hAPP(c_List_Ozip(X1,X2),X4),c_List_OtakeWhile(X2,X3,X5)))). 4.06/4.35 cnf(i_0_5083, plain, (c_List_OtakeWhile(tc_prod(X1,X2),hAPP(c_Fun_Ocomp(X1,tc_HOL_Obool,tc_prod(X1,X2),X3),c_Product__Type_Ofst(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))=hAPP(hAPP(c_List_Ozip(X1,X2),c_List_OtakeWhile(X1,X3,X4)),X5))). 4.06/4.35 cnf(i_0_4037, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2))),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2))),X3))). 4.06/4.35 cnf(i_0_1600, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)),X4))). 4.06/4.35 cnf(i_0_7267, plain, (hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2)),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.06/4.35 cnf(i_0_5530, plain, (c_Lazy__Sequence_Oappend(tc_Option_Ooption(X1),hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)),tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)),c_Lazy__Sequence_Ohit__bound(X1),c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)))),X2),c_Lazy__Sequence_Ohb__flat(X1,X3))=c_Lazy__Sequence_Ohb__flat(X1,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1))),X2,X3)))). 4.06/4.35 cnf(i_0_2294, plain, (hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fdisj),X2)),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.06/4.35 cnf(i_0_1561, plain, (c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1)))). 4.06/4.35 cnf(i_0_4613, plain, (c_New__Random__Sequence_Opos__bind(X1,X2,X3,hAPP(c_Fun_Ocomp(X2,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))))),X1,c_New__Random__Sequence_Opos__single(X2)),X4))=c_New__Random__Sequence_Opos__map(X1,X2,X4,X3))). 4.06/4.35 cnf(i_0_3306, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4))),hAPP(X5,hAPP(c_Product__Type_Osnd(X2,X3),X4))))=c_Product__Type_Oprod_Oprod__size(X2,X3,X1,X5,X4))). 4.06/4.35 cnf(i_0_3153, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Ofilter(X1,X3),X4))=hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)),X4))). 4.06/4.35 cnf(i_0_4114, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.06/4.35 cnf(i_0_776, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4))),c_Map_Odom(X1,X2,X5))=c_Map_Odom(X1,X2,c_Map_Omap__upds(X1,X2,X5,X4,X3)))). 4.06/4.35 cnf(i_0_3462, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,X3),X1),hAPP(c_COMBB(tc_prod(X1,X2),X3,X2),X4)),c_Product__Type_OPair(X1,X2)))=X4)). 4.06/4.35 cnf(i_0_4295, plain, (hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),X1),c_member(X2)),X3)),X4)=hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3))). 4.06/4.35 cnf(i_0_5347, plain, (c_New__Random__Sequence_Oneg__bind(X1,X2,X3,hAPP(c_Fun_Ocomp(X2,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))))),X1,c_New__Random__Sequence_Oneg__single(X2)),X4))=c_New__Random__Sequence_Oneg__map(X1,X2,X4,X3))). 4.06/4.35 cnf(i_0_5928, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X2),X3)),X4))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_1266, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X4))=hAPP(hAPP(c_List_Otake(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)))). 4.06/4.35 cnf(i_0_2438, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3)),hAPP(hAPP(c_List_Odrop(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X4))=hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)))). 4.06/4.35 cnf(i_0_252, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3)))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.06/4.35 cnf(i_0_5698, plain, (c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))). 4.06/4.35 cnf(i_0_4311, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Transitive__Closure_Ortrancl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool))))=c_FunDef_Opair__leq)). 4.06/4.35 cnf(i_0_2950, plain, (hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),hAPP(hAPP(c_List_Omap(X2,tc_prod(X1,X2)),hAPP(c_Product__Type_OPair(X1,X2),X3)),X4)),c_Enum_Oproduct(X1,X2,X5,X4))=c_Enum_Oproduct(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X5),X4))). 4.06/4.35 cnf(i_0_6452, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X4))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X5)),X4))). 4.06/4.35 cnf(i_0_1298, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X4))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X5)),X4))). 4.06/4.35 cnf(i_0_1674, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X4))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X5)),X4))). 4.06/4.35 cnf(i_0_1006, 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)))). 4.06/4.35 cnf(i_0_6800, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2))). 4.06/4.35 cnf(i_0_1964, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))). 4.06/4.35 cnf(i_0_6797, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))). 4.06/4.35 cnf(i_0_964, plain, (c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X3),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBB(tc_fun(X3,X2),tc_fun(tc_Option_Ooption(X3),tc_Option_Ooption(X2)),X1),c_Option_Omap(X3,X2)),X4)),X5))=c_Map_Odom(X1,X3,X5))). 4.06/4.35 cnf(i_0_2377, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.06/4.35 cnf(i_0_530, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))),c_List_Olexord(X1,X5))))). 4.06/4.35 cnf(i_0_1753, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.06/4.35 cnf(i_0_5685, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.06/4.35 cnf(i_0_7550, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.06/4.35 cnf(i_0_5451, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3))). 4.06/4.35 cnf(i_0_3369, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3))). 4.06/4.35 cnf(i_0_7482, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3))). 4.06/4.35 cnf(i_0_2826, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X3)))). 4.06/4.35 cnf(i_0_1922, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3)),X4))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_5895, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.06/4.35 cnf(i_0_4807, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_Ovimage(X2,X4,X5)),X6))=hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6)),X5))). 4.06/4.35 cnf(i_0_962, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_Oimage(X4,X2,X5)),X6))=hAPP(c_Set_Oimage(X4,X2,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6)))). 4.06/4.35 cnf(i_0_6197, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Relation_OImage(X4,X2,X5)),X6))=hAPP(c_Relation_OImage(X4,X2,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6)))). 4.06/4.35 cnf(i_0_1826, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))). 4.06/4.35 cnf(i_0_3120, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_Ovimage(X2,X4,X5)),X6))=hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X6)),X5))). 4.06/4.35 cnf(i_0_959, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2)))))). 4.06/4.35 cnf(i_0_4783, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Ofilter(X1,X2),X3)),hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),X3)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))). 4.06/4.35 cnf(i_0_6381, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))). 4.06/4.35 cnf(i_0_322, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_Map_Omap__of(X1,X2),X3)),hAPP(c_Product__Type_Ofst(X1,X2),X4)),hAPP(c_Option_Ooption_OSome(X2),hAPP(c_Product__Type_Osnd(X1,X2),X4)))=hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),X4),X3)))). 4.06/4.35 cnf(i_0_2319, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X2),X4)),X5))=hAPP(hAPP(c_Set_Oinsert(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)))). 4.06/4.35 cnf(i_0_3325, plain, (c_Enum_Oenum__the(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),hAPP(c_fequal,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=c_Set_Othe__elem(X1,X2))). 4.06/4.35 cnf(i_0_6267, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_Oimage(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oinsert(X1),X3)),hAPP(c_Set_OPow(X1),X2)))=hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)))). 4.06/4.35 cnf(i_0_1309, plain, (c_Random_Opick(X1,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X2))=c_Random_Opick(X1,X2))). 4.06/4.35 cnf(i_0_1283, plain, (c_Random_Oselect__weight(X1,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X2))=c_Random_Oselect__weight(X1,X2))). 4.06/4.35 cnf(i_0_1418, plain, (hAPP(c_Fun_Ocomp(tc_prod(X1,X2),tc_prod(X3,X4),tc_prod(X5,X6),c_Product__Type_Omap__pair(X1,X3,X2,X4,X7,X8)),c_Product__Type_Omap__pair(X5,X1,X6,X2,X9,X10))=c_Product__Type_Omap__pair(X5,X3,X6,X4,hAPP(c_Fun_Ocomp(X1,X3,X5,X7),X9),hAPP(c_Fun_Ocomp(X2,X4,X6,X8),X10)))). 4.06/4.35 cnf(i_0_3077, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3))=hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)),X3))). 4.06/4.35 cnf(i_0_1685, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool))),X4))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)))). 4.06/4.35 cnf(i_0_4724, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool))),X4))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)))). 4.06/4.35 cnf(i_0_7417, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))). 4.06/4.35 cnf(i_0_4905, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X4))=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),c_List_Orotate1(X1)),X4))). 4.06/4.35 cnf(i_0_5309, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(X1),X1,c_List_Omap__filter(X2,X1,X3,X4),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Omap__filter(X2,X1,X3,X4))),hAPP(X3,X5))=c_List_Omap__filter(X2,X1,X3,hAPP(hAPP(c_List_Olist_OCons(X2),X5),X4)))). 4.06/4.35 cnf(i_0_1489, 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),esk114_1(X1)),esk115_1(X1)))))=X1)). 4.06/4.35 cnf(i_0_5543, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),X1),c_Set_OPow(X2)),X4))=hAPP(c_Set_OPow(X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)))). 4.06/4.35 cnf(i_0_2589, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3))),X3))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3))). 4.06/4.35 cnf(i_0_4110, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))),X3))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3))). 4.06/4.35 cnf(i_0_831, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))). 4.06/4.35 cnf(i_0_772, plain, (hAPP(c_Relation_OField(X1),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(c_Relation_OField(X1),X4))))). 4.06/4.35 cnf(i_0_7432, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3)),c_Option_Ooption_ONone(X2)))=c_Map_Odom(X1,X2,X3))). 4.06/4.35 cnf(i_0_2654, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(c_List_Orev(tc_List_Olist(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Orev(X1)),X2)))=hAPP(c_List_Orev(X1),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2)))). 4.06/4.35 cnf(i_0_2638, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X5),X4))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X5)),X4))). 4.06/4.35 cnf(i_0_4219, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X5),X4))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X5)),X4))). 4.06/4.35 cnf(i_0_995, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))). 4.06/4.35 cnf(i_0_803, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))). 4.06/4.35 cnf(i_0_617, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X6))=hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X2),tc_HOL_Obool)),X5),X6)))). 4.06/4.35 cnf(i_0_6220, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))). 4.06/4.35 cnf(i_0_284, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X6),X5))=hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),X4),X6)),X5))). 4.06/4.35 cnf(i_0_5721, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)))),c_Nitpick_Onat__gcd(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)))))=c_Nitpick_Oint__lcm(X1,X2))). 4.06/4.35 cnf(i_0_195, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))). 4.06/4.35 cnf(i_0_6666, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_OPow(X1),X3))),hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)))))). 4.06/4.35 cnf(i_0_896, plain, (hAPP(c_fequal,hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X2))). 4.06/4.35 cnf(i_0_4060, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist__update(X1,X3),X4),hAPP(c_Product__Type_Ofst(X1,X2),X5))),hAPP(hAPP(c_List_Olist__update(X2,X6),X4),hAPP(c_Product__Type_Osnd(X1,X2),X5)))=hAPP(hAPP(c_List_Olist__update(tc_prod(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X6)),X4),X5))). 4.06/4.35 cnf(i_0_3109, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),X1),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1))). 4.06/4.35 cnf(i_0_5567, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)))). 4.06/4.35 cnf(i_0_535, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)))). 4.06/4.35 cnf(i_0_2376, plain, (c_Enum_Oenum__the(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_Enum_Oenum__the(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3)))). 4.06/4.35 cnf(i_0_4886, plain, (c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(hAPP(c_COMBS(tc_prod(X1,X2),X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),tc_prod(X1,X2)),X3),c_Product__Type_Ofst(X1,X2))),c_Product__Type_Osnd(X1,X2)))=c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3)))). 4.06/4.35 cnf(i_0_3838, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5)))). 4.06/4.35 cnf(i_0_3392, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X3)))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X3))))). 4.06/4.35 cnf(i_0_2782, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))). 4.06/4.35 cnf(i_0_224, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))). 4.06/4.35 cnf(i_0_6756, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3))),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))))). 4.06/4.35 cnf(i_0_7209, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))). 4.06/4.35 cnf(i_0_5035, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4))),hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))))). 4.06/4.35 cnf(i_0_4183, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),X3))). 4.06/4.35 cnf(i_0_1902, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),X3)),hAPP(c_Relation_ORange(X2,X1),X4))),hAPP(c_Relation_ORange(X2,X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4)))))). 4.06/4.35 cnf(i_0_427, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4)))))). 4.06/4.35 cnf(i_0_5390, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ORange(X2,X1),X3)),hAPP(c_Relation_ORange(X2,X1),X4)))))). 4.06/4.35 cnf(i_0_4034, 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),esk293_4(X3,X4,X1,X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),X3))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X3))))). 4.06/4.35 cnf(i_0_539, plain, (hAPP(c_List_Olist_Olist__case(tc_List_Olist(X1),X1,hAPP(c_List_Otl(X1),X2),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Oappend(X1)),X2))),X3)=hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Oappend(X1),X3),X2)))). 4.06/4.35 cnf(i_0_6530, plain, (c_Nat_Onat_Onat__case(tc_List_Olist(X1),c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_List_Olist(X1),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X1),X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Otake(X1)),X3)),X4)=hAPP(hAPP(c_List_Otake(X1),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))). 4.06/4.35 cnf(i_0_6758, plain, (hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),c_List_Oset(X1))),X2)=c_List_Olists(X1,X2))). 4.06/4.35 cnf(i_0_4596, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool)),X2))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.06/4.35 cnf(i_0_787, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3)),hAPP(hAPP(c_List_Otake(X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))),X3))=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3))). 4.06/4.35 cnf(i_0_1621, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),hAPP(c_Relation_OField(X1),X2)),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_Relation_OField(X1),X2))))))). 4.06/4.35 cnf(i_0_2411, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5)))))). 4.06/4.35 cnf(i_0_3168, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X3),X5)))))). 4.06/4.35 cnf(i_0_4723, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))=hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 4.06/4.35 cnf(i_0_4098, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5))),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5)))))). 4.06/4.35 cnf(i_0_4268, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool),X1),c_Relation_Oconverse(X3,X2)),X5))=hAPP(c_Relation_Oconverse(X3,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X3,X2),tc_HOL_Obool)),X4),X5)))). 4.06/4.35 cnf(i_0_6168, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool),X1),c_Relation_Oconverse(X3,X2)),X5))=hAPP(c_Relation_Oconverse(X3,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_prod(X3,X2),tc_HOL_Obool)),X4),X5)))). 4.06/4.35 cnf(i_0_130, plain, (hAPP(c_List_Oset(X1),hAPP(c_List_Ofilter(X1,X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X3)),X2))). 4.06/4.35 cnf(i_0_4360, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)))))). 4.06/4.35 cnf(i_0_1044, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))))). 4.06/4.35 cnf(i_0_3075, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)))). 4.06/4.35 cnf(i_0_1699, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),X1),c_Int_Onat)))=X1)). 4.06/4.35 cnf(i_0_3574, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.06/4.35 cnf(i_0_7089, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))). 4.06/4.35 cnf(i_0_138, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),X5),X6)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X4)),X5),X6))). 4.06/4.35 cnf(i_0_1741, plain, (hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),X2)),X3)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.06/4.35 cnf(i_0_3468, plain, (hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X1),hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X1)),c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X1)),X2))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X2)))). 4.06/4.35 cnf(i_0_193, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3))=hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))). 4.06/4.35 cnf(i_0_3089, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),c_Int_OMin)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))). 4.06/4.35 cnf(i_0_2306, plain, (hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X1),X1),c_Wellfounded_Olex__prod(tc_Nat_Onat,X1,c_Wellfounded_Oless__than,X2)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(tc_Nat_Onat,X1)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,tc_prod(tc_Nat_Onat,X1)),X1),c_Product__Type_OPair(tc_Nat_Onat,X1)),X3)),c_COMBI(X1)))=c_Wellfounded_Omlex__prod(X1,X3,X2))). 4.06/4.35 cnf(i_0_441, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool))),X4))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4))). 4.06/4.35 cnf(i_0_1346, plain, (hAPP(c_List_Orev(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),c_List_Orotate1(X1)),X2))=hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),hAPP(c_List_Orev(X1),X2)))). 4.06/4.35 cnf(i_0_4571, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2))),X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2))). 4.06/4.35 cnf(i_0_6595, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2))),X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)),X2))). 4.06/4.35 cnf(i_0_4758, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool))),X4))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4))). 4.06/4.35 cnf(i_0_4588, plain, (c_Nat_Onat_Onat__case(tc_List_Olist(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_List_Olist(X1),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X1),X4)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X1,tc_List_Olist(X1)),c_List_Olist__update(X1,X3)),X2)),X5)=hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)),X5),X2))). 4.06/4.35 cnf(i_0_4595, plain, (c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)))). 4.06/4.35 cnf(i_0_7410, plain, (c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)))). 4.06/4.35 cnf(i_0_5772, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Product__Type_OSigma(X1,X2)),X4))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)),X4))). 4.06/4.35 cnf(i_0_3563, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 4.06/4.35 cnf(i_0_2350, plain, (c_Nitpick_OAbs__Frac(X1,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2)))),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2))))=c_Nitpick_Ouminus__frac(X1,X2))). 4.06/4.35 cnf(i_0_5260, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))=c_Int_Oint__ge__less__than2(X1))). 4.06/4.35 cnf(i_0_2614, plain, (c_Map_Orestrict__map(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=c_Map_Orestrict__map(X1,X2,X3,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))). 4.06/4.35 cnf(i_0_2224, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X4,X5)),tc_fun(X2,X3),X1),hAPP(c_COMBB(tc_prod(X4,X5),X3,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X5,X3),X6))),X7)),X8)=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X5,X3),X6),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X4,X5)),X7),X8)))). 4.06/4.35 cnf(i_0_5490, plain, (hAPP(hAPP(c_COMBS(tc_prod(X1,X2),X2,X3),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,X3),tc_prod(X1,X2)),X5),hAPP(hAPP(c_COMBB(X1,X4,tc_prod(X1,X2)),X6),c_Product__Type_Ofst(X1,X2)))),c_Product__Type_Osnd(X1,X2))=hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,X3),X1),X5),X6)))). 4.06/4.35 cnf(i_0_7274, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Set_Oinsert(X2)),X4)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))=hAPP(c_Set_Oimage(X1,X2,X4),X3))). 4.06/4.35 cnf(i_0_1821, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))). 4.06/4.35 cnf(i_0_6223, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5,X3),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool),X1),hAPP(c_Relation_Orel__comp(X2,X5,X3),X6)),X7))=hAPP(hAPP(c_Relation_Orel__comp(X2,X5,X3),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X5,X3),tc_HOL_Obool)),X4),X7)))). 4.06/4.35 cnf(i_0_4643, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X3),tc_fun(X2,X1)),hAPP(hAPP(c_COMBB(tc_fun(X3,X1),tc_fun(tc_fun(X2,X3),tc_fun(X2,X1)),X1),c_COMBB(X3,X1,X2)),X4)),X5),X6),X7)=hAPP(c_List_Ofoldl(X1,X3,X4,X6),hAPP(hAPP(c_List_Omap(X2,X3),X5),X7)))). 4.06/4.35 cnf(i_0_1340, plain, (hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X4))),hAPP(hAPP(c_List_Ozip(X1,X2),X5),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X4)))=hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X5)),X4))). 4.06/4.35 cnf(i_0_6250, plain, (hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool)))=hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 4.06/4.35 cnf(i_0_6812, plain, (c_Lazy__Sequence_Ohb__not__seq(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),X2)))=hAPP(c_New__DSequence_Opos__not__seq(X1),X2))). 4.06/4.35 cnf(i_0_4362, plain, (hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4)),X3)),hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4)),X5))=hAPP(hAPP(c_List_Ozip(X1,X2),X4),hAPP(hAPP(c_List_Oappend(X2),X3),X5)))). 4.06/4.35 cnf(i_0_1743, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),X5),X6))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),c_Relation_OImage(X2,X1,X3)),X6)))))). 4.06/4.35 cnf(i_0_6996, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))). 4.06/4.35 cnf(i_0_5533, plain, (hAPP(c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Oappend(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1)))),X2)=hAPP(c_List_Orotate1(X1),X2))). 4.06/4.35 cnf(i_0_4808, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))). 4.06/4.35 cnf(i_0_6130, plain, (c_List_Oset__Cons(X1,hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(c_fequal,X4)))=hAPP(c_Relation_OImage(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olistrel(X1,X2)),hAPP(c_fequal,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))))). 4.06/4.35 cnf(i_0_3650, 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))). 4.06/4.35 cnf(i_0_2934, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),tc_prod(X3,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X3,X2)),hAPP(hAPP(c_COMBB(X3,tc_fun(X2,tc_prod(X3,X2)),X1),c_Product__Type_OPair(X3,X2)),X4))),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6))=hAPP(hAPP(c_List_Ozip(X3,X2),hAPP(hAPP(c_List_Omap(X1,X3),X4),X5)),X6))). 4.06/4.35 cnf(i_0_2653, plain, (hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),X3))),c_Option_Ooption_OSome(X2)))=c_Map_Oran(X1,X2,X3))). 4.06/4.35 cnf(i_0_4562, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))=c_Transitive__Closure_Ortrancl(X1,X2))). 4.06/4.35 cnf(i_0_3842, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X3)),X4))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_273, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))). 4.06/4.35 cnf(i_0_3464, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),tc_prod(X2,X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X2,X1)),hAPP(c_COMBC(X2,X1,tc_prod(X2,X1)),c_Product__Type_OPair(X2,X1)))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))=hAPP(hAPP(c_Product__Type_OSigma(X2,X1),X4),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X2),X3)))). 4.06/4.35 cnf(i_0_3449, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),X2),c_Set_OPow(X1)),X4))),hAPP(c_Set_OPow(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)))))). 4.06/4.35 cnf(i_0_2650, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=X1)). 4.06/4.35 cnf(i_0_3784, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))). 4.06/4.35 cnf(i_0_4330, plain, (hAPP(hAPP(c_List_Omap(X1,X2),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2)),X3)),hAPP(c_List_Ofilter(X1,c_Map_Odom(X1,X2,X3)),X4))=c_List_Omap__filter(X1,X2,X3,X4))). 4.06/4.35 cnf(i_0_364, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),hAPP(c_Fun_Ocomp(tc_prod(X2,X4),X2,X1,c_Product__Type_Ofst(X2,X4)),X5))),hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,X1),X6),hAPP(c_Fun_Ocomp(tc_prod(X2,X4),X4,X1,c_Product__Type_Osnd(X2,X4)),X5)))=hAPP(hAPP(c_COMBB(tc_prod(X2,X4),tc_HOL_Obool,X1),hAPP(hAPP(c_Product__Type_OSigma(X2,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X2),X6))),X5))). 4.06/4.35 cnf(i_0_2889, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5))). 4.06/4.35 cnf(i_0_4359, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5))). 4.06/4.35 cnf(i_0_3561, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5))). 4.06/4.35 cnf(i_0_3173, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))). 4.06/4.35 cnf(i_0_4274, plain, (c_Enum_Oenum__the(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBC(X1,X3,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,tc_HOL_Obool),X1),c_fequal),X4)),X5)))=hAPP(c_Fun_Othe__inv__into(X1,X3,X2,X4),X5))). 4.06/4.35 cnf(i_0_6213, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))). 4.06/4.35 cnf(i_0_6957, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat),X3),hAPP(c_List_Onth(X1),X2))))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X3),X2)))). 4.06/4.35 cnf(i_0_4399, plain, (hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X1),X2)),c_Code__Numeral_Onat__of)))=c_Random_Oselect(X1,X2))). 4.06/4.35 cnf(i_0_5785, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)))))=hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X1)))))). 4.06/4.35 cnf(i_0_5767, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))). 4.06/4.35 cnf(i_0_2624, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool))),X5)),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)),X6))). 4.06/4.35 cnf(i_0_4936, plain, (c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),X1),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)=hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X2))). 4.06/4.35 cnf(i_0_6519, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X3)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X4),c_Int_Onat)))=c_Nat_Onat_Onat__case(X1,X3,X4,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))). 4.06/4.35 cnf(i_0_3301, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Osublist(X1,X2,X3)),c_List_Osublist(X1,X4,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X3),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))))=c_List_Osublist(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X4),X3))). 4.06/4.35 cnf(i_0_628, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool))),X5)),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X3),X5)),X6))). 4.06/4.35 cnf(i_0_6175, plain, (c_Wellfounded_Omlex__prod(tc_List_Olist(X1),c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Olex(X1,X2))=c_List_Olenlex(X1,X2))). 4.06/4.35 cnf(i_0_1637, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.06/4.35 cnf(i_0_6598, plain, (hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1)),X2)))),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X1,X2)))=c_Random_Oselect__weight(X1,X2))). 4.06/4.35 cnf(i_0_5671, plain, (hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),X1),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(tc_fun(X1,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(X1,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),X1),c_List_Omap(tc_fun(X1,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(X1,tc_Nat_Onat),X1,tc_Nat_Onat),c_COMBI(tc_fun(X1,tc_Nat_Onat))))),X2))=c_List_Omeasures(X1,X2))). 4.06/4.35 cnf(i_0_2218, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X2)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X2))))). 4.06/4.35 cnf(i_0_7358, plain, (hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_Set_Oinsert(X2),X4),X6)))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X5)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X6))))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X5)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(hAPP(c_Set_Oinsert(X2),X4),X6))))). 4.06/4.35 cnf(i_0_5410, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olists(X1,X2)),c_List_Olists(X1,X3))=c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.06/4.35 cnf(i_0_5202, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),c_fequal))),X2))=c_Relation_OId__on(X1,X2))). 4.06/4.35 cnf(i_0_2591, plain, (c_List_Omap__filter(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_Option_Ooption(X2),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),X1),c_If(tc_Option_Ooption(X2))),X3)),hAPP(hAPP(c_COMBB(X2,tc_Option_Ooption(X2),X1),c_Option_Ooption_OSome(X2)),X4))),c_Option_Ooption_ONone(X2)),X5)=hAPP(hAPP(c_List_Omap(X1,X2),X4),hAPP(c_List_Ofilter(X1,X3),X5)))). 4.06/4.35 cnf(i_0_1849, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X1)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))),c_List_Olist_ONil(X1))),c_List_Osublist(X1,X4,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X2),c_Nat_OSuc)))=c_List_Osublist(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4),X2))). 4.06/4.35 cnf(i_0_3121, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X3,X4)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X4),tc_fun(X2,tc_prod(X3,X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X3,X4)),tc_fun(tc_fun(X2,X4),tc_fun(X2,tc_prod(X3,X4))),X1),c_COMBB(X4,tc_prod(X3,X4),X2)),hAPP(hAPP(c_COMBB(X3,tc_fun(X4,tc_prod(X3,X4)),X1),c_Product__Type_OPair(X3,X4)),X5))),X6))=c_Product__Type_Omap__pair(X1,X3,X2,X4,X5,X6))). 4.06/4.35 cnf(i_0_3476, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X4),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X5,X3),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2,X5),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X5,X3),tc_HOL_Obool),tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),X1),c_Relation_Orel__comp(X2,X5,X3)),X6)),X7))=hAPP(hAPP(c_Relation_Orel__comp(X2,X5,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X5),tc_HOL_Obool)),X4),X6)),X7))). 4.06/4.35 cnf(i_0_3374, plain, (c_New__DSequence_Opos__decr__bind(X1,X2,hAPP(hAPP(hAPP(X3,X4),X5),X6),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))))),X7),X4)),X5)),X6))=c_New__Random__Sequence_Opos__decr__bind(X1,X2,X3,X7,X4,X5,X6))). 4.06/4.35 cnf(i_0_1259, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X2)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2))). 4.06/4.35 cnf(i_0_7072, plain, (hAPP(c_Lazy__Sequence_Obind(X1,tc_prod(X1,X2),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X1,X2))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X1,X2)),X1),c_Lazy__Sequence_Obind(X2,tc_prod(X1,X2),X4)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X1,X2))),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X1,X2)),X2),c_Lazy__Sequence_Osingle(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2))))=c_Lazy__Sequence_Oproduct(X1,X2,X3,X4))). 4.06/4.35 cnf(i_0_5204, plain, (c_New__DSequence_Opos__bind(X1,X2,hAPP(hAPP(hAPP(X3,X4),X5),X6),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2))))),X7),X4)),X5)),X6))=hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X1,X2,X3,X7),X4),X5),X6))). 4.06/4.35 cnf(i_0_1467, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X3),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X4,X2)),tc_fun(X2,X3),X1),hAPP(c_COMBB(tc_prod(X4,X2),X3,X2),X5)),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,tc_prod(X4,X2)),X1),c_Product__Type_OPair(X4,X2)),X6)))),hAPP(hAPP(c_List_Ozip(X1,X2),X7),X8))=hAPP(hAPP(c_List_Omap(tc_prod(X4,X2),X3),X5),hAPP(hAPP(c_List_Ozip(X4,X2),hAPP(hAPP(c_List_Omap(X1,X4),X6),X7)),X8)))). 4.06/4.35 cnf(i_0_309, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X3))),X4))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))). 4.06/4.35 cnf(i_0_3313, plain, (c_New__DSequence_Oneg__decr__bind(X1,X2,hAPP(hAPP(hAPP(X3,X4),X5),X6),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))))),X7),X4)),X5)),X6))=c_New__Random__Sequence_Oneg__decr__bind(X1,X2,X3,X7,X4,X5,X6))). 4.06/4.35 cnf(i_0_4209, plain, (c_Enum_Oenum__the(tc_prod(X1,X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_fequal,X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_fequal,X4))))=hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4))). 4.06/4.35 cnf(i_0_4102, plain, (c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(c_fequal,X3)),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_fequal,X4))))=hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4))). 4.06/4.35 cnf(i_0_6749, plain, (hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_Enum_Osublists(X1,X2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(X1)),tc_fun(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),tc_List_Olist(tc_List_Olist(X1))),c_List_Oappend(tc_List_Olist(X1))),hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(c_List_Olist_OCons(X1),X3)))),c_COMBI(tc_List_Olist(tc_List_Olist(X1)))))=c_Enum_Osublists(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)))). 4.06/4.35 cnf(i_0_4021, plain, (c_New__DSequence_Oneg__bind(X1,X2,hAPP(hAPP(hAPP(X3,X4),X5),X6),hAPP(hAPP(c_COMBC(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2)))))),X7),X4)),X5)),X6))=hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X1,X2,X3,X7),X4),X5),X6))). 4.06/4.35 cnf(i_0_3340, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))). 4.06/4.35 cnf(i_0_880, plain, (c_Fun_Oinj__on(tc_fun(X1,X2),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,X2)),c_Set_OCollect(tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,X2)),c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool)),hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBC(X2,X2,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,X2),tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_2023, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X3))),X4))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),X4)))). 4.06/4.35 cnf(i_0_3305, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X1,tc_Nat_Onat)),X2),c_Product__Type_Osnd(X1,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))))=c_List_Osublist(X1,X3,X2))). 4.06/4.35 cnf(i_0_1707, plain, (hAPP(hAPP(c_Product__Type_OSigma(tc_Int_Oint,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_Set_OCollect(tc_Int_Oint)),c_Orderings_Oord__class_Oless(tc_Int_Oint)))=c_Int_Oint__ge__less__than(X1))). 4.06/4.35 cnf(i_0_935, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X2)),c_Int_Onat))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))). 4.06/4.35 cnf(i_0_7515, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X2)),c_Int_Onat))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))). 4.06/4.35 cnf(i_0_3399, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 4.06/4.35 cnf(i_0_2739, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))). 4.06/4.35 cnf(i_0_6228, plain, (hAPP(c_Set_Oimage(X1,tc_prod(X1,X1),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1))),X2)=c_Relation_OId__on(X1,X2))). 4.06/4.35 cnf(i_0_1492, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),tc_prod(X1,X3)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X1,X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X3),tc_fun(X2,tc_prod(X1,X3))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X1,X3)),tc_fun(tc_fun(X2,X3),tc_fun(X2,tc_prod(X1,X3))),X1),c_COMBB(X3,tc_prod(X1,X3),X2)),c_Product__Type_OPair(X1,X3))),X4))),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6))=hAPP(hAPP(c_List_Ozip(X1,X3),X5),hAPP(hAPP(c_List_Omap(X2,X3),X4),X6)))). 4.06/4.35 cnf(i_0_1976, plain, (hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Omap(tc_prod(X1,X3),tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X3,tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,X2),tc_fun(X3,tc_prod(X1,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(tc_fun(X3,X2),tc_fun(X3,tc_prod(X1,X2))),X1),c_COMBB(X2,tc_prod(X1,X2),X3)),c_Product__Type_OPair(X1,X2))),X4))),X5))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),tc_Option_Ooption(X2),X1,hAPP(c_Option_Omap(X3,X2),X4)),hAPP(c_Map_Omap__of(X1,X3),X5)))). 4.06/4.35 cnf(i_0_4071, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Map_Odom(X1,X3,X4))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X3,X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),c_Map_Odom(X1,X3,X4))))=c_Map_Odom(X1,X3,c_Fun_Ooverride__on(X1,tc_Option_Ooption(X3),X5,X4,X2)))). 4.06/4.35 cnf(i_0_270, plain, (hAPP(hAPP(c_Nitpick_Ofrac(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2))),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X3)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2))),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X3))))=c_Nitpick_Otimes__frac(X1,X2,X3))). 4.06/4.35 cnf(i_0_6563, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),c_COMBK(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))))),X2))=hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),c_List_Ohd(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1)))),X2)))). 4.06/4.35 cnf(i_0_4086, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1)),c_List_Oappend(tc_List_Olist(X1)),c_List_Olist_ONil(tc_List_Olist(X1))),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),tc_List_Olist(X1)),c_List_Omap(X1,tc_List_Olist(X1))),hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)))),X2)),c_Enum_On__lists(X1,X3,X2)))=c_Enum_On__lists(X1,hAPP(c_Nat_OSuc,X3),X2))). 4.06/4.35 cnf(i_0_7073, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq))=c_FunDef_Omax__weak)). 4.06/4.35 cnf(i_0_7307, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat)),c_Int_Onat)),X2))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))). 4.06/4.35 cnf(i_0_1852, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),X3)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X4),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X3,X4)),c_Int_Onat))))=hAPP(c_Nat_Onat_Onat__rec(X1,X3,X4),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))). 4.06/4.35 cnf(i_0_1632, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,X2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)),c_Int_Onat)),X2))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))). 4.06/4.35 cnf(i_0_1740, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq))=c_FunDef_Omin__weak)). 4.06/4.35 cnf(i_0_1920, plain, (hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X1,X1)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBC(tc_prod(X1,X1),tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_HOL_Obool)),tc_prod(X1,X1)),c_COMBB(tc_prod(X1,X1),tc_HOL_Obool,X1)),c_fequal)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1))))=c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_1361, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4)))))=hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4))))))). 4.06/4.35 cnf(i_0_795, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_OCollect(X1)),hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1))))=c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2))). 4.06/4.35 cnf(i_0_501, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1)),c_List_Oappend(tc_List_Olist(X1)),c_List_Olist_ONil(tc_List_Olist(X1))),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X1)),X1,c_List_Olist_ONil(tc_List_Olist(X1)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1))),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(tc_List_Olist(X1)),tc_List_Olist(tc_List_Olist(X1))),c_List_Olist_OCons(tc_List_Olist(X1))),c_List_Olist_ONil(tc_List_Olist(X1)))))),X2))=hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Otl(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1)))),X2)))). 4.06/4.35 cnf(i_0_3346, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X1,X3,X4,X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))))=c_Nat_Onat_Onat__case(X1,X3,X4,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X5)))). 4.06/4.35 cnf(i_0_6411, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),tc_prod(X3,X4)),c_Product__Type_Omap__pair(X1,X3,X2,X4,X5,X6)),hAPP(hAPP(c_List_Ozip(X1,X2),X7),X8))=hAPP(hAPP(c_List_Ozip(X3,X4),hAPP(hAPP(c_List_Omap(X1,X3),X5),X7)),hAPP(hAPP(c_List_Omap(X2,X4),X6),X8)))). 4.06/4.35 cnf(i_0_1493, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X2)),c_List_Olists(X1,hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X2,X3)))). 4.06/4.35 cnf(i_0_4697, plain, (hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),c_Relation_OImage(X1,X1,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3)=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X2))). 4.06/4.35 cnf(i_0_5282, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Nitpick_OFrac)). 4.06/4.35 cnf(i_0_3327, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X3),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X4)),tc_fun(X2,X3),X1),hAPP(c_COMBB(tc_prod(X1,X4),X3,X2),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X4),tc_fun(X2,tc_prod(X1,X4))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X1,X4)),tc_fun(tc_fun(X2,X4),tc_fun(X2,tc_prod(X1,X4))),X1),c_COMBB(X4,tc_prod(X1,X4),X2)),c_Product__Type_OPair(X1,X4))),X6)))),hAPP(hAPP(c_List_Ozip(X1,X2),X7),X8))=hAPP(hAPP(c_List_Omap(tc_prod(X1,X4),X3),X5),hAPP(hAPP(c_List_Ozip(X1,X4),X7),hAPP(hAPP(c_List_Omap(X2,X4),X6),X8))))). 4.06/4.35 cnf(i_0_2633, plain, (hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),X3))),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1)),c_member(X2))),X4)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4))). 4.06/4.35 cnf(i_0_368, plain, (c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))). 4.06/4.35 cnf(i_0_1147, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X2,X1)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X2,X1),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X2,X1)))),hAPP(c_COMBC(X2,X1,tc_prod(X2,X1)),c_Product__Type_OPair(X2,X1))))),X3))=hAPP(c_Relation_Oconverse(X2,X1),X3))). 4.06/4.35 cnf(i_0_7463, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X1)))=c_Wellfounded_Ofinite__psubset(X1))). 4.06/4.35 cnf(i_0_2531, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X1,X3,X4),X5))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X1,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,X1),tc_Int_Oint),X4),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Int_Oint),c_Nat_Onat_Onat__rec(X1,X3,X4)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X5)))))=hAPP(c_Nat_Onat_Onat__rec(X1,X3,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X5)))). 4.06/4.35 cnf(i_0_124, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X4,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X4,tc_fun(X2,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool))),X6))),X7)))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),X5),X7)))). 4.06/4.35 cnf(i_0_3300, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X4,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),tc_fun(tc_fun(X4,tc_fun(X2,tc_HOL_Obool)),tc_fun(X4,tc_fun(X2,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X6))),X7)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),X5),X7)))). 4.06/4.35 cnf(i_0_5278, plain, (hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X1,X2)),X2,c_List_Olist_ONil(tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2)))),X2),c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(X2))),hAPP(hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),X2),c_List_Olist_OCons(tc_prod(X1,X2))),hAPP(c_Product__Type_OPair(X1,X2),X3)))),hAPP(c_List_Ozip(X1,X2),X4))),X5)=hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)),X5))). 4.06/4.35 cnf(i_0_7086, plain, (hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X1),X2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))=hAPP(c_List_Oset(X1),X2))). 4.06/4.35 cnf(i_0_1503, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_List_Olist(X3),hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X3),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X3)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X3)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_List_Orev(tc_List_Olist(X3)),hAPP(c_List_Ofilter(tc_List_Olist(X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X3),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X3)))),X4)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3))),c_List_Otranspose(X3,X4))))). 4.06/4.35 cnf(i_0_1843, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X1,X2),tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X6))),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,tc_fun(X4,tc_HOL_Obool))),tc_fun(X2,tc_fun(tc_prod(X3,X4),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_fun(X3,tc_fun(X4,tc_HOL_Obool))),tc_fun(X2,tc_fun(tc_prod(X3,X4),tc_HOL_Obool))),X1),c_COMBB(tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_prod(X3,X4),tc_HOL_Obool),X2)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),tc_fun(tc_prod(X3,X4),tc_HOL_Obool)),X1),c_Product__Type_OSigma(X3,X4)),X7))),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(X3,tc_fun(X4,tc_HOL_Obool)),X2),c_COMBK(tc_fun(X4,tc_HOL_Obool),X3)),X8))))=hAPP(hAPP(c_Product__Type_OSigma(X3,X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X3,tc_HOL_Obool)),X5),X7)),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X4,tc_HOL_Obool)),X6),X8))))). 4.06/4.35 cnf(i_0_6376, plain, (hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X1,X2)),X1,c_List_Olist_ONil(tc_prod(X1,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2))),tc_fun(tc_List_Olist(X1),tc_List_Olist(tc_prod(X1,X2)))),X1),c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_List_Olist(tc_prod(X1,X2)),tc_List_Olist(tc_prod(X1,X2))),X1),c_List_Olist_OCons(tc_prod(X1,X2))),hAPP(hAPP(c_COMBC(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)),X3)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X2),tc_List_Olist(tc_prod(X1,X2))),c_List_Ozip(X1,X2)),X4))),X5)=hAPP(hAPP(c_List_Ozip(X1,X2),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)))). 4.06/4.35 cnf(i_0_5172, plain, (c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBC(X1,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),X1),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X1),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),X1),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)=hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),X3))). 4.06/4.35 cnf(i_0_4566, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),c_List_Ohd(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1)))),X3)))),c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),X4),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Otl(X1)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1)))),X3)))))=c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),X3)))). 4.06/4.35 cnf(i_0_4730, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X2)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X2,X2),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X2,X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X2),tc_fun(X1,tc_prod(X2,X2))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X2,X2)),tc_fun(tc_fun(X1,X2),tc_fun(X1,tc_prod(X2,X2))),X1),c_COMBB(X2,tc_prod(X2,X2),X1)),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_prod(X2,X2)),X1),c_Product__Type_OPair(X2,X2)),X3))),X3)))),X4))=hAPP(hAPP(c_Relation_Oinv__image(X2,X1),X4),X3))). 4.06/4.35 cnf(i_0_5983, plain, (hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X1),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X1),X2))))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),X3)))=hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3)))). 4.06/4.35 cnf(i_0_1468, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X1),c_Nitpick_Oint__lcm(hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2)),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X3)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X1),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X1),tc_Int_Oint),c_Nitpick_Ofrac(X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X2)))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X3)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),X3))))))),c_COMBI(tc_Int_Oint)))=c_Nitpick_Oplus__frac(X1,X2,X3))). 4.06/4.35 cnf(i_0_4159, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3)),X1)))=hAPP(c_Divides_Oadjust(X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X1)))). 4.06/4.35 cnf(i_0_6781, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,X1))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2)))))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),X2)))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))))=c_Divides_Odivmod__int__rel(X1,X2))). 4.06/4.35 cnf(i_0_5893, plain, (hAPP(c_List_Ofoldl(tc_fun(X1,tc_Option_Ooption(X2)),tc_prod(X1,X2),hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))))),X1),c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2))),X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_Option_Ooption(X2),tc_fun(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,tc_Option_Ooption(X2)))),X1),c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),X1,tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)))))),c_Option_Ooption_OSome(X2)))),X3),hAPP(c_List_Orev(tc_prod(X1,X2)),X4))=c_Map_Omap__add(X1,X2,X3,hAPP(c_Map_Omap__of(X1,X2),X4)))). 4.06/4.35 cnf(i_0_5461, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X4)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X2),c_Set_Oinsert(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4))). 4.06/4.35 cnf(i_0_6439, plain, (hAPP(c_List_Ofoldl(tc_fun(X1,tc_Option_Ooption(X2)),tc_prod(X1,X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(tc_prod(X1,X2),tc_fun(X1,tc_Option_Ooption(X2))),tc_fun(X1,tc_Option_Ooption(X2))),c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(X1,tc_Option_Ooption(X2)))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X1,tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(X1,tc_Option_Ooption(X2))),c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)))),tc_fun(X1,tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2))))),tc_fun(X1,tc_Option_Ooption(X2))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2))),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_fun(X1,tc_Option_Ooption(X2)))),X1),c_COMBB(tc_Option_Ooption(X2),tc_fun(X1,tc_Option_Ooption(X2)),X2))),c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2))))),c_Option_Ooption_OSome(X2))),X3),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))=c_Map_Omap__upds(X1,X2,X3,X4,X5))). 4.06/4.35 cnf(i_0_7272, plain, (hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X1,X2)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X1,X2)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(X1,X2)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(X1,X2),tc_fun(tc_Nat_Onat,tc_prod(X1,X2)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X1,X2)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X1,X2)),c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X2,tc_prod(X1,X2)),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_prod(X1,X2)),tc_Nat_Onat),c_Product__Type_OPair(X1,X2)),hAPP(c_List_Onth(X1),X3))),hAPP(c_List_Onth(X2),X4)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)))))=hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)))). 4.06/4.35 cnf(i_0_1437, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X1,tc_List_Olist(X1)),tc_prod(X1,tc_List_Olist(X1))),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),c_Product__Type_Omap__pair(tc_prod(X1,tc_List_Olist(X1)),tc_List_Olist(X1),tc_prod(X1,tc_List_Olist(X1)),tc_List_Olist(X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)))),c_Wellfounded_Olex__prod(X1,tc_List_Olist(X1),X2,hAPP(c_List_Olexn(X1,X2),X3)))),c_Nitpick_Oprod(tc_List_Olist(X1),tc_List_Olist(X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),hAPP(c_Nat_OSuc,X3)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),hAPP(c_Nat_OSuc,X3))))=hAPP(c_List_Olexn(X1,X2),hAPP(c_Nat_OSuc,X3)))). 4.06/4.35 cnf(i_0_4703, plain, (hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2)),c_Set_OPow(X1))))=hAPP(c_Set_OPow(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))). 4.06/4.35 cnf(i_0_2154, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_fun(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_List_Olist(X1)),hAPP(c_If(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(X2,X3)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_List_Olist(X1)),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(c_List_Olist_OCons(X1),X3))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),c_COMBB(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1))),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(c_List_Olist_OCons(X1),X3)))),c_List_Opartition(X1,X2,X4))=c_List_Opartition(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))). 4.06/4.35 cnf(i_0_1582, plain, (hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))). 4.06/4.35 cnf(i_0_4975, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),X1))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))=c_Divides_Oadjust(X1))). 4.06/4.35 cnf(i_0_6669, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X3))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBC(X3,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X1,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X3),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X1,X3)))),c_Product__Type_OPair(X1,X3)))),X4))))),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X3,X2)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X3,X2),tc_fun(tc_fun(tc_prod(X3,X2),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X3,X2)))),hAPP(c_COMBC(X3,X2,tc_prod(X3,X2)),c_Product__Type_OPair(X3,X2))))),X5))))=hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5))). 4.06/4.35 cnf(i_0_5959, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_COMBS(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),tc_fun(tc_fun(X2,X1),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool))),tc_fun(X2,X1)),c_Product__Type_OPair(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))),c_Relation_Oinv__image(X1,X2))))),c_Relation_Oinv__image(X1,X2)))=c_FunDef_Orp__inv__image(X1,X2))). 4.06/4.35 cnf(i_0_7492, plain, (hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X1)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_List_Olist(X1)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),c_COMBS(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),X1),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool))),tc_List_Olist(X1)),c_COMBB(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_List_Olist(X1),tc_HOL_Obool,tc_List_Olist(X1))),c_fequal))),c_List_Olist_OCons(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2))),X3))))=c_List_Oset__Cons(X1,X2,X3))). 4.06/4.35 cnf(i_0_6977, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X1),tc_Nat_Onat),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1))))),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),tc_List_Olist(X1)),c_COMBC(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X1)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))))),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1))))),c_List_Olex(X1,X2)))))=c_List_Olenlex(X1,X2))). 4.06/4.35 cnf(i_0_886, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))). 4.06/4.35 cnf(i_0_2478, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1))). 4.06/4.35 cnf(i_0_381, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))). 4.06/4.35 cnf(i_0_6253, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1))). 4.06/4.35 cnf(i_0_5978, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))). 4.06/4.35 cnf(i_0_347, plain, (c_Enum_Osublists(X1,c_List_Olist_ONil(X1))=hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(tc_List_Olist(X1))))). 4.06/4.35 cnf(i_0_4239, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=hAPP(c_fequal,X2))). 4.06/4.35 cnf(i_0_7083, plain, (hAPP(c_New__DSequence_Opos__union(X1,X2,X3),X4)=c_Lazy__Sequence_Oappend(X1,hAPP(X2,X4),hAPP(X3,X4)))). 4.06/4.35 cnf(i_0_4028, plain, (c_List_Oremove1(X1,X2,c_List_Oremove1(X1,X3,X4))=c_List_Oremove1(X1,X3,c_List_Oremove1(X1,X2,X4)))). 4.06/4.35 cnf(i_0_4520, plain, (c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool))=hAPP(c_List_Olexn(X1,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))). 4.06/4.35 cnf(i_0_618, 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))))). 4.06/4.35 cnf(i_0_392, plain, (c_Fun_Oid(tc_prod(X1,X2))=hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)))). 4.06/4.35 cnf(i_0_1847, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(c_List_Orev(X1),X3))=hAPP(c_List_Orev(X1),hAPP(c_List_Ofilter(X1,X2),X3)))). 4.06/4.35 cnf(i_0_6573, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))). 4.06/4.35 cnf(i_0_1286, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2))). 4.06/4.35 cnf(i_0_6846, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2))). 4.06/4.35 cnf(i_0_1679, plain, (hAPP(hAPP(X1,X2),hAPP(X3,X2))=hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),X1),X3),X2))). 4.06/4.35 cnf(i_0_5743, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(X1))=c_List_Opartition(X1,X2,c_List_Olist_ONil(X1)))). 4.06/4.35 cnf(i_0_5607, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X1))). 4.06/4.35 cnf(i_0_2952, plain, (hAPP(hAPP(X1,X2),hAPP(c_Nat_Onat_Onat__rec(X3,X4,X1),X2))=hAPP(c_Nat_Onat_Onat__rec(X3,X4,X1),hAPP(c_Nat_OSuc,X2)))). 4.06/4.35 cnf(i_0_4530, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))). 4.06/4.35 cnf(i_0_1787, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)))). 4.06/4.35 cnf(i_0_987, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Obutlast(X2,X4)))). 4.06/4.35 cnf(i_0_5720, plain, (c_Divides_Odivmod__int(X1,X2)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))). 4.06/4.35 cnf(i_0_3756, plain, (hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_List_Oset(X2),X4)))). 4.06/4.35 cnf(i_0_1919, 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)))). 4.06/4.35 cnf(i_0_5115, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))). 4.06/4.35 cnf(i_0_5447, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))=hAPP(c_List_Orotate1(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)))). 4.06/4.35 cnf(i_0_2038, 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)))). 4.06/4.35 cnf(i_0_7296, 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)))). 4.06/4.35 cnf(i_0_5207, plain, (hAPP(hAPP(c_List_Omap(X1,X2),hAPP(c_COMBK(X2,X1),X3)),X4)=c_List_Oreplicate(X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4),X3))). 4.06/4.35 cnf(i_0_1348, plain, (hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_3893, 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))). 4.06/4.35 cnf(i_0_225, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))=hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))). 4.06/4.35 cnf(i_0_109, plain, (hAPP(hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)),hAPP(c_Product__Type_Osnd(X2,X3),X4))=hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X5),X1),X4))). 4.06/4.35 cnf(i_0_3257, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X1,hAPP(X2,X3),c_Option_Ooption_OSome(X1)),hAPP(X4,X3))=hAPP(c_Map_Omap__add(X5,X1,X2,X4),X3))). 4.06/4.35 cnf(i_0_3183, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 4.06/4.35 cnf(i_0_3615, plain, (c_List_Olist_Olist__size(X1,hAPP(c_Fun_Ocomp(X2,tc_Nat_Onat,X1,X3),X4),X5)=c_List_Olist_Olist__size(X2,X3,hAPP(hAPP(c_List_Omap(X1,X2),X4),X5)))). 4.06/4.35 cnf(i_0_7380, plain, (c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X2))=c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X3,X1,X2)))). 4.06/4.35 cnf(i_0_7384, plain, (hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),hAPP(c_Nat_OSuc,X5))=hAPP(hAPP(X3,X4),hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),X5)))). 4.06/4.35 cnf(i_0_5738, plain, (hAPP(hAPP(c_Relation_Oinv__image(X1,X2),hAPP(c_Relation_Oconverse(X1,X1),X3)),X4)=hAPP(c_Relation_Oconverse(X2,X2),hAPP(hAPP(c_Relation_Oinv__image(X1,X2),X3),X4)))). 4.06/4.35 cnf(i_0_2380, 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_Enum_Oenum__the(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2)))). 4.06/4.35 cnf(i_0_755, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Otake(X1),X4),X5))=hAPP(hAPP(c_List_Otake(X2),X4),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)))). 4.06/4.35 cnf(i_0_2155, 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)))). 4.06/4.35 cnf(i_0_7303, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),X4)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),X4)))). 4.06/4.35 cnf(i_0_815, plain, (hAPP(c_List_Ofoldl(X1,X2,X3,X4),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X6))=hAPP(c_List_Ofoldl(X1,X2,X3,hAPP(hAPP(X3,X4),X5)),X6))). 4.06/4.35 cnf(i_0_1199, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X5))=hAPP(hAPP(c_Set_Oinsert(X2),hAPP(X3,X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)))). 4.06/4.35 cnf(i_0_6603, plain, (hAPP(c_Set_Oimage(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6)=hAPP(c_Set_Oimage(X3,X2,X4),hAPP(c_Set_Oimage(X1,X3,X5),X6)))). 4.06/4.35 cnf(i_0_5099, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(c_Fun_Ocomp(X4,X1,X2,X5),X6))=hAPP(hAPP(c_COMBB(X4,tc_HOL_Obool,X2),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X4),X3),X5)),X6))). 4.06/4.35 cnf(i_0_1765, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),hAPP(X2,X3)),hAPP(hAPP(c_List_Omap(X4,X1),X2),X5))=hAPP(hAPP(c_List_Omap(X4,X1),X2),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X5)))). 4.06/4.35 cnf(i_0_822, plain, (hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),X2)=hAPP(c_Set_OPow(X1),X2))). 4.06/4.35 cnf(i_0_3281, plain, (hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X1,X2))=hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X3,X1,X2)))). 4.06/4.35 cnf(i_0_318, 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))). 4.06/4.35 cnf(i_0_5823, plain, (hAPP(hAPP(c_Set_Oinsert(X1),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_Set_Oinsert(X1),X2),X4)))). 4.06/4.35 cnf(i_0_538, 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)))). 4.06/4.35 cnf(i_0_76, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Relation_OField(X1))=hAPP(c_Relation_OField(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2)))). 4.06/4.35 cnf(i_0_2337, 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)))). 4.06/4.35 cnf(i_0_453, plain, (hAPP(hAPP(c_Option_Omap(X1,X2),X3),hAPP(hAPP(c_Option_Omap(X4,X1),X5),X6))=hAPP(hAPP(c_Option_Omap(X4,X2),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)),X6))). 4.06/4.35 cnf(i_0_4419, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(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)))). 4.06/4.35 cnf(i_0_4598, 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)))). 4.06/4.35 cnf(i_0_3366, plain, (hAPP(c_Fun_Ocomp(X1,X2,X3,hAPP(c_Fun_Ocomp(X4,X2,X1,X5),X6)),X7)=hAPP(c_Fun_Ocomp(X4,X2,X3,X5),hAPP(c_Fun_Ocomp(X1,X4,X3,X6),X7)))). 4.06/4.35 cnf(i_0_3887, plain, (hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)),X5),hAPP(X3,X6))=hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(hAPP(c_List_Olist__update(X2,X4),X5),X6)))). 4.06/4.35 cnf(i_0_7336, plain, (hAPP(c_Relation_ORange(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3))=hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X1)),hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X3)))). 4.06/4.35 cnf(i_0_4188, plain, (hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X3,X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,X3)),hAPP(c_Nat_OSuc,hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),X4))))). 4.06/4.35 cnf(i_0_2483, plain, (c_List_Olist_Olist__size(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,X3)),hAPP(c_Nat_OSuc,c_List_Olist_Olist__size(X1,X2,X4))))). 4.06/4.35 cnf(i_0_7140, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),c_Relation_ORange(X1,X2))=hAPP(c_Relation_ORange(X1,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3)))). 4.06/4.35 cnf(i_0_1327, plain, (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))=hAPP(c_Relation_ODomain(X1,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3)))). 4.06/4.35 cnf(i_0_2984, plain, (hAPP(hAPP(c_List_Omap(X1,tc_prod(X1,X1)),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),c_COMBI(X1))),X2)=hAPP(hAPP(c_List_Ozip(X1,X1),X2),X2))). 4.06/4.35 cnf(i_0_7042, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2))=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)))). 4.06/4.35 cnf(i_0_3003, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.06/4.35 cnf(i_0_6015, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.06/4.35 cnf(i_0_181, plain, (c_Map_Orestrict__map(X1,X2,X3,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),c_Option_Ooption_ONone(X2)))). 4.06/4.35 cnf(i_0_1968, 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)))). 4.06/4.35 cnf(i_0_2761, plain, (hAPP(c_Fun_Ocomp(tc_prod(X1,X2),X2,tc_prod(X3,X4),c_Product__Type_Osnd(X1,X2)),c_Product__Type_Omap__pair(X3,X1,X4,X2,X5,X6))=hAPP(c_Fun_Ocomp(X4,X2,tc_prod(X3,X4),X6),c_Product__Type_Osnd(X3,X4)))). 4.06/4.35 cnf(i_0_1132, 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)))). 4.06/4.35 cnf(i_0_3063, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,hAPP(c_Fun_Ocomp(X2,tc_HOL_Obool,X1,X3),X4)),X5))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),hAPP(c_List_Ofilter(X2,X3),hAPP(hAPP(c_List_Omap(X1,X2),X4),X5))))). 4.06/4.35 cnf(i_0_3988, plain, (c_List_Otranspose(X1,hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_List_Olist(X1)),hAPP(c_List_Omap(X2,X1),X3)),X4))=hAPP(hAPP(c_List_Omap(tc_List_Olist(X2),tc_List_Olist(X1)),hAPP(c_List_Omap(X2,X1),X3)),c_List_Otranspose(X2,X4)))). 4.06/4.35 cnf(i_0_6865, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(X5,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X4),X5)))). 4.06/4.35 cnf(i_0_5609, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(c_Fun_Ocomp(X4,tc_fun(X2,X3),X1,X5),X6)),X7)=hAPP(hAPP(X5,hAPP(X6,hAPP(c_Product__Type_Ofst(X1,X2),X7))),hAPP(c_Product__Type_Osnd(X1,X2),X7)))). 4.06/4.35 cnf(i_0_4251, 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))). 4.06/4.35 cnf(i_0_4732, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X3)))). 4.06/4.35 cnf(i_0_1933, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6),hAPP(X4,X7))=hAPP(c_Fun_Ocomp(X3,X2,X1,X4),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X3),X5),X6),X7)))). 4.06/4.35 cnf(i_0_6938, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6))=hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X5)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X6)))). 4.06/4.35 cnf(i_0_4971, 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)))). 4.06/4.35 cnf(i_0_5264, plain, (c_Map_Odom(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),c_Option_Ooption_ONone(X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))). 4.06/4.35 cnf(i_0_3066, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X3)))). 4.06/4.35 cnf(i_0_769, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X1,X4),X5)),X6)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),X3),X6),X4)))). 4.06/4.35 cnf(i_0_5362, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(X4,tc_fun(X2,tc_HOL_Obool),X1),X5),X6))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X6),X3)),X5))). 4.06/4.35 cnf(i_0_2249, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),hAPP(hAPP(c_List_Omap(X3,X1),X4),X5))=hAPP(hAPP(c_List_Omap(X3,X1),X4),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X3),tc_List_Olist(X3)),X2),c_List_Orotate1(X3)),X5)))). 4.06/4.35 cnf(i_0_674, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),hAPP(c_Product__Type_Omap__pair(X5,X1,X3,X3,X6,c_Fun_Oid(X3)),X7))=hAPP(c_Product__Type_Omap__pair(X5,X2,X3,X3,hAPP(c_Fun_Ocomp(X1,X2,X5,X4),X6),c_Fun_Oid(X3)),X7))). 4.06/4.35 cnf(i_0_3950, plain, (hAPP(c_Product__Type_Omap__pair(X1,X1,X2,X3,c_Fun_Oid(X1),X4),hAPP(c_Product__Type_Omap__pair(X1,X1,X5,X2,c_Fun_Oid(X1),X6),X7))=hAPP(c_Product__Type_Omap__pair(X1,X1,X5,X3,c_Fun_Oid(X1),hAPP(c_Fun_Ocomp(X2,X3,X5,X4),X6)),X7))). 4.06/4.35 cnf(i_0_360, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))))). 4.06/4.35 cnf(i_0_5525, plain, (hAPP(c_Set_Oimage(X1,tc_List_Olist(X1),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))),X2)=c_List_Oset__Cons(X1,X2,hAPP(c_fequal,c_List_Olist_ONil(X1))))). 4.06/4.35 cnf(i_0_5355, 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))). 4.06/4.35 cnf(i_0_4542, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),X2))). 4.06/4.35 cnf(i_0_2266, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),hAPP(c_Product__Type_Omap__pair(X1,X1,X5,X3,c_Fun_Oid(X1),X6),X7))=hAPP(c_Product__Type_Omap__pair(X2,X2,X5,X3,c_Fun_Oid(X2),X6),hAPP(c_Product__Type_Omap__pair(X1,X2,X5,X5,X4,c_Fun_Oid(X5)),X7)))). 4.06/4.35 cnf(i_0_907, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),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_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))). 4.06/4.35 cnf(i_0_358, plain, (hAPP(hAPP(c_List_Olist__update(tc_prod(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)),X5),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X7))=hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Olist__update(X1,X3),X5),X6)),hAPP(hAPP(c_List_Olist__update(X2,X4),X5),X7)))). 4.06/4.35 cnf(i_0_6307, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),hAPP(c_Product__Type_Omap__pair(X1,X1,X5,X3,c_Fun_Oid(X1),X6),X7))=hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X5),X7))),hAPP(X6,hAPP(c_Product__Type_Osnd(X1,X5),X7))))). 4.06/4.35 cnf(i_0_6707, plain, (hAPP(c_Product__Type_Omap__pair(X1,X1,X2,X3,c_Fun_Oid(X1),X4),hAPP(c_Product__Type_Omap__pair(X5,X1,X2,X2,X6,c_Fun_Oid(X2)),X7))=hAPP(hAPP(c_Product__Type_OPair(X1,X3),hAPP(X6,hAPP(c_Product__Type_Ofst(X5,X2),X7))),hAPP(X4,hAPP(c_Product__Type_Osnd(X5,X2),X7))))). 4.06/4.35 cnf(i_0_621, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))),X1))). 4.06/4.35 cnf(i_0_1471, 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))))). 4.06/4.35 cnf(i_0_3558, plain, (c_Map_Orestrict__map(X1,X2,hAPP(c_Fun_Ocomp(X2,tc_Option_Ooption(X2),X1,c_Option_Ooption_OSome(X2)),X3),hAPP(c_List_Oset(X1),X4))=hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Omap(X1,tc_prod(X1,X2)),hAPP(hAPP(c_COMBS(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)),X3)),X4)))). 4.06/4.35 cnf(i_0_3555, plain, (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))=hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_List_Olist(X2)),hAPP(c_List_Omap(X1,X2),X3)),X4)))). 4.06/4.35 cnf(i_0_4816, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))))). 4.06/4.35 cnf(i_0_3901, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))))). 4.06/4.35 cnf(i_0_3810, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),hAPP(c_Fun_Ocomp(X3,tc_fun(X1,X1),X2,X4),X5)),X6),hAPP(c_List_Orev(X2),X7))=hAPP(c_List_Ofoldl(X1,X3,hAPP(c_COMBC(X3,X1,X1),X4),X6),hAPP(c_List_Orev(X3),hAPP(hAPP(c_List_Omap(X2,X3),X5),X7))))). 4.06/4.35 cnf(i_0_2118, 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))). 4.06/4.35 cnf(i_0_2246, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))=hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))))). 4.06/4.35 cnf(i_0_7120, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Oappend(X1),hAPP(X2,X3)),hAPP(hAPP(c_List_Omap(X4,tc_List_Olist(X1)),X2),X5))=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(X4,tc_List_Olist(X1)),X2),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X5))))). 4.06/4.35 cnf(i_0_5042, plain, (hAPP(hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3),hAPP(c_Product__Type_OPair(X1,X2),X4))=hAPP(c_Relation_OImage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))). 4.06/4.35 cnf(i_0_7563, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 4.06/4.35 cnf(i_0_844, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X1))). 4.06/4.35 cnf(i_0_2209, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,hAPP(c_Fun_Ocomp(X2,tc_HOL_Obool,X1,X4),X3),X5))),X5))=hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_OtakeWhile(X2,X4,hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)))),hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)))). 4.06/4.35 cnf(i_0_444, plain, (hAPP(c_Set_Oimage(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)))=hAPP(hAPP(c_Product__Type_OSigma(X3,X4),hAPP(c_Set_Oimage(X1,X3,X5),X7)),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),hAPP(c_Set_Oimage(X2,X4,X6),X8))))). 4.06/4.35 cnf(i_0_4089, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))))). 4.06/4.35 cnf(i_0_5894, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),tc_Option_Ooption(X2),X1,hAPP(c_Option_Omap(X3,X2),X4)),X5)),X6),hAPP(c_Option_Ooption_OSome(X2),hAPP(X4,X7)))=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),tc_Option_Ooption(X2),X1,hAPP(c_Option_Omap(X3,X2),X4)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X3)),X5),X6),hAPP(c_Option_Ooption_OSome(X3),X7))))). 4.06/4.35 cnf(i_0_3920, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Osublist(X1,X2,X3))=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)))). 4.06/4.35 cnf(i_0_5719, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,c_List_Otranspose(X1,X2)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1)))),X2)))). 4.06/4.35 cnf(i_0_1110, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X3))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))))). 4.06/4.35 cnf(i_0_2565, 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)))). 4.06/4.35 cnf(i_0_7053, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5))=hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5)))). 4.06/4.35 cnf(i_0_1722, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),X5)))). 4.06/4.35 cnf(i_0_79, 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)))). 4.06/4.35 cnf(i_0_5661, plain, (hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,X4),X5),hAPP(hAPP(c_COMBC(X2,tc_fun(X6,tc_fun(X7,X4)),tc_fun(X3,X4)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X6,X7)),tc_fun(tc_fun(X6,tc_fun(X7,X4)),tc_fun(X3,X4)),X2),c_Product__Type_Oscomp(X3,X6,X7,X4)),X8)),X9))=hAPP(hAPP(c_Product__Type_Oscomp(X1,X6,X7,X4),hAPP(hAPP(c_Product__Type_Oscomp(X1,X2,X3,tc_prod(X6,X7)),X5),X8)),X9))). 4.06/4.35 cnf(i_0_1639, 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)))). 4.06/4.35 cnf(i_0_3902, 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)))))). 4.06/4.35 cnf(i_0_3984, plain, (hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))=c_Nitpick_Oprod(X1,X2,X3,X4))). 4.06/4.35 cnf(i_0_5127, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),c_Set_OCollect(X2)),hAPP(c_COMBC(X2,X1,tc_HOL_Obool),X4)))=hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OAll(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fimplies),X3))),X4)))). 4.06/4.35 cnf(i_0_6192, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(c_Set_Oimage(X2,X1,X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5)))=hAPP(c_Set_Oimage(X2,X1,hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBS(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X5)),X3)),X6)),X4))). 4.06/4.35 cnf(i_0_2658, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X5)),X4))=c_Map_Odom(X1,X2,hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_Option_Ooption(X2)),hAPP(hAPP(c_COMBS(X1,tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_Option_Ooption(X2))),X1),c_If(tc_Option_Ooption(X2))),X4)),X3)),X5)))). 4.06/4.35 cnf(i_0_6667, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))). 4.06/4.35 cnf(i_0_1857, plain, (hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X3))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X4))))))). 4.06/4.35 cnf(i_0_1367, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2)))))). 4.06/4.35 cnf(i_0_7138, plain, (hAPP(c_Set_Oimage(X1,tc_prod(X2,X3),hAPP(hAPP(c_COMBS(X1,X3,tc_prod(X2,X3)),hAPP(hAPP(c_COMBB(X2,tc_fun(X3,tc_prod(X2,X3)),X1),c_Product__Type_OPair(X2,X3)),X4)),X5)),X6)=hAPP(hAPP(c_Product__Type_OSigma(X2,X3),hAPP(c_Set_Oimage(X1,X2,X4),X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X2),c_Set_Oimage(X1,X3,X5)),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),c_Set_Ovimage(X1,X2,X4)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),c_Set_Oinsert(X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))),X6))))). 4.06/4.35 cnf(i_0_4391, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X1,tc_Nat_Onat)),X2),c_Product__Type_Osnd(X1,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))))))=hAPP(hAPP(c_List_Omap(tc_prod(X1,tc_Nat_Onat),X1),c_Product__Type_Ofst(X1,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X1,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X1,tc_Nat_Onat)),X2),hAPP(hAPP(c_COMBC(tc_prod(X1,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(X1,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X1,tc_Nat_Onat))),X4))),hAPP(hAPP(c_List_Ozip(X1,tc_Nat_Onat),X3),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))))))). 4.06/4.35 cnf(i_0_6026, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_HOL_Obool,X1),c_Transitive__Closure_Ortrancl(X1,X2)),hAPP(hAPP(c_COMBC(X1,X1,tc_prod(X1,X1)),c_Product__Type_OPair(X1,X1)),X3))),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBB(tc_prod(X1,X1),tc_HOL_Obool,X1),c_Transitive__Closure_Ortrancl(X1,X2)),hAPP(c_Product__Type_OPair(X1,X1),X4)))))=hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))))). 4.06/4.35 cnf(i_0_3533, negated_conjecture, (~hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)))))). 4.06/4.35 cnf(i_0_7398, plain, (~hBOOL(c_fFalse))). 4.06/4.35 cnf(i_0_1791, plain, (esk136_0!=esk137_0)). 4.06/4.35 cnf(i_0_3608, plain, (esk274_1(X1)!=X1)). 4.06/4.35 cnf(i_0_3147, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.06/4.35 cnf(i_0_2651, plain, (hAPP(c_Nat_OSuc,X1)!=X1)). 4.06/4.35 cnf(i_0_1046, plain, (c_Int_OMin!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.06/4.35 cnf(i_0_1144, plain, (~c_List_Olist__ex1(X1,X2,c_List_Olist_ONil(X1)))). 4.06/4.35 cnf(i_0_5596, plain, (~c_List_Olist__ex(X1,X2,c_List_Olist_ONil(X1)))). 4.06/4.35 cnf(i_0_1341, plain, (hAPP(c_Nat_OSuc,X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.35 cnf(i_0_805, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.06/4.35 cnf(i_0_1215, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.35 cnf(i_0_388, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Int_OMin)))). 4.06/4.35 cnf(i_0_3764, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.35 cnf(i_0_3981, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Int_OMin)))). 4.06/4.35 cnf(i_0_2956, plain, (c_Com_Ocom_OBODY(X1)!=c_Com_Ocom_OWhile(X2,X3))). 4.06/4.35 cnf(i_0_3415, plain, (c_Com_Ocom_OSemi(X1,X2)!=c_Com_Ocom_OBODY(X3))). 4.06/4.35 cnf(i_0_864, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)))). 4.06/4.35 cnf(i_0_1511, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Int_OMin)))). 4.06/4.35 cnf(i_0_4630, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.35 cnf(i_0_5855, plain, (~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))). 4.06/4.35 cnf(i_0_2981, plain, (~c_Option_Ois__none(X1,hAPP(c_Option_Ooption_OSome(X1),X2)))). 4.06/4.35 cnf(i_0_3844, plain, (c_Com_Ocom_OSemi(X1,X2)!=c_Com_Ocom_OWhile(X3,X4))). 4.06/4.35 cnf(i_0_7250, plain, (c_Com_Ocom_OBODY(X1)!=c_Com_Ocom_OCond(X2,X3,X4))). 4.06/4.35 cnf(i_0_1739, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)))). 4.06/4.35 cnf(i_0_242, plain, (c_Com_Ocom_OBODY(X1)!=c_Com_Ocom_OCall(X2,X3,X4))). 4.06/4.35 cnf(i_0_2280, plain, (c_Com_Ocom_OBODY(X1)!=c_Com_Ocom_OLocal(X2,X3,X4))). 4.06/4.35 cnf(i_0_2467, plain, (c_Option_Ooption_ONone(X1)!=hAPP(c_Option_Ooption_OSome(X1),X2))). 4.06/4.35 cnf(i_0_6375, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=X3)). 4.06/4.35 cnf(i_0_5465, plain, (c_Com_Ocom_OWhile(X1,X2)!=c_Com_Ocom_OCall(X3,X4,X5))). 4.06/4.35 cnf(i_0_7295, plain, (c_Com_Ocom_OWhile(X1,X2)!=c_Com_Ocom_OLocal(X3,X4,X5))). 4.06/4.35 cnf(i_0_1957, plain, (c_Com_Ocom_OSemi(X1,X2)!=c_Com_Ocom_OCond(X3,X4,X5))). 4.06/4.35 cnf(i_0_5699, plain, (c_Com_Ocom_OSemi(X1,X2)!=c_Com_Ocom_OCall(X3,X4,X5))). 4.06/4.35 cnf(i_0_6082, plain, (c_Com_Ocom_OSemi(X1,X2)!=c_Com_Ocom_OLocal(X3,X4,X5))). 4.06/4.35 cnf(i_0_173, plain, (c_Com_Ocom_OCond(X1,X2,X3)!=c_Com_Ocom_OWhile(X4,X5))). 4.06/4.35 cnf(i_0_3398, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.06/4.35 cnf(i_0_2875, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)!=c_List_Olist_ONil(X1))). 4.06/4.35 cnf(i_0_2122, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 4.06/4.35 cnf(i_0_4083, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_6681, plain, (c_Com_Ocom_OCall(X1,X2,X3)!=c_Com_Ocom_OCond(X4,X5,X6))). 4.06/4.35 cnf(i_0_843, plain, (c_Com_Ocom_OLocal(X1,X2,X3)!=c_Com_Ocom_OCond(X4,X5,X6))). 4.06/4.35 cnf(i_0_4521, plain, (c_Com_Ocom_OLocal(X1,X2,X3)!=c_Com_Ocom_OCall(X4,X5,X6))). 4.06/4.35 cnf(i_0_1932, plain, (hAPP(c_Set_OPow(X1),X2)!=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_6838, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1)))). 4.06/4.35 cnf(i_0_3524, plain, (~c_Wellfounded_Omax__extp(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.06/4.35 cnf(i_0_4186, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_4926, plain, (~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))). 4.06/4.35 cnf(i_0_4968, plain, (~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))). 4.06/4.35 cnf(i_0_1358, plain, (~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)))). 4.06/4.35 cnf(i_0_3016, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))). 4.06/4.35 cnf(i_0_5987, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.35 cnf(i_0_827, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)))). 4.06/4.35 cnf(i_0_3785, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)))). 4.06/4.35 cnf(i_0_3180, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)))). 4.06/4.35 cnf(i_0_630, plain, (~hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)))). 4.06/4.35 cnf(i_0_5098, plain, (~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))))). 4.06/4.35 cnf(i_0_976, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)))). 4.06/4.35 cnf(i_0_1007, plain, (hAPP(c_Set_OPow(X1),X2)!=hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),X3),X2))). 4.06/4.35 cnf(i_0_745, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))). 4.06/4.35 cnf(i_0_3932, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))). 4.06/4.35 cnf(i_0_5616, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))!=c_List_Olist_ONil(X1))). 4.06/4.35 cnf(i_0_3872, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))))). 4.06/4.35 cnf(i_0_4642, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X1))))))). 4.06/4.35 cnf(i_0_3113, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5))!=hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2)))). 4.06/4.35 cnf(i_0_4896, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.06/4.35 cnf(i_0_6514, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.35 cnf(i_0_7122, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))). 4.06/4.35 cnf(i_0_5964, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,c_List_Olist_ONil(tc_fun(X1,tc_Nat_Onat))))))). 4.06/4.35 cnf(i_0_2447, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olexord(X1,X3))))). 4.06/4.35 cnf(i_0_3900, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olex(X1,X3))))). 4.06/4.35 cnf(i_0_1841, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olistrel1(X1,X3))))). 4.06/4.35 cnf(i_0_677, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olex(X1,X3))))). 4.06/4.35 cnf(i_0_7477, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olistrel1(X1,X3))))). 4.06/4.35 cnf(i_0_4024, plain, (~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot)),c_fequal)),X2),X2)))). 4.06/4.35 cnf(i_0_4823, plain, (~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Wellfounded_Omax__ext(X1,X3))))). 4.06/4.35 cnf(i_0_1673, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)!=c_Int_OMin)). 4.06/4.35 cnf(i_0_857, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))). 4.06/4.35 cnf(i_0_5714, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))). 4.06/4.35 cnf(i_0_1901, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))). 4.06/4.35 cnf(i_0_5210, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))). 4.06/4.35 cnf(i_0_5244, plain, (~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))))). 4.06/4.35 cnf(i_0_6332, plain, (~hBOOL(hAPP(c_fNot,X1))|~hBOOL(X1))). 4.06/4.35 cnf(i_0_595, plain, (c_Groups_Oone__class_Oone(X1)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ozero__neq__one(X1))). 4.06/4.35 cnf(i_0_199, plain, (~c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1))|~class_Rings_Osemiring__1(X1))). 4.06/4.35 cnf(i_0_3727, plain, (hBOOL(X1)|~hBOOL(hAPP(hAPP(c_fconj,X2),X1)))). 4.06/4.35 cnf(i_0_4377, plain, (hBOOL(X1)|~hBOOL(hAPP(hAPP(c_fconj,X1),X2)))). 4.06/4.35 cnf(i_0_6461, plain, (hBOOL(hAPP(c_fNot,X1))|hBOOL(X1))). 4.06/4.35 cnf(i_0_4738, plain, (c_HOL_Oequal__class_Oequal(X1)=c_fequal|~class_HOL_Oequal(X1))). 4.06/4.35 cnf(i_0_511, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X2,X1))))). 4.06/4.35 cnf(i_0_863, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X2,X1))))). 4.06/4.35 cnf(i_0_1142, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Nitpick_Owf_H(X1,X2))). 4.06/4.35 cnf(i_0_862, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X1,X2))))). 4.06/4.35 cnf(i_0_1051, plain, (X1=X2|c_Com_Ocom_OBODY(X1)!=c_Com_Ocom_OBODY(X2))). 4.06/4.35 cnf(i_0_6877, plain, (hBOOL(X1)|~hBOOL(hAPP(hAPP(c_fimplies,X2),X1))|~hBOOL(X2))). 4.06/4.35 cnf(i_0_4072, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_fequal,X1),X2)))). 4.06/4.35 cnf(i_0_4062, plain, (class_Enum_Oenum(tc_Option_Ooption(X1))|~class_Enum_Oenum(X1))). 4.06/4.35 cnf(i_0_3278, plain, (class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X1))|~class_Lazy__Sequence_Osmall__lazy(X1))). 4.06/4.35 cnf(i_0_3723, plain, (hBOOL(hAPP(c_Com_OWT,X1))|hAPP(c_Com_Obody,X2)!=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1))). 4.06/4.35 cnf(i_0_1077, plain, (class_Finite__Set_Ofinite(tc_Option_Ooption(X1))|~class_Finite__Set_Ofinite(X1))). 4.06/4.35 cnf(i_0_4124, plain, (c_Option_Ooption_ONone(X1)=X2|~c_Option_Ois__none(X1,X2))). 4.06/4.35 cnf(i_0_7570, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Wellfounded_Owf(X1,X2))). 4.06/4.35 cnf(i_0_3059, plain, (hBOOL(X1)|hBOOL(X2)|~hBOOL(hAPP(hAPP(c_fdisj,X2),X1)))). 4.06/4.35 cnf(i_0_1318, plain, (c_List_Onat__list(X1)|~c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X1)))). 4.06/4.35 cnf(i_0_2853, plain, (~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin))|~class_Int_Onumber__ring(X1))). 4.06/4.35 cnf(i_0_2192, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X2,X3,X1))))). 4.06/4.35 cnf(i_0_4252, plain, (c_Orderings_Oord__class_Omax(X1)=c_Lattices_Osemilattice__sup__class_Osup(X1)|~class_Lattices_Osemilattice__sup(X1)|~class_Orderings_Olinorder(X1))). 4.06/4.35 cnf(i_0_6182, plain, (c_Orderings_Oord__class_Omin(X1)=c_Lattices_Osemilattice__inf__class_Oinf(X1)|~class_Lattices_Osemilattice__inf(X1)|~class_Orderings_Olinorder(X1))). 4.06/4.35 cnf(i_0_5091, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X3,X1))))). 4.06/4.35 cnf(i_0_5092, plain, (hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X1,X3))))). 4.06/4.35 cnf(i_0_3884, plain, (X1=X2|~c_List_Olist__all2(X3,X3,c_fequal,X1,X2))). 4.06/4.35 cnf(i_0_2946, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|~c_Int_Oiszero(X1,X2)|~class_Rings_Osemiring__1(X1))). 4.06/4.35 cnf(i_0_1368, plain, (hBOOL(hAPP(hAPP(c_fimplies,X1),X2))|~hBOOL(X2))). 4.06/4.35 cnf(i_0_6538, plain, (hBOOL(hAPP(hAPP(c_fdisj,X1),X2))|~hBOOL(X2))). 4.06/4.35 cnf(i_0_7461, plain, (hBOOL(hAPP(hAPP(c_fdisj,X1),X2))|~hBOOL(X1))). 4.06/4.35 cnf(i_0_5040, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.06/4.35 cnf(i_0_2814, plain, (c_Option_Ooption_ONone(tc_Com_Ocom)=hAPP(c_Com_Obody,X1)|hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X1))))). 4.06/4.35 cnf(i_0_3725, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X1,X2)))|~hBOOL(hAPP(c_Com_OWT,X2)))). 4.06/4.35 cnf(i_0_6107, plain, (X1=X2|hAPP(c_Nat_OSuc,X1)!=hAPP(c_Nat_OSuc,X2))). 4.06/4.35 cnf(i_0_3426, plain, (X1=c_List_Olist_ONil(X2)|c_List_Oremdups(X2,X1)!=c_List_Olist_ONil(X2))). 4.06/4.35 cnf(i_0_5659, plain, (X1=X2|c_Com_Ocom_OWhile(X3,X2)!=c_Com_Ocom_OWhile(X4,X1))). 4.06/4.35 cnf(i_0_4382, plain, (X1=X2|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2))). 4.06/4.35 cnf(i_0_366, plain, (X1=X2|hAPP(c_Code__Numeral_Onat__of,X1)!=hAPP(c_Code__Numeral_Onat__of,X2))). 4.06/4.35 cnf(i_0_5658, plain, (X1=X2|c_Com_Ocom_OWhile(X1,X3)!=c_Com_Ocom_OWhile(X2,X4))). 4.06/4.35 cnf(i_0_1875, plain, (X1=X2|c_Com_Ocom_OSemi(X3,X2)!=c_Com_Ocom_OSemi(X4,X1))). 4.06/4.35 cnf(i_0_1874, plain, (X1=X2|c_Com_Ocom_OSemi(X1,X3)!=c_Com_Ocom_OSemi(X2,X4))). 4.06/4.35 cnf(i_0_2137, plain, (X1=X2|hAPP(c_Int_ORep__Integ,X1)!=hAPP(c_Int_ORep__Integ,X2))). 4.06/4.35 cnf(i_0_1798, plain, (hBOOL(hAPP(hAPP(c_fimplies,X1),X2))|hBOOL(X1))). 4.06/4.35 cnf(i_0_1319, plain, (c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X1))|~c_List_Onat__list(X1))). 4.06/4.35 cnf(i_0_2947, plain, (c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))|~class_Rings_Osemiring__1(X1))). 4.06/4.35 cnf(i_0_4957, plain, (~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)))). 4.06/4.35 cnf(i_0_2825, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))|~class_Orderings_Olinorder(X1))). 4.06/4.35 cnf(i_0_5688, plain, (class_Lattices_Olattice(tc_fun(X1,X2))|~class_Lattices_Olattice(X2))). 4.06/4.35 cnf(i_0_3323, plain, (class_Lattices_Osemilattice__sup(tc_fun(X1,X2))|~class_Lattices_Olattice(X2))). 4.06/4.35 cnf(i_0_2487, plain, (class_Orderings_Oord(tc_fun(X1,X2))|~class_Orderings_Oord(X2))). 4.06/4.35 cnf(i_0_5326, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1))). 4.06/4.35 cnf(i_0_5469, plain, (class_Lattices_Osemilattice__inf(tc_fun(X1,X2))|~class_Lattices_Olattice(X2))). 4.06/4.35 cnf(i_0_6985, plain, (class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,X2))|~class_Complete__Lattice_Ocomplete__lattice(X2))). 4.06/4.35 cnf(i_0_3206, plain, (class_Orderings_Oorder(tc_fun(X1,X2))|~class_Orderings_Oorder(X2))). 4.06/4.35 cnf(i_0_2159, plain, (class_Orderings_Opreorder(tc_fun(X1,X2))|~class_Orderings_Opreorder(X2))). 4.06/4.35 cnf(i_0_2917, plain, (class_Orderings_Otop(tc_fun(X1,X2))|~class_Orderings_Otop(X2))). 4.06/4.35 cnf(i_0_3342, plain, (class_Lattices_Oboolean__algebra(tc_fun(X1,X2))|~class_Lattices_Oboolean__algebra(X2))). 4.06/4.35 cnf(i_0_1827, plain, (class_Groups_Ominus(tc_fun(X1,X2))|~class_Groups_Ominus(X2))). 4.06/4.35 cnf(i_0_4370, plain, (class_Lattices_Obounded__lattice(tc_fun(X1,X2))|~class_Lattices_Obounded__lattice(X2))). 4.06/4.35 cnf(i_0_2863, plain, (class_Lattices_Obounded__lattice__top(tc_fun(X1,X2))|~class_Lattices_Obounded__lattice(X2))). 4.06/4.35 cnf(i_0_4811, plain, (class_Groups_Ouminus(tc_fun(X1,X2))|~class_Groups_Ouminus(X2))). 4.06/4.35 cnf(i_0_5198, plain, (class_Lattices_Odistrib__lattice(tc_fun(X1,X2))|~class_Lattices_Odistrib__lattice(X2))). 4.06/4.35 cnf(i_0_7213, plain, (class_Orderings_Obot(tc_fun(X1,X2))|~class_Orderings_Obot(X2))). 4.06/4.35 cnf(i_0_7385, plain, (hBOOL(hAPP(hAPP(c_fconj,X1),X2))|~hBOOL(X2)|~hBOOL(X1))). 4.06/4.35 cnf(i_0_7123, plain, (class_Lattices_Obounded__lattice__bot(tc_fun(X1,X2))|~class_Lattices_Obounded__lattice(X2))). 4.06/4.35 cnf(i_0_2841, plain, (c_Wellfounded_Owf(X1,X2)|esk211_2(X2,X1)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_1168, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),X1)))). 4.06/4.35 cnf(i_0_6569, plain, (c_Nat__Transfer_Ois__nat(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.35 cnf(i_0_2849, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X1)))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X2,X1,X3))))). 4.06/4.35 cnf(i_0_1140, plain, (c_Nitpick_Owf_H(X1,X2)|~c_Nitpick_Ounknown(tc_HOL_Obool)|~c_Wellfounded_Oacyclic(X1,X2))). 4.06/4.35 cnf(i_0_3379, plain, (c_List_Olist_ONil(X1)=X2|hAPP(c_List_Orev(X1),X2)!=c_List_Olist_ONil(X1))). 4.06/4.35 cnf(i_0_489, plain, (c_List_Olist_ONil(X1)=X2|hAPP(c_List_Orotate1(X1),X2)!=c_List_Olist_ONil(X1))). 4.06/4.35 cnf(i_0_861, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X1,X2)))|~hBOOL(hAPP(c_Com_OWT,X1))|~hBOOL(hAPP(c_Com_OWT,X2)))). 4.06/4.35 cnf(i_0_2615, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|c_List_Oremdups(X1,X2)!=X2)). 4.06/4.35 cnf(i_0_2797, plain, (X1=c_Option_Ooption_ONone(X2)|c_Option_Oset(X2,X1)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.35 cnf(i_0_182, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|c_Groups_Osgn__class_Osgn(X2,X1)!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2))). 4.06/4.35 cnf(i_0_1678, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Oreplicate(X2,X1,X3)!=c_List_Olist_ONil(X2))). 4.06/4.35 cnf(i_0_1060, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X1)))|hAPP(c_Com_Obody,X1)!=hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X2))). 4.06/4.35 cnf(i_0_2265, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~class_Finite__Set_Ofinite(X1))). 4.06/4.35 cnf(i_0_1115, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.35 cnf(i_0_3599, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)))). 4.06/4.35 cnf(i_0_2413, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X5)!=c_List_Olist_ONil(X1)|~class_Orderings_Olinorder(X2))). 4.06/4.35 cnf(i_0_1208, plain, (class_Enum_Oenum(tc_fun(X1,X2))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2))). 4.06/4.35 cnf(i_0_4444, plain, (class_Enum_Oenum(tc_prod(X1,X2))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2))). 4.06/4.35 cnf(i_0_5610, plain, (class_Enum_Oenum(tc_sum(X1,X2))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2))). 4.06/4.35 cnf(i_0_2914, plain, (class_Lazy__Sequence_Osmall__lazy(tc_prod(X1,X2))|~class_Lazy__Sequence_Osmall__lazy(X2)|~class_Lazy__Sequence_Osmall__lazy(X1))). 4.06/4.35 cnf(i_0_2835, plain, (c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X1,X2))|~c_Nat__Transfer_Ois__nat(X2)|~c_Nat__Transfer_Ois__nat(X1))). 4.06/4.35 cnf(i_0_6482, plain, (class_Finite__Set_Ofinite(tc_fun(X1,X2))|~class_Finite__Set_Ofinite(X1)|~class_Finite__Set_Ofinite(X2))). 4.06/4.35 cnf(i_0_2933, plain, (class_Finite__Set_Ofinite(tc_prod(X1,X2))|~class_Finite__Set_Ofinite(X1)|~class_Finite__Set_Ofinite(X2))). 4.06/4.35 cnf(i_0_4320, plain, (class_Finite__Set_Ofinite(tc_sum(X1,X2))|~class_Finite__Set_Ofinite(X1)|~class_Finite__Set_Ofinite(X2))). 4.06/4.35 cnf(i_0_3108, plain, (class_HOL_Oequal(tc_fun(X1,X2))|~class_HOL_Oequal(X2)|~class_Enum_Oenum(X1))). 4.06/4.35 cnf(i_0_2561, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.06/4.35 cnf(i_0_6570, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~c_Nat__Transfer_Ois__nat(X1))). 4.06/4.35 cnf(i_0_2402, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X1,X2,X3)))|~hBOOL(hAPP(c_Com_OWT,X3)))). 4.06/4.35 cnf(i_0_5883, plain, (class_Smallcheck_Osmall(tc_prod(X1,X2))|~class_Smallcheck_Osmall(X1)|~class_Smallcheck_Osmall(X2))). 4.06/4.35 cnf(i_0_1782, plain, (~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)))). 4.06/4.35 cnf(i_0_5280, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2))))). 4.06/4.35 cnf(i_0_470, plain, (~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)))). 4.06/4.35 cnf(i_0_7235, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Osemiring__1(X1))). 4.06/4.35 cnf(i_0_2313, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1(X1))). 4.06/4.35 cnf(i_0_4788, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__1(X1))). 4.06/4.35 cnf(i_0_6971, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Osemiring__1(X1))). 4.06/4.35 cnf(i_0_1061, plain, (hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk94_1(X1))=hAPP(c_Com_Obody,X1)|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X1))))). 4.06/4.35 cnf(i_0_3220, plain, (hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),esk244_1(X1))=hAPP(c_Com_Obody,X1)|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X1))))). 4.06/4.35 cnf(i_0_1116, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.06/4.35 cnf(i_0_5365, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,esk385_2(X2,X1)))))). 4.06/4.35 cnf(i_0_7373, plain, (c_List_Oremdups(X1,X2)=X2|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.06/4.35 cnf(i_0_2682, plain, (X1=X2|c_Com_Ocom_OCond(X3,X4,X1)!=c_Com_Ocom_OCond(X5,X6,X2))). 4.06/4.35 cnf(i_0_2683, plain, (X1=X2|c_Com_Ocom_OCond(X3,X2,X4)!=c_Com_Ocom_OCond(X5,X1,X6))). 4.06/4.35 cnf(i_0_2681, plain, (X1=X2|c_Com_Ocom_OCond(X1,X3,X4)!=c_Com_Ocom_OCond(X2,X5,X6))). 4.06/4.35 cnf(i_0_2974, plain, (X1=X2|c_Com_Ocom_OCall(X3,X4,X2)!=c_Com_Ocom_OCall(X5,X6,X1))). 4.06/4.35 cnf(i_0_6226, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|esk444_1(X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.35 cnf(i_0_1581, plain, (c_Orderings_Oord_Omin(X1,c_Orderings_Oord__class_Oless__eq(X1))=c_Orderings_Oord__class_Omin(X1)|~class_Orderings_Oord(X1))). 4.06/4.35 cnf(i_0_2973, plain, (X1=X2|c_Com_Ocom_OCall(X3,X2,X4)!=c_Com_Ocom_OCall(X5,X1,X6))). 4.06/4.35 cnf(i_0_2975, plain, (X1=X2|c_Com_Ocom_OCall(X1,X3,X4)!=c_Com_Ocom_OCall(X2,X5,X6))). 4.06/4.35 cnf(i_0_2188, plain, (X1=X2|c_List_Oreplicate(X3,X1,X4)!=c_List_Oreplicate(X3,X2,X5))). 4.06/4.35 cnf(i_0_357, plain, (X1=X2|c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X1)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X5,X2))). 4.06/4.35 cnf(i_0_2339, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_Enum_Oenum__class_Oenum(X1)))|~class_Enum_Oenum(X1))). 4.06/4.35 cnf(i_0_7217, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)!=X2)). 4.06/4.35 cnf(i_0_4752, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Oappend(X2),X1),X3)!=X3)). 4.06/4.35 cnf(i_0_4557, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Oappend(X2),X3),X1)!=X3)). 4.06/4.35 cnf(i_0_55, plain, (c_Orderings_Oord_Omax(X1,c_Orderings_Oord__class_Oless__eq(X1))=c_Orderings_Oord__class_Omax(X1)|~class_Orderings_Oord(X1))). 4.06/4.36 cnf(i_0_356, plain, (X1=X2|c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X1,X4)!=c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X2,X5))). 4.06/4.36 cnf(i_0_1313, plain, (X1=X2|c_Com_Ocom_OLocal(X3,X4,X2)!=c_Com_Ocom_OLocal(X5,X6,X1))). 4.06/4.36 cnf(i_0_1312, plain, (X1=X2|c_Com_Ocom_OLocal(X3,X1,X4)!=c_Com_Ocom_OLocal(X5,X2,X6))). 4.06/4.36 cnf(i_0_1311, plain, (X1=X2|c_Com_Ocom_OLocal(X1,X3,X4)!=c_Com_Ocom_OLocal(X2,X5,X6))). 4.06/4.36 cnf(i_0_3550, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Osgn__if(X1))). 4.06/4.36 cnf(i_0_807, plain, (c_Relation_Osingle__valued(X1,X2,X3)|esk80_3(X3,X2,X1)!=esk79_3(X3,X2,X1))). 4.06/4.36 cnf(i_0_5724, plain, (c_Relation_Ototal__on(X1,X2,X3)|esk417_3(X3,X2,X1)!=esk416_3(X3,X2,X1))). 4.06/4.36 cnf(i_0_1607, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1))|~class_Lattices_Osemilattice__sup(X1))). 4.06/4.36 cnf(i_0_5562, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Orderings_Oord__class_Omax(X1))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_571, plain, (hBOOL(hAPP(X1,X2))|~class_Enum_Oenum(X3)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X3),X1)))). 4.06/4.36 cnf(i_0_1872, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Groups_Otimes__class_Otimes(X1))|~class_Lattices_Oab__semigroup__idem__mult(X1))). 4.06/4.36 cnf(i_0_3688, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1))|~class_Lattices_Osemilattice__inf(X1))). 4.06/4.36 cnf(i_0_255, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X1,c_Orderings_Oord__class_Omin(X1))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_7186, plain, (c_Finite__Set_Ofun__left__comm(X1,X1,c_Groups_Otimes__class_Otimes(X1))|~class_Groups_Oab__semigroup__mult(X1))). 4.06/4.36 cnf(i_0_6891, plain, (c_List_Olist_ONil(X1)=X2|~c_List_Olist__all2(X1,X3,X4,X2,c_List_Olist_ONil(X3)))). 4.06/4.36 cnf(i_0_4040, plain, (c_List_Olist_ONil(X1)=X2|~c_List_Olist__all2(X3,X1,X4,c_List_Olist_ONil(X3),X2))). 4.06/4.36 cnf(i_0_1003, plain, (c_List_Otranspose(X1,X2)=c_List_Olist_ONil(tc_List_Olist(X1))|esk91_2(X2,X1)!=c_List_Olist_ONil(X1))). 4.06/4.36 cnf(i_0_1169, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(X3,X2)))). 4.06/4.36 cnf(i_0_2878, plain, (hBOOL(hAPP(hAPP(X1,X2),X2))|~c_Equiv__Relations_Oequivp(X3,X1))). 4.06/4.36 cnf(i_0_4448, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_List_Oset(X2),X1)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.36 cnf(i_0_3527, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Wellfounded_Omax__extp(X1,X3,X4,X2))). 4.06/4.36 cnf(i_0_536, plain, (hBOOL(hAPP(hAPP(X1,X2),X2))|~c_Predicate_Oreflp(X3,X1))). 4.06/4.36 cnf(i_0_4684, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(X1,X2,X3)))|~hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X2))))). 4.06/4.36 cnf(i_0_522, plain, (X1=X2|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))). 4.06/4.36 cnf(i_0_3523, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Wellfounded_Omax__extp(X1,X3,X2,X4))). 4.06/4.36 cnf(i_0_363, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)!=X2|~class_Groups_Olinordered__ab__group__add(X1))). 4.06/4.36 cnf(i_0_943, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.36 cnf(i_0_4125, plain, (X1=X2|hAPP(c_Option_Ooption_OSome(X3),X1)!=hAPP(c_Option_Ooption_OSome(X3),X2))). 4.06/4.36 cnf(i_0_4689, plain, (X1=X2|hAPP(c_List_Orev(X3),X1)!=hAPP(c_List_Orev(X3),X2))). 4.06/4.36 cnf(i_0_2766, plain, (X1=X2|~c_Natural_Oevalc(X3,X4,X2)|~c_Natural_Oevalc(X3,X4,X1))). 4.06/4.36 cnf(i_0_4357, plain, (c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,hAPP(c_List_Orev(X1),X3)))). 4.06/4.36 cnf(i_0_4828, plain, (c_List_Olist__ex(X1,X2,X3)|~c_List_Olist__ex(X1,X2,hAPP(c_List_Orev(X1),X3)))). 4.06/4.36 cnf(i_0_7214, plain, (~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_584, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|esk54_2(X2,X1)!=esk55_2(X2,X1))). 4.06/4.36 cnf(i_0_939, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.06/4.36 cnf(i_0_5665, plain, (hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X1,X2,X3)))|~hBOOL(hAPP(c_Com_OWT,X2))|~hBOOL(hAPP(c_Com_OWT,X3)))). 4.06/4.36 cnf(i_0_183, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1))). 4.06/4.36 cnf(i_0_620, plain, (~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_682, plain, (c_List_Olist__all(X1,X2,X3)|~hBOOL(hAPP(X2,esk66_3(X2,X3,X1))))). 4.06/4.36 cnf(i_0_1013, plain, (c_List_Olist__all(X1,X2,X3)|~hBOOL(hAPP(X2,esk92_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_1828, plain, (c_List_Olist__all(X1,X2,X3)|~hBOOL(hAPP(X2,esk138_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_219, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)))). 4.06/4.36 cnf(i_0_2637, plain, (X1=X2|~class_HOL_Oequal(X3)|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X3),X1),X2)))). 4.06/4.36 cnf(i_0_1165, plain, (c_Natural_Oevalc(X1,X2,X3)|~c_Natural_Oevaln(X1,X2,X4,X3))). 4.06/4.36 cnf(i_0_5976, plain, (c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))|~c_Nat__Transfer_Ois__nat(X1))). 4.06/4.36 cnf(i_0_1709, plain, (c_Wellfounded_OwfP(X1,X2)|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk129_2(X2,X1))))). 4.06/4.36 cnf(i_0_1121, 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)),esk100_1(X1))))). 4.06/4.36 cnf(i_0_2071, 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))). 4.06/4.36 cnf(i_0_7024, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.06/4.36 cnf(i_0_362, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Olinordered__ab__group__add(X1))). 4.06/4.36 cnf(i_0_6935, plain, (X1=X2|~c_Map_Omap__le(X3,X4,X2,X1)|~c_Map_Omap__le(X3,X4,X1,X2))). 4.06/4.36 cnf(i_0_1098, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(c_Groups_Oabs__class_Oabs(X2),X1)!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Oordered__ab__group__add__abs(X2))). 4.06/4.36 cnf(i_0_1359, 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))). 4.06/4.36 cnf(i_0_4666, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.36 cnf(i_0_4665, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.36 cnf(i_0_6550, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Oappend(X2),X3),X1)!=c_List_Olist_ONil(X2))). 4.06/4.36 cnf(i_0_6551, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Oappend(X2),X1),X3)!=c_List_Olist_ONil(X2))). 4.06/4.36 cnf(i_0_1473, plain, (X1=X2|c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X1)!=c_Nitpick_Opair__box_OPairBox(X3,X4,X6,X2))). 4.06/4.36 cnf(i_0_5380, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X2))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(X2,X3)))). 4.06/4.36 cnf(i_0_7099, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))|~class_Orderings_Opreorder(X1))). 4.06/4.36 cnf(i_0_3169, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X2),X2))|~class_HOL_Oequal(X1))). 4.06/4.36 cnf(i_0_1474, plain, (X1=X2|c_Nitpick_Opair__box_OPairBox(X3,X4,X1,X5)!=c_Nitpick_Opair__box_OPairBox(X3,X4,X2,X6))). 4.06/4.36 cnf(i_0_7136, plain, (c_Divides_Odiv__class_Omod(X1,X2,X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.06/4.36 cnf(i_0_2177, plain, (c_Relation_Orefl__on(X1,X2,X3)|~c_Relation_Orefl__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3)))). 4.06/4.36 cnf(i_0_6123, plain, (c_Relation_Ototal__on(X1,X2,X3)|~c_Relation_Ototal__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3)))). 4.06/4.36 cnf(i_0_5225, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X2))))). 4.06/4.36 cnf(i_0_462, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X2))))). 4.06/4.36 cnf(i_0_895, plain, (hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1)))|~hBOOL(hAPP(X1,X3)))). 4.06/4.36 cnf(i_0_7284, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Oring__char__0(X1))). 4.06/4.36 cnf(i_0_5349, plain, (X1=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X1),X2)!=c_Groups_Ozero__class_Ozero(X3)|~class_Groups_Oab__group__add(X3))). 4.06/4.36 cnf(i_0_7439, plain, (X1=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X3),X1),X2)!=c_Groups_Ozero__class_Ozero(X3)|~class_Groups_Ogroup__add(X3))). 4.06/4.36 cnf(i_0_1819, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.06/4.36 cnf(i_0_5728, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2)=X2|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_2217, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2)=X2|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_7283, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)!=c_Groups_Ozero__class_Ozero(X2)|~class_Int_Oring__char__0(X2))). 4.06/4.36 cnf(i_0_53, plain, (hAPP(c_Int_Onat,X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_4135, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Oremdups(X1,X2))|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_2441, plain, (X1=X2|hAPP(c_SetInterval_Oord__class_OatLeast(X3),X1)!=hAPP(c_SetInterval_Oord__class_OatLeast(X3),X2)|~class_Orderings_Olinorder(X3))). 4.06/4.36 cnf(i_0_5516, plain, (X1=X2|hAPP(c_SetInterval_Oord__class_OatMost(X3),X1)!=hAPP(c_SetInterval_Oord__class_OatMost(X3),X2)|~class_Orderings_Olinorder(X3))). 4.06/4.36 cnf(i_0_6652, plain, (X1=X2|hAPP(c_SetInterval_Oord__class_OlessThan(X3),X1)!=hAPP(c_SetInterval_Oord__class_OlessThan(X3),X2)|~class_Orderings_Olinorder(X3))). 4.06/4.36 cnf(i_0_1839, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_4122, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Oone__class_Oone(X1))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1))). 4.06/4.36 cnf(i_0_3151, plain, (X1=X2|hAPP(c_SetInterval_Oord__class_OgreaterThan(X3),X1)!=hAPP(c_SetInterval_Oord__class_OgreaterThan(X3),X2)|~class_Orderings_Olinorder(X3))). 4.06/4.36 cnf(i_0_3914, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(c_List_Omap(X2,X3),X4),X1)!=c_List_Olist_ONil(X3))). 4.06/4.36 cnf(i_0_6837, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_4555, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.06/4.36 cnf(i_0_3912, plain, (c_List_Olist_ONil(X1)=X2|hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)!=c_List_Olist_ONil(X1))). 4.06/4.36 cnf(i_0_1460, plain, (c_Option_Ooption_ONone(X1)=X2|hAPP(hAPP(c_Option_Omap(X1,X3),X4),X2)!=c_Option_Ooption_ONone(X3))). 4.06/4.36 cnf(i_0_5573, plain, (c_List_OtakeWhile(X1,X2,X3)=X3|~hBOOL(hAPP(X2,esk397_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_5041, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.06/4.36 cnf(i_0_6102, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),c_List_Olist_ONil(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Omonoid__add(X1))). 4.06/4.36 cnf(i_0_267, plain, (c_Enum_Oall__n__lists(X1,X2,X3)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(X2,esk21_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_1711, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.06/4.36 cnf(i_0_6330, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_3977, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1))=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Oboolean__algebra(X1))). 4.06/4.36 cnf(i_0_986, plain, (c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))|~c_Nat__Transfer_Ois__nat(X2)|~c_Nat__Transfer_Ois__nat(X1))). 4.06/4.36 cnf(i_0_7080, plain, (c_Wellfounded_Owf(X1,c_Wellfounded_Omlex__prod(X1,X2,X3))|~c_Wellfounded_Owf(X1,X3))). 4.06/4.36 cnf(i_0_4681, plain, (hBOOL(hAPP(X1,c_Option_Ooption_ONone(X2)))|~class_Enum_Oenum(X2)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X2)),X1)))). 4.06/4.36 cnf(i_0_570, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X2))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(X2,esk52_2(X2,X1))))). 4.06/4.36 cnf(i_0_4646, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X2))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(X2,esk336_2(X2,X1))))). 4.06/4.36 cnf(i_0_7454, plain, (c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X2))|~c_Wellfounded_Owf(X1,X2))). 4.06/4.36 cnf(i_0_6493, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_1671, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X2))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_4294, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_2305, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1))=c_Orderings_Otop__class_Otop(X1)|~class_Lattices_Oboolean__algebra(X1))). 4.06/4.36 cnf(i_0_1672, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_6542, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|esk462_4(X4,X3,X2,X1)!=esk463_4(X4,X3,X2,X1))). 4.06/4.36 cnf(i_0_6357, plain, (X1=X2|hAPP(X1,esk448_2(X2,X1))!=hAPP(X2,esk448_2(X2,X1)))). 4.06/4.36 cnf(i_0_702, plain, (c_Fun_Oinj__on(X1,X1,c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Groups_Oordered__ab__group__add(X1))). 4.06/4.36 cnf(i_0_5290, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_95, plain, (hAPP(c_Nat_OSuc,esk8_1(X1))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.06/4.36 cnf(i_0_3949, plain, (hBOOL(hAPP(X1,esk288_2(X2,X1)))|~hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1))))). 4.06/4.36 cnf(i_0_4635, plain, (hBOOL(hAPP(X1,esk334_1(X1)))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))). 4.06/4.36 cnf(i_0_4500, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 4.06/4.36 cnf(i_0_4641, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.06/4.36 cnf(i_0_1484, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)))). 4.06/4.36 cnf(i_0_3264, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Ois__nat(X1))). 4.06/4.36 cnf(i_0_1247, plain, (X1=X2|hAPP(c_Groups_Ouminus__class_Ouminus(X3),X1)!=hAPP(c_Groups_Ouminus__class_Ouminus(X3),X2)|~class_Groups_Ogroup__add(X3))). 4.06/4.36 cnf(i_0_665, plain, (X1=X2|hAPP(c_Groups_Ouminus__class_Ouminus(X3),X1)!=hAPP(c_Groups_Ouminus__class_Ouminus(X3),X2)|~class_Lattices_Oboolean__algebra(X3))). 4.06/4.36 cnf(i_0_7182, plain, (X1=X2|hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2)|~class_Nat_Osemiring__char__0(X3))). 4.06/4.36 cnf(i_0_4092, plain, (~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.06/4.36 cnf(i_0_2450, plain, (X1=X2|hAPP(c_Int_Oring__1__class_Oof__int(X3),X1)!=hAPP(c_Int_Oring__1__class_Oof__int(X3),X2)|~class_Int_Oring__char__0(X3))). 4.06/4.36 cnf(i_0_2929, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X3),X1)!=X3|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2))). 4.06/4.36 cnf(i_0_1009, plain, (c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Ozero__class_Ozero(X1))=X2|~class_Divides_Osemiring__div(X1))). 4.06/4.36 cnf(i_0_1735, plain, (c_Nat__Transfer_Ois__nat(X1)|~c_Nat__Transfer_Onat__set(X2)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_6262, plain, (~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.06/4.36 cnf(i_0_4041, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2)=X2|~class_Lattices_Olattice(X1))). 4.06/4.36 cnf(i_0_3824, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)=X2|~class_Lattices_Oab__semigroup__idem__mult(X1))). 4.06/4.36 cnf(i_0_7528, plain, (c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)))). 4.06/4.36 cnf(i_0_845, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2)=X2|~class_Lattices_Osemilattice__sup(X1))). 4.06/4.36 cnf(i_0_235, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2)=X2|~class_Lattices_Olattice(X1))). 4.06/4.36 cnf(i_0_911, plain, (c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X4),X3)))). 4.06/4.36 cnf(i_0_910, plain, (c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4)))). 4.06/4.36 cnf(i_0_4503, plain, (~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_6642, plain, (~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_66, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2)=X2|~class_Lattices_Osemilattice__inf(X1))). 4.06/4.36 cnf(i_0_6709, plain, (c_Nitpick_Ocard_H(X1,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_2417, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.06/4.36 cnf(i_0_2462, plain, (c_Option_Ooption_ONone(X1)!=hAPP(X2,X3)|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_Map_Odom(X4,X1,X2))))). 4.06/4.36 cnf(i_0_1521, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Oacyclic(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)))). 4.06/4.36 cnf(i_0_2195, plain, (c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olex(X1,X2))|~c_Wellfounded_Owf(X1,X2))). 4.06/4.36 cnf(i_0_6210, plain, (c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olenlex(X1,X2))|~c_Wellfounded_Owf(X1,X2))). 4.06/4.36 cnf(i_0_2355, plain, (X1=X2|hBOOL(hAPP(X3,X1))|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X4),X1,X2))). 4.06/4.36 cnf(i_0_5492, plain, (c_Natural_Oevalc(X1,X2,X3)|~c_Natural_Oevalc(c_Com_Ocom_OCond(X4,X1,X5),X2,X3)|~hBOOL(hAPP(X4,X2)))). 4.06/4.36 cnf(i_0_2093, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),esk157_1(X1)))))). 4.06/4.36 cnf(i_0_5703, plain, (c_Map_Omap__le(X1,X2,X3,X4)|~c_Map_Omap__le(X1,X2,c_Map_Omap__add(X1,X2,X5,X3),X4))). 4.06/4.36 cnf(i_0_6617, plain, (X1=c_Orderings_Obot__class_Obot(X2)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X3)!=c_Orderings_Obot__class_Obot(X2)|~class_Lattices_Obounded__lattice__bot(X2))). 4.06/4.36 cnf(i_0_5679, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.36 cnf(i_0_2656, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Olinordered__ab__group__add(X1))). 4.06/4.36 cnf(i_0_2206, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__1__no__zero__divisors(X1))). 4.06/4.36 cnf(i_0_6618, plain, (c_Orderings_Obot__class_Obot(X1)=X2|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)!=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Obounded__lattice__bot(X1))). 4.06/4.36 cnf(i_0_4609, plain, (hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),esk331_1(X1))))|~hBOOL(hAPP(X1,X2)))). 4.06/4.36 cnf(i_0_7529, plain, (hBOOL(hAPP(X1,X2))|~c_List_Olist__all(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)))). 4.06/4.36 cnf(i_0_1054, plain, (c_List_Oupto(X1,X2)=c_List_Olist_ONil(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 4.06/4.36 cnf(i_0_6697, plain, (c_Random_Olog(X1,X2)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X2),X1)))). 4.06/4.36 cnf(i_0_1807, plain, (X1=X2|hAPP(X3,X1)!=hAPP(X3,X2)|~c_Typedef_Otype__definition(X4,X5,X3,X6,X7))). 4.06/4.36 cnf(i_0_1710, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~c_Wellfounded_OwfP(X1,X2))). 4.06/4.36 cnf(i_0_802, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osorted__list__of__set(X1,X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_5538, plain, (c_List_Olinorder__class_Osorted(X1,esk396_2(X2,X1))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_3494, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 4.06/4.36 cnf(i_0_6453, plain, (c_List_Olinorder__class_Osorted(X1,c_List_OtakeWhile(X1,X2,X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_4534, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Oremove1(X1,X2,X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_3536, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.06/4.36 cnf(i_0_5133, plain, (hAPP(c_List_Ofilter(X1,X2),X3)=X3|~hBOOL(hAPP(X2,esk373_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_1139, plain, (c_Nitpick_Owf_H(X1,X2)|~c_Wellfounded_Oacyclic(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)))). 4.06/4.36 cnf(i_0_2254, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))). 4.06/4.36 cnf(i_0_697, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(X2,esk67_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_579, plain, (X1=X2|hBOOL(hAPP(X3,X1))|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X4),X1,X5,X2))). 4.06/4.36 cnf(i_0_4084, plain, (c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Oone__class_Oone(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.06/4.36 cnf(i_0_6337, plain, (c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.06/4.36 cnf(i_0_4004, plain, (hBOOL(hAPP(c_Predicate_OPowp(X1,X2),X3))|~hBOOL(hAPP(X2,esk291_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_5633, plain, (X1=X2|hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)!=hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)|~class_Int_Oring__char__0(X3)|~class_Int_Onumber__ring(X3))). 4.06/4.36 cnf(i_0_828, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=X1|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.06/4.36 cnf(i_0_7342, plain, (c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X2))=c_Groups_Osgn__class_Osgn(X1,X2)|~class_Rings_Olinordered__idom(X1))). 4.06/4.36 cnf(i_0_3204, plain, (c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),esk241_2(X2,X1)),c_Wellfounded_Oacc(X1,X2))))). 4.06/4.36 cnf(i_0_3171, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))). 4.06/4.36 cnf(i_0_3320, plain, (X1=X2|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X3,X4,X5,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X2)))). 4.06/4.36 cnf(i_0_1529, plain, (c_Natural_Oevalc(c_Com_Ocom_OBODY(X1),X2,X3)|~c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3))). 4.06/4.36 cnf(i_0_1758, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk132_2(X1,X2)),X2)))). 4.06/4.36 cnf(i_0_7554, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk528_2(X1,X2)),X2)))). 4.06/4.36 cnf(i_0_3076, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))=hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_627, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_1973, plain, (hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4))|~hBOOL(hAPP(X3,X4)))). 4.06/4.36 cnf(i_0_3808, plain, (c_Orderings_Otop__class_Otop(X1)=X2|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)!=c_Orderings_Otop__class_Otop(X1)|~class_Lattices_Obounded__lattice__top(X1))). 4.06/4.36 cnf(i_0_3807, 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))). 4.06/4.36 cnf(i_0_1974, plain, (X1=X2|hBOOL(hAPP(X3,X2))|~hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X4),X1),X3),X2)))). 4.06/4.36 cnf(i_0_7443, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))))). 4.06/4.36 cnf(i_0_3835, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))))). 4.06/4.36 cnf(i_0_2283, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_7298, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Otl(X1),X2))|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_5287, plain, (hAPP(hAPP(X1,X2),X2)=X2|~c_Finite__Set_Ofolding__one__idem(X3,X1,X4))). 4.06/4.36 cnf(i_0_4380, plain, (hAPP(X1,X2)=c_Option_Ooption_ONone(X3)|hAPP(c_Map_Omap__add(X4,X3,X5,X1),X2)!=c_Option_Ooption_ONone(X3))). 4.06/4.36 cnf(i_0_4379, plain, (hAPP(X1,X2)=c_Option_Ooption_ONone(X3)|hAPP(c_Map_Omap__add(X4,X3,X1,X5),X2)!=c_Option_Ooption_ONone(X3))). 4.06/4.36 cnf(i_0_3007, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X3),X2))))). 4.06/4.36 cnf(i_0_3006, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))))). 4.06/4.36 cnf(i_0_7126, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(c_List_Olistsp(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))))). 4.06/4.36 cnf(i_0_6696, plain, (c_Random_Olog(X1,X2)=c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))). 4.06/4.36 cnf(i_0_6520, plain, (c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)=X3|~class_Rings_Osemiring__1(X1))). 4.06/4.36 cnf(i_0_2989, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X2),X6)))). 4.06/4.36 cnf(i_0_1800, plain, (hAPP(X1,X2)=X3|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X4,X5),X1),X2),X3)!=X1)). 4.06/4.36 cnf(i_0_1605, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X4,X5,X1),X3),X2)))). 4.06/4.36 cnf(i_0_110, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X1),X2)))). 4.06/4.36 cnf(i_0_3598, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))|~c_Wellfounded_Oacyclic(X1,X2))). 4.06/4.36 cnf(i_0_1822, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X1),X4),X2)))). 4.06/4.36 cnf(i_0_1154, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)))). 4.06/4.36 cnf(i_0_736, plain, (X1=X2|hAPP(hAPP(c_List_Oappend(X3),X4),X1)!=hAPP(hAPP(c_List_Oappend(X3),X4),X2))). 4.06/4.36 cnf(i_0_251, plain, (X1=X2|hAPP(hAPP(c_List_Oappend(X3),X1),X4)!=hAPP(hAPP(c_List_Oappend(X3),X2),X4))). 4.06/4.36 cnf(i_0_3934, plain, (X1=X2|hAPP(hAPP(c_List_Olist_OCons(X3),X4),X1)!=hAPP(hAPP(c_List_Olist_OCons(X3),X5),X2))). 4.06/4.36 cnf(i_0_3335, 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,esk254_2(X2,X1))))). 4.06/4.36 cnf(i_0_1563, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(X1,esk118_1(X1))))). 4.06/4.36 cnf(i_0_3587, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))))). 4.06/4.36 cnf(i_0_3935, plain, (X1=X2|hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4)!=hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))). 4.06/4.36 cnf(i_0_694, plain, (~class_Rings_Olinordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_648, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.36 cnf(i_0_2935, plain, (c_List_Olinorder__class_Osort__key(X1,X2,X3,c_List_Olist_ONil(X1))=c_List_Olist_ONil(X1)|~class_Orderings_Olinorder(X2))). 4.06/4.36 cnf(i_0_773, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)))). 4.06/4.36 cnf(i_0_64, plain, (hAPP(c_Option_Ooption_OSome(X1),esk4_2(X1,X2))=X2|X2=c_Option_Ooption_ONone(X1))). 4.06/4.36 cnf(i_0_3237, plain, (c_Natural_Oevaln(X1,X2,X3,X4)|~c_Natural_Oevaln(c_Com_Ocom_OCond(X5,X1,X6),X2,X3,X4)|~hBOOL(hAPP(X5,X2)))). 4.06/4.36 cnf(i_0_3394, plain, (hAPP(c_Option_Ooption_OSome(X1),esk256_2(X1,X2))=X2|c_Option_Ooption_ONone(X1)=X2)). 4.06/4.36 cnf(i_0_5866, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.36 cnf(i_0_3633, plain, (hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.06/4.36 cnf(i_0_2836, 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))). 4.06/4.36 cnf(i_0_2189, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|X2=X3|c_List_Oreplicate(X4,X1,X3)!=c_List_Oreplicate(X4,X5,X2))). 4.06/4.36 cnf(i_0_1268, plain, (~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1)))))). 4.06/4.36 cnf(i_0_4958, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_2099, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))|~class_Orderings_Oorder(X1))). 4.06/4.36 cnf(i_0_3445, plain, (c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),X2))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_7510, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X1,X5,hAPP(c_Fun_Ocomp(X2,X5,X1,X6),X3),X4))). 4.06/4.36 cnf(i_0_4358, plain, (c_List_Olist__all(X1,X2,hAPP(c_List_Orev(X1),X3))|~c_List_Olist__all(X1,X2,X3))). 4.06/4.36 cnf(i_0_4829, plain, (c_List_Olist__ex(X1,X2,hAPP(c_List_Orev(X1),X3))|~c_List_Olist__ex(X1,X2,X3))). 4.06/4.36 cnf(i_0_160, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X1)),X2))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(X2,c_Option_Ooption_ONone(X1))))). 4.06/4.36 cnf(i_0_5381, plain, (hBOOL(hAPP(X1,esk386_2(X1,X2)))|~class_Enum_Oenum(X2)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X2),X1)))). 4.06/4.36 cnf(i_0_2936, plain, (hBOOL(hAPP(X1,esk218_3(X2,X1,X3)))|~c_List_Olist__ex(X3,X1,X2))). 4.06/4.36 cnf(i_0_4772, plain, (hBOOL(hAPP(X1,esk346_3(X2,X1,X3)))|~c_List_Olist__ex1(X3,X1,X2))). 4.06/4.36 cnf(i_0_5493, plain, (c_Natural_Oevalc(X1,X2,X3)|c_Natural_Oevalc(X4,X2,X3)|~c_Natural_Oevalc(c_Com_Ocom_OCond(X5,X4,X1),X2,X3))). 4.06/4.36 cnf(i_0_7211, plain, (hBOOL(hAPP(X1,esk506_2(X1,X2)))|~class_Enum_Oenum(X2)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X2),X1)))). 4.06/4.36 cnf(i_0_1122, plain, (c_Nat__Transfer_Onat__set(X1)|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk100_1(X1)),X1)))). 4.06/4.36 cnf(i_0_439, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Orderings_Otop__class_Otop(X1)))|~class_Orderings_Otop(X1))). 4.06/4.36 cnf(i_0_3041, plain, (hAPP(c_Nat_OSuc,esk225_4(X1,X2,X3,X4))=X2|~c_Natural_Oevaln(c_Com_Ocom_OBODY(X4),X3,X2,X1))). 4.06/4.36 cnf(i_0_6982, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Orderings_Obot__class_Obot(X1)),X2))|~class_Orderings_Obot(X1))). 4.06/4.36 cnf(i_0_1480, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)=X3|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.06/4.36 cnf(i_0_6248, 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_Ono__zero__divisors(X1)|~class_Rings_Omult__zero(X1)|~class_Rings_Ozero__neq__one(X1)|~class_Power_Opower(X1))). 4.06/4.36 cnf(i_0_836, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(c_Set_Oimage(X2,X3,X4),X1)!=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))). 4.06/4.36 cnf(i_0_3333, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))))). 4.06/4.36 cnf(i_0_7021, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Otl(X1),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.06/4.36 cnf(i_0_5224, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.06/4.36 cnf(i_0_463, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.06/4.36 cnf(i_0_2931, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_List_Oset(X3),c_List_Oreplicate(X3,X4,X2)))))). 4.06/4.36 cnf(i_0_1900, plain, (c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3)|~c_Natural_Oevalc(c_Com_Ocom_OBODY(X1),X2,X3))). 4.06/4.36 cnf(i_0_4959, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.06/4.36 cnf(i_0_1879, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1))). 4.06/4.36 cnf(i_0_6713, plain, (c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X2))|~c_Wellfounded_Owf(X1,X2))). 4.06/4.36 cnf(i_0_6844, plain, (c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X2))|~c_Wellfounded_Owf(X1,X2))). 4.06/4.36 cnf(i_0_5663, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 4.06/4.36 cnf(i_0_3513, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.06/4.36 cnf(i_0_660, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))). 4.06/4.36 cnf(i_0_7088, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))). 4.06/4.36 cnf(i_0_1303, plain, (X1=X2|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),X1)!=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),X2))). 4.06/4.36 cnf(i_0_2886, plain, (X1=X2|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X4),X2))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X4),X1)))). 4.06/4.36 cnf(i_0_2244, 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)))). 4.06/4.36 cnf(i_0_2076, plain, (X1=hAPP(c_Option_Ooption_OSome(X2),X3)|~hBOOL(hAPP(hAPP(c_member(X2),X3),c_Option_Oset(X2,X1))))). 4.06/4.36 cnf(i_0_1337, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_4027, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_3754, plain, (~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.06/4.36 cnf(i_0_794, plain, (~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.06/4.36 cnf(i_0_1476, plain, (~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.06/4.36 cnf(i_0_4600, plain, (c_Nat__Transfer_Otsub(X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1)))). 4.06/4.36 cnf(i_0_6403, plain, (X1=X2|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X1)))!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X2))))). 4.06/4.36 cnf(i_0_1934, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)!=X3|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_2800, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)!=X2|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_1111, plain, (hAPP(X1,X2)=hAPP(X1,X3)|~c_Equiv__Relations_Oequivp(X4,X1)|~hBOOL(hAPP(hAPP(X1,X2),X3)))). 4.06/4.36 cnf(i_0_1840, plain, (hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~class_Enum_Oenum(X1))). 4.06/4.36 cnf(i_0_503, plain, (c_List_Oupto(X1,X2)=c_List_Olist_ONil(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_3407, plain, (c_Fun_Oid(X1)=hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))|~c_Finite__Set_Ofolding(X3,X1,X4,X2))). 4.06/4.36 cnf(i_0_7130, plain, (c_Random_Oinc__shift(X1,X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))|X2=X1)). 4.06/4.36 cnf(i_0_6850, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2))))). 4.06/4.36 cnf(i_0_2275, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Ois__nat(X2)|~c_Nat__Transfer_Ois__nat(X1))). 4.06/4.36 cnf(i_0_2787, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Ois__nat(X2)|~c_Nat__Transfer_Ois__nat(X1))). 4.06/4.36 cnf(i_0_1771, plain, (c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Ois__nat(X2)|~c_Nat__Transfer_Ois__nat(X1))). 4.06/4.36 cnf(i_0_290, 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))). 4.06/4.36 cnf(i_0_123, plain, (c_Power_Opower_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1))=c_Power_Opower__class_Opower(X1)|~class_Power_Opower(X1))). 4.06/4.36 cnf(i_0_5142, plain, (c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2),X3,X3)|hBOOL(hAPP(X1,X3)))). 4.06/4.36 cnf(i_0_491, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk42_1(X1))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_7071, plain, (c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_5384, plain, (c_Natural_Oevalc(X1,X2,X3)|hBOOL(hAPP(X4,X2))|~c_Natural_Oevalc(c_Com_Ocom_OCond(X4,X5,X1),X2,X3))). 4.06/4.36 cnf(i_0_2182, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_3296, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_7552, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_306, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X2))))). 4.06/4.36 cnf(i_0_1354, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X2))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_992, plain, (c_Natural_Oevaln(X1,X2,hAPP(c_Nat_OSuc,X3),X4)|~c_Natural_Oevaln(X1,X2,X3,X4))). 4.06/4.36 cnf(i_0_6859, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,esk482_4(X2,X1,hAPP(c_Option_Ooption_OSome(X3),X2),X3))))). 4.06/4.36 cnf(i_0_2371, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))). 4.06/4.36 cnf(i_0_1166, plain, (c_Natural_Oevaln(X1,X2,esk101_3(X3,X2,X1),X3)|~c_Natural_Oevalc(X1,X2,X3))). 4.06/4.36 cnf(i_0_5314, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk381_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_3787, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThan(X4,X1,X2))))). 4.06/4.36 cnf(i_0_4212, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeast(X4,X1,X2))))). 4.06/4.36 cnf(i_0_1704, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OlessThan(X4,X1,X3))))). 4.06/4.36 cnf(i_0_3500, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatMost(X4,X1,X3))))). 4.06/4.36 cnf(i_0_6327, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk447_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_456, plain, (c_List_Olist__all(X1,X2,X3)|~hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),esk36_3(X3,X2,X1)))))). 4.06/4.36 cnf(i_0_7094, plain, (hAPP(X1,hAPP(X2,X3))=X3|~c_Typedef_Otype__definition(X4,X5,X2,X1,X6))). 4.06/4.36 cnf(i_0_6345, plain, (c_SMT_Oz3mod(X1,X2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.06/4.36 cnf(i_0_116, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X3),hAPP(hAPP(c_List_Omap(X1,X3),X4),X2))))). 4.06/4.36 cnf(i_0_3836, plain, (~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.06/4.36 cnf(i_0_2100, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.06/4.36 cnf(i_0_7240, plain, (c_Wellfounded_OwfP(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))). 4.06/4.36 cnf(i_0_4200, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X2),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.06/4.36 cnf(i_0_2961, plain, (c_Wellfounded_Owf(X1,X2)|hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))). 4.06/4.36 cnf(i_0_1249, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=X2|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Odivision__ring(X1))). 4.06/4.36 cnf(i_0_5686, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.06/4.36 cnf(i_0_905, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2|~class_Groups_Omonoid__mult(X1))). 4.06/4.36 cnf(i_0_2063, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=X2|~class_Groups_Ogroup__add(X1))). 4.06/4.36 cnf(i_0_5682, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~class_Orderings_Olinorder(X3)|~hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osort__key(X1,X3,X4,X2))))). 4.06/4.36 cnf(i_0_610, plain, (X1=X2|hAPP(hAPP(c_Product__Type_OPair(X3,X4),X5),X1)!=hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X2))). 4.06/4.36 cnf(i_0_611, plain, (X1=X2|hAPP(hAPP(c_Product__Type_OPair(X3,X4),X1),X5)!=hAPP(hAPP(c_Product__Type_OPair(X3,X4),X2),X6))). 4.06/4.36 cnf(i_0_5476, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X2|~class_Rings_Ocomm__semiring__1(X1))). 4.06/4.36 cnf(i_0_3923, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=X2|~class_Lattices_Oboolean__algebra(X1))). 4.06/4.36 cnf(i_0_2168, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Groups_Ocomm__monoid__add(X1))). 4.06/4.36 cnf(i_0_568, plain, (X1=X2|hAPP(X3,X1)!=hAPP(X3,X2)|~c_Fun_Oinj__on(X4,X5,X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))). 4.06/4.36 cnf(i_0_1686, plain, (hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X2)),X3)=c_Orderings_Obot__class_Obot(X2)|~class_Orderings_Obot(X2))). 4.06/4.36 cnf(i_0_7471, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Groups_Ocomm__monoid__mult(X1))). 4.06/4.36 cnf(i_0_7003, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Groups_Omonoid__mult(X1))). 4.06/4.36 cnf(i_0_3593, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Orderings_Otop__class_Otop(X1))=X2|~class_Lattices_Obounded__lattice__top(X1))). 4.06/4.36 cnf(i_0_1143, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Groups_Ogroup__add(X1))). 4.06/4.36 cnf(i_0_4949, plain, (hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),X3)=c_Orderings_Otop__class_Otop(X2)|~class_Orderings_Otop(X2))). 4.06/4.36 cnf(i_0_2672, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Olist_ONil(X2)=X3|hAPP(hAPP(c_List_Otake(X2),X1),X3)!=c_List_Olist_ONil(X2))). 4.06/4.36 cnf(i_0_6022, plain, (c_List_Olast(X1,c_List_Oreplicate(X1,X2,X3))=X3|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.36 cnf(i_0_6391, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Rings_Odivision__ring(X1))). 4.06/4.36 cnf(i_0_6200, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Divides_Osemiring__div(X1))). 4.06/4.36 cnf(i_0_5590, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Rings_Ocomm__semiring__1(X1))). 4.06/4.36 cnf(i_0_1508, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Groups_Omonoid__add(X1))). 4.06/4.36 cnf(i_0_4420, plain, (c_List_Olist_ONil(X1)=X2|c_List_Olinorder__class_Osorted(X1,c_List_Obutlast(X1,X2))|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_5598, plain, (c_List_Olist_ONil(X1)=X2|c_List_Olinorder__class_Osorted(X1,esk401_2(X2,X1))|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_3316, plain, (c_Complete__Lattice_OInf__class_OInf(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.06/4.36 cnf(i_0_493, plain, (c_Complete__Lattice_OSup__class_OSup(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.06/4.36 cnf(i_0_6256, plain, (hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_5208, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1))=X2|~class_Lattices_Obounded__lattice__bot(X1))). 4.06/4.36 cnf(i_0_7488, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1))=X2|~class_Rings_Ocomm__semiring__1(X1))). 4.06/4.36 cnf(i_0_6151, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=X2|~class_Groups_Omonoid__add(X1))). 4.06/4.36 cnf(i_0_3117, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2)=X2|~class_Lattices_Obounded__lattice__top(X1))). 4.06/4.36 cnf(i_0_2744, plain, (c_Complete__Lattice_OInf__class_OInf(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.06/4.36 cnf(i_0_1855, plain, (c_Complete__Lattice_OSup__class_OSup(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(X1)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.06/4.36 cnf(i_0_472, plain, (c_List_Olinorder__class_Osorted__list__of__set(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_List_Olist_ONil(X1)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_3056, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))). 4.06/4.36 cnf(i_0_2960, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.06/4.36 cnf(i_0_3668, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=X2|~class_Rings_Ocomm__semiring__1(X1))). 4.06/4.36 cnf(i_0_6313, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=X2|~class_Groups_Ocomm__monoid__add(X1))). 4.06/4.36 cnf(i_0_3865, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2)=X2|~class_Lattices_Obounded__lattice__bot(X1))). 4.06/4.36 cnf(i_0_1027, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)=X2|~class_Rings_Ocomm__semiring__1(X1))). 4.06/4.36 cnf(i_0_6943, plain, (hBOOL(hAPP(X1,esk487_3(X2,X1,X3)))|~c_Enum_Oex__n__lists(X3,X1,X2)|~class_Enum_Oenum(X3))). 4.06/4.36 cnf(i_0_752, plain, (~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,X1)),X4),X3)))). 4.06/4.36 cnf(i_0_5449, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=X1)). 4.06/4.36 cnf(i_0_1650, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)=X2|~class_Groups_Ocomm__monoid__mult(X1))). 4.06/4.36 cnf(i_0_2235, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2)=X2|~class_Groups_Omonoid__mult(X1))). 4.06/4.36 cnf(i_0_3497, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X1)|~class_Power_Opower(X1))). 4.06/4.36 cnf(i_0_354, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X2)|~class_Groups_Ocancel__semigroup__add(X3))). 4.06/4.36 cnf(i_0_3983, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X4),X2)|~class_Groups_Ocancel__ab__semigroup__add(X3))). 4.06/4.36 cnf(i_0_1893, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X1),X4)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),X2),X4)|~class_Groups_Ocancel__semigroup__add(X3))). 4.06/4.36 cnf(i_0_638, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_7084, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Ocomm__semiring__1(X1))). 4.06/4.36 cnf(i_0_7110, plain, (X1=X2|hAPP(hAPP(c_List_Olist_OCons(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),X4)))). 4.06/4.36 cnf(i_0_2176, plain, (c_Relation_Orefl__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3))|~c_Relation_Orefl__on(X1,X2,X3))). 4.06/4.36 cnf(i_0_6122, plain, (c_Relation_Ototal__on(X1,X2,hAPP(c_Relation_Oconverse(X1,X1),X3))|~c_Relation_Ototal__on(X1,X2,X3))). 4.06/4.36 cnf(i_0_5350, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oab__group__add(X1))). 4.06/4.36 cnf(i_0_2597, plain, (c_List_Omember(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))))). 4.06/4.36 cnf(i_0_265, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.06/4.36 cnf(i_0_4260, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.06/4.36 cnf(i_0_1112, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|hAPP(X1,X2)!=hAPP(X1,X3)|~c_Equiv__Relations_Oequivp(X4,X1))). 4.06/4.36 cnf(i_0_2420, plain, (hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1))). 4.06/4.36 cnf(i_0_2834, plain, (c_Map_Omap__le(X1,X2,X3,X4)|~c_Map_Omap__le(X1,X2,X5,X4)|~c_Map_Omap__le(X1,X2,X3,X5))). 4.06/4.36 cnf(i_0_1569, plain, (hAPP(hAPP(X1,X2),X2)=X2|~c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X1,X5,X6,X7))). 4.06/4.36 cnf(i_0_3565, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)))). 4.06/4.36 cnf(i_0_3496, plain, (hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Oone__class_Oone(X1)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Rings_Osemiring__1(X1))). 4.06/4.36 cnf(i_0_3763, plain, (hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1))). 4.06/4.36 cnf(i_0_340, plain, (hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Rings_Osemiring__1(X1))). 4.06/4.36 cnf(i_0_1622, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X3,X1)),c_Sum__Type_OPlus(X3,X1,X4,X2))))). 4.06/4.36 cnf(i_0_5916, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4))))). 4.06/4.36 cnf(i_0_4140, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2))))). 4.06/4.36 cnf(i_0_1195, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2))))). 4.06/4.36 cnf(i_0_2418, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))))). 4.06/4.36 cnf(i_0_7291, 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))). 4.06/4.36 cnf(i_0_3860, 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))). 4.06/4.36 cnf(i_0_2663, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.36 cnf(i_0_662, plain, (c_Wellfounded_Owf(tc_List_Olist(X1),hAPP(c_List_Olexn(X1,X2),X3))|~c_Wellfounded_Owf(X1,X2))). 4.06/4.36 cnf(i_0_1374, plain, (c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X2,X3),X4,X5)|~c_Natural_Oevalc(X2,X4,X5)|~hBOOL(hAPP(X1,X4)))). 4.06/4.36 cnf(i_0_3404, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2))))). 4.06/4.36 cnf(i_0_6822, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2))))). 4.06/4.36 cnf(i_0_4465, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))))). 4.06/4.36 cnf(i_0_4143, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X2)=c_Groups_Oone__class_Oone(X1)|c_Groups_Ozero__class_Ozero(X1)=X2|~class_Rings_Odivision__ring__inverse__zero(X1))). 4.06/4.36 cnf(i_0_5521, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X5),X4)))). 4.06/4.36 cnf(i_0_5522, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5)))). 4.06/4.36 cnf(i_0_386, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X2)=c_Groups_Oone__class_Oone(X1)|c_Groups_Ozero__class_Ozero(X1)=X2|~class_Divides_Osemiring__div(X1))). 4.06/4.36 cnf(i_0_6395, 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)))). 4.06/4.36 cnf(i_0_2314, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool))|hAPP(c_Relation_ODomain(X2,X3),X1)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.36 cnf(i_0_2506, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_3586, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_2928, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1))=X2|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1))). 4.06/4.36 cnf(i_0_554, plain, (hAPP(c_Nat_OSuc,X1)!=hAPP(c_Finite__Set_Ocard(X2),X3)|~hBOOL(hAPP(hAPP(c_member(X2),esk48_3(X1,X3,X2)),esk49_3(X1,X3,X2))))). 4.06/4.36 cnf(i_0_4900, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(X2,esk356_4(X2,X3,X1,X4))))). 4.06/4.36 cnf(i_0_1074, plain, (~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2)))). 4.06/4.36 cnf(i_0_3794, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_5269, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Omult__zero(X1))). 4.06/4.36 cnf(i_0_2634, plain, (hAPP(c_List_Ohd(X1),c_List_Oreplicate(X1,X2,X3))=X3|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2)). 4.06/4.36 cnf(i_0_2312, plain, (~c_Relation_Oirrefl(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2)))). 4.06/4.36 cnf(i_0_4248, 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))). 4.06/4.36 cnf(i_0_4249, 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),X1))!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))). 4.06/4.36 cnf(i_0_1065, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Odivision__ring__inverse__zero(X1))). 4.06/4.36 cnf(i_0_6247, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ono__zero__divisors(X1)|~class_Rings_Omult__zero(X1)|~class_Rings_Ozero__neq__one(X1)|~class_Power_Opower(X1))). 4.06/4.36 cnf(i_0_2200, plain, (hBOOL(hAPP(X1,esk168_2(X1,X2)))|~c_List_Olist__ex1(X2,X1,c_Enum_Oenum__class_Oenum(X2))|~class_Enum_Oenum(X2))). 4.06/4.36 cnf(i_0_856, plain, (c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X3,X4,X3)|hBOOL(hAPP(X1,X3)))). 4.06/4.36 cnf(i_0_1851, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_5865, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_2448, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Orderings_Otop__class_Otop(X1))=c_Orderings_Otop__class_Otop(X1)|~class_Lattices_Obounded__lattice__top(X1))). 4.06/4.36 cnf(i_0_5512, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_6560, plain, (c_Natural_Oevalc(X1,X2,esk466_4(X3,X2,X4,X1))|~c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4),X2,X3))). 4.06/4.36 cnf(i_0_6561, plain, (c_Natural_Oevalc(X1,esk466_4(X2,X3,X1,X4),X2)|~c_Natural_Oevalc(c_Com_Ocom_OSemi(X4,X1),X3,X2))). 4.06/4.36 cnf(i_0_2202, plain, (c_List_Olist__ex1(X1,X2,c_Enum_Oenum__class_Oenum(X1))|esk167_3(X2,X1,X3)!=X3|~class_Enum_Oenum(X1)|~hBOOL(hAPP(X2,X3)))). 4.06/4.36 cnf(i_0_1630, plain, (hAPP(c_Int_ORep__Integ,esk123_1(X1))=X1|~hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg)))). 4.06/4.36 cnf(i_0_960, plain, (hBOOL(hAPP(c_Predicate_ODomainP(X1,X2,X3),X4))|~hBOOL(hAPP(hAPP(X3,X4),X5)))). 4.06/4.36 cnf(i_0_326, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.06/4.36 cnf(i_0_4113, plain, (c_Nat__Transfer_Otsub(X1,X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1)))). 4.06/4.36 cnf(i_0_6554, 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),X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.36 cnf(i_0_4007, plain, (hBOOL(hAPP(c_Predicate_ORangeP(X1,X2,X3),X4))|~hBOOL(hAPP(hAPP(X3,X5),X4)))). 4.06/4.36 cnf(i_0_4199, plain, (hAPP(c_List_Orotate1(X1),X2)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 4.06/4.36 cnf(i_0_2428, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ocomm__semiring__1(X1))). 4.06/4.36 cnf(i_0_5821, plain, (hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.06/4.36 cnf(i_0_6559, plain, (c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X2),X3,X4)|~c_Natural_Oevalc(X1,X3,X5)|~c_Natural_Oevalc(X2,X5,X4))). 4.06/4.36 cnf(i_0_6454, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)!=X2|~class_Lattices_Osemilattice__inf(X1))). 4.06/4.36 cnf(i_0_741, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)!=X3|~class_Lattices_Osemilattice__sup(X1))). 4.06/4.36 cnf(i_0_6257, plain, (hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_4221, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1))=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Obounded__lattice__bot(X1))). 4.06/4.36 cnf(i_0_3680, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X1),c_Divides_Odivmod__int(X2,X1))))). 4.06/4.36 cnf(i_0_1114, plain, (c_Equiv__Relations_Oequivp(X1,X2)|hAPP(X2,esk98_1(X2))!=hAPP(X2,esk99_1(X2))|~hBOOL(hAPP(hAPP(X2,esk98_1(X2)),esk99_1(X2))))). 4.06/4.36 cnf(i_0_7472, plain, (c_List_Olist__ex(X1,X2,X3)|c_List_Olist__ex(X1,X2,X4)|~c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4)))). 4.06/4.36 cnf(i_0_3238, plain, (c_Natural_Oevaln(X1,X2,X3,X4)|hBOOL(hAPP(X5,X2))|~c_Natural_Oevaln(c_Com_Ocom_OCond(X5,X6,X1),X2,X3,X4))). 4.06/4.36 cnf(i_0_2201, plain, (X1=esk168_2(X2,X3)|~c_List_Olist__ex1(X3,X2,c_Enum_Oenum__class_Oenum(X3))|~class_Enum_Oenum(X3)|~hBOOL(hAPP(X2,X1)))). 4.06/4.36 cnf(i_0_609, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.06/4.36 cnf(i_0_2407, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__no__zero__divisors(X1))). 4.06/4.36 cnf(i_0_2065, plain, (hAPP(c_List_Ohd(X1),X2)=hAPP(hAPP(c_List_Onth(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_List_Olist_ONil(X1)=X2)). 4.06/4.36 cnf(i_0_2539, plain, (X1=c_List_Olist_ONil(X2)|hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X2),tc_List_Olist(X2)),X3),c_List_Orotate1(X2)),X1)!=c_List_Olist_ONil(X2))). 4.06/4.36 cnf(i_0_5424, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),c_List_OtakeWhile(X3,X1,X4)))))). 4.06/4.36 cnf(i_0_2262, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|~hBOOL(hAPP(X1,X2)))). 4.06/4.36 cnf(i_0_801, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X2)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_5537, plain, (hBOOL(hAPP(c_List_Odistinct(X1),esk396_2(X2,X1)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_3830, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2)=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Obounded__lattice__bot(X1))). 4.06/4.36 cnf(i_0_4396, plain, (X1=X2|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X4,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X2)))). 4.06/4.36 cnf(i_0_3898, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|~c_List_Olist__all2(X1,X2,X3,hAPP(c_List_Orev(X1),X4),hAPP(c_List_Orev(X2),X5)))). 4.06/4.36 cnf(i_0_1349, 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))). 4.06/4.36 cnf(i_0_2408, 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))). 4.06/4.36 cnf(i_0_3067, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.06/4.36 cnf(i_0_5873, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.06/4.36 cnf(i_0_6836, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_1188, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2)=c_Orderings_Otop__class_Otop(X1)|~class_Lattices_Obounded__lattice__top(X1))). 4.06/4.36 cnf(i_0_6610, plain, (X1=X2|c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)!=hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))|~class_Orderings_Oorder(X3))). 4.06/4.36 cnf(i_0_6609, plain, (X1=X2|c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X2)!=hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))|~class_Orderings_Oorder(X3))). 4.06/4.36 cnf(i_0_800, plain, (hAPP(c_List_Oset(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X2))=X2|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_604, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Ocomm__semiring__1(X1))). 4.06/4.36 cnf(i_0_7170, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Equiv__Relations_Oequivp(X4,X1)|~hBOOL(hAPP(hAPP(X1,X3),X2)))). 4.06/4.36 cnf(i_0_6946, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Omult__zero(X1))). 4.06/4.36 cnf(i_0_5539, plain, (hAPP(c_List_Oset(X1),esk396_2(X2,X1))=X2|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_3790, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeastAtMost(X4,X1,X2,X5))))). 4.06/4.36 cnf(i_0_4068, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThanLessThan(X4,X1,X2,X5))))). 4.06/4.36 cnf(i_0_3791, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatLeastAtMost(X4,X1,X5,X3))))). 4.06/4.36 cnf(i_0_1026, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Odivision__ring(X1))). 4.06/4.36 cnf(i_0_1270, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Relation_OField(X1),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)))). 4.06/4.36 cnf(i_0_2184, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_OtakeWhile(X1,X2,X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.06/4.36 cnf(i_0_2583, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oinsert(X1,X2,X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.06/4.36 cnf(i_0_5357, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Osublist(X1,X2,X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.06/4.36 cnf(i_0_1645, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_3877, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2)=c_Groups_Oone__class_Oone(X1)|~class_Groups_Omonoid__mult(X1))). 4.06/4.36 cnf(i_0_4067, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OgreaterThanLessThan(X4,X1,X5,X3))))). 4.06/4.36 cnf(i_0_2966, plain, (c_Finite__Set_Ofun__left__comm(X1,tc_List_Olist(X1),c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_7337, plain, (c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.06/4.36 cnf(i_0_1175, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.06/4.36 cnf(i_0_3882, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremove1(X1,X2,X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.06/4.36 cnf(i_0_4692, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)=X2|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.06/4.36 cnf(i_0_1935, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.06/4.36 cnf(i_0_6245, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.06/4.36 cnf(i_0_2027, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.36 cnf(i_0_2026, 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)))). 4.06/4.36 cnf(i_0_5376, plain, (c_List_Olist__ex1(X1,X2,X3)|hBOOL(hAPP(X2,X4))|~c_List_Olist__ex1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)))). 4.06/4.36 cnf(i_0_1729, plain, (c_List_Olist__ex(X1,X2,X3)|hBOOL(hAPP(X2,X4))|~c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3)))). 4.06/4.36 cnf(i_0_3246, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)=X2|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.06/4.36 cnf(i_0_3205, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~c_Wellfounded_Owf(X1,X3))). 4.06/4.36 cnf(i_0_4785, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))))). 4.06/4.36 cnf(i_0_3236, plain, (c_Natural_Oevaln(X1,X2,X3,X4)|c_Natural_Oevaln(X5,X2,X3,X4)|~c_Natural_Oevaln(c_Com_Ocom_OCond(X6,X5,X1),X2,X3,X4))). 4.06/4.36 cnf(i_0_2020, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__semidom(X1))). 4.06/4.36 cnf(i_0_4091, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__semidom(X1))). 4.06/4.36 cnf(i_0_2183, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_2655, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Olinordered__ab__group__add(X1))). 4.06/4.36 cnf(i_0_6807, 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))). 4.06/4.36 cnf(i_0_2162, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1))))). 4.06/4.36 cnf(i_0_2233, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)))). 4.06/4.36 cnf(i_0_3211, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 4.06/4.36 cnf(i_0_2256, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)))|~hBOOL(hAPP(X1,esk174_3(X3,X2,X1)))|~hBOOL(hAPP(X1,X2)))). 4.06/4.36 cnf(i_0_6914, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|c_Sum__Type_OPlus(X2,X3,X1,X4)!=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X2,X3),tc_HOL_Obool)))). 4.06/4.36 cnf(i_0_6913, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Sum__Type_OPlus(X3,X1,X4,X2)!=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X3,X1),tc_HOL_Obool)))). 4.06/4.36 cnf(i_0_2152, plain, (hBOOL(hAPP(X1,X2))|hAPP(c_List_Ofilter(X3,X1),X4)!=hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))). 4.06/4.36 cnf(i_0_7273, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Ofilter(X1,X2),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.06/4.36 cnf(i_0_7127, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))))). 4.06/4.36 cnf(i_0_2132, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Otake(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_3362, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Odrop(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_5141, plain, (c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2),X3,X3)|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2),X4,X3)|~c_Natural_Oevalc(X2,X3,X4))). 4.06/4.36 cnf(i_0_5140, plain, (c_Natural_Oevalc(X1,X2,esk374_3(X2,X1,X3))|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X1),X2,X2)|~hBOOL(hAPP(X3,X2)))). 4.06/4.36 cnf(i_0_4679, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X4),X3))))). 4.06/4.36 cnf(i_0_4678, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4))))). 4.06/4.36 cnf(i_0_6898, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2))))). 4.06/4.36 cnf(i_0_6899, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))))). 4.06/4.36 cnf(i_0_2406, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__no__zero__divisors(X1))). 4.06/4.36 cnf(i_0_6644, plain, (c_Map_Omap__le(X1,X2,X3,X4)|hAPP(X4,esk471_4(X4,X3,X2,X1))!=hAPP(X3,esk471_4(X4,X3,X2,X1)))). 4.06/4.36 cnf(i_0_5897, plain, (X1=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.36 cnf(i_0_6433, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.06/4.36 cnf(i_0_657, plain, (c_SMT_Oz3div(X1,X2)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.06/4.36 cnf(i_0_423, plain, (X1=X2|~class_Orderings_Oorder(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),X2)))). 4.06/4.36 cnf(i_0_1606, plain, (hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))|~hBOOL(hAPP(hAPP(X3,X5),X4)))). 4.06/4.36 cnf(i_0_3905, 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))). 4.06/4.36 cnf(i_0_4608, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk331_1(X1)))|~hBOOL(hAPP(X1,X2)))). 4.06/4.36 cnf(i_0_1179, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))))). 4.06/4.36 cnf(i_0_4451, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Oinv__image(X2,X1),X3),X4))|~c_Wellfounded_Owf(X2,X3))). 4.06/4.36 cnf(i_0_4267, plain, (c_FunDef_Oreduction__pair(X1,hAPP(hAPP(c_FunDef_Orp__inv__image(X2,X1),X3),X4))|~c_FunDef_Oreduction__pair(X2,X3))). 4.06/4.36 cnf(i_0_3002, plain, (X1=X2|hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)!=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))). 4.06/4.36 cnf(i_0_2688, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))))). 4.06/4.36 cnf(i_0_4607, plain, (hBOOL(hAPP(X1,esk332_1(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))))). 4.06/4.36 cnf(i_0_2603, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1))). 4.06/4.36 cnf(i_0_6208, plain, (c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3)=c_Divides_Odiv__class_Omod(X1,X2,X3)|~class_Divides_Osemiring__div(X1))). 4.06/4.36 cnf(i_0_1760, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.06/4.36 cnf(i_0_4075, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.06/4.36 cnf(i_0_1911, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.06/4.36 cnf(i_0_3228, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.06/4.36 cnf(i_0_4523, plain, (c_List_Oinsert(X1,X2,X3)=X3|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.06/4.36 cnf(i_0_1464, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.06/4.36 cnf(i_0_2095, 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,esk156_1(X1))))). 4.06/4.36 cnf(i_0_2884, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))))). 4.06/4.36 cnf(i_0_4464, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))))). 4.06/4.36 cnf(i_0_3384, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2)))). 4.06/4.36 cnf(i_0_6364, plain, (c_List_Olast(X1,hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Ohd(X1),X2)|X2=c_List_Olist_ONil(X1))). 4.06/4.36 cnf(i_0_1810, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeastLessThan(X4,X1,X5,X2,X6))))). 4.06/4.36 cnf(i_0_1929, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThanAtMost(X4,X5,X1,X2,X6))))). 4.06/4.36 cnf(i_0_1811, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatLeastLessThan(X4,X5,X1,X6,X3))))). 4.06/4.36 cnf(i_0_1181, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),X2)))). 4.06/4.36 cnf(i_0_7462, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)))). 4.06/4.36 cnf(i_0_1928, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OgreaterThanAtMost(X4,X1,X5,X6,X3))))). 4.06/4.36 cnf(i_0_2768, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_1251, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))))). 4.06/4.36 cnf(i_0_1715, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)))). 4.06/4.36 cnf(i_0_6041, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))))). 4.06/4.36 cnf(i_0_923, plain, (hBOOL(hAPP(X1,X2))|hBOOL(hAPP(X3,X2))|~hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X1),X3),X2)))). 4.06/4.36 cnf(i_0_7375, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X1))|~c_Nat__Transfer_Onat__set(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1))))). 4.06/4.36 cnf(i_0_3441, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_1275, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)))). 4.06/4.36 cnf(i_0_4891, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)))). 4.06/4.36 cnf(i_0_3469, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(X1,esk261_2(X1,X3))))). 4.06/4.36 cnf(i_0_6116, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(X1,esk437_2(X1,X3))))). 4.06/4.36 cnf(i_0_4006, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),X4))|~hBOOL(hAPP(c_Predicate_OPowp(X3,X1),X4)))). 4.06/4.36 cnf(i_0_622, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X4),X1))|~hBOOL(hAPP(X4,X2)))). 4.06/4.36 cnf(i_0_2166, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~c_Fun_Oinj__on(X1,X3,X4,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2))))). 4.06/4.36 cnf(i_0_3717, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)|~c_List_Olist__all2(X1,X3,X5,X2,X4))). 4.06/4.36 cnf(i_0_4705, plain, (hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)=c_Groups_Oone__class_Oone(tc_Int_Oint)|hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))!=c_Groups_Oone__class_Oone(tc_Int_Oint))). 4.06/4.36 cnf(i_0_12, 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))). 4.06/4.36 cnf(i_0_3553, plain, (c_Equiv__Relations_Oequiv(tc_List_Olist(X1),c_List_Olists(X1,X2),c_List_Olistrel(X1,X3))|~c_Equiv__Relations_Oequiv(X1,X2,X3))). 4.06/4.36 cnf(i_0_4809, plain, (c_Relation_Orefl__on(tc_List_Olist(X1),c_List_Olists(X1,X2),c_List_Olistrel(X1,X3))|~c_Relation_Orefl__on(X1,X2,X3))). 4.06/4.36 cnf(i_0_4776, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2))))). 4.06/4.36 cnf(i_0_2349, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3))))). 4.06/4.36 cnf(i_0_6522, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2))))). 4.06/4.36 cnf(i_0_4748, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3))))). 4.06/4.36 cnf(i_0_1727, plain, (c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~c_List_Olist__ex(X1,X2,X4))). 4.06/4.36 cnf(i_0_7474, plain, (c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))|~c_List_Olist__ex(X1,X2,X4))). 4.06/4.36 cnf(i_0_7473, plain, (c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))|~c_List_Olist__ex(X1,X2,X3))). 4.06/4.36 cnf(i_0_4173, plain, (X1=c_Divides_Odiv__class_Omod(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),X4),X1))))). 4.06/4.36 cnf(i_0_7455, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)|~class_Rings_Oring__1(X1))). 4.06/4.36 cnf(i_0_1697, plain, (hAPP(c_List_Ohd(X1),hAPP(c_List_Orev(X1),X2))=c_List_Olast(X1,X2)|c_List_Olist_ONil(X1)=X2)). 4.06/4.36 cnf(i_0_2888, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)|~class_Rings_Olinordered__idom(X1))). 4.06/4.36 cnf(i_0_166, plain, (c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X2,X3),X4,X5,X6)|~c_Natural_Oevaln(X2,X4,X5,X6)|~hBOOL(hAPP(X1,X4)))). 4.06/4.36 cnf(i_0_1090, plain, (c_Wellfounded_OwfP(X1,X2)|~c_Wellfounded_OwfP(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X2),X3)))). 4.06/4.36 cnf(i_0_1698, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))=hAPP(c_Groups_Oabs__class_Oabs(X1),X2)|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.06/4.36 cnf(i_0_5846, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)|~class_Groups_Ocomm__monoid__add(X1))). 4.06/4.36 cnf(i_0_6455, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)=X2|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.06/4.36 cnf(i_0_5844, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)=X2|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.06/4.36 cnf(i_0_740, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)=X3|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.06/4.36 cnf(i_0_3085, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_Owf(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.06/4.36 cnf(i_0_4398, plain, (c_Wellfounded_Oacyclic(X1,X2)|~c_Wellfounded_Oacyclic(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.06/4.36 cnf(i_0_6173, plain, (c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X2,X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_6673, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)=X3|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.06/4.36 cnf(i_0_5124, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk370_3(X3,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.06/4.36 cnf(i_0_5339, plain, (~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk382_3(X3,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.06/4.36 cnf(i_0_7040, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Relation_OId__on(X3,X4))))). 4.06/4.36 cnf(i_0_6444, plain, (X1=c_Int_OMin|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))!=c_Int_OMin)). 4.06/4.36 cnf(i_0_1728, plain, (c_List_Olist__ex(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~hBOOL(hAPP(X2,X3)))). 4.06/4.36 cnf(i_0_2247, plain, (c_Nitpick_Osetsum_H(X1,X2,X3,X4)=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Ocomm__monoid__add(X2))). 4.06/4.36 cnf(i_0_4280, plain, (c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))|~c_Wellfounded_Oacyclic(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)))). 4.06/4.36 cnf(i_0_6488, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~class_Orderings_Olinorder(X3)|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X3,X4),X5),X2))))). 4.06/4.36 cnf(i_0_1764, plain, (hAPP(hAPP(c_List_Otake(X1),X2),X3)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)))). 4.06/4.36 cnf(i_0_6489, plain, (~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_List_Odistinct(X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X5))))). 4.06/4.36 cnf(i_0_72, plain, (X1=hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ogroup__add(X2))). 4.06/4.36 cnf(i_0_2862, plain, (X1=hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X3),X1)!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ogroup__add(X2))). 4.06/4.36 cnf(i_0_7016, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.06/4.36 cnf(i_0_6179, 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)). 4.06/4.36 cnf(i_0_2883, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2)))). 4.06/4.36 cnf(i_0_2185, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=X2|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_2165, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=X2|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.06/4.36 cnf(i_0_3252, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=X2|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.06/4.36 cnf(i_0_6003, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X2)=X2|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_218, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)))). 4.06/4.36 cnf(i_0_5496, plain, (c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X2,X3),X4,X5)|hBOOL(hAPP(X1,X4))|~c_Natural_Oevalc(X3,X4,X5))). 4.06/4.36 cnf(i_0_2416, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.06/4.36 cnf(i_0_3349, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1))))|~class_Enum_Oenum(X1))). 4.06/4.36 cnf(i_0_2388, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Int_Oring__1__class_OInts(X1)))|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_5262, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1))). 4.06/4.36 cnf(i_0_2269, plain, (c_Wellfounded_Owf(tc_prod(X1,X2),c_Wellfounded_Olex__prod(X1,X2,X3,X4))|~c_Wellfounded_Owf(X2,X4)|~c_Wellfounded_Owf(X1,X3))). 4.06/4.36 cnf(i_0_4329, plain, (c_Map_Omap__add(X1,X2,X3,X4)=c_Map_Omap__add(X1,X2,X4,X3)|~c_Map_Omap__le(X1,X2,X3,c_Map_Omap__add(X1,X2,X3,X4)))). 4.06/4.36 cnf(i_0_1392, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Rings_Osemiring__1(X1))). 4.06/4.36 cnf(i_0_5854, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1))). 4.06/4.36 cnf(i_0_1477, plain, (X1=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X1)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X2))). 4.06/4.36 cnf(i_0_1990, plain, (c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))=c_Smallcheck_Osmall_H(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)))). 4.06/4.36 cnf(i_0_588, plain, (c_List_Olistrelp(X1,X2,X3,X4)|~c_List_Olistrelp(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4)))). 4.06/4.36 cnf(i_0_7504, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|hAPP(c_Finite__Set_Ocard(X2),hAPP(c_Set_Oimage(X1,X2,X3),X4))!=hAPP(c_Finite__Set_Ocard(X1),X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.06/4.36 cnf(i_0_952, plain, (hAPP(c_List_Ofilter(X1,X2),X3)=c_List_Olist_ONil(X1)|hBOOL(hAPP(X2,esk88_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_563, 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),esk50_2(X3,X1)))|~hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(X1,X2)))). 4.06/4.36 cnf(i_0_556, plain, (esk49_3(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X2),X1)!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.06/4.36 cnf(i_0_2431, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2)=c_Big__Operators_Olattice__class_OSup__fin(X1,X2)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_4417, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2)=c_Big__Operators_Olattice__class_OInf__fin(X1,X2)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_5344, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omax(X1)),X2)=c_Big__Operators_Olinorder__class_OMax(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_6725, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)=c_Big__Operators_Olinorder__class_OMin(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_2057, plain, (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4))|~hBOOL(hAPP(X3,X4)))). 4.06/4.36 cnf(i_0_4787, plain, (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4))|~hBOOL(hAPP(X2,X4)))). 4.06/4.36 cnf(i_0_555, plain, (hAPP(c_Finite__Set_Ocard(X1),esk49_3(X2,X3,X1))=X2|hAPP(c_Nat_OSuc,X2)!=hAPP(c_Finite__Set_Ocard(X1),X3))). 4.06/4.36 cnf(i_0_1288, plain, (c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1))=c_List_Omonoid__add__class_Olistsum(X1)|~class_Groups_Omonoid__add(X1))). 4.06/4.36 cnf(i_0_954, plain, (hAPP(c_List_Ofilter(X1,X2),X3)!=c_List_Olist_ONil(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 4.06/4.36 cnf(i_0_782, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2,X1)),hAPP(c_Relation_Oconverse(X1,X2),X3))))). 4.06/4.36 cnf(i_0_375, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_5758, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_4717, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X3))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_2356, plain, (c_Natural_Oevalc(X1,X2,esk179_4(X3,X2,X1,X4))|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X4,X1),X2,X3)|~hBOOL(hAPP(X4,X2)))). 4.06/4.36 cnf(i_0_6146, plain, (c_Natural_Oevaln(X1,X2,X3,X4)|~c_Natural_Oevaln(X1,X2,X5,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X3)))). 4.06/4.36 cnf(i_0_6926, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))). 4.06/4.36 cnf(i_0_5957, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X2))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_3181, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.06/4.36 cnf(i_0_6956, plain, (~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_1752, plain, (c_Divides_OposDivAlg(X1,X2)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_1485, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2))|~c_Wellfounded_Owf(X1,X2))). 4.06/4.36 cnf(i_0_2357, plain, (X1=X2|c_Natural_Oevalc(X3,X1,esk179_4(X2,X1,X3,X4))|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X4,X3),X1,X2))). 4.06/4.36 cnf(i_0_5136, plain, (c_Natural_Oevaln(c_Com_Ocom_OBODY(X1),X2,hAPP(c_Nat_OSuc,X3),X4)|~c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3,X4))). 4.06/4.36 cnf(i_0_430, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_631, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(X1,esk58_1(X1))))). 4.06/4.36 cnf(i_0_3421, plain, (X1=X2|hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)!=hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1))). 4.06/4.36 cnf(i_0_1913, plain, (c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1)=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_1992, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 4.06/4.36 cnf(i_0_78, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_4019, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(X1,esk292_1(X1))))). 4.06/4.36 cnf(i_0_1196, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),X2)))). 4.06/4.36 cnf(i_0_4139, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_2419, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_4310, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=hAPP(c_Groups_Oabs__class_Oabs(X1),X2)|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.06/4.36 cnf(i_0_3127, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))!=X2)). 4.06/4.36 cnf(i_0_5457, plain, (c_Fun_Oinj__on(tc_Nat_Onat,X1,c_Nat_Osemiring__1__class_Oof__nat(X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))|~class_Nat_Osemiring__char__0(X1))). 4.06/4.36 cnf(i_0_6821, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),hAPP(c_Code__Numeral_Onat__of,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2)))). 4.06/4.36 cnf(i_0_3405, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_1759, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk132_2(X1,X2)),X1))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)))). 4.06/4.36 cnf(i_0_7555, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk528_2(X1,X2)),X1))|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)))). 4.06/4.36 cnf(i_0_532, plain, (c_List_Oremdups(X1,X2)=X2|hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))). 4.06/4.36 cnf(i_0_5405, plain, (c_Predicate_Oreflp(X1,X2)|~c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))). 4.06/4.36 cnf(i_0_1455, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=X3|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))). 4.06/4.36 cnf(i_0_3517, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=X3|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1))). 4.06/4.36 cnf(i_0_646, 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)|esk60_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.36 cnf(i_0_3866, plain, (c_List_Oremove1(X1,X2,c_List_Oremdups(X1,X3))=c_List_Oremdups(X1,c_List_Oremove1(X1,X2,X3))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.06/4.36 cnf(i_0_6215, plain, (c_Enum_Oproduct(X1,X2,c_Enum_Oenum__class_Oenum(X1),c_Enum_Oenum__class_Oenum(X2))=c_Enum_Oenum__class_Oenum(tc_prod(X1,X2))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1))). 4.06/4.36 cnf(i_0_2257, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X1)))|~hBOOL(hAPP(X2,esk174_3(X1,X3,X2))))). 4.06/4.36 cnf(i_0_2811, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))). 4.06/4.36 cnf(i_0_5842, plain, (~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_4572, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)=hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omax(X1)),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_1995, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)))). 4.06/4.36 cnf(i_0_5050, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)))). 4.06/4.36 cnf(i_0_2363, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(X1,esk180_3(X3,X2,X1)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.06/4.36 cnf(i_0_924, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)=hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_2938, plain, (c_List_Olist__ex(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 4.06/4.36 cnf(i_0_2571, plain, (hAPP(c_Map_Orestrict__map(X1,X2,X3,X4),X5)=hAPP(X3,X5)|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4)))). 4.06/4.36 cnf(i_0_1949, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(X1,esk146_3(X3,X2,X1)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.06/4.36 cnf(i_0_2229, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(X1,esk171_3(X3,X2,X1)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.06/4.36 cnf(i_0_1755, plain, (X1=hAPP(c_Nat_OSuc,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),X1),hAPP(c_Nat_OSuc,X2))))). 4.06/4.36 cnf(i_0_1859, 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))). 4.06/4.36 cnf(i_0_514, plain, (c_Natural_Oevaln(c_Com_Ocom_OSemi(X1,X2),X3,X4,X5)|~c_Natural_Oevaln(X2,X6,X4,X5)|~c_Natural_Oevaln(X1,X3,X4,X6))). 4.06/4.36 cnf(i_0_4923, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))))). 4.06/4.36 cnf(i_0_3475, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))))). 4.06/4.36 cnf(i_0_4340, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))))). 4.06/4.36 cnf(i_0_780, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))))). 4.06/4.36 cnf(i_0_1788, plain, (hAPP(c_List_Oset(X1),c_List_Olinorder__class_Osort__key(X1,X2,X3,X4))=hAPP(c_List_Oset(X1),X4)|~class_Orderings_Olinorder(X2))). 4.06/4.36 cnf(i_0_1124, plain, (~c_Fun_Oinj__on(X1,X2,X3,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),hAPP(c_Set_Oimage(X1,X2,X3),X4))),hAPP(c_Finite__Set_Ocard(X1),X4))))). 4.06/4.36 cnf(i_0_4761, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X1)!=c_Groups_Ozero__class_Ozero(X2)|~class_Int_Oring__char__0(X2)|~hBOOL(hAPP(hAPP(c_member(X2),X1),c_Int_Oring__1__class_OInts(X2))))). 4.06/4.36 cnf(i_0_4573, plain, (hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),c_Enum_On__lists(X1,X2,X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.06/4.36 cnf(i_0_3695, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))). 4.06/4.36 cnf(i_0_3698, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))). 4.06/4.36 cnf(i_0_2001, plain, (c_Divides_Odivmod__int(X1,X2)=c_Divides_OposDivAlg(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.06/4.36 cnf(i_0_513, plain, (c_Natural_Oevaln(X1,X2,X3,esk46_5(X4,X3,X2,X5,X1))|~c_Natural_Oevaln(c_Com_Ocom_OSemi(X1,X5),X2,X3,X4))). 4.06/4.36 cnf(i_0_512, plain, (c_Natural_Oevaln(X1,esk46_5(X2,X3,X4,X1,X5),X3,X2)|~c_Natural_Oevaln(c_Com_Ocom_OSemi(X5,X1),X4,X3,X2))). 4.06/4.36 cnf(i_0_2920, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Groups_Ogroup__add(X1))). 4.06/4.36 cnf(i_0_5213, 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))). 4.06/4.36 cnf(i_0_1141, plain, (c_Nitpick_Ounknown(tc_HOL_Obool)|hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))|~c_Nitpick_Owf_H(X1,X2))). 4.06/4.36 cnf(i_0_4374, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.06/4.36 cnf(i_0_7450, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_3826, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)))). 4.06/4.36 cnf(i_0_2094, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk157_1(X1)))|hBOOL(hAPP(X1,X2)))). 4.06/4.36 cnf(i_0_1271, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_681, plain, (hBOOL(hAPP(X1,X2))|~c_List_Olist__all(X3,X1,X4)|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))))). 4.06/4.36 cnf(i_0_3336, 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,esk254_2(X1,X2))))). 4.06/4.36 cnf(i_0_6399, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3))|hAPP(hAPP(c_List_Odrop(X1),X3),X2)!=c_List_Olist_ONil(X1))). 4.06/4.36 cnf(i_0_6185, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,X2)=c_Complete__Lattice_OSup__class_OSup(X1,X2)|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_136, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,X2)=c_Complete__Lattice_OInf__class_OInf(X1,X2)|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_1751, plain, (c_Divides_OposDivAlg(X1,X2)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_114, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X2)))). 4.06/4.36 cnf(i_0_855, plain, (c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X3,X4,X3)|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X5,X4,X3)|~c_Natural_Oevaln(X2,X3,X4,X5))). 4.06/4.36 cnf(i_0_626, plain, (hBOOL(hAPP(X1,esk56_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(X1,X3)))). 4.06/4.36 cnf(i_0_4278, plain, (hBOOL(hAPP(X1,esk310_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(X1,X3)))). 4.06/4.36 cnf(i_0_1656, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=c_Groups_Ozero__class_Ozero(X1)|hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)!=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber(X1))). 4.06/4.36 cnf(i_0_2385, plain, (X1=X2|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_2241, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Relation_ORange(X2,X1),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2,X1)),X3)))). 4.06/4.36 cnf(i_0_1850, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Relation_ODomain(X1,X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),X3)))). 4.06/4.36 cnf(i_0_7141, plain, (c_List_Olist_ONil(X1)=X2|hBOOL(hAPP(c_List_Odistinct(X1),c_List_Obutlast(X1,X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.06/4.36 cnf(i_0_2074, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)!=X3)). 4.06/4.36 cnf(i_0_4486, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.06/4.36 cnf(i_0_4587, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1)))). 4.06/4.36 cnf(i_0_490, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk42_1(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_5135, plain, (c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3,X4)|~c_Natural_Oevaln(c_Com_Ocom_OBODY(X1),X2,hAPP(c_Nat_OSuc,X3),X4))). 4.06/4.36 cnf(i_0_6080, 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,esk435_2(X1,X2)))))). 4.06/4.36 cnf(i_0_4328, plain, (c_Map_Omap__le(X1,X2,X3,c_Map_Omap__add(X1,X2,X3,X4))|c_Map_Omap__add(X1,X2,X3,X4)!=c_Map_Omap__add(X1,X2,X4,X3))). 4.06/4.36 cnf(i_0_1005, plain, (c_List_Olist_ONil(X1)=X2|c_List_Otranspose(X1,X3)!=c_List_Olist_ONil(tc_List_Olist(X1))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),hAPP(c_List_Oset(tc_List_Olist(X1)),X3))))). 4.06/4.36 cnf(i_0_1757, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk133_1(X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2)))). 4.06/4.36 cnf(i_0_7553, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),esk529_1(X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2)))). 4.06/4.36 cnf(i_0_909, plain, (c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))|~c_List_Olist__all(X1,X2,X3)|~c_List_Olist__all(X1,X2,X4))). 4.06/4.36 cnf(i_0_6950, plain, (c_List_OtakeWhile(X1,X2,X3)=hAPP(c_List_Ofilter(X1,X2),X3)|hBOOL(hAPP(X2,esk488_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_5681, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osort__key(X1,X2,X3,X4)))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X4)))). 4.06/4.36 cnf(i_0_2317, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2)))). 4.06/4.36 cnf(i_0_518, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk47_2(X2,X1))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_6849, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_6663, plain, (c_Relation_Osingle__valued(X1,X2,X3)|~c_Relation_Osingle__valued(X1,X2,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))). 4.06/4.36 cnf(i_0_7070, 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))). 4.06/4.36 cnf(i_0_3506, plain, (X1=c_Groups_Oone__class_Oone(tc_Int_Oint)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.06/4.36 cnf(i_0_3505, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_999, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(X2,X1,X3),X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.06/4.36 cnf(i_0_4977, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)))|~class_Rings_Olinordered__semidom(X1))). 4.06/4.36 cnf(i_0_5454, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.06/4.36 cnf(i_0_5220, 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)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.06/4.36 cnf(i_0_6225, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X2))))). 4.06/4.36 cnf(i_0_7567, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Osgn__class_Osgn(X1,X2))=hAPP(c_Groups_Oabs__class_Oabs(X1),X2)|~class_Rings_Olinordered__idom(X1))). 4.06/4.36 cnf(i_0_7387, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|c_Groups_Osgn__class_Osgn(X1,X2)!=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1))). 4.06/4.36 cnf(i_0_418, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|~c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4),hAPP(hAPP(c_List_Olist_OCons(X2),X7),X5)))). 4.06/4.36 cnf(i_0_637, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_2687, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_2512, plain, (hAPP(hAPP(c_List_Odrop(X1),X2),X3)=c_List_Olist_ONil(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2)))). 4.06/4.36 cnf(i_0_3788, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OgreaterThan(X1,X3,X4)))|~hBOOL(hAPP(hAPP(X3,X4),X2)))). 4.06/4.36 cnf(i_0_6292, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=c_List_Olast(X1,X3)|X3=c_List_Olist_ONil(X1))). 4.06/4.36 cnf(i_0_2534, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk186_2(X1,X2))=X2|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.36 cnf(i_0_277, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk22_2(X1,X2))=X2|c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.06/4.36 cnf(i_0_3773, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.06/4.36 cnf(i_0_2990, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3))=c_List_Olast(X1,X3)|X3=c_List_Olist_ONil(X1))). 4.06/4.36 cnf(i_0_4211, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatLeast(X1,X3,X4)))|~hBOOL(hAPP(hAPP(X3,X4),X2)))). 4.06/4.36 cnf(i_0_1705, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OlessThan(X1,X3,X4)))|~hBOOL(hAPP(hAPP(X3,X2),X4)))). 4.06/4.36 cnf(i_0_3501, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatMost(X1,X3,X4)))|~hBOOL(hAPP(hAPP(X3,X2),X4)))). 4.06/4.36 cnf(i_0_3853, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3))))). 4.06/4.36 cnf(i_0_71, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 4.06/4.36 cnf(i_0_4549, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.06/4.36 cnf(i_0_7413, plain, (hAPP(c_List_Ofilter(X1,X2),c_List_Oreplicate(X1,X3,X4))=c_List_Oreplicate(X1,X3,X4)|~hBOOL(hAPP(X2,X4)))). 4.06/4.36 cnf(i_0_6955, plain, (c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1))). 4.06/4.36 cnf(i_0_3854, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))))). 4.06/4.36 cnf(i_0_4812, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3))))). 4.06/4.36 cnf(i_0_5335, plain, (X1=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Int_OMin=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)!=c_Groups_Oone__class_Oone(tc_Int_Oint))). 4.06/4.36 cnf(i_0_3612, plain, (c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1))). 4.06/4.36 cnf(i_0_7527, plain, (c_List_Olist__all(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~c_List_Olist__all(X1,X2,X4)|~hBOOL(hAPP(X2,X3)))). 4.06/4.36 cnf(i_0_167, plain, (c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X2,X3),X4,X5,X6)|hBOOL(hAPP(X1,X4))|~c_Natural_Oevaln(X3,X4,X5,X6))). 4.06/4.36 cnf(i_0_4813, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))))). 4.06/4.36 cnf(i_0_2382, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3)))). 4.06/4.36 cnf(i_0_2381, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)))). 4.06/4.36 cnf(i_0_5332, plain, (X1=c_Groups_Oone__class_Oone(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))). 4.06/4.36 cnf(i_0_2794, 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),esk206_3(X3,X1,X2))))). 4.06/4.36 cnf(i_0_3286, 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))). 4.06/4.36 cnf(i_0_2954, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3)))). 4.06/4.36 cnf(i_0_2955, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)))). 4.06/4.36 cnf(i_0_5480, plain, (hBOOL(hAPP(hAPP(X1,X2),esk393_2(X2,X1)))|~hBOOL(hAPP(c_Predicate_ODomainP(X3,X4,X1),X2)))). 4.06/4.36 cnf(i_0_5601, 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),esk400_4(hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),X1,X3,X2))))). 4.06/4.36 cnf(i_0_274, plain, (X1=X2|hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))!=hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))). 4.06/4.36 cnf(i_0_7258, plain, (X1=X2|hAPP(c_Set_Oimage(X3,X4,X5),X1)!=hAPP(c_Set_Oimage(X3,X4,X5),X2)|~c_Fun_Oinj__on(X3,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))). 4.06/4.36 cnf(i_0_875, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.06/4.36 cnf(i_0_2034, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.06/4.36 cnf(i_0_6806, plain, (hBOOL(hAPP(hAPP(X1,esk478_2(X2,X1)),X2))|~hBOOL(hAPP(c_Predicate_ORangeP(X3,X4,X1),X2)))). 4.06/4.36 cnf(i_0_7205, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)))|~class_Lattices_Olattice(X1))). 4.06/4.36 cnf(i_0_5173, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)))|~class_Lattices_Osemilattice__sup(X1))). 4.06/4.36 cnf(i_0_5333, plain, (X1=c_Groups_Oone__class_Oone(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))). 4.06/4.36 cnf(i_0_7412, plain, (hAPP(c_List_Ofilter(X1,X2),c_List_Oreplicate(X1,X3,X4))=c_List_Olist_ONil(X1)|hBOOL(hAPP(X2,X4)))). 4.06/4.36 cnf(i_0_4301, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X3)=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.06/4.36 cnf(i_0_589, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_List_Olistrelp(X4,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6)))). 4.06/4.36 cnf(i_0_4794, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|~c_Fun_Oinj__on(X1,X2,X3,X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5)))). 4.06/4.36 cnf(i_0_4546, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Oboolean__algebra(X1))). 4.06/4.36 cnf(i_0_1284, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)))|~class_Lattices_Olattice(X1))). 4.06/4.36 cnf(i_0_3740, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)))|~class_Lattices_Osemilattice__sup(X1))). 4.06/4.36 cnf(i_0_2563, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X3))|~class_Lattices_Olattice(X1))). 4.06/4.36 cnf(i_0_3268, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X3))|~class_Lattices_Osemilattice__inf(X1))). 4.06/4.36 cnf(i_0_5334, plain, (X1=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Int_OMin=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)!=c_Groups_Oone__class_Oone(tc_Int_Oint))). 4.06/4.36 cnf(i_0_6929, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=c_Orderings_Otop__class_Otop(X1)|~class_Lattices_Oboolean__algebra(X1))). 4.06/4.36 cnf(i_0_7305, plain, (X1=X2|hAPP(c_Set_Oimage(X3,X4,X5),X1)!=hAPP(c_Set_Oimage(X3,X4,X5),X2)|~c_Fun_Oinj__on(X3,X4,X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X1),X2)))). 4.06/4.36 cnf(i_0_5620, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,esk405_4(X1,X3,X4,X5)))|~hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))). 4.06/4.36 cnf(i_0_5619, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,esk405_4(X1,X3,X4,X5)))|~hBOOL(hAPP(hAPP(c_member(X5),X2),X3)))). 4.06/4.36 cnf(i_0_6005, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ogroup__add(X1))). 4.06/4.36 cnf(i_0_4121, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X2))|~class_Lattices_Olattice(X1))). 4.06/4.36 cnf(i_0_4515, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X2))|~class_Lattices_Osemilattice__inf(X1))). 4.06/4.36 cnf(i_0_6268, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3))=X2|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_7533, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3))=X2|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_1279, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oab__group__add(X1))). 4.06/4.36 cnf(i_0_3875, 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,esk285_3(X2,X3,X1))!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.06/4.36 cnf(i_0_6153, 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,esk441_3(X2,X3,X1))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.06/4.36 cnf(i_0_601, plain, (c_Orderings_Oord_Omax(X1,hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1)))=c_Orderings_Oord__class_Omin(X1)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_614, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)=c_Orderings_Obot__class_Obot(X1)|~class_Lattices_Oboolean__algebra(X1))). 4.06/4.36 cnf(i_0_4096, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)=c_Orderings_Otop__class_Otop(X1)|~class_Lattices_Oboolean__algebra(X1))). 4.06/4.36 cnf(i_0_1559, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X1))|~class_Orderings_Oorder(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),X1)))). 4.06/4.36 cnf(i_0_3155, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))|~class_Orderings_Olinorder(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),X2)))). 4.06/4.36 cnf(i_0_2472, plain, (c_Orderings_Oord_Omin(X1,hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1)))=c_Orderings_Oord__class_Omax(X1)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_2546, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2))))). 4.06/4.36 cnf(i_0_5566, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_1056, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool)))))). 4.06/4.36 cnf(i_0_6249, 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_Ono__zero__divisors(X1)|~class_Rings_Omult__zero(X1)|~class_Rings_Ozero__neq__one(X1)|~class_Power_Opower(X1))). 4.06/4.36 cnf(i_0_6434, plain, (c_Groups_Oone__class_Oone(tc_Int_Oint)=X1|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X3))))). 4.06/4.36 cnf(i_0_3259, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|c_Groups_Ozero__class_Ozero(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),X3),X2))))). 4.06/4.36 cnf(i_0_4653, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))))). 4.06/4.36 cnf(i_0_636, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,esk59_4(X2,X3,X1,X4)))|~hBOOL(hAPP(X2,X3)))). 4.06/4.36 cnf(i_0_2308, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))))). 4.06/4.36 cnf(i_0_854, plain, (c_Natural_Oevaln(X1,X2,X3,esk84_4(X3,X2,X1,X4))|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X1),X2,X3,X2)|~hBOOL(hAPP(X4,X2)))). 4.06/4.36 cnf(i_0_2998, plain, (c_Nitpick_Orefl_H(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk221_2(X2,X1)),esk221_2(X2,X1))),X2)))). 4.06/4.36 cnf(i_0_5572, plain, (hBOOL(hAPP(X1,X2))|c_List_OtakeWhile(X3,X1,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))))). 4.06/4.36 cnf(i_0_2253, plain, (c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2),X3,X4)|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2),X5,X4)|~c_Natural_Oevalc(X2,X3,X5)|~hBOOL(hAPP(X1,X3)))). 4.06/4.36 cnf(i_0_2307, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))))). 4.06/4.36 cnf(i_0_1567, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)=X3|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))))). 4.06/4.36 cnf(i_0_1803, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(c_Divides_OnegateSnd,X3)))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)),X3)))). 4.06/4.36 cnf(i_0_2364, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1)))|~hBOOL(hAPP(X2,esk180_3(X1,X3,X2))))). 4.06/4.36 cnf(i_0_4554, plain, (c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X2,X3)=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.06/4.36 cnf(i_0_5139, plain, (c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2),esk374_3(X3,X2,X1),X3)|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2),X3,X3)|~hBOOL(hAPP(X1,X3)))). 4.06/4.36 cnf(i_0_4378, plain, (hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5)=c_Option_Ooption_ONone(X2)|hAPP(X3,X5)!=c_Option_Ooption_ONone(X2)|hAPP(X4,X5)!=c_Option_Ooption_ONone(X2))). 4.06/4.36 cnf(i_0_6053, plain, (hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)))). 4.06/4.36 cnf(i_0_2596, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~c_List_Omember(X1,X3,X2))). 4.06/4.36 cnf(i_0_4064, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),esk294_2(X1,X2)),X1)))). 4.06/4.36 cnf(i_0_215, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.06/4.36 cnf(i_0_1732, plain, (c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),X3,c_Map_Odom(X1,X2,X3))|~c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),c_Map_Omap__add(X1,X2,X4,X3),c_Map_Odom(X1,X2,X3)))). 4.06/4.36 cnf(i_0_1845, plain, (hAPP(c_Fun_Ooverride__on(X1,X2,X3,X4,X5),X6)=hAPP(X4,X6)|~hBOOL(hAPP(hAPP(c_member(X1),X6),X5)))). 4.06/4.36 cnf(i_0_565, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),esk51_2(X1,X2)),X1)))). 4.06/4.36 cnf(i_0_4178, plain, (hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)))). 4.06/4.36 cnf(i_0_3250, plain, (hAPP(c_Nat_OSuc,esk246_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))))). 4.06/4.36 cnf(i_0_5315, plain, (hBOOL(hAPP(hAPP(X1,esk381_3(X2,X1,X3)),X2))|hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)))). 4.06/4.36 cnf(i_0_6328, plain, (hBOOL(hAPP(hAPP(X1,esk447_3(X2,X1,X3)),X2))|hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)))). 4.06/4.36 cnf(i_0_2965, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.06/4.36 cnf(i_0_725, plain, (X1=hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2))|hAPP(c_List_Orev(X2),X1)!=hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Olist_ONil(X2)))). 4.06/4.36 cnf(i_0_1599, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OInf__class_OInf(X1,X2)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2)))). 4.06/4.36 cnf(i_0_2174, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.06/4.36 cnf(i_0_4769, plain, (c_List_Olist__ex1(X1,X2,X3)|esk347_4(X3,X2,X1,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 4.06/4.36 cnf(i_0_1665, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X1))))). 4.06/4.36 cnf(i_0_230, 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)))). 4.06/4.36 cnf(i_0_1780, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.06/4.36 cnf(i_0_5273, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)))). 4.06/4.36 cnf(i_0_7265, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2)))). 4.06/4.36 cnf(i_0_4634, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk334_1(X1)))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))). 4.06/4.36 cnf(i_0_3747, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_5748, plain, (hAPP(c_Finite__Set_Ofold1(X1,X2),X3)=hAPP(X4,X3)|~c_Finite__Set_Ofolding__one(X1,X2,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.06/4.36 cnf(i_0_753, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4))|~class_Orderings_Oord(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4)))). 4.06/4.36 cnf(i_0_5741, plain, (c_Divides_Odivmod__int(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.06/4.36 cnf(i_0_6134, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))))). 4.06/4.36 cnf(i_0_6135, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))))). 4.06/4.36 cnf(i_0_3284, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(X3),X1),X4))|~hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X2),X4))))). 4.06/4.36 cnf(i_0_6348, plain, (c_Random_Ominus__shift(X1,X2,X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X2),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X2),X3)))). 4.06/4.36 cnf(i_0_997, plain, (hAPP(c_COMBK(tc_Option_Ooption(X1),X2),c_Option_Ooption_ONone(X1))=X3|c_Map_Odom(X2,X1,X3)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.36 cnf(i_0_701, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_171, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_3999, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Groups_Oabs__if(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_3933, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X1)))). 4.06/4.36 cnf(i_0_6172, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))))). 4.06/4.36 cnf(i_0_407, 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))). 4.06/4.36 cnf(i_0_3072, 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),esk229_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_4833, plain, (hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))|~hBOOL(hAPP(X1,esk353_3(X3,X2,X1)))|~hBOOL(hAPP(X1,esk355_3(X3,X2,X1)))|~hBOOL(hAPP(X1,X2)))). 4.06/4.36 cnf(i_0_4432, 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),esk320_3(X3,X2,X1)),X3)))). 4.06/4.36 cnf(i_0_271, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))))). 4.06/4.36 cnf(i_0_7144, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),X4))|~c_Typedef_Otype__definition(X5,X1,X2,X6,X4))). 4.06/4.36 cnf(i_0_419, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_List_Olist__all2(X4,X5,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X6),hAPP(hAPP(c_List_Olist_OCons(X5),X3),X7)))). 4.06/4.36 cnf(i_0_1955, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))))). 4.06/4.36 cnf(i_0_3261, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3)))). 4.06/4.36 cnf(i_0_2604, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1)))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1))). 4.06/4.36 cnf(i_0_187, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X3,X4),esk14_3(X4,X3,X1)),esk15_3(X4,X3,X1)))))). 4.06/4.36 cnf(i_0_5346, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X6),X1),X2),X3)))). 4.06/4.36 cnf(i_0_2804, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X1),X6),X2),X3)))). 4.06/4.36 cnf(i_0_2494, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_256, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_7392, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)|~class_Rings_Ocomm__semiring__1(X1))). 4.06/4.36 cnf(i_0_7353, 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))). 4.06/4.36 cnf(i_0_4775, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.06/4.36 cnf(i_0_6523, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.06/4.36 cnf(i_0_2348, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.06/4.36 cnf(i_0_4431, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)|~class_Lattices_Olattice(X1))). 4.06/4.36 cnf(i_0_1820, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oorder(X1))). 4.06/4.36 cnf(i_0_2330, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=c_Groups_Oone__class_Oone(X1)|c_Groups_Ozero__class_Ozero(X1)=X2|~class_Groups_Osgn__if(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.06/4.36 cnf(i_0_7506, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.06/4.36 cnf(i_0_837, plain, (c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=c_List_Olist_ONil(X1)|hBOOL(hAPP(X2,X3)))). 4.06/4.36 cnf(i_0_4747, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.06/4.36 cnf(i_0_727, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3))))). 4.06/4.36 cnf(i_0_728, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))))). 4.06/4.36 cnf(i_0_3751, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X2)|~class_Lattices_Osemilattice__sup(X1))). 4.06/4.36 cnf(i_0_684, plain, (c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),c_List_Oremdups(X1,X2))=c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(c_List_Oset(X1),X2))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_4654, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)=X2|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.36 cnf(i_0_2080, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Oring__char__0(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))))). 4.06/4.36 cnf(i_0_2647, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X2)),X3)))). 4.06/4.36 cnf(i_0_5564, plain, (c_Fun_Oinj__on(X1,X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Set_Oimage(X1,X1,X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.06/4.36 cnf(i_0_2784, plain, (hBOOL(hAPP(c_List_Odistinct(X1),X2))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X3),c_List_Orotate1(X1)),X2))))). 4.06/4.36 cnf(i_0_2648, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3)))). 4.06/4.36 cnf(i_0_2763, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.06/4.36 cnf(i_0_5474, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)|~class_Rings_Ocomm__semiring__1(X1))). 4.06/4.36 cnf(i_0_3115, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)!=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)|~hBOOL(hAPP(X2,X4)))). 4.06/4.36 cnf(i_0_641, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))=c_List_Olist_ONil(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.06/4.36 cnf(i_0_4728, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))|~hBOOL(hAPP(hAPP(X2,X3),X4))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X4)))). 4.06/4.36 cnf(i_0_196, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))=X2|~class_Rings_Olinordered__idom(X1))). 4.06/4.36 cnf(i_0_485, 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),esk41_3(X2,X3,X1))))). 4.06/4.36 cnf(i_0_6495, 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),esk460_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_6620, 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),esk468_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_2692, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),esk194_3(X3,X2,X1)),X3)))). 4.06/4.36 cnf(i_0_4368, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))=c_List_Olist_ONil(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_6699, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(c_List_Oset(X1),X2))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.06/4.36 cnf(i_0_5726, plain, (c_Relation_Ototal__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk416_3(X3,X2,X1)),X2)))). 4.06/4.36 cnf(i_0_7433, plain, (X1=c_Enum_Oenum__the(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X2,X3))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X3),X1)))). 4.06/4.36 cnf(i_0_790, 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))))). 4.06/4.36 cnf(i_0_4172, plain, (hAPP(X1,hAPP(X2,X3))=X3|~c_Typedef_Otype__definition(X4,X5,X1,X2,X6)|~hBOOL(hAPP(hAPP(c_member(X5),X3),X6)))). 4.06/4.36 cnf(i_0_5725, plain, (c_Relation_Ototal__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk417_3(X3,X2,X1)),X2)))). 4.06/4.36 cnf(i_0_1562, 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),esk119_1(X1)))))). 4.06/4.36 cnf(i_0_696, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4)))|~hBOOL(hAPP(c_List_Olistsp(X3,X1),X4)))). 4.06/4.36 cnf(i_0_4548, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3))=X2|~class_Lattices_Olattice(X1))). 4.06/4.36 cnf(i_0_947, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)|~class_Lattices_Olattice(X1))). 4.06/4.36 cnf(i_0_1236, plain, (hAPP(c_Map_Orestrict__map(X1,X2,X3,X4),X5)=c_Option_Ooption_ONone(X2)|hBOOL(hAPP(hAPP(c_member(X1),X5),X4)))). 4.06/4.36 cnf(i_0_68, plain, (hAPP(X1,esk5_5(X2,X3,X1,X4,X5))=X2|hAPP(c_Option_Ooption_OSome(X4),X2)!=hAPP(hAPP(c_Option_Omap(X5,X4),X1),X3))). 4.06/4.36 cnf(i_0_3749, plain, (hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Oinsort__insert__key(X1,X2,X3,X4,X5)))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X5)))). 4.06/4.36 cnf(i_0_834, plain, (X1=hAPP(hAPP(c_Finite__Set_Ofold(X2,X3,X4),X5),X6)|~c_Finite__Set_Ofun__left__comm(X2,X3,X4)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X2,X3,X4,X5,X6),X1)))). 4.06/4.36 cnf(i_0_1717, plain, (~hBOOL(hAPP(hAPP(c_member(X1),esk130_5(X2,X3,X4,X5,X1)),esk131_5(X2,X3,X4,X5,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2)))). 4.06/4.36 cnf(i_0_3982, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3))=X2|~class_Lattices_Olattice(X1))). 4.06/4.36 cnf(i_0_6911, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X3)=X2|~class_Groups_Ogroup__add(X1))). 4.06/4.36 cnf(i_0_5915, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X3)=X2|~class_Groups_Ogroup__add(X1))). 4.06/4.36 cnf(i_0_7168, plain, (~hBOOL(hAPP(hAPP(c_member(X1),esk501_5(X2,X3,X4,X5,X1)),esk502_5(X2,X3,X4,X5,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2)))). 4.06/4.36 cnf(i_0_3707, plain, (X1=X2|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3,X4),X1)!=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3,X5),X2)|~class_Orderings_Olinorder(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X5),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X4),X1)))). 4.06/4.36 cnf(i_0_2717, plain, (X1=X2|hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3,X1),X4)!=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X3,X2),X5)|~class_Orderings_Olinorder(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X4)))). 4.06/4.36 cnf(i_0_3341, plain, (hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))=hAPP(c_List_Ohd(X1),X2)|X2=c_List_Olist_ONil(X1))). 4.06/4.36 cnf(i_0_3337, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk254_2(X1,X2))=X1|hBOOL(hAPP(X2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))|~hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.06/4.36 cnf(i_0_3389, plain, (hAPP(c_Nat_OSuc,X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_6186, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1))))). 4.06/4.36 cnf(i_0_1597, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1))))). 4.06/4.36 cnf(i_0_3212, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)|~class_Lattices_Osemilattice__inf(X1))). 4.06/4.36 cnf(i_0_2776, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_5132, plain, (hBOOL(hAPP(X1,X2))|hAPP(c_List_Ofilter(X3,X1),X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))))). 4.06/4.36 cnf(i_0_4271, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)),c_Groups_Ozero__class_Ozero(X2))))). 4.06/4.36 cnf(i_0_3396, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Oring__1__class_Oof__int(X2),X1)),c_Groups_Ozero__class_Ozero(X2))))). 4.06/4.36 cnf(i_0_6628, plain, (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4))|~hBOOL(hAPP(X3,X4))|~hBOOL(hAPP(X2,X4)))). 4.06/4.36 cnf(i_0_1456, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.06/4.36 cnf(i_0_3541, plain, (hAPP(X1,esk267_3(X1,X2,X3))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 4.06/4.36 cnf(i_0_4147, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),esk300_3(X3,X2,X1)),c_Wellfounded_Oacc(X1,X3))))). 4.06/4.36 cnf(i_0_4966, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),esk360_3(X3,X2,X1)),c_Wellfounded_Oacc(X1,X3))))). 4.06/4.36 cnf(i_0_2409, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_2461, plain, (c_Option_Ooption_ONone(X1)=hAPP(X2,X3)|hBOOL(hAPP(hAPP(c_member(X4),X3),c_Map_Odom(X4,X1,X2))))). 4.06/4.36 cnf(i_0_6472, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),esk458_3(X3,X2,X1)),c_Wellfounded_Oacc(X1,X3))))). 4.06/4.36 cnf(i_0_4640, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1))). 4.06/4.36 cnf(i_0_4830, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.06/4.36 cnf(i_0_4731, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_343, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_3192, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3)=c_Divides_Odiv__class_Omod(X1,X2,X3)|~class_Divides_Osemiring__div(X1))). 4.06/4.36 cnf(i_0_119, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X2)=c_Divides_Odiv__class_Omod(X1,X3,X2)|~class_Divides_Osemiring__div(X1))). 4.06/4.36 cnf(i_0_820, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_4151, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2))=hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_2695, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.06/4.36 cnf(i_0_3383, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_5214, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=X1|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))). 4.06/4.36 cnf(i_0_593, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_5066, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Ozero__class_Ozero(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_2698, plain, (c_List_Olist__ex(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|~hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),X4))))). 4.06/4.36 cnf(i_0_4243, 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)))))). 4.06/4.36 cnf(i_0_6112, 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))). 4.06/4.36 cnf(i_0_2226, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2))=hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_1706, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.06/4.36 cnf(i_0_6040, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.06/4.36 cnf(i_0_2476, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~class_Rings_Olinordered__semidom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2))))). 4.06/4.36 cnf(i_0_1038, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~class_Rings_Olinordered__idom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Oring__1__class_Oof__int(X3),X1)),hAPP(c_Int_Oring__1__class_Oof__int(X3),X2))))). 4.06/4.36 cnf(i_0_4408, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2))=hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_6113, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3))!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__ring__strict(X2))). 4.06/4.36 cnf(i_0_3672, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2,X1),tc_HOL_Obool)))))). 4.06/4.36 cnf(i_0_3582, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2,X1),tc_HOL_Obool)))))). 4.06/4.36 cnf(i_0_3581, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool)))))). 4.06/4.36 cnf(i_0_6897, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(X2)|~class_Groups_Ocomm__monoid__mult(X2))). 4.06/4.36 cnf(i_0_3917, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~class_Rings_Olinordered__semidom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2))))). 4.06/4.36 cnf(i_0_6305, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~class_Rings_Olinordered__idom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Oring__1__class_Oof__int(X3),X1)),hAPP(c_Int_Oring__1__class_Oof__int(X3),X2))))). 4.06/4.36 cnf(i_0_577, plain, (c_Natural_Oevaln(X1,X2,X3,esk53_5(X4,X3,X2,X1,X5))|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X5,X1),X2,X3,X4)|~hBOOL(hAPP(X5,X2)))). 4.06/4.36 cnf(i_0_639, 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))). 4.06/4.36 cnf(i_0_5102, plain, (hAPP(hAPP(c_List_Onth(X1),c_List_Oreplicate(X1,X2,X3)),X4)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X2)))). 4.06/4.36 cnf(i_0_159, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X1)),X2))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1)))))). 4.06/4.36 cnf(i_0_6346, plain, (c_SMT_Oz3mod(X1,X2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.06/4.36 cnf(i_0_562, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk50_2(X1,X2)),X1))|hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X2,X1)))). 4.06/4.36 cnf(i_0_5215, plain, (X1=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))). 4.06/4.36 cnf(i_0_1123, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~c_Nat__Transfer_Onat__set(X2)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_3226, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_5759, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1))=hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X1)|~c_Nat__Transfer_Onat__set(X1))). 4.06/4.36 cnf(i_0_7112, 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)))). 4.06/4.36 cnf(i_0_5884, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.06/4.36 cnf(i_0_5485, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.06/4.36 cnf(i_0_708, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.06/4.36 cnf(i_0_710, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_7104, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_349, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_3446, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X3))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_2358, plain, (c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2),esk179_4(X3,X4,X2,X1),X3)|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2),X4,X3)|~hBOOL(hAPP(X1,X4)))). 4.06/4.36 cnf(i_0_1167, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.06/4.36 cnf(i_0_7013, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,esk494_3(X1,X3,X2)))|~hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X1))))). 4.06/4.36 cnf(i_0_4337, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2))=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))|~class_Rings_Oring__1(X1))). 4.06/4.36 cnf(i_0_6000, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X3,X1,X4),X5)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5)))). 4.06/4.36 cnf(i_0_580, plain, (X1=X2|c_Natural_Oevaln(X3,X1,X4,esk53_5(X2,X4,X1,X3,X5))|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X5,X3),X1,X4,X2))). 4.06/4.36 cnf(i_0_1462, plain, (X1=X2|~c_Finite__Set_Ofun__left__comm(X3,X4,X5)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X7),X2))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X7),X1)))). 4.06/4.36 cnf(i_0_5536, plain, (esk396_2(hAPP(c_List_Oset(X1),X2),X1)=X2|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.06/4.36 cnf(i_0_3512, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)))). 4.06/4.36 cnf(i_0_2075, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.06/4.36 cnf(i_0_4586, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_4960, 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),esk359_2(X2,X1))))). 4.06/4.36 cnf(i_0_7056, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=X3|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X3))))). 4.06/4.36 cnf(i_0_3299, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)))). 4.06/4.36 cnf(i_0_4105, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.06/4.36 cnf(i_0_429, plain, (hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_7475, plain, (hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5),X6)=hAPP(X3,X6)|X6=X4)). 4.06/4.36 cnf(i_0_2359, plain, (X1=X2|c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X4),esk179_4(X2,X1,X4,X3),X2)|~c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X4),X1,X2))). 4.06/4.36 cnf(i_0_1784, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X4),esk135_4(X2,X1,X4,X3))))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))))). 4.06/4.36 cnf(i_0_2150, plain, (hAPP(c_List_Ofilter(X1,X2),X3)!=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)|~hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),esk163_5(X5,X4,X3,X2,X1))))|~hBOOL(hAPP(X2,X6)))). 4.06/4.36 cnf(i_0_5838, plain, (hAPP(c_List_Ofilter(X1,X2),X3)!=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)|~hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),esk422_5(X3,X2,X5,X4,X1))))|~hBOOL(hAPP(X2,X6)))). 4.06/4.36 cnf(i_0_5555, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_484, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_2602, plain, (X1=hAPP(c_Groups_Ouminus__class_Ouminus(X2),c_Groups_Oone__class_Oone(X2))|c_Groups_Oone__class_Oone(X2)=X1|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)!=c_Groups_Oone__class_Oone(X2)|~class_Rings_Oring__1__no__zero__divisors(X2))). 4.06/4.36 cnf(i_0_2626, plain, (X1=X2|hAPP(hAPP(c_List_Omap(X3,X4),X5),X1)!=hAPP(hAPP(c_List_Omap(X3,X4),X5),X2)|~c_Fun_Oinj__on(X3,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))). 4.06/4.36 cnf(i_0_3819, plain, (hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,X2)),X3),X4)=hAPP(c_Groups_Ouminus__class_Ouminus(X2),hAPP(X3,X4))|~class_Groups_Ouminus(X2))). 4.06/4.36 cnf(i_0_262, plain, (c_Wellfounded_Owf(X1,X2)|hBOOL(hAPP(hAPP(c_member(X1),esk18_2(X2,X1)),esk17_2(X2,X1))))). 4.06/4.36 cnf(i_0_7537, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.06/4.36 cnf(i_0_4170, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_2144, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.06/4.36 cnf(i_0_4531, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.06/4.36 cnf(i_0_5216, 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),X2),X1))). 4.06/4.36 cnf(i_0_600, plain, (c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3))=X2|~c_Equiv__Relations_Oequiv(X1,X2,X3))). 4.06/4.36 cnf(i_0_2812, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.06/4.36 cnf(i_0_2219, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 4.06/4.36 cnf(i_0_1062, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.06/4.36 cnf(i_0_1405, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Lattices_Oboolean__algebra(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.06/4.36 cnf(i_0_507, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.06/4.36 cnf(i_0_7486, 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),esk524_3(X1,X3,X2)))|~hBOOL(hAPP(hAPP(c_member(X2),X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.06/4.36 cnf(i_0_7497, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_4424, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_3742, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_4899, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),c_List_Oreplicate(X3,X4,X5))))|~hBOOL(hAPP(X1,X5)))). 4.06/4.36 cnf(i_0_634, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),c_List_Oreplicate(X3,X5,X2))))|~hBOOL(hAPP(X1,X4)))). 4.06/4.36 cnf(i_0_7012, plain, (hBOOL(hAPP(X1,esk494_3(X2,X3,X1)))|hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2))))). 4.06/4.36 cnf(i_0_4499, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3))))). 4.06/4.36 cnf(i_0_7351, 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))). 4.06/4.36 cnf(i_0_2702, 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,esk196_4(X4,X3,X1,X2))!=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.36 cnf(i_0_3736, 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,esk282_4(X4,X3,X2,X1))!=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.36 cnf(i_0_6973, 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,esk491_4(X4,X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.36 cnf(i_0_2963, 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,esk219_4(X4,X3,X1,X2))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.06/4.36 cnf(i_0_4010, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~c_Equiv__Relations_Oequivp(X4,X1)|~hBOOL(hAPP(hAPP(X1,X5),X3))|~hBOOL(hAPP(hAPP(X1,X2),X5)))). 4.06/4.36 cnf(i_0_2010, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk151_2(X2,X1)))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_3303, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.06/4.36 cnf(i_0_3302, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_3453, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),c_List_Olists(X1,X3))))). 4.06/4.36 cnf(i_0_6457, plain, (c_Big__Operators_Olinorder__class_OMax(X1,X2)=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk456_3(X3,X2,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_2031, plain, (c_Wellfounded_Owf(tc_prod(X1,X2),c_Recdef_Osame__fst(X1,X2,X3,X4))|~c_Wellfounded_Owf(X2,hAPP(X4,esk152_4(X1,X4,X2,X3))))). 4.06/4.36 cnf(i_0_2119, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_7019, plain, (c_List_Olist__all2(X1,X2,X3,X4,hAPP(c_List_Orev(X2),X5))|~c_List_Olist__all2(X1,X2,X3,hAPP(c_List_Orev(X1),X4),X5))). 4.06/4.36 cnf(i_0_7018, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(c_List_Orev(X1),X4),X5)|~c_List_Olist__all2(X1,X2,X3,X4,hAPP(c_List_Orev(X2),X5)))). 4.06/4.36 cnf(i_0_5372, plain, (c_List_Olist__ex1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|hBOOL(hAPP(X2,X3))|~c_List_Olist__ex1(X1,X2,X4))). 4.06/4.36 cnf(i_0_7263, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Olinorder__class_Osort__key(X1,X2,X3,X4))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)|~class_Orderings_Olinorder(X2))). 4.06/4.36 cnf(i_0_5734, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~class_Rings_Olinordered__semidom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1))))). 4.06/4.36 cnf(i_0_1786, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))))|~class_Rings_Olinordered__semidom(X1))). 4.06/4.36 cnf(i_0_2056, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)))|~class_Rings_Olinordered__ring(X1))). 4.06/4.36 cnf(i_0_1914, plain, (c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1)=c_Int_OMin|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_7561, plain, (X1=X2|hAPP(c_List_Oset(X3),X1)!=hAPP(c_List_Oset(X3),X2)|~c_List_Olinorder__class_Osorted(X3,X2)|~c_List_Olinorder__class_Osorted(X3,X1)|~class_Orderings_Olinorder(X3)|~hBOOL(hAPP(c_List_Odistinct(X3),X2))|~hBOOL(hAPP(c_List_Odistinct(X3),X1)))). 4.06/4.36 cnf(i_0_2712, 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(X2)|~class_Lazy__Sequence_Osmall__lazy(X1))). 4.06/4.36 cnf(i_0_6347, plain, (c_Random_Ominus__shift(X1,X2,X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X1),X2)),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X2),X3)))). 4.06/4.36 cnf(i_0_2147, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Lattices_Olattice(X1))). 4.06/4.36 cnf(i_0_3648, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.06/4.36 cnf(i_0_4924, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_3361, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))))). 4.06/4.36 cnf(i_0_185, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,X3)))))). 4.06/4.36 cnf(i_0_3235, plain, (c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.06/4.36 cnf(i_0_7568, 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),esk530_3(X2,X3,X1))))). 4.06/4.36 cnf(i_0_5411, 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)))). 4.06/4.36 cnf(i_0_1887, plain, (X1=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))). 4.06/4.36 cnf(i_0_1532, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.06/4.36 cnf(i_0_5701, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Wellfounded_Oless__than)))). 4.06/4.36 cnf(i_0_188, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X5)))|~hBOOL(hAPP(X1,esk13_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_4290, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Rings_Oidom(X1))). 4.06/4.36 cnf(i_0_3576, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Lattices_Olattice(X1))). 4.06/4.36 cnf(i_0_6104, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1))))). 4.06/4.36 cnf(i_0_4032, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1))))). 4.06/4.36 cnf(i_0_3201, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Ozero__class_Ozero(X2))))). 4.06/4.36 cnf(i_0_2289, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Ozero__class_Ozero(X2))))). 4.06/4.36 cnf(i_0_6513, plain, (c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_1994, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)))). 4.06/4.36 cnf(i_0_5049, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)))). 4.06/4.36 cnf(i_0_1542, plain, (c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_2505, plain, (c_Relation_Osingle__valued(X1,X2,hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5))|~c_Relation_Osingle__valued(X3,X2,X5)|~c_Relation_Osingle__valued(X1,X3,X4))). 4.06/4.36 cnf(i_0_1539, plain, (c_Relation_Ototal__on(X1,X2,X3)|~c_Relation_Ototal__on(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))))). 4.06/4.36 cnf(i_0_5723, 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),esk416_3(X3,X2,X1)),esk417_3(X3,X2,X1))),X3)))). 4.06/4.36 cnf(i_0_5379, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_3481, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.06/4.36 cnf(i_0_316, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X4)=c_Groups_Oone__class_Oone(X2)|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Ocomm__monoid__mult(X2))). 4.06/4.36 cnf(i_0_5722, 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),esk417_3(X3,X2,X1)),esk416_3(X3,X2,X1))),X3)))). 4.06/4.36 cnf(i_0_5155, plain, (X1=hAPP(hAPP(c_List_Onth(X2),X3),X4)|hAPP(hAPP(c_List_Olist__update(X2,X3),X4),X1)!=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))))). 4.06/4.36 cnf(i_0_1878, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)))). 4.06/4.36 cnf(i_0_1825, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 4.06/4.36 cnf(i_0_1948, 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,esk146_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_4582, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X4)=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~class_Groups_Ocomm__monoid__add(X2))). 4.06/4.36 cnf(i_0_6167, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(c_Set_Oimage(X2,X1,X3),X4))=hAPP(c_Finite__Set_Ocard(X2),X4)|~c_Fun_Oinj__on(X2,X1,X3,X4))). 4.06/4.36 cnf(i_0_6811, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_HOL_Obool))))))). 4.06/4.36 cnf(i_0_2011, 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))))). 4.06/4.36 cnf(i_0_2230, 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,esk171_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_3457, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2))))). 4.06/4.36 cnf(i_0_6547, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),X2)))). 4.06/4.36 cnf(i_0_2110, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))))). 4.06/4.36 cnf(i_0_6831, plain, (c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))=X2|hAPP(c_Finite__Set_Ocard(X1),X2)!=hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 4.06/4.36 cnf(i_0_7175, plain, (X1=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1)!=hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)|~class_Rings_Olinordered__semidom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Oone__class_Oone(X3)),X4)))). 4.06/4.36 cnf(i_0_4003, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ocomm__monoid__add(X2))). 4.06/4.36 cnf(i_0_3348, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))))). 4.06/4.36 cnf(i_0_1119, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))))). 4.06/4.36 cnf(i_0_2040, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))))). 4.06/4.36 cnf(i_0_879, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_4000, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),X2)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oabs__if(X1))). 4.06/4.36 cnf(i_0_7210, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(hAPP(c_member(X2),c_List_Olast(X2,X1)),hAPP(c_List_Oset(X2),X1))))). 4.06/4.36 cnf(i_0_5511, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1))),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.06/4.36 cnf(i_0_1662, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.06/4.36 cnf(i_0_6437, plain, (c_Equiv__Relations_Oequiv(X1,hAPP(c_Relation_ODomain(X1,X1),X2),X2)|hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X2)),X2)!=X2)). 4.06/4.36 cnf(i_0_5184, plain, (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(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),X1))))). 4.06/4.36 cnf(i_0_4858, 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,esk353_3(X1,X3,X2)))|~hBOOL(hAPP(X2,esk355_3(X1,X3,X2))))). 4.06/4.36 cnf(i_0_3781, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X3)))). 4.06/4.36 cnf(i_0_4005, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk291_3(X2,X3,X1)),X2))|hBOOL(hAPP(c_Predicate_OPowp(X1,X3),X2)))). 4.06/4.36 cnf(i_0_2175, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_1779, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_6462, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)|~class_Groups_Ogroup__add(X1))). 4.06/4.36 cnf(i_0_917, plain, (~class_Rings_Olinordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_6889, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2)=c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_List_Oset(X1),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.06/4.36 cnf(i_0_5258, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Olinorder__class_Osort__key(X2,X1,X3,X4)))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_6750, 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),esk475_3(X3,X2,X1)))))). 4.06/4.36 cnf(i_0_5272, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.06/4.36 cnf(i_0_7264, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.06/4.36 cnf(i_0_6948, plain, (hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X2),X3))=hAPP(hAPP(X1,X2),X3)|~c_Finite__Set_Ofun__left__comm__idem(X4,X5,X1))). 4.06/4.36 cnf(i_0_2700, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk195_3(X3,X1,X2))))|~c_List_Olist__ex(X2,X1,X3))). 4.06/4.36 cnf(i_0_714, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Lattices_Oboolean__algebra(X1))). 4.06/4.36 cnf(i_0_3664, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3))))). 4.06/4.36 cnf(i_0_1201, 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),esk103_3(X3,X2,X1)),X2)),X3)))). 4.06/4.36 cnf(i_0_619, plain, (c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool))))). 4.06/4.36 cnf(i_0_3857, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Groups_Oab__group__add(X1))). 4.06/4.36 cnf(i_0_1675, plain, (c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X3,X4,X5)|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X6,X4,X5)|~c_Natural_Oevaln(X2,X3,X4,X6)|~hBOOL(hAPP(X1,X3)))). 4.06/4.36 cnf(i_0_6543, plain, (hAPP(X1,esk462_4(X2,X1,X3,X4))=hAPP(X1,esk463_4(X2,X1,X3,X4))|c_Fun_Oinj__on(X4,X3,X1,X2))). 4.06/4.36 cnf(i_0_447, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.06/4.36 cnf(i_0_2582, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_4130, 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,esk299_1(X1))))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_7125, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),X4))|~hBOOL(hAPP(X2,X3)))). 4.06/4.36 cnf(i_0_2567, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Groups_Ogroup__add(X1))). 4.06/4.36 cnf(i_0_3591, plain, (c_Relation_Osingle__valued(X1,X1,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X3))|~c_Relation_Osingle__valued(X1,X1,X3))). 4.06/4.36 cnf(i_0_3471, 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,esk260_2(X1,X3))))). 4.06/4.36 cnf(i_0_115, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(c_List_Oset(X1),X4))|~hBOOL(hAPP(c_List_Odistinct(X2),hAPP(hAPP(c_List_Omap(X1,X2),X3),X4))))). 4.06/4.36 cnf(i_0_7201, plain, (hBOOL(hAPP(X1,esk503_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X4),X5),X3))|~hBOOL(hAPP(X1,X5)))). 4.06/4.36 cnf(i_0_3729, plain, (hBOOL(hAPP(X1,esk280_3(X2,X1,X3)))|hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(X1,X2)))). 4.06/4.36 cnf(i_0_6227, 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),esk444_1(X1)),hAPP(c_List_Oset(tc_Nat_Onat),X1))))). 4.06/4.36 cnf(i_0_3635, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.06/4.36 cnf(i_0_2389, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Rings_Ocomm__ring__1(X1))). 4.06/4.36 cnf(i_0_7199, plain, (hBOOL(hAPP(X1,esk503_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X4),X5),X2))|~hBOOL(hAPP(X1,X5)))). 4.06/4.36 cnf(i_0_1287, 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))). 4.06/4.36 cnf(i_0_69, plain, (hAPP(c_Option_Ooption_OSome(X1),esk5_5(X2,X3,X4,X5,X1))=X3|hAPP(c_Option_Ooption_OSome(X5),X2)!=hAPP(hAPP(c_Option_Omap(X1,X5),X4),X3))). 4.06/4.36 cnf(i_0_4502, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.06/4.36 cnf(i_0_6700, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.06/4.36 cnf(i_0_1030, plain, (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_3309, plain, (X1=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)))). 4.06/4.36 cnf(i_0_5209, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X1,X3))=c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.06/4.36 cnf(i_0_5737, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.06/4.36 cnf(i_0_4801, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.06/4.36 cnf(i_0_1880, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X3)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1))). 4.06/4.36 cnf(i_0_3312, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3))=c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.06/4.36 cnf(i_0_4179, plain, (hAPP(c_List_Ofilter(X1,X2),c_List_Oremove1(X1,X3,X4))=hAPP(c_List_Ofilter(X1,X2),X4)|hBOOL(hAPP(X2,X3)))). 4.06/4.36 cnf(i_0_4670, plain, (hAPP(hAPP(c_List_Onth(X1),X2),esk338_3(X2,X3,X1))=X3|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))))). 4.06/4.36 cnf(i_0_6353, plain, (c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X3))=X3|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_11, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.06/4.36 cnf(i_0_1146, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.06/4.36 cnf(i_0_1881, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)),X2)=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1))). 4.06/4.36 cnf(i_0_1528, plain, (hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),hAPP(X4,X5))=X5|~c_Fun_Oinj__on(X1,X2,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3)))). 4.06/4.36 cnf(i_0_2105, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Wellfounded_Owf(X1,X3))). 4.06/4.36 cnf(i_0_5593, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Wellfounded_Owf(X1,X2))). 4.06/4.36 cnf(i_0_6969, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),esk489_3(X1,X2,X3)),esk490_3(X1,X2,X3)))|~hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 4.06/4.36 cnf(i_0_2016, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.06/4.36 cnf(i_0_3632, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.06/4.36 cnf(i_0_2211, 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),esk170_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk169_2(X2,X1)))))). 4.06/4.36 cnf(i_0_2675, 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),esk192_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk193_2(X2,X1)))))). 4.06/4.36 cnf(i_0_3897, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(c_List_Orev(X1),X4),hAPP(c_List_Orev(X2),X5))|~c_List_Olist__all2(X1,X2,X3,X4,X5))). 4.06/4.36 cnf(i_0_3044, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))!=c_Groups_Osgn__class_Osgn(X1,X2)|~class_Rings_Olinordered__idom(X1))). 4.06/4.36 cnf(i_0_3943, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X2)=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.06/4.36 cnf(i_0_2022, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X1)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.06/4.36 cnf(i_0_3535, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oorder(X1))). 4.06/4.36 cnf(i_0_4633, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk335_1(X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,X2)))). 4.06/4.36 cnf(i_0_9, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2)|~class_Groups_Oab__group__add(X1))). 4.06/4.36 cnf(i_0_4602, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.06/4.36 cnf(i_0_2660, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_6928, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3)=X2|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Odivision__ring(X1))). 4.06/4.36 cnf(i_0_4773, plain, (X1=esk346_3(X2,X3,X4)|~c_List_Olist__ex1(X4,X3,X2)|~hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_List_Oset(X4),X2)))|~hBOOL(hAPP(X3,X1)))). 4.06/4.36 cnf(i_0_1547, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2))))). 4.06/4.36 cnf(i_0_6724, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2))))). 4.06/4.36 cnf(i_0_4339, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_3474, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_3360, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_781, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)))). 4.06/4.36 cnf(i_0_6643, plain, (hAPP(X1,X2)=hAPP(X3,X2)|~c_Map_Omap__le(X4,X5,X1,X3)|~hBOOL(hAPP(hAPP(c_member(X4),X2),c_Map_Odom(X4,X5,X1))))). 4.06/4.36 cnf(i_0_6679, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_6012, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_6019, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_2661, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_3696, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_5751, 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))). 4.06/4.36 cnf(i_0_4533, plain, (hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5)=hAPP(X4,X5)|~hBOOL(hAPP(hAPP(c_member(X1),X5),c_Map_Odom(X1,X2,X4))))). 4.06/4.36 cnf(i_0_3128, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X3),X1)),hAPP(c_Finite__Set_Ocard(X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)))). 4.06/4.36 cnf(i_0_1701, plain, (hAPP(X1,esk128_4(X2,X1,X3,X4))=X4|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Set_Oimage(X3,X5,X1),X2))))). 4.06/4.36 cnf(i_0_3699, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_7039, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Relation_OId__on(X1,X3))))). 4.06/4.36 cnf(i_0_6660, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),X4)!=c_Option_Ooption_ONone(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)))))). 4.06/4.36 cnf(i_0_649, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X3))))). 4.06/4.36 cnf(i_0_6234, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_7451, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_3825, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_3179, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool)),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X1),X2)))). 4.06/4.36 cnf(i_0_6471, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(hAPP(c_member(X2),hAPP(c_List_Ohd(X2),X1)),hAPP(c_List_Oset(X2),X1))))). 4.06/4.36 cnf(i_0_7419, 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))|esk520_3(X3,X2,X1)=esk521_3(X3,X2,X1))). 4.06/4.36 cnf(i_0_2295, plain, (c_List_Oremdups(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=c_List_Oremdups(X1,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.06/4.36 cnf(i_0_3738, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~c_Fun_Oinj__on(X1,X2,X3,X4))). 4.06/4.36 cnf(i_0_6968, plain, (hBOOL(hAPP(X1,esk490_3(X1,X2,X3)))|hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 4.06/4.36 cnf(i_0_1034, plain, (hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_2180, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2))))). 4.06/4.36 cnf(i_0_6988, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2))))). 4.06/4.36 cnf(i_0_3140, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3))))). 4.06/4.36 cnf(i_0_757, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3))))). 4.06/4.36 cnf(i_0_3891, plain, (c_List_Oremove1(X1,X2,X3)=X3|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.06/4.36 cnf(i_0_2468, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_6260, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.06/4.36 cnf(i_0_6217, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(X3,c_List_Olast(X2,X4))|c_List_Olist_ONil(X2)=X4)). 4.06/4.36 cnf(i_0_7467, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3))))). 4.06/4.36 cnf(i_0_853, plain, (c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk84_4(X3,X4,X2,X1),X3,X4)|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X4,X3,X4)|~hBOOL(hAPP(X1,X4)))). 4.06/4.36 cnf(i_0_7293, 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,esk513_5(X5,X4,X3,X2,X1)),X5)))). 4.06/4.36 cnf(i_0_6585, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~class_Rings_Olinordered__idom(X3)|~class_Int_Onumber__ring(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2))))). 4.06/4.36 cnf(i_0_5425, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_OtakeWhile(X1,X4,X3)))))). 4.06/4.36 cnf(i_0_5641, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Osublist(X1,X3,X4)))))). 4.06/4.36 cnf(i_0_2452, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~class_Rings_Olinordered__idom(X3)|~class_Int_Onumber__ring(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2))))). 4.06/4.36 cnf(i_0_4511, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X4,X3)))))). 4.06/4.36 cnf(i_0_4760, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Oring__char__0(X1)|~hBOOL(hAPP(hAPP(c_member(X1),c_Groups_Ozero__class_Ozero(X1)),c_Int_Oring__1__class_OInts(X1))))). 4.06/4.36 cnf(i_0_3145, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))))). 4.06/4.36 cnf(i_0_3262, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)),X3)))). 4.06/4.36 cnf(i_0_1844, plain, (hAPP(c_Fun_Ooverride__on(X1,X2,X3,X4,X5),X6)=hAPP(X3,X6)|hBOOL(hAPP(hAPP(c_member(X1),X6),X5)))). 4.06/4.36 cnf(i_0_2203, plain, (c_List_Olist__ex1(X1,X2,c_Enum_Oenum__class_Oenum(X1))|hBOOL(hAPP(X2,esk167_3(X2,X1,X3)))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(X2,X3)))). 4.06/4.36 cnf(i_0_783, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),hAPP(c_Relation_Oconverse(X2,X1),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2,X1)),X3)))). 4.06/4.36 cnf(i_0_2523, plain, (c_Finite__Set_Ofun__left__comm__idem(X1,X2,hAPP(hAPP(c_COMBB(X3,tc_fun(X2,X2),X1),X4),X5))|~c_Finite__Set_Ofun__left__comm__idem(X3,X2,X4))). 4.06/4.36 cnf(i_0_2547, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Osgn__class_Osgn(X1,X2)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.06/4.36 cnf(i_0_5565, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_3895, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)|~class_Rings_Ocomm__ring__1(X1))). 4.06/4.36 cnf(i_0_888, plain, (c_Finite__Set_Ofun__left__comm(X1,X2,hAPP(hAPP(c_COMBB(X3,tc_fun(X2,X2),X1),X4),X5))|~c_Finite__Set_Ofun__left__comm(X3,X2,X4))). 4.06/4.36 cnf(i_0_6961, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),c_List_Olist_ONil(X1))=hAPP(hAPP(c_List_Olist_OCons(X1),X4),c_List_Olist_ONil(X1))|~class_Orderings_Olinorder(X2))). 4.06/4.36 cnf(i_0_1039, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Oran(X3,X1,X4)))|hAPP(X4,X5)!=hAPP(c_Option_Ooption_OSome(X1),X2))). 4.06/4.36 cnf(i_0_3625, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Map_Odom(X1,X3,X4)))|hAPP(c_Option_Ooption_OSome(X3),X5)!=hAPP(X4,X2))). 4.06/4.36 cnf(i_0_6717, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Big__Operators_Olinorder__class_OMax(X1,X3)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.06/4.36 cnf(i_0_6648, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_2581, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_330, plain, (hAPP(X1,esk25_3(X1,X2,X3))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,tc_Nat_Onat),X1),X2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 4.06/4.36 cnf(i_0_6545, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|hBOOL(hAPP(hAPP(c_member(X1),esk462_4(X4,X3,X2,X1)),X4)))). 4.06/4.36 cnf(i_0_6544, plain, (c_Fun_Oinj__on(X1,X2,X3,X4)|hBOOL(hAPP(hAPP(c_member(X1),esk463_4(X4,X3,X2,X1)),X4)))). 4.06/4.36 cnf(i_0_1276, plain, (~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),c_Transitive__Closure_Ortrancl(X1,X4))))). 4.06/4.36 cnf(i_0_1564, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk118_1(X1)))|hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))))). 4.06/4.36 cnf(i_0_92, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Int_OMin),X1)=c_Int_OMin|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_6572, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.06/4.36 cnf(i_0_4890, plain, (~c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),c_Transitive__Closure_Ortrancl(X1,X4))))). 4.06/4.36 cnf(i_0_6568, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))=X2|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.06/4.36 cnf(i_0_4204, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))=X2|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.06/4.36 cnf(i_0_6855, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_6118, 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,esk436_2(X1,X3))))). 4.06/4.36 cnf(i_0_3467, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))))). 4.06/4.36 cnf(i_0_2994, plain, (hAPP(c_Option_Ooption_OSome(X1),esk220_3(X2,X1,X3))=hAPP(X2,X3)|~hBOOL(hAPP(hAPP(c_member(X4),X3),c_Map_Odom(X4,X1,X2))))). 4.06/4.36 cnf(i_0_1381, plain, (c_Partial__Function_Oflat__lub(X1,X2,X3)=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))). 4.06/4.36 cnf(i_0_3728, 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,esk280_3(X2,X1,X3)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(X1,X2)))). 4.06/4.36 cnf(i_0_3466, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))))). 4.06/4.36 cnf(i_0_2041, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1))))). 4.06/4.36 cnf(i_0_1118, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))))). 4.06/4.36 cnf(i_0_4539, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),X4),X3)))))). 4.06/4.36 cnf(i_0_2913, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),esk217_3(X3,X2,X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3))))). 4.06/4.36 cnf(i_0_6593, plain, (hAPP(X1,esk467_4(X1,X2,X3,X4))=c_Groups_Ozero__class_Ozero(X4)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X4),X1),X2)!=c_Groups_Ozero__class_Ozero(X4)|~class_Rings_Ono__zero__divisors(X4)|~class_Rings_Ocomm__semiring__1(X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 4.06/4.36 cnf(i_0_5802, plain, (c_List_Olinorder__class_Osort__key(X1,X2,X3,hAPP(c_List_Ofilter(X1,X4),X5))=hAPP(c_List_Ofilter(X1,X4),c_List_Olinorder__class_Osort__key(X1,X2,X3,X5))|~class_Orderings_Olinorder(X2))). 4.06/4.36 cnf(i_0_1876, plain, (X1=c_List_Olist_ONil(X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X1),c_List_Olist_ONil(X2))),c_List_Olistrel(X2,X3))))). 4.06/4.36 cnf(i_0_4356, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),X4),X3)))))). 4.06/4.36 cnf(i_0_474, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))). 4.06/4.36 cnf(i_0_956, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))). 4.06/4.36 cnf(i_0_7327, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))). 4.06/4.36 cnf(i_0_1882, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3)=X2|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Fields_Ofield__inverse__zero(X1))). 4.06/4.36 cnf(i_0_4161, 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)),c_List_Olist_ONil(X1)),X2)),c_List_Olistrel(X1,X3))))). 4.06/4.36 cnf(i_0_7418, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2)))). 4.06/4.36 cnf(i_0_606, 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)))). 4.06/4.36 cnf(i_0_2666, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))=c_List_Olist_ONil(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_3578, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))). 4.06/4.36 cnf(i_0_1293, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))). 4.06/4.36 cnf(i_0_5369, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))))). 4.06/4.36 cnf(i_0_1550, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin)))). 4.06/4.36 cnf(i_0_4980, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(X1,esk361_3(X3,X2,X1)))|~hBOOL(hAPP(X1,esk363_3(X3,X2,X1)))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_6137, 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,esk439_4(X1,X3,X2,X4))))). 4.06/4.36 cnf(i_0_3270, 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),esk249_5(X3,X5,X4,X2,X1))))). 4.06/4.36 cnf(i_0_5803, 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),esk420_5(X5,X4,X3,X2,X1))))). 4.06/4.36 cnf(i_0_3126, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)=hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))|hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))=X2)). 4.06/4.36 cnf(i_0_52, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_6389, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_1909, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin)))). 4.06/4.36 cnf(i_0_6386, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin)))). 4.06/4.36 cnf(i_0_200, plain, (X1=X2|hAPP(X3,X1)!=hAPP(X3,X2)|~c_Fun_Oinj__on(X4,X5,X3,X6)|~hBOOL(hAPP(hAPP(c_member(X4),X2),X6))|~hBOOL(hAPP(hAPP(c_member(X4),X1),X6)))). 4.06/4.36 cnf(i_0_6187, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.06/4.36 cnf(i_0_1598, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.06/4.36 cnf(i_0_4270, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_1999, plain, (c_Divides_Odivmod__int(X1,X2)=c_Divides_OnegDivAlg(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.06/4.36 cnf(i_0_2830, plain, (c_List_Olast(X1,hAPP(hAPP(c_List_Odrop(X1),X2),X3))=c_List_Olast(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.06/4.36 cnf(i_0_3395, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.06/4.36 cnf(i_0_6410, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))))). 4.06/4.36 cnf(i_0_2664, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X1),esk191_2(X2,X1)),X2)))). 4.06/4.36 cnf(i_0_2618, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.06/4.36 cnf(i_0_6740, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_2414, plain, (X1=hAPP(hAPP(X2,X3),X4)|hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~c_Big__Operators_Ocomm__monoid__big(X6,X5,X7,X1,X2))). 4.06/4.36 cnf(i_0_2151, plain, (hAPP(c_List_Ofilter(X1,X2),esk164_5(X3,X4,X5,X2,X1))=X3|hAPP(c_List_Ofilter(X1,X2),X5)!=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))). 4.06/4.36 cnf(i_0_3251, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk246_2(X2,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))))). 4.06/4.36 cnf(i_0_3930, plain, (hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=X1|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.06/4.36 cnf(i_0_2544, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_6109, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2)))). 4.06/4.36 cnf(i_0_5836, plain, (hAPP(c_List_Ofilter(X1,X2),esk423_5(X3,X2,X4,X5,X1))=X4|hAPP(c_List_Ofilter(X1,X2),X3)!=hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4))). 4.06/4.36 cnf(i_0_526, plain, (hAPP(X1,X2)=hAPP(c_Option_Ooption_OSome(X3),X4)|c_Option_Ooption_ONone(X3)=hAPP(X1,X2)|hAPP(c_Map_Omap__add(X5,X3,X6,X1),X2)!=hAPP(c_Option_Ooption_OSome(X3),X4))). 4.06/4.36 cnf(i_0_1267, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.06/4.36 cnf(i_0_2187, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~class_Rings_Oring__1(X1))). 4.06/4.36 cnf(i_0_5993, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.06/4.36 cnf(i_0_3357, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.06/4.36 cnf(i_0_4682, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X1)),X2))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1))))|~hBOOL(hAPP(X2,c_Option_Ooption_ONone(X1))))). 4.06/4.36 cnf(i_0_3090, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3,X3),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4))))). 4.06/4.36 cnf(i_0_2212, plain, (c_List_Olinorder__class_Osorted(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk170_2(X2,X1)),esk169_2(X2,X1)))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_50, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.06/4.36 cnf(i_0_3084, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.06/4.36 cnf(i_0_4579, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.06/4.36 cnf(i_0_2685, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.06/4.36 cnf(i_0_2677, plain, (c_List_Olinorder__class_Osorted(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk192_2(X2,X1)),esk193_2(X2,X1)))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_1057, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X1),tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 4.06/4.36 cnf(i_0_5634, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),c_Divides_OnegDivAlg(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.06/4.36 cnf(i_0_3371, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),c_Divides_OposDivAlg(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.06/4.36 cnf(i_0_1546, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.06/4.36 cnf(i_0_6352, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.06/4.36 cnf(i_0_989, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Nat_OSuc,X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))|~class_Rings_Osemiring__1(X1))). 4.06/4.36 cnf(i_0_7239, plain, (c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Wellfounded_OwfP(X1,X2))). 4.06/4.36 cnf(i_0_504, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Wellfounded_OwfP(X1,X2))). 4.06/4.36 cnf(i_0_3213, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)=X3|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4))))). 4.06/4.36 cnf(i_0_965, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(c_COMBK(X2,X1),c_Groups_Ozero__class_Ozero(X2))),X3)=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ocomm__monoid__add(X2))). 4.06/4.36 cnf(i_0_892, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_4466, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_2508, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(c_COMBK(X2,X1),c_Groups_Oone__class_Oone(X2))),X3)=c_Groups_Oone__class_Oone(X2)|~class_Groups_Ocomm__monoid__mult(X2))). 4.06/4.36 cnf(i_0_4288, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)=X3|X3=X2|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Rings_Oidom(X1))). 4.06/4.36 cnf(i_0_4331, plain, (X1=X2|hAPP(hAPP(c_List_Oappend(X3),X4),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3)))!=hAPP(hAPP(c_List_Oappend(X3),X5),hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_Olist_ONil(X3))))). 4.06/4.36 cnf(i_0_4332, plain, (X1=X2|hAPP(hAPP(c_List_Oappend(X3),X1),hAPP(hAPP(c_List_Olist_OCons(X3),X4),c_List_Olist_ONil(X3)))!=hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X5),c_List_Olist_ONil(X3))))). 4.06/4.36 cnf(i_0_5302, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X1,X2)),X3),X4))|hAPP(X3,esk380_4(X4,X3,X1,X2))!=hAPP(X4,esk380_4(X4,X3,X1,X2))|~class_HOL_Oequal(X2)|~class_Enum_Oenum(X1))). 4.06/4.36 cnf(i_0_3678, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk278_2(X2,X1)))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.06/4.36 cnf(i_0_7280, plain, (hBOOL(hAPP(c_List_Odistinct(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)))|~hBOOL(hAPP(c_List_Odistinct(X2),X4)))). 4.06/4.36 cnf(i_0_6796, plain, (hBOOL(hAPP(c_List_Odistinct(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.06/4.36 cnf(i_0_2816, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X2,c_Option_Ooption_ONone(X1),X3),hAPP(X4,X5))=c_Option_Ooption_ONone(X1)|hAPP(X4,X5)!=c_Option_Ooption_ONone(X2))). 4.06/4.36 cnf(i_0_624, plain, (hBOOL(hAPP(X1,esk57_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))|~hBOOL(hAPP(X1,X3)))). 4.06/4.36 cnf(i_0_2807, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X2,X3))=hAPP(X2,X3)|~c_Finite__Set_Ofun__left__comm__idem(X4,X1,X2))). 4.06/4.36 cnf(i_0_6546, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))))). 4.06/4.36 cnf(i_0_3458, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)))). 4.06/4.36 cnf(i_0_412, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_7082, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X2)|~class_Orderings_Oorder(X1))). 4.06/4.36 cnf(i_0_3890, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)))). 4.06/4.36 cnf(i_0_3546, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(c_Set_Oimage(X4,X1,X5),X6))|~c_Fun_Oinj__on(X4,X2,hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5),X6))). 4.06/4.36 cnf(i_0_6300, plain, (X1=X2|hAPP(hAPP(c_List_Onth(X3),X1),esk446_3(X3,X1,X2))!=hAPP(hAPP(c_List_Onth(X3),X2),esk446_3(X3,X1,X2))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2))). 4.06/4.36 cnf(i_0_5420, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Obutlast(X1,X3))|c_List_Olist_ONil(X1)=X3)). 4.06/4.36 cnf(i_0_5888, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.06/4.36 cnf(i_0_4442, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_1160, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.06/4.36 cnf(i_0_5600, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk402_2(X2,X1)),esk401_2(X2,X1))=X2|c_List_Olist_ONil(X1)=X2|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_540, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3))=hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Obutlast(X1,X3))|c_List_Olist_ONil(X1)=X3)). 4.06/4.36 cnf(i_0_1514, 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)|esk116_2(X2,X1)!=c_List_Olist_ONil(X1))). 4.06/4.36 cnf(i_0_1544, 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)|esk117_2(X2,X1)!=c_List_Olist_ONil(X1))). 4.06/4.36 cnf(i_0_1530, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3)))). 4.06/4.36 cnf(i_0_314, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X2)),c_Sum__Type_OPlus(X1,X2,X3,X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.06/4.36 cnf(i_0_6069, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.06/4.36 cnf(i_0_916, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_3123, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_6745, plain, (hBOOL(hAPP(c_List_Odistinct(tc_prod(X1,X2)),c_Enum_Oproduct(X1,X2,X3,X4)))|~hBOOL(hAPP(c_List_Odistinct(X2),X4))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.06/4.36 cnf(i_0_1667, 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),esk126_3(X3,X2,X1)),esk127_3(X3,X2,X1))))). 4.06/4.36 cnf(i_0_3428, plain, (c_Fun_Oinj__on(X1,X2,c_Fun_Othe__inv__into(X2,X1,X3,X4),hAPP(c_Set_Oimage(X2,X1,X4),X3))|~c_Fun_Oinj__on(X2,X1,X4,X3))). 4.06/4.36 cnf(i_0_983, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Ois__nat(X1)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2))))). 4.06/4.36 cnf(i_0_4952, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_fun(X5,tc_HOL_Obool))),X6),X1))|~hBOOL(hAPP(hAPP(X6,X2),X3)))). 4.06/4.36 cnf(i_0_578, plain, (c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk53_5(X3,X4,X5,X2,X1),X4,X3)|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X5,X4,X3)|~hBOOL(hAPP(X1,X5)))). 4.06/4.36 cnf(i_0_3525, plain, (hBOOL(hAPP(hAPP(X1,X2),esk266_5(X3,X4,X1,X5,X2)))|~c_Wellfounded_Omax__extp(X5,X1,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X5),X2),X4)))). 4.06/4.36 cnf(i_0_409, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)),X5)!=c_Option_Ooption_ONone(X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),X3))))). 4.06/4.36 cnf(i_0_4484, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.06/4.36 cnf(i_0_5733, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.06/4.36 cnf(i_0_5885, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_7540, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(c_List_Ofilter(X1,X2),X4)|hBOOL(hAPP(X2,X3)))). 4.06/4.36 cnf(i_0_6255, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X5),X4)))|~class_Orderings_Olinorder(X1))). 4.06/4.36 cnf(i_0_6967, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X3),esk489_3(X1,X2,X3)),esk490_3(X1,X2,X3))))|~hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 4.06/4.36 cnf(i_0_5268, plain, (X1=X2|hAPP(X3,X1)!=hAPP(X3,X2)|~c_Typedef_Otype__definition(X4,X5,X6,X3,X7)|~hBOOL(hAPP(hAPP(c_member(X5),X2),X7))|~hBOOL(hAPP(hAPP(c_member(X5),X1),X7)))). 4.06/4.36 cnf(i_0_1193, plain, (hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))=X3|~c_Finite__Set_Ofolding__one(X2,X4,X1))). 4.06/4.36 cnf(i_0_2894, plain, (hAPP(c_Finite__Set_Ocard(tc_sum(X1,X2)),c_Sum__Type_OPlus(X1,X2,X3,X4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.06/4.36 cnf(i_0_5484, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.06/4.36 cnf(i_0_7103, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.06/4.36 cnf(i_0_348, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.06/4.36 cnf(i_0_3645, plain, (hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))|hBOOL(hAPP(X1,esk277_3(X1,X3,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(X1,X3)))). 4.06/4.36 cnf(i_0_6110, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))|~class_Int_Onumber__ring(X1))). 4.06/4.36 cnf(i_0_2895, plain, (hAPP(c_Finite__Set_Ocard(tc_sum(X1,X2)),c_Sum__Type_OPlus(X1,X2,X3,X4))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.06/4.36 cnf(i_0_732, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),c_Orderings_Otop__class_Otop(X1)),X2)=c_Complete__Lattice_OInf__class_OInf(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_925, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),c_Orderings_Obot__class_Obot(X1)),X2)=c_Complete__Lattice_OSup__class_OSup(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_4605, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X2)),X2)=X2|~c_Equiv__Relations_Oequiv(X1,X3,X2))). 4.06/4.36 cnf(i_0_6450, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),esk455_3(X3,X2,X1)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3))))). 4.06/4.36 cnf(i_0_4677, 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)))). 4.06/4.36 cnf(i_0_2937, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk218_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex(X1,X3,X2))). 4.06/4.36 cnf(i_0_4774, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk346_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olist__ex1(X1,X3,X2))). 4.06/4.36 cnf(i_0_4688, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.06/4.36 cnf(i_0_6449, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk455_3(X2,X3,X1)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Complete__Lattice_OSup__class_OSup(X1,X2))))). 4.06/4.36 cnf(i_0_6754, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk476_3(X2,X3,X1)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X2)))). 4.06/4.36 cnf(i_0_6755, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk476_3(X2,X3,X1)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X3)),X2)))). 4.06/4.36 cnf(i_0_2404, 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)). 4.06/4.36 cnf(i_0_5886, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X1))))). 4.06/4.36 cnf(i_0_254, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))))). 4.06/4.36 cnf(i_0_2205, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.06/4.36 cnf(i_0_581, plain, (X1=X2|c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X4),esk53_5(X1,X5,X2,X4,X3),X5,X1)|~c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X4),X2,X5,X1))). 4.06/4.36 cnf(i_0_5452, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)|hAPP(hAPP(c_List_Omap(X1,X5),X6),X2)!=hAPP(hAPP(c_List_Omap(X3,X5),X7),X4))). 4.06/4.36 cnf(i_0_7036, plain, (c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,hAPP(c_Nat_OSuc,X3),X4)=c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,X3,hAPP(X2,X4))|~class_Rings_Osemiring__1(X1))). 4.06/4.36 cnf(i_0_4066, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OgreaterThanLessThan(X1,X3,X4,X5)))|~hBOOL(hAPP(hAPP(X3,X2),X5))|~hBOOL(hAPP(hAPP(X3,X4),X2)))). 4.06/4.36 cnf(i_0_3789, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatLeastAtMost(X1,X3,X4,X5)))|~hBOOL(hAPP(hAPP(X3,X4),X2))|~hBOOL(hAPP(hAPP(X3,X2),X5)))). 4.06/4.36 cnf(i_0_4373, 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),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.06/4.36 cnf(i_0_1835, plain, (hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(X3,hAPP(c_List_Ohd(X2),X4))|c_List_Olist_ONil(X2)=X4)). 4.06/4.36 cnf(i_0_7221, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk507_4(X2,X3,X4,X1)),X3))|hAPP(c_Nat_OSuc,X2)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3))). 4.06/4.36 cnf(i_0_7498, plain, (X1=hAPP(c_Groups_Ouminus__class_Ouminus(X2),X3)|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X3),X1)!=c_Orderings_Otop__class_Otop(X2)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X3),X1)!=c_Orderings_Obot__class_Obot(X2)|~class_Lattices_Oboolean__algebra(X2))). 4.06/4.36 cnf(i_0_1997, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)))). 4.06/4.36 cnf(i_0_264, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))|hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.06/4.36 cnf(i_0_3600, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X5)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)))). 4.06/4.36 cnf(i_0_258, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk20_3(X2,X1,X3)),X3))|~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3)))). 4.06/4.36 cnf(i_0_6887, plain, (hBOOL(hAPP(hAPP(X1,esk486_5(X2,X1,X3,X4,X5)),X2))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X4,tc_HOL_Obool)),X3),X1),X2)))). 4.06/4.36 cnf(i_0_3234, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X3))|~class_Groups_Omonoid__add(X1))). 4.06/4.36 cnf(i_0_4281, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Olinordered__idom(X1))). 4.06/4.36 cnf(i_0_4277, plain, (hBOOL(hAPP(X1,esk311_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))|~hBOOL(hAPP(X1,X3)))). 4.06/4.36 cnf(i_0_2475, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)))). 4.06/4.36 cnf(i_0_5389, 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,esk387_3(X3,X2,X1)))),hAPP(X3,esk387_3(X3,X2,X1)))),X2)))). 4.06/4.36 cnf(i_0_6857, 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,esk481_3(X2,X1,X3)))),hAPP(X3,esk481_3(X2,X1,X3)))),X2)))). 4.06/4.36 cnf(i_0_3322, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3)|~class_Divides_Oring__div(X1))). 4.06/4.36 cnf(i_0_1037, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3)))). 4.06/4.36 cnf(i_0_3918, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)))). 4.06/4.36 cnf(i_0_6306, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)))). 4.06/4.36 cnf(i_0_4981, 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,esk361_3(X1,X3,X2)))|~hBOOL(hAPP(X2,esk363_3(X1,X3,X2))))). 4.06/4.36 cnf(i_0_7324, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X2,X3))=hAPP(X2,X3)|~c_Finite__Set_Ofolding__idem(X4,X1,X2,X5))). 4.06/4.36 cnf(i_0_5096, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))))). 4.06/4.36 cnf(i_0_3368, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X1))|~class_Orderings_Olinorder(X3))). 4.06/4.36 cnf(i_0_1113, plain, (hAPP(X1,esk98_1(X1))=hAPP(X1,esk99_1(X1))|c_Equiv__Relations_Oequivp(X2,X1)|hBOOL(hAPP(hAPP(X1,esk98_1(X1)),esk99_1(X1))))). 4.06/4.36 cnf(i_0_4620, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))))). 4.06/4.36 cnf(i_0_5571, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))))). 4.06/4.36 cnf(i_0_3878, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X1))|~class_Rings_Olinordered__idom(X3))). 4.06/4.36 cnf(i_0_3486, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))))). 4.06/4.36 cnf(i_0_6059, plain, (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|~hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))))))). 4.06/4.36 cnf(i_0_2087, 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))). 4.06/4.36 cnf(i_0_3233, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2)=X3|c_Groups_Ozero__class_Ozero(X1)=X2|~class_Divides_Osemiring__div(X1))). 4.06/4.36 cnf(i_0_2331, plain, (c_Groups_Osgn__class_Osgn(X1,X2)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))|c_Groups_Ozero__class_Ozero(X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Groups_Osgn__if(X1))). 4.06/4.36 cnf(i_0_1411, 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),esk113_2(X1,X2))))). 4.06/4.36 cnf(i_0_5356, plain, (c_Map_Omap__add(X1,X2,X3,X4)=c_Map_Omap__add(X1,X2,X4,X3)|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),c_Map_Odom(X1,X2,X4))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.06/4.36 cnf(i_0_6944, plain, (c_Enum_Oex__n__lists(X1,X2,X3)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X3,c_Enum_Oenum__class_Oenum(X1)))))|~hBOOL(hAPP(X2,X4)))). 4.06/4.36 cnf(i_0_3344, plain, (X1=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),hAPP(c_List_Oset(tc_prod(X3,X3)),hAPP(hAPP(c_List_Ozip(X3,X3),X4),X4)))))). 4.06/4.36 cnf(i_0_458, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)))|~c_List_Olist__all(X2,X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))))). 4.06/4.36 cnf(i_0_608, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.06/4.36 cnf(i_0_304, plain, (c_Map_Omap__le(X1,X2,c_Map_Omap__upds(X1,X2,X3,X4,X5),c_Map_Omap__upds(X1,X2,X6,X4,X5))|~c_Map_Omap__le(X1,X2,X3,X6))). 4.06/4.36 cnf(i_0_3655, plain, (hAPP(c_Option_Ooption_OSome(X1),X2)=hAPP(c_Map_Omap__add(X3,X1,X4,X5),X6)|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(X5,X6))). 4.06/4.36 cnf(i_0_607, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.06/4.36 cnf(i_0_2333, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),X5)))|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5)))). 4.06/4.36 cnf(i_0_2689, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),X2)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.06/4.36 cnf(i_0_3543, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk267_3(X2,X3,X1)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.36 cnf(i_0_3454, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X2)),c_List_Olists(X1,X3))))). 4.07/4.36 cnf(i_0_4626, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X4),X2)),c_List_Olists(X1,X3))))). 4.07/4.36 cnf(i_0_6882, plain, (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(tc_Int_Oint),X1),X2))|hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.07/4.36 cnf(i_0_663, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.07/4.36 cnf(i_0_583, plain, (hAPP(hAPP(c_List_Onth(X1),X2),esk54_2(X2,X1))=hAPP(hAPP(c_List_Onth(X1),X2),esk55_2(X2,X1))|hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.07/4.36 cnf(i_0_3338, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk254_2(X1,X2))=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(X2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))))). 4.07/4.36 cnf(i_0_4627, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X4)),c_List_Olists(X1,X3))))). 4.07/4.36 cnf(i_0_3539, 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)|esk268_4(X2,X3,X1,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.36 cnf(i_0_5229, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))=c_Big__Operators_Olattice__class_OSup__fin(X1,X3)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.36 cnf(i_0_5240, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))=c_Big__Operators_Olattice__class_OInf__fin(X1,X3)|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.36 cnf(i_0_7027, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.07/4.36 cnf(i_0_2659, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))))). 4.07/4.36 cnf(i_0_2054, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olinorder__class_OMax(X1,X3))=c_Big__Operators_Olinorder__class_OMax(X1,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.36 cnf(i_0_7128, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olinorder__class_OMin(X1,X3))=c_Big__Operators_Olinorder__class_OMin(X1,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.36 cnf(i_0_4415, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|hBOOL(hAPP(hAPP(X4,X2),X3))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X6,tc_HOL_Obool))),X1),X4),X2),X3)))). 4.07/4.36 cnf(i_0_1131, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))=X3|~class_Groups_Ogroup__add(X1))). 4.07/4.36 cnf(i_0_3827, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))=X3|~class_Groups_Ogroup__add(X1))). 4.07/4.36 cnf(i_0_6867, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)),X2))))). 4.07/4.36 cnf(i_0_1985, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2),X3),hAPP(c_COMBK(X2,X1),X4))=X4|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Complete__Lattice_Ocomplete__lattice(X2))). 4.07/4.36 cnf(i_0_1733, plain, (c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),c_Map_Omap__add(X1,X2,X3,X4),c_Map_Odom(X1,X2,X4))|~c_Fun_Oinj__on(X1,tc_Option_Ooption(X2),X4,c_Map_Odom(X1,X2,X4)))). 4.07/4.36 cnf(i_0_6856, plain, (c_Transitive__Closure_Ortrancl(X1,X2)=c_Transitive__Closure_Ortrancl(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Transitive__Closure_Ortrancl(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.07/4.36 cnf(i_0_1962, plain, (hAPP(c_Set_Oimage(X1,X1,X2),X3)=X3|~c_Fun_Oinj__on(X1,X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X1,X2),X3)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.36 cnf(i_0_1273, plain, (c_Equiv__Relations_Ocongruent(X1,X2,X3,hAPP(X4,X5))|~c_Equiv__Relations_Oequiv(X6,X7,X8)|~c_Equiv__Relations_Ocongruent2(X6,X1,X2,X8,X3,X4)|~hBOOL(hAPP(hAPP(c_member(X6),X5),X7)))). 4.07/4.36 cnf(i_0_592, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)))). 4.07/4.36 cnf(i_0_7043, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.07/4.36 cnf(i_0_3440, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3)))). 4.07/4.36 cnf(i_0_4012, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X2),X3),hAPP(c_COMBK(X2,X1),X4))=X4|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Complete__Lattice_Ocomplete__lattice(X2))). 4.07/4.36 cnf(i_0_5527, plain, (hBOOL(hAPP(hAPP(X1,X2),esk395_4(X3,X2,X4,X1)))|~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X6,X7,X1,X4),X2),X3)))). 4.07/4.36 cnf(i_0_5528, plain, (hBOOL(hAPP(hAPP(X1,esk395_4(X2,X3,X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X6,X7,X4,X1),X3),X2)))). 4.07/4.36 cnf(i_0_900, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2))=hAPP(c_SetInterval_Oord__class_OatMost(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1))). 4.07/4.36 cnf(i_0_2599, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2))=hAPP(c_SetInterval_Oord__class_OatLeast(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1))). 4.07/4.36 cnf(i_0_4255, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.36 cnf(i_0_6972, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3)))). 4.07/4.36 cnf(i_0_3387, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.36 cnf(i_0_2729, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3)))). 4.07/4.36 cnf(i_0_2029, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1))). 4.07/4.36 cnf(i_0_3718, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2))=hAPP(c_SetInterval_Oord__class_OlessThan(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1))). 4.07/4.36 cnf(i_0_269, plain, (hBOOL(hAPP(X1,X2))|~c_Enum_Oall__n__lists(X3,X1,X4)|~class_Enum_Oenum(X3)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3)),X2),hAPP(c_List_Oset(tc_List_Olist(X3)),c_Enum_On__lists(X3,X4,c_Enum_Oenum__class_Oenum(X3))))))). 4.07/4.36 cnf(i_0_3381, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Map_Odom(X1,X3,X4))=c_Map_Odom(X1,X3,X4)|hAPP(c_Option_Ooption_OSome(X3),X5)!=hAPP(X4,X2))). 4.07/4.36 cnf(i_0_5366, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk385_2(X1,X2)),c_Int_OInteg))|hBOOL(hAPP(X2,X1)))). 4.07/4.36 cnf(i_0_1189, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Orderings_Opreorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.36 cnf(i_0_6331, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),X2))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1))). 4.07/4.36 cnf(i_0_6970, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk490_3(X2,X3,X1)))|hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.36 cnf(i_0_7459, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)|~class_Lattices_Osemilattice__sup(X1))). 4.07/4.36 cnf(i_0_4305, plain, (c_Nitpick_Onorm__frac(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.36 cnf(i_0_6415, plain, (c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|hAPP(c_Set_Oimage(X1,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 4.07/4.36 cnf(i_0_3809, plain, (hAPP(c_Set_Oimage(X1,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 4.07/4.36 cnf(i_0_5999, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~c_Fun_Oinj__on(X1,X2,X3,X5)|~c_Fun_Oinj__on(X1,X2,X3,X4))). 4.07/4.36 cnf(i_0_2488, plain, (c_Map_Omap__le(X1,X2,c_Map_Omap__add(X1,X2,X3,X4),X5)|~c_Map_Omap__le(X1,X2,X3,c_Map_Omap__add(X1,X2,X3,X4))|~c_Map_Omap__le(X1,X2,X4,X5)|~c_Map_Omap__le(X1,X2,X3,X5))). 4.07/4.36 cnf(i_0_2805, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)|~class_Lattices_Olattice(X1))). 4.07/4.36 cnf(i_0_6793, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)|~class_Lattices_Olattice(X1))). 4.07/4.36 cnf(i_0_6735, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)|~class_Lattices_Oab__semigroup__idem__mult(X1))). 4.07/4.36 cnf(i_0_5090, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X6)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X7)|~c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X6),X4),hAPP(hAPP(c_List_Oappend(X2),X7),X5)))). 4.07/4.36 cnf(i_0_5089, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)|~c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X6),hAPP(hAPP(c_List_Oappend(X2),X5),X7)))). 4.07/4.36 cnf(i_0_4894, plain, (X1=X2|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X4)),X5),X6),hAPP(c_Option_Ooption_OSome(X4),X1))!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,tc_Option_Ooption(X4)),X7),X6),hAPP(c_Option_Ooption_OSome(X4),X2)))). 4.07/4.36 cnf(i_0_4046, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)|~class_Lattices_Osemilattice__inf(X1))). 4.07/4.36 cnf(i_0_4303, plain, (c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=c_Nitpick_Onorm__frac(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.36 cnf(i_0_1376, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)))|~class_Rings_Olinordered__idom(X1))). 4.07/4.36 cnf(i_0_1634, plain, (~c_Wellfounded_Oacyclic(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))))). 4.07/4.36 cnf(i_0_4853, 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,esk355_3(X1,X3,X2)))|~hBOOL(hAPP(X2,X3)))). 4.07/4.36 cnf(i_0_1776, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))))). 4.07/4.36 cnf(i_0_6719, plain, (c_Divides_OnegDivAlg(X1,X2)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.36 cnf(i_0_4837, 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,esk353_3(X1,X3,X2)))|~hBOOL(hAPP(X2,X3)))). 4.07/4.36 cnf(i_0_5629, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))|~c_Wellfounded_Owf(X1,X2))). 4.07/4.36 cnf(i_0_586, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk54_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))|hBOOL(hAPP(c_List_Odistinct(X2),X1)))). 4.07/4.36 cnf(i_0_585, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk55_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))|hBOOL(hAPP(c_List_Odistinct(X2),X1)))). 4.07/4.36 cnf(i_0_2993, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1))). 4.07/4.36 cnf(i_0_4708, plain, (c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X1)))|~class_Orderings_Owellorder(X1))). 4.07/4.36 cnf(i_0_1086, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3))))). 4.07/4.36 cnf(i_0_1543, plain, (X1=c_List_Olist_ONil(X2)|hAPP(c_List_Ofoldl(tc_List_Olist(X2),tc_List_Olist(X2),c_List_Oappend(X2),c_List_Olist_ONil(X2)),X3)!=c_List_Olist_ONil(X2)|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X1),hAPP(c_List_Oset(tc_List_Olist(X2)),X3))))). 4.07/4.36 cnf(i_0_564, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk50_2(X2,X1))))|hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X1,X2)))). 4.07/4.36 cnf(i_0_3107, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.36 cnf(i_0_3037, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.36 cnf(i_0_838, plain, (c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_OtakeWhile(X1,X2,X4))|~hBOOL(hAPP(X2,X3)))). 4.07/4.36 cnf(i_0_331, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk25_3(X2,X3,X1)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.36 cnf(i_0_372, 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,esk29_3(X1,X3,X2)),esk30_3(X1,X3,X2))))). 4.07/4.36 cnf(i_0_467, 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,esk38_3(X1,X3,X2)),esk39_3(X1,X3,X2))))). 4.07/4.36 cnf(i_0_6176, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.36 cnf(i_0_1161, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.36 cnf(i_0_3104, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.36 cnf(i_0_3771, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.36 cnf(i_0_3448, 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),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))|~class_Rings_Oring(X1))). 4.07/4.36 cnf(i_0_823, 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,esk81_3(X1,X3,X2)),esk82_3(X1,X3,X2))))). 4.07/4.36 cnf(i_0_2864, 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,esk214_3(X1,X3,X2)),esk215_3(X1,X3,X2))))). 4.07/4.36 cnf(i_0_7145, 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,esk499_3(X1,X3,X2)),esk500_3(X1,X3,X2))))). 4.07/4.36 cnf(i_0_7338, 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,esk516_3(X1,X3,X2)),esk517_3(X1,X3,X2))))). 4.07/4.36 cnf(i_0_6103, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.36 cnf(i_0_4033, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.36 cnf(i_0_3202, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.36 cnf(i_0_2290, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.36 cnf(i_0_1109, plain, (hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X1))=X1|~c_List_Onat__list(X1))). 4.07/4.36 cnf(i_0_553, plain, (hAPP(hAPP(c_Set_Oinsert(X1),esk48_3(X2,X3,X1)),esk49_3(X2,X3,X1))=X3|hAPP(c_Nat_OSuc,X2)!=hAPP(c_Finite__Set_Ocard(X1),X3))). 4.07/4.36 cnf(i_0_2992, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Oremove1(X2,X4,X5)))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))|~class_Orderings_Olinorder(X1))). 4.07/4.36 cnf(i_0_3011, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X4),esk222_3(X1,X4,X3))))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))))). 4.07/4.36 cnf(i_0_2891, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Osgn__class_Osgn(X1,X2)),c_Groups_Osgn__class_Osgn(X1,X3))=c_Groups_Osgn__class_Osgn(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__idom(X1))). 4.07/4.36 cnf(i_0_3314, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Orderings_Olinorder(X1))). 4.07/4.36 cnf(i_0_4055, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(c_Finite__Set_Ocard(X1),X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.36 cnf(i_0_7030, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))|~class_Fields_Ofield__inverse__zero(X1))). 4.07/4.36 cnf(i_0_5954, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X2|~class_Orderings_Olinorder(X1))). 4.07/4.36 cnf(i_0_4636, plain, (c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Oremove1(X1,X2,X4))|X2=X3)). 4.07/4.36 cnf(i_0_2491, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3))))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,c_Wellfounded_Oacc(X1,X3)))))). 4.07/4.36 cnf(i_0_658, plain, (c_SMT_Oz3div(X1,X2)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.36 cnf(i_0_7532, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))))). 4.07/4.36 cnf(i_0_6791, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))))). 4.07/4.36 cnf(i_0_4800, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3)))). 4.07/4.36 cnf(i_0_1014, plain, (c_List_Olist__all(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk92_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 4.07/4.36 cnf(i_0_3800, plain, (~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))))))). 4.07/4.36 cnf(i_0_4293, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__ring__strict(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X3))),c_Groups_Ozero__class_Ozero(X2))))). 4.07/4.36 cnf(i_0_4292, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2))),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.36 cnf(i_0_257, 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)|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.07/4.36 cnf(i_0_1829, plain, (c_List_Olist__all(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk138_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 4.07/4.36 cnf(i_0_4912, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3)))). 4.07/4.36 cnf(i_0_1918, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))))). 4.07/4.36 cnf(i_0_471, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))|~class_Rings_Oring(X1))). 4.07/4.36 cnf(i_0_5769, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oring(X1))). 4.07/4.36 cnf(i_0_683, plain, (c_List_Olist__all(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk66_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3))))). 4.07/4.36 cnf(i_0_6743, plain, (c_Enum_Oenum__the(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))=hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.07/4.37 cnf(i_0_4655, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool))|c_Fun_Oinj__on(X2,X3,X4,c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_HOL_Obool),X1))|~c_Fun_Oinj__on(X2,X3,X4,esk337_4(X4,X3,X2,X1)))). 4.07/4.37 cnf(i_0_1837, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))|~hBOOL(hAPP(c_List_Olistsp(X1,X3),X2)))). 4.07/4.37 cnf(i_0_5270, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3)=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))|~class_Rings_Odivision__ring(X1))). 4.07/4.37 cnf(i_0_1063, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.07/4.37 cnf(i_0_1406, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))|~class_Lattices_Oboolean__algebra(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.07/4.37 cnf(i_0_5617, plain, (hAPP(hAPP(c_List_Oappend(X1),c_List_Obutlast(X1,X2)),hAPP(hAPP(c_List_Olist_OCons(X1),c_List_Olast(X1,X2)),c_List_Olist_ONil(X1)))=X2|X2=c_List_Olist_ONil(X1))). 4.07/4.37 cnf(i_0_3776, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))). 4.07/4.37 cnf(i_0_525, plain, (hAPP(c_Option_Ooption_OSome(X1),X2)=hAPP(X3,X4)|hAPP(X5,X4)=hAPP(c_Option_Ooption_OSome(X1),X2)|hAPP(c_Map_Omap__add(X6,X1,X3,X5),X4)!=hAPP(c_Option_Ooption_OSome(X1),X2))). 4.07/4.37 cnf(i_0_506, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.07/4.37 cnf(i_0_4423, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.37 cnf(i_0_3741, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.07/4.37 cnf(i_0_1214, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Odivision__ring(X1))). 4.07/4.37 cnf(i_0_5574, plain, (c_List_OtakeWhile(X1,X2,X3)=X3|hBOOL(hAPP(hAPP(c_member(X1),esk397_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 4.07/4.37 cnf(i_0_2260, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk174_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.37 cnf(i_0_2112, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X5,tc_HOL_Obool)),X6),X1),X3))|~hBOOL(hAPP(hAPP(c_member(X4),X2),X6)))). 4.07/4.37 cnf(i_0_2861, 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,esk212_4(X4,X1,X2,hAPP(c_Set_Oimage(X1,X2,X3),X4)),hAPP(c_Set_Oimage(X1,X2,X3),X4)))). 4.07/4.37 cnf(i_0_129, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Otl(X1),X2)),X3)=hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))|c_List_Olist_ONil(X1)=X2)). 4.07/4.37 cnf(i_0_3455, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X3),X6))))). 4.07/4.37 cnf(i_0_6055, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_4436, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))))|~class_Rings_Olinordered__semidom(X1))). 4.07/4.37 cnf(i_0_6236, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_OMin,X1)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_1254, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_1383, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),X2)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.07/4.37 cnf(i_0_5251, 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)))). 4.07/4.37 cnf(i_0_1301, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.37 cnf(i_0_4903, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Rings_Olinordered__idom(X1))). 4.07/4.37 cnf(i_0_5468, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),c_Big__Operators_Olinorder__class_OMax(X2,X1)),X1))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.07/4.37 cnf(i_0_716, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_717, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|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),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_4712, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2)))). 4.07/4.37 cnf(i_0_7034, 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,esk495_2(X2,X1))))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.07/4.37 cnf(i_0_7135, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X1)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)))). 4.07/4.37 cnf(i_0_73, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)))). 4.07/4.37 cnf(i_0_2564, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)|~class_Fields_Ofield__inverse__zero(X1))). 4.07/4.37 cnf(i_0_3665, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X5,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2)))). 4.07/4.37 cnf(i_0_4711, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.07/4.37 cnf(i_0_3667, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.07/4.37 cnf(i_0_6129, plain, (hAPP(c_List_Oset(X1),c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X2,X3))=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3))|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_487, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4),X5),X6))|~hBOOL(hAPP(hAPP(X4,X5),X6)))). 4.07/4.37 cnf(i_0_768, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)|~class_Rings_Oring(X1))). 4.07/4.37 cnf(i_0_7359, 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)). 4.07/4.37 cnf(i_0_2066, plain, (c_List_Olinorder__class_Oinsort__insert__key(X1,X2,X3,X4,X5)=X5|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X4)),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_List_Oset(X1),X5)))))). 4.07/4.37 cnf(i_0_3526, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk266_5(X2,X3,X4,X1,X5)),X2))|~c_Wellfounded_Omax__extp(X1,X4,X3,X2)|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3)))). 4.07/4.37 cnf(i_0_3957, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4),X5),X6))|~hBOOL(hAPP(hAPP(X3,X5),X6)))). 4.07/4.37 cnf(i_0_4632, plain, (hAPP(hAPP(c_List_Otake(X1),X2),c_List_Obutlast(X1,X3))=hAPP(hAPP(c_List_Otake(X1),X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.37 cnf(i_0_2170, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk166_3(X2,X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),c_Relation_OId__on(X1,X2))))). 4.07/4.37 cnf(i_0_1927, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OgreaterThanAtMost(X1,X3,X4,X5,X6)))|~hBOOL(hAPP(hAPP(X3,X2),X6))|~hBOOL(hAPP(hAPP(X4,X5),X2)))). 4.07/4.37 cnf(i_0_1812, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatLeastLessThan(X1,X3,X4,X5,X6)))|~hBOOL(hAPP(hAPP(X3,X5),X2))|~hBOOL(hAPP(hAPP(X4,X2),X6)))). 4.07/4.37 cnf(i_0_3222, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4))=X2|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X4)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.07/4.37 cnf(i_0_4614, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_1253, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),X4)=hAPP(hAPP(c_List_Onth(X1),X3),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X2)))). 4.07/4.37 cnf(i_0_3874, plain, (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(X1,X2)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Nat_Onat),X1),X4)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X3),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)))). 4.07/4.37 cnf(i_0_6152, 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)))). 4.07/4.37 cnf(i_0_7148, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_2714, plain, (hAPP(c_Fun_Othe__inv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(X3,X4))=X4|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))). 4.07/4.37 cnf(i_0_2930, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X3)))))). 4.07/4.37 cnf(i_0_2277, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.07/4.37 cnf(i_0_2422, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))))). 4.07/4.37 cnf(i_0_2622, plain, (c_List_Olist_ONil(X1)=X2|hBOOL(hAPP(hAPP(c_member(X1),esk188_3(X3,X2,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3))))). 4.07/4.37 cnf(i_0_5869, plain, (c_Equiv__Relations_Ocongruent(X1,X2,X3,X4)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk427_4(X4,X3,X2,X1)),X3)))). 4.07/4.37 cnf(i_0_977, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk89_4(X2,X3,X4,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X2))))). 4.07/4.37 cnf(i_0_5826, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2)))). 4.07/4.37 cnf(i_0_4563, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~class_Groups_Oordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2)))). 4.07/4.37 cnf(i_0_6888, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk486_5(X2,X3,X4,X5,X1)),X4))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X4),X3),X2)))). 4.07/4.37 cnf(i_0_1016, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))=X2|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_5506, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))=X2|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_5134, plain, (hAPP(c_List_Ofilter(X1,X2),X3)=X3|hBOOL(hAPP(hAPP(c_member(X1),esk373_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 4.07/4.37 cnf(i_0_6884, 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))). 4.07/4.37 cnf(i_0_6883, 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))). 4.07/4.37 cnf(i_0_5020, 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,esk363_3(X1,X3,X2)))|~hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_3086, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_5739, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X2),X3)=c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_6986, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X2),X3)=c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_4988, 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,esk361_3(X1,X3,X2)))|~hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_3317, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(X4,X3)))|~class_Orderings_Oord(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X1)),X2),X4)))). 4.07/4.37 cnf(i_0_4016, 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)|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Odivision__ring(X1))). 4.07/4.37 cnf(i_0_4410, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~c_Fun_Oinj__on(X1,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3))))). 4.07/4.37 cnf(i_0_2298, plain, (hAPP(c_Relation_OImage(X1,X1,c_Transitive__Closure_Ortrancl(X1,X2)),X3)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X2),X3)),X3)))). 4.07/4.37 cnf(i_0_1203, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk103_3(X2,X3,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Fields_Olinordered__field__inverse__zero(X1))). 4.07/4.37 cnf(i_0_6751, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk475_3(X2,X3,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Fields_Olinordered__field(X1))). 4.07/4.37 cnf(i_0_1300, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=c_Groups_Ozero__class_Ozero(X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~class_Int_Onumber__ring(X1))). 4.07/4.37 cnf(i_0_6839, plain, (hAPP(c_Set_Oimage(X1,X2,X3),esk479_5(X4,X3,X1,X5,X2))=X5|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X5),hAPP(c_Set_Oimage(X1,X2,X3),X4))))). 4.07/4.37 cnf(i_0_7278, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3))=c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1))). 4.07/4.37 cnf(i_0_3269, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3))=c_SetInterval_Oord__class_OgreaterThanLessThan(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1))). 4.07/4.37 cnf(i_0_1202, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk103_3(X2,X3,X1)),c_Groups_Oone__class_Oone(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2))|~class_Fields_Olinordered__field__inverse__zero(X1))). 4.07/4.37 cnf(i_0_4160, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))))). 4.07/4.37 cnf(i_0_6862, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.07/4.37 cnf(i_0_3356, 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))). 4.07/4.37 cnf(i_0_3040, plain, (c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,esk225_4(X3,X4,X2,X1),X3)|~c_Natural_Oevaln(c_Com_Ocom_OBODY(X1),X2,X4,X3))). 4.07/4.37 cnf(i_0_605, 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))))). 4.07/4.37 cnf(i_0_3979, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.37 cnf(i_0_5817, plain, (c_Groups_Ozero__class_Ozero(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),X2)),X1))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X3,X1),X2)))). 4.07/4.37 cnf(i_0_3837, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.07/4.37 cnf(i_0_3647, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk277_3(X2,X3,X1)))|hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(X2,X3)))). 4.07/4.37 cnf(i_0_305, 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)))). 4.07/4.37 cnf(i_0_4473, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.37 cnf(i_0_2822, plain, (c_List_Osublist(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)),X3)=c_List_Olist_ONil(X1)|hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))). 4.07/4.37 cnf(i_0_259, plain, (~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),esk20_3(X2,X1,X4))),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X4)))). 4.07/4.37 cnf(i_0_3017, 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,esk224_5(X4,X3,X5,X1,X2)))))). 4.07/4.37 cnf(i_0_2699, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk195_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)))|~c_List_Olist__ex(X3,X2,X1))). 4.07/4.37 cnf(i_0_2032, plain, (c_Wellfounded_Owf(tc_prod(X1,X2),c_Recdef_Osame__fst(X1,X2,X3,X4))|hBOOL(hAPP(X3,esk152_4(X1,X4,X2,X3))))). 4.07/4.37 cnf(i_0_698, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk67_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))|hBOOL(hAPP(c_List_Olistsp(X1,X3),X2)))). 4.07/4.37 cnf(i_0_3009, 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,esk223_3(X1,X3,X2))))). 4.07/4.37 cnf(i_0_3719, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_2785, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_6680, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),X2)))). 4.07/4.37 cnf(i_0_4947, plain, (hAPP(X1,X2)=hAPP(X1,X3)|~c_Equiv__Relations_Ocongruent(X4,X5,X6,X1)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),X6)))). 4.07/4.37 cnf(i_0_5676, 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,esk410_5(X1,X6,X5,X4,X3))))). 4.07/4.37 cnf(i_0_3318, 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,esk251_4(X4,X3,X1,X2))),hAPP(X4,esk251_4(X4,X3,X1,X2)))))). 4.07/4.37 cnf(i_0_1548, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_6464, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_6723, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_5131, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_567, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_COMBI(X1)),hAPP(c_List_Oset(X1),X2))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.07/4.37 cnf(i_0_3074, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Complete__Lattice_OInf__class_OInf(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X4)))). 4.07/4.37 cnf(i_0_6678, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_6013, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_6018, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_6508, plain, (X1=X2|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))). 4.07/4.37 cnf(i_0_860, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2)=c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_List_Oset(X1),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.07/4.37 cnf(i_0_4434, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OSup__class_OSup(X1,X4)),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.07/4.37 cnf(i_0_7149, plain, (c_Fun_Oinj__on(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),X6)|~c_Fun_Oinj__on(X3,X2,X4,hAPP(c_Set_Oimage(X1,X3,X5),X6))|~c_Fun_Oinj__on(X1,X3,X5,X6))). 4.07/4.37 cnf(i_0_6726, plain, (hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),X3)|~class_Rings_Osemiring__1(X1))). 4.07/4.37 cnf(i_0_3122, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_6485, plain, (c_Fun_Oinj__on(X1,X2,esk459_4(X3,X2,X4,X1),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X4)),hAPP(c_Finite__Set_Ocard(X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.37 cnf(i_0_3538, 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,esk268_4(X2,X3,X1,X4))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X2,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_1899, plain, (hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X2),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),X3)|~class_Rings_Oring__1(X1))). 4.07/4.37 cnf(i_0_5599, plain, (c_List_Olist_ONil(X1)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk402_2(X2,X1)),X3))|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),esk401_2(X2,X1)))))). 4.07/4.37 cnf(i_0_1769, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_814, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_4447, 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_Oone__class_Oone(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.07/4.37 cnf(i_0_4604, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.07/4.37 cnf(i_0_291, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3)))). 4.07/4.37 cnf(i_0_414, 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,esk33_4(X4,X1,X3,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.07/4.37 cnf(i_0_652, 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,esk62_4(X4,X1,X3,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.07/4.37 cnf(i_0_5994, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.07/4.37 cnf(i_0_1917, 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_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)),X1)))). 4.07/4.37 cnf(i_0_2216, 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),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.37 cnf(i_0_3102, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=c_List_Olist_ONil(X1)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.07/4.37 cnf(i_0_6525, 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)))). 4.07/4.37 cnf(i_0_7556, plain, (c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omax(X1),X2),X3)|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_6528, plain, (c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omin(X1),X2),X3)|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_2261, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk174_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1))))). 4.07/4.37 cnf(i_0_4814, 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),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.07/4.37 cnf(i_0_2383, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.07/4.37 cnf(i_0_2213, plain, (c_List_Olinorder__class_Osorted(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk169_2(X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_7190, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)|~class_Lattices_Olattice(X1))). 4.07/4.37 cnf(i_0_7022, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)|~class_Lattices_Olattice(X1))). 4.07/4.37 cnf(i_0_2912, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk217_3(X2,X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2))))). 4.07/4.37 cnf(i_0_1984, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3))))). 4.07/4.37 cnf(i_0_2676, plain, (c_List_Olinorder__class_Osorted(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk193_2(X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_2953, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.37 cnf(i_0_6646, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5))=X3|hAPP(X3,X4)!=hAPP(c_Option_Ooption_OSome(X2),X5))). 4.07/4.37 cnf(i_0_3307, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)),X3)=X4|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.07/4.37 cnf(i_0_7456, 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,esk522_5(X5,X4,X3,X2,X1)))))). 4.07/4.37 cnf(i_0_4931, 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,esk358_5(X5,X4,X3,X2,X1))),X5)))). 4.07/4.37 cnf(i_0_2940, plain, (hAPP(X1,X2)=hAPP(c_Option_Ooption_OSome(X3),X4)|X4=X5|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6,tc_Option_Ooption(X3)),X1),X7),hAPP(c_Option_Ooption_OSome(X3),X5)),X2)!=hAPP(c_Option_Ooption_OSome(X3),X4))). 4.07/4.37 cnf(i_0_953, plain, (hAPP(c_List_Ofilter(X1,X2),X3)=c_List_Olist_ONil(X1)|hBOOL(hAPP(hAPP(c_member(X1),esk88_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 4.07/4.37 cnf(i_0_6639, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.07/4.37 cnf(i_0_2535, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_1816, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_2873, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.07/4.37 cnf(i_0_457, plain, (c_List_Olist__all(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk36_3(X3,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.37 cnf(i_0_2941, plain, (hAPP(X1,X2)=hAPP(c_Option_Ooption_OSome(X3),X4)|X5=X2|hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X6,tc_Option_Ooption(X3)),X1),X5),hAPP(c_Option_Ooption_OSome(X3),X7)),X2)!=hAPP(c_Option_Ooption_OSome(X3),X4))). 4.07/4.37 cnf(i_0_4972, plain, (hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X1,X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.37 cnf(i_0_1690, plain, (hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X1,X2))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_333, 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)|esk24_4(X2,X3,X1,X4)!=X4|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_7421, 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),esk520_3(X3,X2,X1)),X2)))). 4.07/4.37 cnf(i_0_7436, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.07/4.37 cnf(i_0_2367, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk181_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.07/4.37 cnf(i_0_4319, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))). 4.07/4.37 cnf(i_0_7420, 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),esk521_3(X3,X2,X1)),X3)))). 4.07/4.37 cnf(i_0_4940, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Ofilter(X2,X4),X5)))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_1724, plain, (hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1,X2,X3),X4),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X3)))). 4.07/4.37 cnf(i_0_383, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))). 4.07/4.37 cnf(i_0_5782, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))). 4.07/4.37 cnf(i_0_5193, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))). 4.07/4.37 cnf(i_0_4908, plain, (X1=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X3),X4)),hAPP(c_List_Olexn(X2,X5),X1))))). 4.07/4.37 cnf(i_0_4907, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X2)),hAPP(c_List_Olexn(X1,X5),X3))))). 4.07/4.37 cnf(i_0_5674, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(X4,X5)))|~hBOOL(hAPP(X1,esk411_5(X1,X4,X6,X7,X3)))|~hBOOL(hAPP(hAPP(c_member(X7),X5),X6)))). 4.07/4.37 cnf(i_0_5526, plain, (hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X1,X2,X3,X4,X5),X6),X7))|~hBOOL(hAPP(hAPP(X4,X6),X8))|~hBOOL(hAPP(hAPP(X5,X8),X7)))). 4.07/4.37 cnf(i_0_5182, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),X2))))). 4.07/4.37 cnf(i_0_3730, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk280_3(X1,X2,X3)),X3))|hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3))|~hBOOL(hAPP(X2,X1)))). 4.07/4.37 cnf(i_0_5702, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Wellfounded_Oless__than))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.07/4.37 cnf(i_0_3073, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk229_3(X2,X3,X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Complete__Lattice_OInf__class_OInf(X1,X2)))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.07/4.37 cnf(i_0_4433, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk320_3(X2,X3,X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Complete__Lattice_OSup__class_OSup(X1,X3)),X2))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.07/4.37 cnf(i_0_552, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),X3))|hAPP(c_Finite__Set_Ocard(X1),X3)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.07/4.37 cnf(i_0_5793, plain, (hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2))|~class_Groups_Oordered__ab__group__add(X1))). 4.07/4.37 cnf(i_0_7476, plain, (hAPP(c_Set_Oimage(X1,X2,c_Fun_Othe__inv__into(X2,X1,X3,X4)),hAPP(c_Set_Oimage(X2,X1,X4),X3))=X3|~c_Fun_Oinj__on(X2,X1,X4,X3))). 4.07/4.37 cnf(i_0_156, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X2)),c_Wellfounded_Ofinite__psubset(X1))))). 4.07/4.37 cnf(i_0_1594, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1))). 4.07/4.37 cnf(i_0_6906, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)))). 4.07/4.37 cnf(i_0_4878, 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,esk355_3(X1,X3,X2))))). 4.07/4.37 cnf(i_0_4862, 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,esk353_3(X1,X3,X2))))). 4.07/4.37 cnf(i_0_2999, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),X3))|~c_Nitpick_Orefl_H(X1,X3))). 4.07/4.37 cnf(i_0_4493, plain, (X1=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X3)),X4)|c_Groups_Ozero__class_Ozero(X2)=X4|hAPP(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))). 4.07/4.37 cnf(i_0_3656, plain, (hAPP(c_Option_Ooption_OSome(X1),X2)=hAPP(c_Map_Omap__add(X3,X1,X4,X5),X6)|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(X4,X6)|c_Option_Ooption_ONone(X1)!=hAPP(X5,X6))). 4.07/4.37 cnf(i_0_1378, plain, (c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))|~c_FunDef_Oreduction__pair(X1,X2))). 4.07/4.37 cnf(i_0_4771, plain, (c_List_Olist__ex1(X1,X2,X3)|hBOOL(hAPP(X2,esk347_4(X3,X2,X1,X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 4.07/4.37 cnf(i_0_6645, plain, (c_Map_Omap__le(X1,X2,X3,X4)|hBOOL(hAPP(hAPP(c_member(X1),esk471_4(X4,X3,X2,X1)),c_Map_Odom(X1,X2,X3))))). 4.07/4.37 cnf(i_0_1692, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.07/4.37 cnf(i_0_1996, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))|~class_Groups_Oordered__ab__group__add__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.37 cnf(i_0_5051, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.07/4.37 cnf(i_0_466, plain, (hBOOL(hAPP(X1,X2))|hAPP(hAPP(c_List_Odrop(X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),c_List_OtakeWhile(X3,X1,X4))),X4)!=c_List_Olist_ONil(X3)|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))))). 4.07/4.37 cnf(i_0_3163, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~c_Relation_Orefl__on(X1,X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X2)),X4)))). 4.07/4.37 cnf(i_0_3814, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~c_Relation_Orefl__on(X1,X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),X4)))). 4.07/4.37 cnf(i_0_2091, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.07/4.37 cnf(i_0_1031, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.07/4.37 cnf(i_0_2037, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.07/4.37 cnf(i_0_7068, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~c_Equiv__Relations_Oequiv(X1,X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X2)),X4)))). 4.07/4.37 cnf(i_0_7069, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~c_Equiv__Relations_Oequiv(X1,X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),X4)))). 4.07/4.37 cnf(i_0_3070, plain, (~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2)))). 4.07/4.37 cnf(i_0_4524, plain, (c_List_Oinsert(X1,X2,X3)=hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.07/4.37 cnf(i_0_2109, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)))). 4.07/4.37 cnf(i_0_4956, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.07/4.37 cnf(i_0_2251, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)))). 4.07/4.37 cnf(i_0_6030, plain, (hAPP(X1,esk430_5(X2,X1,X3,X4,X5))=hAPP(c_Option_Ooption_OSome(X5),X4)|~hBOOL(hAPP(hAPP(c_member(X5),X4),c_Map_Oran(X3,X5,c_Map_Orestrict__map(X3,X5,X1,X2)))))). 4.07/4.37 cnf(i_0_1182, plain, (hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X5))=hAPP(hAPP(c_Set_Oinsert(X1),X4),hAPP(c_List_Oset(X1),X5))|~class_Orderings_Olinorder(X2))). 4.07/4.37 cnf(i_0_6747, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),c_Map_Odom(X1,X2,X4)))|~c_Map_Omap__le(X1,X2,X3,X4))). 4.07/4.37 cnf(i_0_1004, plain, (c_List_Otranspose(X1,X2)=c_List_Olist_ONil(tc_List_Olist(X1))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk91_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))))). 4.07/4.37 cnf(i_0_384, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.07/4.37 cnf(i_0_4686, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.07/4.37 cnf(i_0_6438, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.07/4.37 cnf(i_0_3813, 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)). 4.07/4.37 cnf(i_0_6592, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk467_4(X2,X3,X1,X4)),X3))|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X4),X2),X3)!=c_Groups_Ozero__class_Ozero(X4)|~class_Rings_Ono__zero__divisors(X4)|~class_Rings_Ocomm__semiring__1(X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_117, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)))|~c_Fun_Oinj__on(X2,X1,X3,hAPP(c_List_Oset(X2),X4))|~hBOOL(hAPP(c_List_Odistinct(X2),X4)))). 4.07/4.37 cnf(i_0_4409, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X4),X2)),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X6),X3))))). 4.07/4.37 cnf(i_0_5324, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3)))). 4.07/4.37 cnf(i_0_3347, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)))). 4.07/4.37 cnf(i_0_1085, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.07/4.37 cnf(i_0_2657, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)))). 4.07/4.37 cnf(i_0_7415, plain, (hAPP(hAPP(X1,X2),hAPP(X3,X4))=hAPP(X3,X4)|~c_Finite__Set_Ofolding__one__idem(X5,X1,X3)|~hBOOL(hAPP(hAPP(c_member(X5),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))). 4.07/4.37 cnf(i_0_7535, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)=X3|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.07/4.37 cnf(i_0_2368, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk181_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))))). 4.07/4.37 cnf(i_0_5191, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.07/4.37 cnf(i_0_5021, 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,esk363_3(X1,X3,X2))))). 4.07/4.37 cnf(i_0_4989, 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,esk361_3(X1,X3,X2))))). 4.07/4.37 cnf(i_0_5180, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(X3),X4),X1))|hBOOL(hAPP(hAPP(c_member(X3),X4),X2))|hAPP(hAPP(c_Set_Oinsert(X3),X4),X1)!=hAPP(hAPP(c_Set_Oinsert(X3),X4),X2))). 4.07/4.37 cnf(i_0_6819, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2))))). 4.07/4.37 cnf(i_0_7546, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_Predicate_Oconversep(X1,X1,X2))))). 4.07/4.37 cnf(i_0_5697, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))))). 4.07/4.37 cnf(i_0_2741, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2)),X3))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.37 cnf(i_0_3638, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.37 cnf(i_0_6586, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3)))). 4.07/4.37 cnf(i_0_1702, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk128_4(X2,X3,X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Set_Oimage(X1,X5,X3),X2))))). 4.07/4.37 cnf(i_0_1339, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Olinorder__class_Oinsort__insert__key(X2,X1,X3,X4,X5)))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_2555, plain, (c_Nitpick_Oless__frac(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_5228, plain, (c_Nitpick_Oless__eq__frac(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_2451, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)))). 4.07/4.37 cnf(i_0_1371, 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)))). 4.07/4.37 cnf(i_0_5710, plain, (hAPP(X1,hAPP(c_Fun_Othe__inv__into(X2,X3,X4,X1),X5))=X5|~c_Fun_Oinj__on(X2,X3,X1,X4)|~hBOOL(hAPP(hAPP(c_member(X3),X5),hAPP(c_Set_Oimage(X2,X3,X1),X4))))). 4.07/4.37 cnf(i_0_4822, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X2)),c_Wellfounded_Omax__ext(X1,X4))))). 4.07/4.37 cnf(i_0_3062, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(c_COMBK(X1,X2),c_Groups_Ozero__class_Ozero(X1))),X3))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Omonoid__add(X1))). 4.07/4.37 cnf(i_0_6704, 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)))). 4.07/4.37 cnf(i_0_750, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3))|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_4821, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Omax__ext(X1,X4))))). 4.07/4.37 cnf(i_0_6939, plain, (hAPP(X1,hAPP(X2,X3))=hAPP(X4,hAPP(X5,X3))|hAPP(c_Fun_Ocomp(X6,X7,X8,X1),X2)!=hAPP(c_Fun_Ocomp(X9,X7,X8,X4),X5))). 4.07/4.37 cnf(i_0_5515, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_2018, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_1157, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))))). 4.07/4.37 cnf(i_0_74, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)))). 4.07/4.37 cnf(i_0_3980, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.37 cnf(i_0_6718, plain, (c_Divides_OnegDivAlg(X1,X2)=hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))))). 4.07/4.37 cnf(i_0_2036, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),X5)=hAPP(hAPP(X6,X5),X4)|~c_Finite__Set_Ofolding(X1,X2,X3,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.37 cnf(i_0_2507, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4)))). 4.07/4.37 cnf(i_0_4974, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,c_Wellfounded_Oacc(X1,X3))))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3)))))). 4.07/4.37 cnf(i_0_260, plain, (c_Wellfounded_Owf(X1,X2)|hBOOL(hAPP(hAPP(c_member(X1),esk19_3(X2,X1,X3)),esk17_2(X2,X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),esk17_2(X2,X1))))). 4.07/4.37 cnf(i_0_3365, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3)))|~hBOOL(hAPP(c_Predicate_OPowp(X1,X3),X2)))). 4.07/4.37 cnf(i_0_3765, plain, (c_Groups_Ozero__class_Ozero(X1)=X2|X3=X4|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1))). 4.07/4.37 cnf(i_0_6691, plain, (hAPP(hAPP(c_List_Omap(X1,X2),X3),X4)=hAPP(hAPP(c_List_Omap(X1,X2),X5),X4)|hAPP(X3,esk472_5(X3,X4,X5,X2,X1))!=hAPP(X5,esk472_5(X3,X4,X5,X2,X1)))). 4.07/4.37 cnf(i_0_6494, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X4))))). 4.07/4.37 cnf(i_0_5253, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X5))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5))|~class_Orderings_Olinorder(X2))). 4.07/4.37 cnf(i_0_6661, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremove1(X1,X2,X3))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.07/4.37 cnf(i_0_1412, 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),esk113_2(X1,X2)),X2)))). 4.07/4.37 cnf(i_0_5754, plain, (hAPP(X1,esk418_3(X1,X2,X3))=c_Option_Ooption_ONone(X2)|hBOOL(hAPP(c_Finite__Set_Ofinite(X3),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),c_Map_Odom(X3,X2,X1))))). 4.07/4.37 cnf(i_0_1274, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_4599, plain, (c_List_Olast(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.07/4.37 cnf(i_0_4441, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1)))). 4.07/4.37 cnf(i_0_6054, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3))))|~hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_1951, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk146_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.07/4.37 cnf(i_0_2231, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk171_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.07/4.37 cnf(i_0_2169, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk166_3(X2,X3,X1)),esk166_3(X2,X3,X1))=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),c_Relation_OId__on(X1,X2))))). 4.07/4.37 cnf(i_0_1870, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2,X3)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4)))))). 4.07/4.37 cnf(i_0_3459, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OSigma(X3,X1),X4),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X3),X2)))))). 4.07/4.37 cnf(i_0_5119, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2)))). 4.07/4.37 cnf(i_0_6863, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X1),X5),X2)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5)))). 4.07/4.37 cnf(i_0_547, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3))=X3|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)!=X2)). 4.07/4.37 cnf(i_0_5261, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.07/4.37 cnf(i_0_6854, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X2)))). 4.07/4.37 cnf(i_0_671, 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,esk65_5(X5,X4,X3,X2,X1)))))). 4.07/4.37 cnf(i_0_6995, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X1),X2)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X1))))). 4.07/4.37 cnf(i_0_2426, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),hAPP(c_List_Oset(X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.07/4.37 cnf(i_0_6722, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),X4)),hAPP(X4,X5)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_member(X2),X5),X3)))). 4.07/4.37 cnf(i_0_2783, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.07/4.37 cnf(i_0_2821, plain, (c_List_Osublist(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)),X3)=hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))). 4.07/4.37 cnf(i_0_7254, plain, (c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))=hAPP(hAPP(c_List_Oappend(X1),c_List_Oremove1(X1,X2,X3)),X4)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.07/4.37 cnf(i_0_6466, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),c_List_Olinorder__class_Osort__key(X1,X2,X3,X5))=c_List_Olinorder__class_Osort__key(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))|~class_Orderings_Olinorder(X2))). 4.07/4.37 cnf(i_0_2061, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),X1))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),X1),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))))). 4.07/4.37 cnf(i_0_3382, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Nat__Transfer_Otsub(X1,X2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_3203, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_3175, plain, (c_Map_Omap__upds(X1,X2,X3,X4,hAPP(hAPP(c_List_Oappend(X2),X5),X6))=c_Map_Omap__upds(X1,X2,X3,X4,X5)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5))). 4.07/4.37 cnf(i_0_1572, plain, (c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X5),X6)=c_Map_Omap__upds(X1,X2,X3,X4,X6)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X6))). 4.07/4.37 cnf(i_0_3544, 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,esk269_4(X3,X4,X2,X1)))))). 4.07/4.37 cnf(i_0_3876, 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),esk285_3(X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_6154, 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),esk441_3(X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_1795, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.37 cnf(i_0_5631, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4)=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_6860, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk482_4(X2,X3,hAPP(c_Option_Ooption_OSome(X1),X2),X1)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))|hBOOL(hAPP(X3,X2)))). 4.07/4.37 cnf(i_0_5222, 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,esk378_4(X3,X4,X2,X1)))))). 4.07/4.37 cnf(i_0_5749, plain, (hAPP(hAPP(c_List_Onth(X1),c_List_OtakeWhile(X1,X2,X3)),X4)=hAPP(hAPP(c_List_Onth(X1),X3),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3)))))). 4.07/4.37 cnf(i_0_6124, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~class_Rings_Olinordered__semidom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Oone__class_Oone(X3)),X4)))). 4.07/4.37 cnf(i_0_2220, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4)=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_5672, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~class_Rings_Olinordered__semidom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Oone__class_Oone(X3)),X4)))). 4.07/4.37 cnf(i_0_2793, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_fequal),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X3)))))). 4.07/4.37 cnf(i_0_645, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 4.07/4.37 cnf(i_0_6587, plain, (hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4))|~hBOOL(hAPP(c_List_Olistsp(X1,X3),X4))|~hBOOL(hAPP(c_List_Olistsp(X1,X2),X4)))). 4.07/4.37 cnf(i_0_2568, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.37 cnf(i_0_1072, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.07/4.37 cnf(i_0_7383, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Otake(X1),X4),X5),hAPP(hAPP(c_List_Otake(X2),X4),X6))|~c_List_Olist__all2(X1,X2,X3,X5,X6))). 4.07/4.37 cnf(i_0_4069, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Odrop(X1),X4),X5),hAPP(hAPP(c_List_Odrop(X2),X4),X6))|~c_List_Olist__all2(X1,X2,X3,X5,X6))). 4.07/4.37 cnf(i_0_1938, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(hAPP(c_member(X3),esk144_4(X1,X4,X2,X3)),esk145_4(X1,X4,X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),X4))|~hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 4.07/4.37 cnf(i_0_416, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X4)=c_Divides_Odiv__class_Omod(X1,X2,X4)|~class_Divides_Osemiring__div(X1))). 4.07/4.37 cnf(i_0_4803, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.37 cnf(i_0_3694, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.07/4.37 cnf(i_0_5038, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.37 cnf(i_0_6157, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X3)=c_Divides_Odiv__class_Omod(X1,X2,X3)|~class_Divides_Osemiring__div(X1))). 4.07/4.37 cnf(i_0_3714, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X2),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_5568, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X2),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_4680, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1))))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(X1)),X2)))). 4.07/4.37 cnf(i_0_3735, plain, (hAPP(X1,X2)=c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X3,tc_HOL_Obool)),X5),X1)!=c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X4),X2),X5)))). 4.07/4.37 cnf(i_0_2962, plain, (hAPP(X1,X2)=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X3,tc_HOL_Obool)),X5),X1)!=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X4),X2),X5)))). 4.07/4.37 cnf(i_0_3036, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_4042, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_6177, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.37 cnf(i_0_4621, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_7237, 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),esk509_3(X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.07/4.37 cnf(i_0_3165, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_5232, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_3564, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.37 cnf(i_0_4797, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_6133, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.07/4.37 cnf(i_0_4429, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.37 cnf(i_0_7393, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_7286, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.07/4.37 cnf(i_0_1585, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.37 cnf(i_0_6061, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.37 cnf(i_0_2566, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.37 cnf(i_0_2743, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.37 cnf(i_0_3103, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_3770, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.37 cnf(i_0_4669, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk338_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X1))))). 4.07/4.37 cnf(i_0_1035, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_7035, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.37 cnf(i_0_6184, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.37 cnf(i_0_5650, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|~class_Rings_Olinordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.37 cnf(i_0_7501, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X4)=c_Groups_Ozero__class_Ozero(X2)|c_Groups_Ozero__class_Ozero(X2)!=hAPP(X3,X5)|~class_Rings_Ocomm__semiring__1(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.37 cnf(i_0_982, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))|~c_Nat__Transfer_Onat__set(X2)|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X2)))). 4.07/4.37 cnf(i_0_821, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1))). 4.07/4.37 cnf(i_0_5067, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Int_Onumber__ring(X1))). 4.07/4.37 cnf(i_0_6918, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.07/4.37 cnf(i_0_774, 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)))). 4.07/4.37 cnf(i_0_915, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_2592, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_6769, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_3419, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3))=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))|~class_Rings_Oring__1(X1))). 4.07/4.37 cnf(i_0_35, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_1219, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_6270, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.37 cnf(i_0_6239, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),X2)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber__ring(X1))). 4.07/4.37 cnf(i_0_5171, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3))=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3))|~class_Rings_Oring__1(X1))). 4.07/4.37 cnf(i_0_2696, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_1700, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_3279, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Oaccp(X1,X2)),c_Wellfounded_Oaccp(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X3),X2)))). 4.07/4.37 cnf(i_0_3272, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Oacc(X1,X2)),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)))). 4.07/4.37 cnf(i_0_335, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3))=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))|~class_Rings_Oring__1(X1))). 4.07/4.37 cnf(i_0_5577, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.37 cnf(i_0_6917, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.07/4.37 cnf(i_0_118, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))|~class_Int_Onumber__ring(X1))). 4.07/4.37 cnf(i_0_4937, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__idom(X1))). 4.07/4.37 cnf(i_0_3528, 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,esk265_4(X1,X4,X3,X2)),X5))|~hBOOL(hAPP(hAPP(c_member(X2),X5),X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.07/4.37 cnf(i_0_3961, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X1,X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.37 cnf(i_0_882, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X1,X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_2008, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X2=X3|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5),X3)))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X6),X2))))). 4.07/4.37 cnf(i_0_7101, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X3))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))|~class_Groups_Omonoid__add(X1))). 4.07/4.37 cnf(i_0_5081, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))))). 4.07/4.37 cnf(i_0_6987, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.07/4.37 cnf(i_0_758, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.37 cnf(i_0_3141, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.37 cnf(i_0_5858, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))|~class_Fields_Olinordered__field__inverse__zero(X1))). 4.07/4.37 cnf(i_0_5238, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|X2=X3|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X5)))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X4,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X6))))). 4.07/4.37 cnf(i_0_7438, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3),X4)|~class_Divides_Oring__div(X1))). 4.07/4.37 cnf(i_0_2173, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4)|~class_Divides_Osemiring__div(X1))). 4.07/4.37 cnf(i_0_2179, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.07/4.37 cnf(i_0_7468, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.07/4.37 cnf(i_0_4857, 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)))). 4.07/4.37 cnf(i_0_3078, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Rings_Olinordered__idom(X1))). 4.07/4.37 cnf(i_0_3993, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)|~class_Divides_Osemiring__div(X1))). 4.07/4.37 cnf(i_0_3592, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))|~class_Int_Onumber__ring(X1))). 4.07/4.37 cnf(i_0_2691, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X3))))). 4.07/4.37 cnf(i_0_3319, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X4),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4),X3)|~class_Divides_Osemiring__div(X1))). 4.07/4.37 cnf(i_0_865, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X4),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)|~class_Divides_Osemiring__div(X1))). 4.07/4.37 cnf(i_0_3504, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.07/4.37 cnf(i_0_2210, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))|~class_Rings_Osemiring__1(X1))). 4.07/4.37 cnf(i_0_5930, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),X4),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4),X3)|~class_Divides_Oring__div(X1))). 4.07/4.37 cnf(i_0_7487, plain, (X1=c_Big__Operators_Olinorder__class_OMin(X2,X3)|hBOOL(hAPP(hAPP(c_member(X2),esk524_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)))). 4.07/4.37 cnf(i_0_5860, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_623, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk57_2(X1,X2)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))|~hBOOL(hAPP(X1,X3)))). 4.07/4.37 cnf(i_0_4056, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),X3))|hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_5831, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)=c_Int_OMin|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_5271, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3))|~class_Rings_Osemiring__1(X1))). 4.07/4.37 cnf(i_0_6711, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_6458, plain, (c_Big__Operators_Olinorder__class_OMax(X1,X2)=X3|hBOOL(hAPP(hAPP(c_member(X1),esk456_3(X3,X2,X1)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.37 cnf(i_0_1261, 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,esk108_4(X4,X2,X3,X1))))). 4.07/4.37 cnf(i_0_3111, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk233_5(X2,X3,X1,X4,X5)),X2))|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Relation_OImage(X1,X5,X3),X2))))). 4.07/4.37 cnf(i_0_3605, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk273_5(X2,X3,X1,X4,X5)),X2))|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_Relation_OImage(X1,X5,X3),X2))))). 4.07/4.37 cnf(i_0_339, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_1045, plain, (hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4))=hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X2),X4))|~c_Finite__Set_Ofun__left__comm(X5,X6,X1))). 4.07/4.37 cnf(i_0_6798, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),X4)=hAPP(hAPP(c_List_Onth(X1),X2),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.07/4.37 cnf(i_0_4276, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk311_2(X1,X2)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))|~hBOOL(hAPP(X1,X3)))). 4.07/4.37 cnf(i_0_3873, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_1944, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),c_List_Oremove1(X1,X2,X3))=X3|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.07/4.37 cnf(i_0_6448, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Complete__Lattice_OSup__class_OSup(X1,X3)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.37 cnf(i_0_6753, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Complete__Lattice_OInf__class_OInf(X1,X2)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3)))). 4.07/4.37 cnf(i_0_5156, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_1483, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))))). 4.07/4.37 cnf(i_0_3567, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4),X5),X6))|~hBOOL(hAPP(hAPP(X4,X5),X6))|~hBOOL(hAPP(hAPP(X3,X5),X6)))). 4.07/4.37 cnf(i_0_3020, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.07/4.37 cnf(i_0_1433, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3))|~class_Int_Onumber__ring(X1))). 4.07/4.37 cnf(i_0_3634, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_2432, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1)),X2),X3)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_1937, plain, (hBOOL(hAPP(X1,esk145_4(X1,X2,X3,X4)))|hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),X2))|~hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))). 4.07/4.37 cnf(i_0_5623, 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,esk403_4(X1,X5,X4,X3)))|~hBOOL(hAPP(X1,esk404_4(X1,X5,X4,X3))))). 4.07/4.37 cnf(i_0_2327, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~class_Int_Onumber__ring(X1))). 4.07/4.37 cnf(i_0_6886, plain, (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X3))|~hBOOL(hAPP(hAPP(X4,X6),X5)))). 4.07/4.37 cnf(i_0_1866, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_List_Oset(X3),c_List_Oremove1(X3,X2,X4))))|~hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_List_Oset(X3),X4))))). 4.07/4.37 cnf(i_0_473, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_191, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)|X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.07/4.37 cnf(i_0_6058, plain, (hAPP(X1,X2)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X3,X4,X5),X6),X7),X2)|~c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X7,X6,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)))). 4.07/4.37 cnf(i_0_332, 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,esk24_4(X2,X3,X1,X4))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(X2,X4)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_6295, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_2500, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_7326, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X1)))). 4.07/4.37 cnf(i_0_955, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_3577, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)))). 4.07/4.37 cnf(i_0_1294, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),X1)))). 4.07/4.37 cnf(i_0_4928, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.07/4.37 cnf(i_0_897, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_1084, plain, (c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))|~c_Wellfounded_Owf(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)))). 4.07/4.37 cnf(i_0_5370, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.07/4.37 cnf(i_0_51, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_1551, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)))). 4.07/4.37 cnf(i_0_6388, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_5197, 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|c_Groups_Ozero__class_Ozero(X1)=X3|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X5)!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)|~class_Fields_Ofield(X1))). 4.07/4.37 cnf(i_0_1345, plain, (hAPP(X1,esk109_4(X2,X1,X3,X4))=X2|~c_Fun_Oinj__on(X4,X3,X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_Set_Oimage(X4,X3,X1),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))))). 4.07/4.37 cnf(i_0_58, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk3_5(X3,X4,X5,X2,X1))=X4|X4=c_List_Olist_ONil(X1)|hAPP(hAPP(c_List_Oappend(X1),X4),X3)!=hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5))). 4.07/4.37 cnf(i_0_5900, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk428_5(X3,X2,X4,X5,X1))=X5|X5=c_List_Olist_ONil(X1)|hAPP(hAPP(c_List_Oappend(X1),X5),X4)!=hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))). 4.07/4.37 cnf(i_0_60, plain, (hAPP(hAPP(c_List_Oappend(X1),esk3_5(X2,X3,X4,X5,X1)),X2)=X4|X3=c_List_Olist_ONil(X1)|hAPP(hAPP(c_List_Oappend(X1),X3),X2)!=hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4))). 4.07/4.37 cnf(i_0_1908, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OMin)))). 4.07/4.37 cnf(i_0_6385, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Int_OMin)))). 4.07/4.37 cnf(i_0_6128, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))|~class_Groups_Omonoid__mult(X1))). 4.07/4.37 cnf(i_0_5706, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4))|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.37 cnf(i_0_5196, 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)=X5|c_Groups_Ozero__class_Ozero(X1)=X3|hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)|~class_Fields_Ofield(X1))). 4.07/4.37 cnf(i_0_5901, plain, (hAPP(hAPP(c_List_Oappend(X1),esk428_5(X2,X3,X4,X5,X1)),X4)=X2|X5=c_List_Olist_ONil(X1)|hAPP(hAPP(c_List_Oappend(X1),X5),X4)!=hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))). 4.07/4.37 cnf(i_0_2264, plain, (hAPP(X1,X2)=hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X3),X4,c_Option_Ooption_ONone(X3),X1),hAPP(X5,X6))|hAPP(X5,X6)!=hAPP(c_Option_Ooption_OSome(X4),X2))). 4.07/4.37 cnf(i_0_7161, plain, (hAPP(c_List_Ofilter(X1,X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X3,X4),X5),X6))=hAPP(c_List_Ofilter(X1,X2),X6)|hBOOL(hAPP(X2,X5))|~class_Orderings_Olinorder(X3))). 4.07/4.37 cnf(i_0_3132, plain, (hAPP(hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Orotate1(X1)),X3)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))). 4.07/4.37 cnf(i_0_16, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.37 cnf(i_0_3954, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))|~class_Groups_Oab__semigroup__add(X1))). 4.07/4.37 cnf(i_0_241, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.37 cnf(i_0_3390, plain, (c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)))=c_List_OtakeWhile(X1,X2,X3)|hBOOL(hAPP(X2,X4)))). 4.07/4.37 cnf(i_0_3215, 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,esk243_7(X7,X6,X5,X4,X3,X2,X1)),X6),X7)))). 4.07/4.37 cnf(i_0_6241, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olistsp(X1,X2)),c_List_Olistsp(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.07/4.37 cnf(i_0_1592, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olists(X1,X2)),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.07/4.37 cnf(i_0_4218, 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)))))). 4.07/4.37 cnf(i_0_2703, 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),esk196_4(X4,X3,X1,X2)),X3)))). 4.07/4.37 cnf(i_0_7124, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))|~class_Lattices_Osemilattice__inf(X1))). 4.07/4.37 cnf(i_0_5732, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))|~class_Lattices_Olattice(X1))). 4.07/4.37 cnf(i_0_1019, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))|~class_Lattices_Osemilattice__sup(X1))). 4.07/4.37 cnf(i_0_1620, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.07/4.37 cnf(i_0_3737, 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),esk282_4(X4,X3,X2,X1)),X3)))). 4.07/4.37 cnf(i_0_4217, 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)))))). 4.07/4.37 cnf(i_0_6894, plain, (c_Nat_Osemiring__1__class_Oof__nat__aux(X1,hAPP(hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_Groups_Oone__class_Oone(X1)),X2,c_Groups_Ozero__class_Ozero(X1))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)|~class_Rings_Osemiring__1(X1))). 4.07/4.37 cnf(i_0_2964, 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),esk219_4(X4,X3,X1,X2)),X3)))). 4.07/4.37 cnf(i_0_5164, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))|~class_Groups_Oab__semigroup__mult(X1))). 4.07/4.37 cnf(i_0_5752, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Groups_Omonoid__mult(X1))). 4.07/4.37 cnf(i_0_151, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))|~class_Lattices_Olattice(X1))). 4.07/4.37 cnf(i_0_6974, 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),esk491_4(X4,X3,X2,X1)),X3)))). 4.07/4.37 cnf(i_0_1712, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),X5)))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.37 cnf(i_0_1941, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3)=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_1773, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4))|~class_Rings_Odivision__ring(X1))). 4.07/4.37 cnf(i_0_7222, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk507_4(X2,X3,X1,X4))))|hAPP(c_Nat_OSuc,X2)!=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X3))). 4.07/4.37 cnf(i_0_2186, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))=hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_464, 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,esk37_3(X3,X2,X1))))). 4.07/4.37 cnf(i_0_370, 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,esk28_4(X4,X2,X3,X1))),hAPP(X4,esk28_4(X4,X2,X3,X1)))))). 4.07/4.37 cnf(i_0_912, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Fun_Oinj__on(X3,X4,X5,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X3,tc_HOL_Obool)),X2),X6))|~c_Fun_Oinj__on(X3,X4,X5,hAPP(X6,esk85_6(X6,X5,X4,X3,X1,X2))))). 4.07/4.37 cnf(i_0_5037, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2))=hAPP(c_Nat_OSuc,X2)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.07/4.37 cnf(i_0_5876, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))))). 4.07/4.37 cnf(i_0_5879, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))))). 4.07/4.37 cnf(i_0_5418, plain, (hAPP(hAPP(X1,X2),esk390_7(X2,X3,X4,X5,X1,X6,X7))=X3|~c_Finite__Set_Ofun__left__comm(X7,X6,X1)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X6,X1,X5,X4),X3))|~hBOOL(hAPP(hAPP(c_member(X7),X2),X4)))). 4.07/4.37 cnf(i_0_6662, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremove1(X1,X2,X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.07/4.37 cnf(i_0_6174, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omax(X1),X2),X3)|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_3899, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omin(X1),X2),X3)|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_5878, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))))). 4.07/4.37 cnf(i_0_5877, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))))). 4.07/4.37 cnf(i_0_3940, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))))). 4.07/4.37 cnf(i_0_3941, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))))). 4.07/4.37 cnf(i_0_5304, plain, (hAPP(X1,X2)=hAPP(X3,X2)|~class_HOL_Oequal(X4)|~class_Enum_Oenum(X5)|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(X5,X4)),X1),X3)))). 4.07/4.37 cnf(i_0_3051, plain, (c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)))|~c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))). 4.07/4.37 cnf(i_0_590, plain, (c_List_Olistrelp(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X6))|~c_List_Olistrelp(X1,X2,X4,X6)|~hBOOL(hAPP(hAPP(X2,X3),X5)))). 4.07/4.37 cnf(i_0_5985, plain, (X1=X2|hAPP(hAPP(c_List_Omap(X3,X4),X5),X1)!=hAPP(hAPP(c_List_Omap(X3,X4),X5),X2)|~c_Fun_Oinj__on(X3,X4,X5,hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Oappend(X3),X2),X1))))). 4.07/4.37 cnf(i_0_3942, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2))))). 4.07/4.37 cnf(i_0_3939, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3))))). 4.07/4.37 cnf(i_0_1022, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_3670, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_4737, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_6038, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_1848, plain, (hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5)=hAPP(X4,X5)|hBOOL(hAPP(hAPP(c_member(X1),X5),c_Map_Odom(X1,X2,X3))))). 4.07/4.37 cnf(i_0_2733, 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))))). 4.07/4.37 cnf(i_0_1024, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_1023, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_2732, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_3840, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2))|~class_Groups_Ogroup__add(X1))). 4.07/4.37 cnf(i_0_3375, plain, (hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5)=hAPP(X3,X5)|hBOOL(hAPP(hAPP(c_member(X1),X5),c_Map_Odom(X1,X2,X4))))). 4.07/4.37 cnf(i_0_3138, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_5744, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.37 cnf(i_0_1524, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.37 cnf(i_0_5761, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_2731, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_1025, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_2730, 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))))). 4.07/4.37 cnf(i_0_2541, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_3879, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))|~class_Groups_Oab__group__add(X1))). 4.07/4.37 cnf(i_0_2623, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk188_3(X2,X3,X1)),esk189_3(X2,X3,X1))=X3|c_List_Olist_ONil(X1)=X3|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2))))). 4.07/4.37 cnf(i_0_5970, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_7247, 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))))). 4.07/4.37 cnf(i_0_2831, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(X1),X2))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X1)))). 4.07/4.37 cnf(i_0_2133, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)))). 4.07/4.37 cnf(i_0_6817, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)))). 4.07/4.37 cnf(i_0_4269, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3))|~class_Lattices_Oboolean__algebra(X1))). 4.07/4.37 cnf(i_0_5466, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3))|~class_Groups_Olinordered__ab__group__add(X1))). 4.07/4.37 cnf(i_0_2526, 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))))). 4.07/4.37 cnf(i_0_848, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4))))). 4.07/4.37 cnf(i_0_1936, plain, (hBOOL(hAPP(X1,X2))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X3),esk144_4(X1,X4,X2,X3)),esk145_4(X1,X4,X2,X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X2),X4))|~hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)))). 4.07/4.37 cnf(i_0_3657, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_1297, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3))|~class_Lattices_Oboolean__algebra(X1))). 4.07/4.37 cnf(i_0_2142, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3))|~class_Groups_Olinordered__ab__group__add(X1))). 4.07/4.37 cnf(i_0_1954, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist__update(X1,X3),X4),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.37 cnf(i_0_5669, 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))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_5064, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_587, plain, (X1=X2|hAPP(hAPP(c_List_Onth(X3),X4),X1)!=hAPP(hAPP(c_List_Onth(X3),X4),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)))|~hBOOL(hAPP(c_List_Odistinct(X3),X4)))). 4.07/4.37 cnf(i_0_7176, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(c_COMBK(X2,X1),X3)),X4)=hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Finite__Set_Ocard(X1),X4))|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.37 cnf(i_0_2296, plain, (c_List_Oremdups(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))=hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Oremdups(X1,X3))|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.07/4.37 cnf(i_0_1344, plain, (esk109_4(hAPP(X1,X2),X1,X3,X4)=X2|~c_Fun_Oinj__on(X4,X3,X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))). 4.07/4.37 cnf(i_0_5028, 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))))). 4.07/4.37 cnf(i_0_5285, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X2)|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.37 cnf(i_0_1069, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olinorder__class_OMin(X1,X3))=c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_2693, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk194_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2))))). 4.07/4.37 cnf(i_0_4581, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Oplus__class_Oplus(X1)),X3),c_Groups_Ozero__class_Ozero(X1)),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.37 cnf(i_0_317, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.37 cnf(i_0_3637, 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))). 4.07/4.37 cnf(i_0_2713, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))|~class_Groups_Oordered__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.07/4.37 cnf(i_0_5097, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.07/4.37 cnf(i_0_1570, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))|~class_Groups_Oordered__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.07/4.37 cnf(i_0_6565, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))=c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_1777, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X2)))). 4.07/4.37 cnf(i_0_5589, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Omap(X4,X1),X5),X6),X7)|~c_List_Olist__all2(X4,X2,hAPP(hAPP(c_COMBB(X1,tc_fun(X2,tc_HOL_Obool),X4),X3),X5),X6,X7))). 4.07/4.37 cnf(i_0_4619, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.07/4.37 cnf(i_0_2605, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.07/4.37 cnf(i_0_6189, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.07/4.37 cnf(i_0_5266, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.37 cnf(i_0_4450, 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)))). 4.07/4.37 cnf(i_0_1153, plain, (~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X4)),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))))). 4.07/4.37 cnf(i_0_6029, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk430_5(X2,X3,X1,X4,X5)),X2))|~hBOOL(hAPP(hAPP(c_member(X5),X4),c_Map_Oran(X1,X5,c_Map_Orestrict__map(X1,X5,X3,X2)))))). 4.07/4.37 cnf(i_0_6693, plain, (hAPP(X1,X2)=hAPP(X3,X2)|hAPP(hAPP(c_List_Omap(X4,X5),X1),X6)!=hAPP(hAPP(c_List_Omap(X4,X5),X3),X6)|~hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X6))))). 4.07/4.37 cnf(i_0_5404, plain, (c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))|~c_Predicate_Oreflp(X1,X2))). 4.07/4.37 cnf(i_0_6590, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))). 4.07/4.37 cnf(i_0_1522, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_5764, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.07/4.37 cnf(i_0_5, plain, (X1=X2|hAPP(hAPP(c_Product__Type_OSigma(X3,X4),X1),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),X5))!=hAPP(hAPP(c_Product__Type_OSigma(X3,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X3),X5))|~hBOOL(hAPP(hAPP(c_member(X4),X6),X5)))). 4.07/4.37 cnf(i_0_87, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Groups_Otimes__class_Otimes(X1)),X2),X3)|~class_Lattices_Oab__semigroup__idem__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_5747, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))). 4.07/4.37 cnf(i_0_4194, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)))). 4.07/4.37 cnf(i_0_344, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))). 4.07/4.37 cnf(i_0_602, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))). 4.07/4.37 cnf(i_0_3131, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_2013, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_6766, plain, (hAPP(c_Set_Oimage(X1,X2,hAPP(c_COMBK(X2,X1),X3)),X4)=hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4)))). 4.07/4.37 cnf(i_0_4101, plain, (hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),X5))=hAPP(c_Set_Oimage(X4,X1,X2),X5)|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5)))). 4.07/4.37 cnf(i_0_83, 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,esk7_5(X3,X2,X5,X4,X1))))|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.07/4.37 cnf(i_0_4162, plain, (c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),X2))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2))|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Groups_Olinordered__ab__group__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.37 cnf(i_0_4230, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))). 4.07/4.37 cnf(i_0_431, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))). 4.07/4.37 cnf(i_0_7064, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))). 4.07/4.37 cnf(i_0_3487, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.37 cnf(i_0_4759, 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))|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)))). 4.07/4.37 cnf(i_0_4541, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_1373, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_6315, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))). 4.07/4.37 cnf(i_0_2469, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_6502, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.07/4.37 cnf(i_0_6358, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(c_Set_Oimage(X2,X1,X3),X4))),hAPP(c_Finite__Set_Ocard(X2),X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.37 cnf(i_0_4316, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,X1))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))))). 4.07/4.37 cnf(i_0_3583, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X1,X2),tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))). 4.07/4.37 cnf(i_0_6144, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk440_7(X2,X3,X4,X5,X6,X7,X1)),X5))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X7,tc_fun(X6,tc_HOL_Obool))),X5),X4),X3),X2)))). 4.07/4.37 cnf(i_0_3966, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),X2)!=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X2)))). 4.07/4.37 cnf(i_0_6741, 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))). 4.07/4.37 cnf(i_0_7569, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk530_3(X2,X3,X1)),X3))|hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3))))). 4.07/4.37 cnf(i_0_1040, 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,esk93_3(X2,X3,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_4713, 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,esk339_3(X2,X3,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_3472, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk260_2(X1,X2)),X2))|hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))))). 4.07/4.37 cnf(i_0_5966, 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))|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Fields_Olinordered__field(X1))). 4.07/4.37 cnf(i_0_2178, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_5149, 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,esk376_3(X2,X1,X3)),esk377_3(X2,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_2707, 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,esk197_3(X2,X1,X3)),esk198_3(X2,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.07/4.37 cnf(i_0_1950, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk146_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)))). 4.07/4.37 cnf(i_0_6281, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_5582, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_40, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.37 cnf(i_0_1230, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.37 cnf(i_0_2340, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.07/4.37 cnf(i_0_2232, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk171_3(X1,X2,X3))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)))). 4.07/4.37 cnf(i_0_2817, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X2,c_Option_Ooption_ONone(X1),X3),hAPP(X4,X5))=c_Option_Ooption_ONone(X1)|hAPP(X4,X5)!=hAPP(c_Option_Ooption_OSome(X2),X6)|c_Option_Ooption_ONone(X1)!=hAPP(X3,X6))). 4.07/4.37 cnf(i_0_3548, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ORange(X3,X1),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X2)),X4)))). 4.07/4.37 cnf(i_0_2390, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X3),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),X5)),X4)))). 4.07/4.37 cnf(i_0_6534, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))))). 4.07/4.37 cnf(i_0_6535, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))))). 4.07/4.37 cnf(i_0_6536, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))))). 4.07/4.37 cnf(i_0_6533, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))))). 4.07/4.37 cnf(i_0_1302, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))|~class_Int_Onumber__ring(X1))). 4.07/4.37 cnf(i_0_5075, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))=X4|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3)). 4.07/4.37 cnf(i_0_5798, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Oone__class_Oone(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))|~class_Int_Onumber__ring(X1))). 4.07/4.37 cnf(i_0_2335, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)=c_Groups_Oone__class_Oone(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))|~class_Int_Onumber__ring(X1))). 4.07/4.37 cnf(i_0_6412, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,esk452_5(X3,X4,X5,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3))))). 4.07/4.37 cnf(i_0_249, 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|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3)). 4.07/4.37 cnf(i_0_1385, 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))))). 4.07/4.37 cnf(i_0_1384, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_1387, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_1386, 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))))). 4.07/4.37 cnf(i_0_1966, plain, (hAPP(c_Set_Oimage(X1,X2,hAPP(c_COMBK(X2,X1),X3)),X4)=hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X4)). 4.07/4.37 cnf(i_0_4575, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_4145, plain, (hAPP(hAPP(c_List_Onth(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_List_Olast(X1,X2)|c_List_Olist_ONil(X1)=X2)). 4.07/4.37 cnf(i_0_5880, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_3938, 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))))). 4.07/4.37 cnf(i_0_5881, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_3937, 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)))). 4.07/4.37 cnf(i_0_2594, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))))). 4.07/4.37 cnf(i_0_5774, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2))))). 4.07/4.37 cnf(i_0_6920, 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))))). 4.07/4.37 cnf(i_0_2123, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X5),X4),X2))))). 4.07/4.37 cnf(i_0_4043, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(c_COMBK(X1,X2),X4))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3)))). 4.07/4.37 cnf(i_0_1793, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.37 cnf(i_0_1087, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.07/4.37 cnf(i_0_120, plain, (hAPP(c_Map_Omap__upds(X1,X2,X3,X4,X5),X6)=hAPP(X3,X6)|hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),X4))))). 4.07/4.37 cnf(i_0_6350, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_COMBB(X3,tc_HOL_Obool,X1),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(X3),hAPP(X5,X2)),X4)))). 4.07/4.37 cnf(i_0_4342, plain, (hAPP(X1,X2)=X3|~hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,X4),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X1))))). 4.07/4.37 cnf(i_0_7289, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Int_Oring__1__class_OInts(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))))). 4.07/4.37 cnf(i_0_5467, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Rings_Osemiring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Nat_Osemiring__1__class_ONats(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Nat_Osemiring__1__class_ONats(X1))))). 4.07/4.37 cnf(i_0_4044, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(c_COMBK(X1,X2),X4))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1),X4),X3)))). 4.07/4.37 cnf(i_0_5779, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2))),X3)=c_List_Oremove1(X1,X2,X3)|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.07/4.37 cnf(i_0_591, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X1),c_Fun_Oid(X1)),hAPP(c_Set_Oimage(X2,X1,X3),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)|~c_Fun_Oinj__on(X2,X1,X3,X4)|~class_Groups_Ocomm__monoid__mult(X1))). 4.07/4.37 cnf(i_0_7490, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_Fun_Oid(X1)),hAPP(c_Set_Oimage(X2,X1,X3),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)|~c_Fun_Oinj__on(X2,X1,X3,X4)|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.37 cnf(i_0_2621, plain, (c_List_Olist_ONil(X1)=X2|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk189_3(X3,X2,X1)),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3))))). 4.07/4.37 cnf(i_0_1940, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk145_4(X2,X3,X4,X1)))|hBOOL(hAPP(X2,X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.37 cnf(i_0_1427, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Int_Oring__1__class_OInts(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))))). 4.07/4.37 cnf(i_0_3998, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Nat_Osemiring__1__class_ONats(X1)))|~class_Rings_Osemiring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Nat_Osemiring__1__class_ONats(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Nat_Osemiring__1__class_ONats(X1))))). 4.07/4.37 cnf(i_0_141, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),c_Int_Oring__1__class_OInts(X1)))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Int_Oring__1__class_OInts(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))))). 4.07/4.37 cnf(i_0_1321, plain, (hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4))=hAPP(X5,hAPP(c_Product__Type_Ofst(X2,X3),X4))|hAPP(c_Product__Type_Omap__pair(X2,X6,X3,X3,X1,c_Fun_Oid(X3)),X4)!=hAPP(c_Product__Type_Omap__pair(X2,X6,X3,X3,X5,c_Fun_Oid(X3)),X4))). 4.07/4.37 cnf(i_0_4095, plain, (hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4))=hAPP(X5,hAPP(c_Product__Type_Osnd(X2,X3),X4))|hAPP(c_Product__Type_Omap__pair(X2,X2,X3,X6,c_Fun_Oid(X2),X1),X4)!=hAPP(c_Product__Type_Omap__pair(X2,X2,X3,X6,c_Fun_Oid(X2),X5),X4))). 4.07/4.37 cnf(i_0_5968, plain, (X1=c_Big__Operators_Olinorder__class_OMax(X2,X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_member(X2),X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.07/4.37 cnf(i_0_1021, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_1020, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_2735, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_2734, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_6084, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|hAPP(c_Set_Oimage(X3,X1,X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X3),X2),X4))))). 4.07/4.37 cnf(i_0_6984, plain, (X1=c_Big__Operators_Olattice__class_OSup__fin(X2,X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~class_Lattices_Olattice(X2)|~hBOOL(hAPP(hAPP(c_member(X2),X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.07/4.37 cnf(i_0_7008, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,X2)=X3|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.37 cnf(i_0_5190, 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)))). 4.07/4.37 cnf(i_0_6930, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X1)))). 4.07/4.37 cnf(i_0_934, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.07/4.37 cnf(i_0_6815, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.07/4.37 cnf(i_0_5834, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)))|~c_Fun_Oinj__on(X1,X2,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.07/4.37 cnf(i_0_4556, plain, (c_List_Olinorder__class_Oinsort__insert__key(X1,X1,c_COMBI(X1),X2,X3)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X3)|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_5472, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2))))). 4.07/4.37 cnf(i_0_4051, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2))))). 4.07/4.37 cnf(i_0_5630, plain, (hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3))=hAPP(hAPP(c_List_Onth(X1),X3),X2)|X3=c_List_Olist_ONil(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.37 cnf(i_0_6119, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk436_2(X1,X2)),X2))|hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))))). 4.07/4.37 cnf(i_0_1742, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OField(X1),X2)),hAPP(c_Relation_OField(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.07/4.37 cnf(i_0_302, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X4)))). 4.07/4.37 cnf(i_0_3263, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.07/4.37 cnf(i_0_7346, plain, (hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3))=X4|hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))). 4.07/4.37 cnf(i_0_5962, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X5))))). 4.07/4.37 cnf(i_0_5963, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X5),X3))))). 4.07/4.37 cnf(i_0_7294, 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),esk513_5(X5,X4,X3,X2,X1)),X3)))). 4.07/4.37 cnf(i_0_502, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X1),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))=c_List_Oupto(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.07/4.37 cnf(i_0_5236, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X2))))). 4.07/4.37 cnf(i_0_385, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.07/4.37 cnf(i_0_4318, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.07/4.37 cnf(i_0_2810, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),hAPP(c_Set_Oimage(X2,X1,X3),X4)),X3)=X4|~c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))). 4.07/4.37 cnf(i_0_5406, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X4),X5),hAPP(hAPP(c_List_Oappend(X2),X6),X7))|~c_List_Olist__all2(X1,X2,X3,X5,X7)|~c_List_Olist__all2(X1,X2,X3,X4,X6))). 4.07/4.37 cnf(i_0_5144, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X4),X3)|c_Divides_Odiv__class_Omod(X1,X2,X3)!=c_Divides_Odiv__class_Omod(X1,X4,X3)|~class_Divides_Oring__div(X1))). 4.07/4.37 cnf(i_0_6509, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2)))). 4.07/4.37 cnf(i_0_6372, 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),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))))). 4.07/4.37 cnf(i_0_2754, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))))). 4.07/4.37 cnf(i_0_6760, plain, (hAPP(X1,esk477_7(X2,X3,X4,X1,X5,X6,X7))=hAPP(c_Option_Ooption_OSome(X6),X2)|hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X7,c_Option_Ooption_ONone(X6),X1),hAPP(X4,X3))!=hAPP(c_Option_Ooption_OSome(X6),X2))). 4.07/4.37 cnf(i_0_3542, plain, (hAPP(X1,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|X2=esk267_3(X1,X3,X4)|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X3)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X4),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))). 4.07/4.37 cnf(i_0_2323, 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),X2),X4)),hAPP(hAPP(c_List_Olist_OCons(X5),X1),X3))),c_List_Olistrel1(X5,X6))))). 4.07/4.37 cnf(i_0_3575, plain, (c_List_Obutlast(X1,hAPP(hAPP(c_List_Otake(X1),X2),X3))=hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.37 cnf(i_0_2092, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.07/4.37 cnf(i_0_6056, plain, (hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))))). 4.07/4.37 cnf(i_0_1721, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.07/4.37 cnf(i_0_253, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.07/4.37 cnf(i_0_1211, 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)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_3005, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(X1),X3))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.07/4.37 cnf(i_0_1263, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.07/4.37 cnf(i_0_7051, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.07/4.37 cnf(i_0_6510, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2)))). 4.07/4.37 cnf(i_0_2957, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.07/4.37 cnf(i_0_5569, plain, (c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Code__Numeral_Onat__of,X1))))). 4.07/4.37 cnf(i_0_3610, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.37 cnf(i_0_4786, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),X3)))). 4.07/4.37 cnf(i_0_5297, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.07/4.37 cnf(i_0_7181, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X1,X2)),c_Predicate_OPowp(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.07/4.37 cnf(i_0_6254, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5)))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_1351, plain, (hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),X5))|hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,X3,X4),X5)))). 4.07/4.37 cnf(i_0_1666, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(X4,X2)))). 4.07/4.37 cnf(i_0_4831, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X3))=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.07/4.37 cnf(i_0_13, plain, (X1=X2|~c_Relation_Osingle__valued(X3,X4,X5)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X2)),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X4)),hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X1)),X5)))). 4.07/4.37 cnf(i_0_2748, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk200_5(X2,X3,X4,X5,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X5)),X4),hAPP(hAPP(c_Product__Type_OSigma(X1,X5),X3),X2))))). 4.07/4.37 cnf(i_0_3624, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.07/4.37 cnf(i_0_6571, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.07/4.37 cnf(i_0_3953, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.07/4.37 cnf(i_0_4944, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)))). 4.07/4.37 cnf(i_0_715, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_2237, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk172_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X2),X4))))). 4.07/4.37 cnf(i_0_2882, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|hAPP(c_Option_Ooption_OSome(X4),X5)!=hAPP(hAPP(c_Map_Omap__of(X1,X4),hAPP(hAPP(c_List_Ozip(X1,X4),X3),X6)),X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X6)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))). 4.07/4.37 cnf(i_0_2635, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.07/4.37 cnf(i_0_4443, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)))). 4.07/4.37 cnf(i_0_3671, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_4736, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_3697, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))|~class_Lattices_Olattice(X1))). 4.07/4.37 cnf(i_0_413, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5),X2)))|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.07/4.37 cnf(i_0_4979, 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)))). 4.07/4.37 cnf(i_0_5160, plain, (hAPP(hAPP(X1,X2),X3)=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X4,X5,X6),X2),X7),X3)|~c_Big__Operators_Ocomm__monoid__big(X4,X5,X6,X7,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)))). 4.07/4.37 cnf(i_0_417, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X6),X7))|~c_List_Olist__all2(X1,X2,X3,X5,X7)|~hBOOL(hAPP(hAPP(X3,X4),X6)))). 4.07/4.37 cnf(i_0_5718, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_6577, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_175, plain, (hAPP(hAPP(c_List_Otake(X1),X2),X3)=c_List_OtakeWhile(X1,X4,X3)|hBOOL(hAPP(X4,hAPP(hAPP(c_List_Onth(X1),X3),X2)))|~hBOOL(hAPP(X4,hAPP(hAPP(c_List_Onth(X1),X3),esk12_4(X4,X3,X1,X2)))))). 4.07/4.37 cnf(i_0_1610, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(X3,esk122_5(X3,X4,X5,X2,X1))))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X1),X4),X3))))). 4.07/4.37 cnf(i_0_4176, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk306_5(X3,X2,X4,X5,X1))),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X1),X4),X2)),X3)))). 4.07/4.37 cnf(i_0_2255, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X3),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X1)))). 4.07/4.37 cnf(i_0_1439, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.37 cnf(i_0_4334, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.37 cnf(i_0_5979, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))|~class_Lattices_Osemilattice__sup(X1))). 4.07/4.37 cnf(i_0_3774, 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))). 4.07/4.37 cnf(i_0_754, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X4),X3))|~class_Orderings_Oord(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2)),X3),X4)))). 4.07/4.37 cnf(i_0_5456, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X3))=hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2),X3)|~class_Groups_Omonoid__add(X1))). 4.07/4.37 cnf(i_0_5762, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_2542, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_5114, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk368_4(X3,X4,X2,X1)),esk367_4(X3,X4,X2,X1))=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),X4),hAPP(c_Relation_Oconverse(X2,X1),X3))))). 4.07/4.37 cnf(i_0_157, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Ofinite__psubset(X1))))). 4.07/4.37 cnf(i_0_6413, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk452_5(X2,X3,X1,X4,X5)),X3))|~hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X3),X2))))). 4.07/4.37 cnf(i_0_2818, plain, (hAPP(X1,esk208_6(X2,X3,X1,X4,X5,X6))=c_Option_Ooption_ONone(X5)|hAPP(X3,X2)=c_Option_Ooption_ONone(X6)|hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X5),X6,c_Option_Ooption_ONone(X5),X1),hAPP(X3,X2))!=c_Option_Ooption_ONone(X5))). 4.07/4.37 cnf(i_0_5241, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_985, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_3424, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_2590, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X4))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_2740, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.07/4.37 cnf(i_0_647, 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),esk60_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_List_Oset(tc_Nat_Onat),X1))))). 4.07/4.37 cnf(i_0_6531, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_744, 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),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_3978, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_7349, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),X3)=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1)|~class_Int_Onumber(X1))). 4.07/4.37 cnf(i_0_2207, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))),c_Divides_Odiv__class_Omod(X1,X3,X2))=X3|~class_Divides_Osemiring__div(X1))). 4.07/4.37 cnf(i_0_2342, 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,esk178_5(X3,X4,X5,X1,X2))!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.37 cnf(i_0_3157, 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,esk238_5(X3,X4,X5,X1,X2))!=c_Groups_Oone__class_Oone(X2)|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.37 cnf(i_0_7389, 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,esk518_5(X3,X4,X5,X1,X2))!=c_Groups_Ozero__class_Ozero(X2)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.37 cnf(i_0_7005, 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,esk493_5(X3,X4,X5,X1,X2))!=c_Groups_Oone__class_Oone(X2)|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.37 cnf(i_0_3373, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3))=X2|~class_Divides_Osemiring__div(X1))). 4.07/4.37 cnf(i_0_5111, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_1557, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_6323, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2)))). 4.07/4.37 cnf(i_0_46, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3)),c_Divides_Odiv__class_Omod(X1,X2,X3))=X2|~class_Divides_Osemiring__div(X1))). 4.07/4.37 cnf(i_0_6143, plain, (hBOOL(hAPP(hAPP(hAPP(X1,esk440_7(X2,X3,X1,X4,X5,X6,X7)),X3),X2))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X6,tc_fun(X5,tc_HOL_Obool))),X4),X1),X3),X2)))). 4.07/4.37 cnf(i_0_329, plain, (hAPP(X1,X2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|esk25_3(X1,X3,X4)=X2|hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X3)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X4),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))). 4.07/4.37 cnf(i_0_1609, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk122_5(X2,X3,X1,X4,X5)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X5)|~class_Orderings_Olinorder(X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X5),X3),X2))))). 4.07/4.37 cnf(i_0_4175, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk306_5(X2,X3,X4,X1,X5)),X4))|~class_Complete__Lattice_Ocomplete__lattice(X5)|~class_Orderings_Olinorder(X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X5),X4),X3)),X2)))). 4.07/4.37 cnf(i_0_743, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_6532, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_5391, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Oordered__cancel__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_3911, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_5778, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2))),X3)=X3|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.07/4.37 cnf(i_0_6132, plain, (X1=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),hAPP(c_Nat_OSuc,X4))!=hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),hAPP(c_Nat_OSuc,X4))|~class_Rings_Olinordered__semidom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),X1)))). 4.07/4.37 cnf(i_0_1625, plain, (hAPP(c_Random_Opick(X1,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X1)),X2),X3)),X4)=hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X4),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1),X2))))). 4.07/4.37 cnf(i_0_1725, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))|~hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1,X2,X5),X3),X4)))). 4.07/4.37 cnf(i_0_2079, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)|~c_Nat__Transfer_Ois__nat(X2)|~c_Nat__Transfer_Ois__nat(X1))). 4.07/4.37 cnf(i_0_2131, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2)))). 4.07/4.37 cnf(i_0_5899, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_3916, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.37 cnf(i_0_4672, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1)). 4.07/4.37 cnf(i_0_1888, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)=c_List_Olist_ONil(X1)|~hBOOL(hAPP(X2,hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)))))). 4.07/4.37 cnf(i_0_6761, plain, (hAPP(c_Option_Ooption_OSome(X1),esk477_7(X2,X3,X4,X5,X6,X7,X1))=hAPP(X4,X3)|hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X7),X1,c_Option_Ooption_ONone(X7),X5),hAPP(X4,X3))!=hAPP(c_Option_Ooption_OSome(X7),X2))). 4.07/4.37 cnf(i_0_2163, 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)))). 4.07/4.37 cnf(i_0_4171, 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))),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.37 cnf(i_0_4435, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_523, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_1910, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_3786, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_7028, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))|~class_Lattices_Olattice(X1))). 4.07/4.37 cnf(i_0_7269, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X1),X2)),hAPP(c_Relation_ORange(X1,X1),X3))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~c_Wellfounded_Owf(X1,X3)|~c_Wellfounded_Owf(X1,X2))). 4.07/4.37 cnf(i_0_4482, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),hAPP(c_Relation_Oconverse(X1,X2),X5))))). 4.07/4.37 cnf(i_0_921, 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),esk86_5(X3,X5,X2,X4,X1))),hAPP(hAPP(c_List_Onth(X2),X5),esk86_5(X3,X5,X2,X4,X1)))))). 4.07/4.37 cnf(i_0_4942, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_5429, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.37 cnf(i_0_941, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Oordered__cancel__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_5683, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))|~class_Lattices_Osemilattice__inf(X1))). 4.07/4.37 cnf(i_0_6193, 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),esk442_5(X5,X4,X3,X2,X1))),hAPP(hAPP(c_List_Onth(X2),X5),esk442_5(X5,X4,X3,X2,X1)))))). 4.07/4.37 cnf(i_0_75, 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)))). 4.07/4.37 cnf(i_0_7231, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X2),X3)=c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_4594, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2),X3)=c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_942, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Oordered__cancel__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_1389, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_1127, plain, (hBOOL(hAPP(hAPP(hAPP(X1,X2),X3),X4))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X6,tc_fun(X7,tc_HOL_Obool))),X8),X1),X3),X4))|~hBOOL(hAPP(hAPP(c_member(X5),X2),X8)))). 4.07/4.37 cnf(i_0_1388, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_7509, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_3557, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_4142, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_2786, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_6301, plain, (X1=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk446_3(X3,X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2))). 4.07/4.37 cnf(i_0_4848, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk353_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk355_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.37 cnf(i_0_4836, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk353_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.37 cnf(i_0_945, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_3451, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_6635, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_2705, plain, (c_Random_Oselect__weight(X1,hAPP(hAPP(c_List_Omap(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,X1)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X2))=c_Random_Oselect(X1,X2)|X2=c_List_Olist_ONil(X1))). 4.07/4.37 cnf(i_0_4412, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4)))))). 4.07/4.37 cnf(i_0_3170, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),X3)=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.07/4.37 cnf(i_0_4953, plain, (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.07/4.37 cnf(i_0_625, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk56_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(X1,X3)))). 4.07/4.37 cnf(i_0_5937, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_5602, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk400_4(hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),X1,X3,X2)),hAPP(c_List_Oset(X1),X3)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_49, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4))|~class_Divides_Osemiring__div(X1))). 4.07/4.37 cnf(i_0_6071, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X4)),X3)|~class_Divides_Osemiring__div(X1))). 4.07/4.37 cnf(i_0_2236, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.07/4.37 cnf(i_0_4279, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk310_2(X1,X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(X1,X3)))). 4.07/4.37 cnf(i_0_6875, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)))). 4.07/4.37 cnf(i_0_850, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X2),c_Product__Type_Osnd(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))=X4|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))). 4.07/4.37 cnf(i_0_3621, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(X1)),c_Option_Ooption_ONone(X1)),hAPP(hAPP(c_List_Omap(X1,tc_Option_Ooption(X1)),c_Option_Ooption_OSome(X1)),c_Enum_Oenum__class_Oenum(X1)))=c_Enum_Oenum__class_Oenum(tc_Option_Ooption(X1))|~class_Enum_Oenum(X1))). 4.07/4.37 cnf(i_0_481, 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,esk40_4(X3,X4,X2,X1))!=c_Groups_Oone__class_Oone(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.37 cnf(i_0_1536, plain, (c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X2),hAPP(c_List_Omap(X1,X2),X3),X4)|~c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool)),X4),c_List_Oset(X1))))). 4.07/4.37 cnf(i_0_1658, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~c_Fun_Oinj__on(X1,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X4,X5),X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3))))). 4.07/4.37 cnf(i_0_5588, plain, (c_List_Olist__all2(X1,X2,hAPP(hAPP(c_COMBB(X3,tc_fun(X2,tc_HOL_Obool),X1),X4),X5),X6,X7)|~c_List_Olist__all2(X3,X2,X4,hAPP(hAPP(c_List_Omap(X1,X3),X5),X6),X7))). 4.07/4.37 cnf(i_0_2842, plain, (c_Wellfounded_Owf(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk211_2(X2,X1)),hAPP(c_Relation_OImage(X1,X1,X2),esk211_2(X2,X1)))))). 4.07/4.37 cnf(i_0_6052, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3))))|~hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.07/4.37 cnf(i_0_6919, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.07/4.37 cnf(i_0_7011, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk494_3(X1,X2,X3))),X2))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))))). 4.07/4.37 cnf(i_0_6371, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))))). 4.07/4.37 cnf(i_0_851, plain, (hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))=X3|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))). 4.07/4.37 cnf(i_0_5337, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X4,X5))=hAPP(X4,X5)|~c_Finite__Set_Ofolding__image__simple__idem(X6,X7,X1,X8,X2,X4)|~hBOOL(hAPP(hAPP(c_member(X7),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X5)))). 4.07/4.37 cnf(i_0_737, 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,esk74_5(X5,X4,X3,X2,X1)))))). 4.07/4.37 cnf(i_0_4917, 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,esk357_5(X5,X4,X3,X2,X1))),X5)))). 4.07/4.37 cnf(i_0_2756, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))))). 4.07/4.37 cnf(i_0_2755, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))))). 4.07/4.37 cnf(i_0_6374, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))))). 4.07/4.37 cnf(i_0_2282, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1))!=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)))). 4.07/4.37 cnf(i_0_7539, 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)))). 4.07/4.37 cnf(i_0_3596, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X1),X2),c_List_Oupto(X3,X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X3,X4))|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.37 cnf(i_0_1731, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3),X4)|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_328, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_476, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X2,X3)),hAPP(X4,X3))=hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,X1)),X2),X4),X3)|~class_Lattices_Olattice(X1))). 4.07/4.37 cnf(i_0_2086, 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))). 4.07/4.37 cnf(i_0_779, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(X2,X3)),hAPP(X4,X3))=hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,X1)),X2),X4),X3)|~class_Groups_Ominus(X1))). 4.07/4.37 cnf(i_0_6931, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_7400, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3))=hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.37 cnf(i_0_6246, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3))=hAPP(c_SetInterval_Oord__class_OatMost(X1),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.37 cnf(i_0_5871, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3))=hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.07/4.37 cnf(i_0_5087, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))=X2|~class_Int_Onumber__ring(X1))). 4.07/4.37 cnf(i_0_1108, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X1)))). 4.07/4.37 cnf(i_0_2532, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.07/4.37 cnf(i_0_3106, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_4938, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)=X2|~class_Int_Onumber__ring(X1))). 4.07/4.37 cnf(i_0_3955, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X4))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_63, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X4))=c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),X3)|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_1912, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.07/4.37 cnf(i_0_6068, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3))=hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.37 cnf(i_0_5263, plain, (c_Map_Odom(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),X5))=hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Map_Odom(X1,X2,X3))|X5=c_Option_Ooption_ONone(X2))). 4.07/4.37 cnf(i_0_5392, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X3)))). 4.07/4.37 cnf(i_0_1117, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)))). 4.07/4.37 cnf(i_0_1761, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3))=hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.37 cnf(i_0_4111, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_4192, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_2893, 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)))). 4.07/4.37 cnf(i_0_2042, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.07/4.37 cnf(i_0_4699, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)))). 4.07/4.37 cnf(i_0_3435, plain, (c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3))=hAPP(c_Set_Oimage(X1,X1,c_Groups_Ouminus__class_Ouminus(X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X2))|~class_Groups_Oordered__ab__group__add(X1))). 4.07/4.37 cnf(i_0_7323, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),c_Divides_Odiv__class_Omod(X1,X4,X3)),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4),X3)|~class_Divides_Osemiring__div(X1))). 4.07/4.37 cnf(i_0_3713, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),c_Divides_Odiv__class_Omod(X1,X4,X3)),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),X3)|~class_Divides_Osemiring__div(X1))). 4.07/4.37 cnf(i_0_6447, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))))). 4.07/4.37 cnf(i_0_6487, plain, (hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X5)))|hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X5)))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(c_List_Odistinct(X1),X5)))). 4.07/4.37 cnf(i_0_7010, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk494_3(X1,X2,X3))),X2))|hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))))). 4.07/4.37 cnf(i_0_7038, plain, (X1=hAPP(c_List_Orev(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4))|hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)!=hAPP(c_List_Orev(X2),X1))). 4.07/4.37 cnf(i_0_2662, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2))=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_6496, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk460_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_6621, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk468_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_486, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk41_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_4951, plain, (X1=hAPP(X2,X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))|~c_Finite__Set_Ofolding__one(X4,X5,X2)|~hBOOL(hAPP(hAPP(c_member(X4),X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)))). 4.07/4.37 cnf(i_0_6861, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.07/4.37 cnf(i_0_1041, 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),esk93_3(X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_4714, 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),esk339_3(X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_6140, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)),X5)=hAPP(X3,hAPP(hAPP(c_List_Onth(X2),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))))). 4.07/4.37 cnf(i_0_7255, plain, (c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))=hAPP(hAPP(c_List_Oappend(X1),X3),c_List_Oremove1(X1,X2,X4))|hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.07/4.37 cnf(i_0_5955, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,X3))))). 4.07/4.37 cnf(i_0_2090, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X1)),hAPP(hAPP(c_Product__Type_OPair(X4,X1),X5),X2)),hAPP(c_List_Oset(tc_prod(X4,X1)),hAPP(hAPP(c_List_Ozip(X4,X1),X6),X3)))))). 4.07/4.37 cnf(i_0_2415, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),hAPP(c_List_Oset(tc_prod(X1,X4)),hAPP(hAPP(c_List_Ozip(X1,X4),X3),X6)))))). 4.07/4.37 cnf(i_0_5363, plain, (c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.07/4.37 cnf(i_0_5906, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X4,X5)))|~hBOOL(hAPP(hAPP(c_member(X2),X5),X3)))). 4.07/4.37 cnf(i_0_2537, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_6792, 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)))). 4.07/4.37 cnf(i_0_7391, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.07/4.37 cnf(i_0_890, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),X2)),X3)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))|~class_Fields_Ofield__inverse__zero(X1))). 4.07/4.37 cnf(i_0_3812, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=X3|c_List_Olast(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))=c_List_Olast(X1,X2)|c_List_Olist_ONil(X1)=X2)). 4.07/4.37 cnf(i_0_6115, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),c_List_Olist_Olist__size(X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_List_Oset(X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(X3,X5))))). 4.07/4.37 cnf(i_0_1073, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_List_Olist_Olist__size(X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_List_Oset(X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(X3,X5))))). 4.07/4.37 cnf(i_0_3142, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,X3))),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Oone__class_Oone(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_3676, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Relation_OId__on(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.07/4.37 cnf(i_0_930, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk87_2(X2,X1)),esk87_2(X2,X1))=X2|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))))). 4.07/4.37 cnf(i_0_2069, plain, (X1=X2|hAPP(hAPP(c_Power_Opower__class_Opower(X3),X1),X4)!=hAPP(hAPP(c_Power_Opower__class_Opower(X3),X2),X4)|~class_Rings_Olinordered__semidom(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),X1)))). 4.07/4.37 cnf(i_0_5069, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2)),hAPP(c_Set_OPow(X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.07/4.37 cnf(i_0_1576, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk120_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)))). 4.07/4.37 cnf(i_0_4574, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1))). 4.07/4.37 cnf(i_0_1831, 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,esk139_5(X4,X2,X3,X3,X1))!=hAPP(X4,esk139_5(X4,X2,X3,X3,X1))|~c_Nat__Transfer_Onat__set(X3)|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.37 cnf(i_0_6738, 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,esk474_5(X4,X2,X3,X3,X1))!=hAPP(X4,esk474_5(X4,X2,X3,X3,X1))|~c_Nat__Transfer_Onat__set(X3)|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.37 cnf(i_0_3465, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)))). 4.07/4.37 cnf(i_0_2361, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)))). 4.07/4.37 cnf(i_0_673, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X6),X3)))|~hBOOL(hAPP(hAPP(c_member(X5),X4),X6)))). 4.07/4.37 cnf(i_0_7434, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2)))). 4.07/4.37 cnf(i_0_3666, 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,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.07/4.37 cnf(i_0_5443, plain, (c_Fun_Oinj__on(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~c_Fun_Oinj__on(X1,X3,X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~c_Fun_Oinj__on(X3,X2,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))). 4.07/4.37 cnf(i_0_1836, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2))))). 4.07/4.37 cnf(i_0_6242, 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),esk445_4(X4,X2,X3,X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))))). 4.07/4.37 cnf(i_0_3904, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X4)))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,X4)))))). 4.07/4.37 cnf(i_0_3903, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X3),X4)))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,X3)))))). 4.07/4.37 cnf(i_0_5080, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X4))))). 4.07/4.37 cnf(i_0_47, 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,esk2_4(X4,X2,X3,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.37 cnf(i_0_125, plain, (c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4))=c_List_OtakeWhile(X1,X2,X3)|hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),X3))))). 4.07/4.37 cnf(i_0_2372, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X2,X3))|~hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X1)))). 4.07/4.37 cnf(i_0_161, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X1),tc_HOL_Obool,X1),X2),c_Option_Ooption_OSome(X1))))|hBOOL(hAPP(X2,c_Option_Ooption_ONone(X1)))|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(X1)),X2)))). 4.07/4.37 cnf(i_0_4852, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk353_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)))). 4.07/4.37 cnf(i_0_5856, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Divides_Odiv__class_Omod(X1,X2,X3)),c_Divides_Odiv__class_Omod(X1,X4,X3)),X3)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4),X3)|~class_Divides_Oring__div(X1))). 4.07/4.37 cnf(i_0_7458, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(X3,X4)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X1),X6),X3)))|~hBOOL(hAPP(hAPP(c_member(X5),X4),X6)))). 4.07/4.37 cnf(i_0_3118, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))=X3|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)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))). 4.07/4.37 cnf(i_0_4856, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_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)))). 4.07/4.37 cnf(i_0_3000, plain, (hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),X2)))). 4.07/4.37 cnf(i_0_4933, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X2,X3)),X4))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X1),X6),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(X5),X3),X6)))). 4.07/4.37 cnf(i_0_1423, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.07/4.37 cnf(i_0_7106, 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))). 4.07/4.37 cnf(i_0_5796, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),X3),X4),c_List_Oremdups(X2,X5))=hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,X3),X4),hAPP(c_List_Oset(X2),X5))|~c_Finite__Set_Ofun__left__comm(X2,X1,X3))). 4.07/4.37 cnf(i_0_7547, plain, (c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_Predicate_Oconversep(X1,X1,X2)))|~c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))). 4.07/4.37 cnf(i_0_2801, 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_Wellfounded_Owf(X2,X4)|~c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))). 4.07/4.37 cnf(i_0_4152, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1))!=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.07/4.37 cnf(i_0_4187, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2)))). 4.07/4.37 cnf(i_0_6672, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2)),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1))))). 4.07/4.37 cnf(i_0_4961, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk359_2(X2,X1)),X2))|hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2)))). 4.07/4.37 cnf(i_0_5902, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk428_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))). 4.07/4.37 cnf(i_0_59, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk3_5(X3,X4,X5,X2,X1))=X4|hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)=X3|hAPP(hAPP(c_List_Oappend(X1),X4),X3)!=hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5))). 4.07/4.37 cnf(i_0_3470, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk261_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))|hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.07/4.37 cnf(i_0_4009, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X5)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.07/4.37 cnf(i_0_5249, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X5)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.07/4.37 cnf(i_0_5544, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4)))). 4.07/4.37 cnf(i_0_509, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_OImage(X1,X2,X5),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))))). 4.07/4.37 cnf(i_0_5903, plain, (hAPP(hAPP(c_List_Oappend(X1),esk428_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))). 4.07/4.37 cnf(i_0_61, plain, (hAPP(hAPP(c_List_Oappend(X1),esk3_5(X2,X3,X4,X5,X1)),X2)=X4|hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)=X2|hAPP(hAPP(c_List_Oappend(X1),X3),X2)!=hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4))). 4.07/4.37 cnf(i_0_2311, plain, (c_Relation_Oirrefl(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk177_2(X2,X1)),esk177_2(X2,X1))),X2)))). 4.07/4.37 cnf(i_0_5382, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5),X2)))|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5)))). 4.07/4.37 cnf(i_0_5188, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),hAPP(X4,X5)))|~hBOOL(hAPP(hAPP(c_member(X2),X5),X3)))). 4.07/4.37 cnf(i_0_1463, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.07/4.37 cnf(i_0_6117, plain, (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk437_2(X1,X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))|hBOOL(hAPP(X1,X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)))). 4.07/4.37 cnf(i_0_6114, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__ring__strict(X1))). 4.07/4.37 cnf(i_0_359, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2),X3),hAPP(hAPP(c_COMBC(X1,X4,X2),X5),X6))=hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,X2)),X3),X5),X6)|~class_Complete__Lattice_Ocomplete__lattice(X2))). 4.07/4.37 cnf(i_0_6947, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X2),X3),hAPP(hAPP(c_COMBC(X1,X4,X2),X5),X6))=hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,X2)),X3),X5),X6)|~class_Complete__Lattice_Ocomplete__lattice(X2))). 4.07/4.37 cnf(i_0_6584, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),X3))|~c_Relation_Orefl__on(X1,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.07/4.37 cnf(i_0_932, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))))). 4.07/4.37 cnf(i_0_311, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))))). 4.07/4.37 cnf(i_0_2000, plain, (hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))=c_Divides_Odivmod__int(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.37 cnf(i_0_6377, plain, (X1=X2|X3=X4|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X4))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X2),X3))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5))). 4.07/4.37 cnf(i_0_7055, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))))). 4.07/4.37 cnf(i_0_2757, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2))))). 4.07/4.37 cnf(i_0_6373, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))))). 4.07/4.37 cnf(i_0_7137, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(c_List_Onth(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2)|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.37 cnf(i_0_4710, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1))). 4.07/4.37 cnf(i_0_3297, 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)))). 4.07/4.37 cnf(i_0_5695, 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_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)))). 4.07/4.37 cnf(i_0_4709, 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),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5)))). 4.07/4.37 cnf(i_0_2969, plain, (hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),X2),hAPP(c_List_Orev(X1),X3))=hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2),X3)|~class_Groups_Oab__semigroup__add(X1))). 4.07/4.37 cnf(i_0_6093, 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)). 4.07/4.37 cnf(i_0_7113, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X2)))). 4.07/4.37 cnf(i_0_3452, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_List_Olists(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.07/4.37 cnf(i_0_6196, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)),hAPP(hAPP(c_List_Onth(X5),X6),X4)))|~c_List_Olist__all2(X2,X5,X1,X3,X6)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))))). 4.07/4.37 cnf(i_0_6727, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)=hAPP(hAPP(c_List_Odrop(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2)). 4.07/4.37 cnf(i_0_2607, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X2)). 4.07/4.37 cnf(i_0_721, plain, (hBOOL(hAPP(X1,esk73_2(X1,X2)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk71_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,esk70_2(X1,X2)))|~hBOOL(hAPP(X1,X3)))). 4.07/4.37 cnf(i_0_635, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_member(X2),esk59_4(X3,X4,X1,X2)),hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X4))))|~hBOOL(hAPP(X3,X4)))). 4.07/4.37 cnf(i_0_3479, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X4,X5))=hAPP(X2,X3)|~c_Finite__Set_Ofolding__idem(X6,X1,X4,X2)|~hBOOL(hAPP(hAPP(c_member(X6),X5),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X3)))). 4.07/4.37 cnf(i_0_2850, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X3),X4))|~class_Groups_Osemigroup__add(X1))). 4.07/4.37 cnf(i_0_936, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X2)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X1)). 4.07/4.37 cnf(i_0_3772, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),X4)),hAPP(hAPP(c_List_Onth(X5),X6),X4)))|~c_List_Olist__all2(X2,X5,X1,X3,X6)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X6))))). 4.07/4.37 cnf(i_0_4446, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.07/4.37 cnf(i_0_7331, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk514_3(X3,X2,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk515_3(X3,X2,X1)),esk515_3(X3,X2,X1))),X3)))). 4.07/4.37 cnf(i_0_239, 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),esk16_3(X3,X2,X1)),esk16_3(X3,X2,X1))),X3)))). 4.07/4.37 cnf(i_0_1257, 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),esk107_3(X2,X3,X1)),esk107_3(X2,X3,X1))),X3)))). 4.07/4.37 cnf(i_0_5071, plain, (X1=c_List_Olist_ONil(X2)|hBOOL(hAPP(hAPP(c_member(X2),hAPP(c_Product__Type_Ofst(X2,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X2,X1),X3))),hAPP(c_List_Oset(X2),X1))))). 4.07/4.37 cnf(i_0_1785, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk135_4(X1,X2,X3,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)))|hBOOL(hAPP(X2,X1))|~hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_List_Oset(X4),X3))))). 4.07/4.37 cnf(i_0_2948, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3))|~class_Rings_Oring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.07/4.37 cnf(i_0_3008, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(c_List_Oset(X1),X3))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3))))). 4.07/4.37 cnf(i_0_712, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk69_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.37 cnf(i_0_2378, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))))). 4.07/4.37 cnf(i_0_3646, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk276_3(X2,X3,X1)),esk277_3(X2,X3,X1)))|hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(X2,X3)))). 4.07/4.37 cnf(i_0_1939, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk144_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(X2,X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.37 cnf(i_0_2243, plain, (c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X1),c_Lazy__Sequence_Osmall__lazy_H(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Lazy__Sequence_Osmall__lazy_H(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 4.07/4.37 cnf(i_0_4990, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk362_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk363_3(X1,X2,X3)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_4984, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk361_3(X1,X2,X3)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.37 cnf(i_0_6219, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2)))). 4.07/4.37 cnf(i_0_6206, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)))). 4.07/4.37 cnf(i_0_6423, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk454_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.37 cnf(i_0_3210, plain, (hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 4.07/4.37 cnf(i_0_5407, plain, (c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__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)))). 4.07/4.37 cnf(i_0_4107, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)=X3|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.37 cnf(i_0_5991, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_HOL_Obool),X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),esk429_3(X3,X1,X2)),X3)))). 4.07/4.37 cnf(i_0_2632, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)|hBOOL(hAPP(hAPP(c_member(X1),X3),X2)))). 4.07/4.37 cnf(i_0_4976, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)))). 4.07/4.37 cnf(i_0_5780, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4)))). 4.07/4.37 cnf(i_0_3779, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.07/4.37 cnf(i_0_281, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk23_3(X1,X2,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),X2),hAPP(hAPP(c_Relation_Orel__comp(X3,X3,X3),X1),c_Transitive__Closure_Ortrancl(X3,X1)))))). 4.07/4.37 cnf(i_0_2819, plain, (hAPP(c_Option_Ooption_OSome(X1),esk208_6(X2,X3,X4,X5,X6,X1))=hAPP(X3,X2)|hAPP(X3,X2)=c_Option_Ooption_ONone(X1)|hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X6),X1,c_Option_Ooption_ONone(X6),X4),hAPP(X3,X2))!=c_Option_Ooption_ONone(X6))). 4.07/4.37 cnf(i_0_1669, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk126_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X2)))|~c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_6096, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)|hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.07/4.37 cnf(i_0_3907, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.07/4.37 cnf(i_0_3652, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))|~class_Groups_Oordered__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.07/4.37 cnf(i_0_4052, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X5)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.07/4.37 cnf(i_0_3693, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X5)))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.07/4.37 cnf(i_0_1668, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk127_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3)))|~c_List_Olinorder__class_Osorted(X1,X2)|~c_List_Olinorder__class_Osorted(X1,X3)|~class_Orderings_Olinorder(X1))). 4.07/4.37 cnf(i_0_1708, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBB(X2,X2,X1),c_Groups_Oabs__class_Oabs(X2)),X3)),X4)=hAPP(c_Groups_Oabs__class_Oabs(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X4))|~class_Fields_Olinordered__field(X2))). 4.07/4.37 cnf(i_0_2829, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3)))). 4.07/4.37 cnf(i_0_3529, 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),esk265_4(X1,X4,X3,X2)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.07/4.37 cnf(i_0_6479, plain, (hAPP(c_Set_Oimage(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5)),X6)=hAPP(c_Set_Oimage(X1,X2,X3),X6)|hBOOL(hAPP(hAPP(c_member(X1),X4),X6)))). 4.07/4.37 cnf(i_0_6309, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.37 cnf(i_0_4104, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X5)))). 4.07/4.37 cnf(i_0_6767, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))|~class_Groups_Oordered__cancel__ab__semigroup__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.37 cnf(i_0_4998, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk362_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))))). 4.07/4.37 cnf(i_0_4901, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_member(X2),esk356_4(X3,X4,X1,X2)),hAPP(c_List_Oset(X2),c_List_Oreplicate(X2,X1,X4))))|hBOOL(hAPP(X3,X4)))). 4.07/4.37 cnf(i_0_240, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk16_3(X3,X2,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))))). 4.07/4.37 cnf(i_0_1258, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk107_3(X2,X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))))). 4.07/4.37 cnf(i_0_3364, plain, (hBOOL(hAPP(c_Predicate_OPowp(X1,X2),X3))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Set_OPow(X1),X2))))). 4.07/4.37 cnf(i_0_4873, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk353_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk355_3(X1,X2,X3))))). 4.07/4.37 cnf(i_0_4877, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk353_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))))). 4.07/4.37 cnf(i_0_5024, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_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))))). 4.07/4.37 cnf(i_0_7015, plain, (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,esk494_3(X1,X2,X3)))))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1))))). 4.07/4.37 cnf(i_0_6076, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Oone__class_Oone(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.37 cnf(i_0_4881, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_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))))). 4.07/4.37 cnf(i_0_4861, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk353_3(X1,X2,X3))))). 4.07/4.37 cnf(i_0_3644, 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)),esk277_3(X1,X3,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk276_3(X1,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(X1,X3)))). 4.07/4.37 cnf(i_0_2120, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk159_3(X1,X2,X3)))=X3|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)!=c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.07/4.37 cnf(i_0_5829, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|~class_Orderings_Oord(X1)|~class_Int_Onumber(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))). 4.07/4.37 cnf(i_0_5613, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X2))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Oone__class_Oone(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.37 cnf(i_0_7271, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)),hAPP(c_Nat_OSuc,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.07/4.37 cnf(i_0_5110, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.07/4.37 cnf(i_0_7017, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),hAPP(c_Nat_OSuc,X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X2))|~hBOOL(hAPP(X1,X4)))). 4.07/4.37 cnf(i_0_4927, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(c_List_Oset(X2),X4))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_List_Odistinct(X2),X4)))). 4.07/4.37 cnf(i_0_6048, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|~class_Orderings_Oord(X1)|~class_Int_Onumber(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))))). 4.07/4.38 cnf(i_0_3490, plain, (c_Map_Orestrict__map(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),X5),X6)=c_Map_Orestrict__map(X1,X2,X3,X6)|hBOOL(hAPP(hAPP(c_member(X1),X4),X6)))). 4.07/4.38 cnf(i_0_4770, plain, (c_List_Olist__ex1(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk347_4(X3,X2,X1,X4)),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 4.07/4.38 cnf(i_0_176, plain, (hAPP(hAPP(c_List_Otake(X1),X2),X3)=c_List_OtakeWhile(X1,X4,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|~hBOOL(hAPP(X4,hAPP(hAPP(c_List_Onth(X1),X3),esk12_4(X4,X3,X1,X2)))))). 4.07/4.38 cnf(i_0_7152, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.38 cnf(i_0_5549, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.38 cnf(i_0_5896, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)))). 4.07/4.38 cnf(i_0_5971, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)))). 4.07/4.38 cnf(i_0_3124, 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)). 4.07/4.38 cnf(i_0_4583, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(X2,X4)|~c_Finite__Set_Ofolding__image__simple__idem(X5,X6,X1,X7,X8,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X4)))). 4.07/4.38 cnf(i_0_6840, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk479_5(X2,X3,X1,X4,X5)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X5,X3),X2))))). 4.07/4.38 cnf(i_0_1718, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk130_5(X3,X4,X5,X2,X1),esk131_5(X3,X4,X5,X2,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)),X3)))). 4.07/4.38 cnf(i_0_7169, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk501_5(X3,X4,X5,X2,X1),esk502_5(X3,X4,X5,X2,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)),X3)))). 4.07/4.38 cnf(i_0_2671, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.38 cnf(i_0_6291, 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))). 4.07/4.38 cnf(i_0_7014, 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,esk494_3(X2,X1,X3)))))|hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2))))). 4.07/4.38 cnf(i_0_4909, 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)|X2=c_List_Olist_ONil(X1))). 4.07/4.38 cnf(i_0_1856, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3))=hAPP(c_SetInterval_Oord__class_OlessThan(X1),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.38 cnf(i_0_6655, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3))=hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.38 cnf(i_0_3560, plain, (hAPP(hAPP(c_List_Oappend(X1),esk271_3(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),esk272_3(X2,X3,X1)))=X2|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))))). 4.07/4.38 cnf(i_0_465, 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),esk37_3(X3,X2,X1)),hAPP(c_List_Oset(X1),X3))))). 4.07/4.38 cnf(i_0_5811, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.07/4.38 cnf(i_0_4180, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X1,X2),X3)),hAPP(c_Relation_ODomain(X1,X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))). 4.07/4.38 cnf(i_0_3285, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X3))))|~class_Rings_Olinordered__ring(X1))). 4.07/4.38 cnf(i_0_901, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.38 cnf(i_0_6937, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Lattices_Oab__semigroup__idem__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_7238, 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)),esk509_3(X3,X2,X1)),X2)))). 4.07/4.38 cnf(i_0_5340, plain, (hAPP(hAPP(c_List_Oappend(X1),esk382_3(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),esk383_3(X2,X3,X1)))=X2|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))))). 4.07/4.38 cnf(i_0_5125, plain, (hAPP(hAPP(c_List_Oappend(X1),esk369_3(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),esk370_3(X2,X3,X1)))=X2|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X2))))). 4.07/4.38 cnf(i_0_4834, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk353_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.38 cnf(i_0_4843, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_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,esk355_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.38 cnf(i_0_2978, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_Relation_ODomain(X3,X3),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,X4))))). 4.07/4.38 cnf(i_0_5321, plain, (X1=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))). 4.07/4.38 cnf(i_0_449, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_245, plain, (c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_2088, plain, (hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)))=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.07/4.38 cnf(i_0_1555, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X4),c_Wellfounded_Oless__than),X1))))). 4.07/4.38 cnf(i_0_292, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))))). 4.07/4.38 cnf(i_0_4661, plain, (hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OPow(X1),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Finite__Set_Ocard(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_2760, plain, (c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_1790, plain, (c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_5927, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBB(X2,X2,X1),c_Groups_Ouminus__class_Ouminus(X2)),X3)),X4)=hAPP(c_Groups_Ouminus__class_Ouminus(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X4))|~class_Groups_Oab__group__add(X2))). 4.07/4.38 cnf(i_0_315, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3))))). 4.07/4.38 cnf(i_0_6490, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.38 cnf(i_0_5203, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))|~class_Orderings_Olinorder(X1))). 4.07/4.38 cnf(i_0_1081, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))|~class_Orderings_Olinorder(X1))). 4.07/4.38 cnf(i_0_6419, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3)|~class_Groups_Oordered__ab__group__add(X1))). 4.07/4.38 cnf(i_0_6417, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X4)|X2=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.07/4.38 cnf(i_0_1716, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))=c_Big__Operators_Olattice__class_OSup__fin(X1,X3)|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_569, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.38 cnf(i_0_2923, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)|~class_Groups_Ocomm__monoid__mult(X1))). 4.07/4.38 cnf(i_0_3273, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)),X3)|~class_Fields_Ofield__inverse__zero(X1))). 4.07/4.38 cnf(i_0_1079, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)|~class_Groups_Oordered__ab__group__add(X1))). 4.07/4.38 cnf(i_0_6816, 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)|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Fields_Ofield__inverse__zero(X1))). 4.07/4.38 cnf(i_0_6687, 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)|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_2715, 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)|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_5988, 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)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_4376, 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)))). 4.07/4.38 cnf(i_0_3370, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)|~class_Orderings_Olinorder(X1))). 4.07/4.38 cnf(i_0_6842, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3)|~class_Orderings_Olinorder(X1))). 4.07/4.38 cnf(i_0_4854, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_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)))). 4.07/4.38 cnf(i_0_4847, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_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)))). 4.07/4.38 cnf(i_0_4481, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)|c_Groups_Ozero__class_Ozero(X1)=X2|~class_Fields_Ofield__inverse__zero(X1))). 4.07/4.38 cnf(i_0_6942, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk487_3(X2,X3,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X2,c_Enum_Oenum__class_Oenum(X1)))))|~c_Enum_Oex__n__lists(X1,X3,X2)|~class_Enum_Oenum(X1))). 4.07/4.38 cnf(i_0_2995, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X4),X5)),X6)=hAPP(hAPP(X3,X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X5),X6))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.07/4.38 cnf(i_0_4115, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)))). 4.07/4.38 cnf(i_0_3166, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)))). 4.07/4.38 cnf(i_0_3049, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2)))). 4.07/4.38 cnf(i_0_3492, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3)))). 4.07/4.38 cnf(i_0_2722, 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,esk199_6(X3,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),X5),X2,X5,X4,X1))))|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.07/4.38 cnf(i_0_731, plain, (hAPP(hAPP(X1,hAPP(c_Fun_Ocomp(X2,X3,X2,X4),X5)),X6)=hAPP(hAPP(X1,X4),hAPP(c_Set_Oimage(X2,X2,X5),X6))|~c_Finite__Set_Ofolding__image(X3,X2,X7,X8,X1)|~c_Fun_Oinj__on(X2,X2,X5,X6)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 4.07/4.38 cnf(i_0_6235, plain, (X1=X2|hAPP(c_Map_Omap__of(X3,X4),hAPP(hAPP(c_List_Ozip(X3,X4),X5),X1))!=hAPP(c_Map_Omap__of(X3,X4),hAPP(hAPP(c_List_Ozip(X3,X4),X5),X2))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X5)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X1)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X5)|~hBOOL(hAPP(c_List_Odistinct(X3),X5)))). 4.07/4.38 cnf(i_0_6429, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBB(tc_Int_Oint,X2,X1),c_Int_Oring__1__class_Oof__int(X2)),X3)),X4)=hAPP(c_Int_Oring__1__class_Oof__int(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Int_Oint),X3),X4))|~class_Rings_Oring__1(X2))). 4.07/4.38 cnf(i_0_2753, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2)))). 4.07/4.38 cnf(i_0_4756, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X4)|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Divides_Osemiring__div(X1))). 4.07/4.38 cnf(i_0_2, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)=hAPP(c_Finite__Set_Ocard(X1),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_2746, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk200_5(X3,X4,X5,X2,X1)),esk201_5(X3,X4,X5,X2,X1))=X5|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),X5),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X4),X3))))). 4.07/4.38 cnf(i_0_4401, 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)))|esk319_2(X2,X1)!=esk318_2(X2,X1)|~hBOOL(hAPP(c_List_Odistinct(X1),esk317_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 4.07/4.38 cnf(i_0_4087, 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,esk297_6(X5,X2,X1,X4,X3,X6)),esk298_6(X5,X2,X1,X4,X3,X6)))))). 4.07/4.38 cnf(i_0_1481, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2)))). 4.07/4.38 cnf(i_0_706, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Oordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.07/4.38 cnf(i_0_2617, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Oordered__comm__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.07/4.38 cnf(i_0_1584, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.07/4.38 cnf(i_0_6979, plain, (hBOOL(hAPP(c_List_Odistinct(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool)),c_List_Oset(X1)),c_Enum_Osublists(X1,X2))))|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.07/4.38 cnf(i_0_1232, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_7516, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_6232, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.38 cnf(i_0_3473, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4))=c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.07/4.38 cnf(i_0_4999, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk362_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))))). 4.07/4.38 cnf(i_0_2553, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Oordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.07/4.38 cnf(i_0_5845, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.07/4.38 cnf(i_0_2742, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.07/4.38 cnf(i_0_4522, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~class_Rings_Olinordered__comm__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.07/4.38 cnf(i_0_5025, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_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))))). 4.07/4.38 cnf(i_0_5059, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.07/4.38 cnf(i_0_6778, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.38 cnf(i_0_4198, 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))))). 4.07/4.38 cnf(i_0_6775, plain, (c_Fun_Oinj__on(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5),X6)|hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X3),X6)))|~c_Fun_Oinj__on(X1,X2,X3,X6))). 4.07/4.38 cnf(i_0_7097, 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)|X3=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). 4.07/4.38 cnf(i_0_2752, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Olinordered__ring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.38 cnf(i_0_4766, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.38 cnf(i_0_4117, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.38 cnf(i_0_2536, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_7460, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel(X1,X2)),c_List_Olistrel(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.07/4.38 cnf(i_0_1560, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel1(X1,X2)),c_List_Olistrel1(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.07/4.38 cnf(i_0_2301, plain, (hAPP(c_Nat_OSuc,esk176_5(X1,X2,X3,X4,X5))=X2|X3=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X2),X1))))). 4.07/4.38 cnf(i_0_5396, plain, (hAPP(c_Nat_OSuc,esk389_5(X1,X2,X3,X4,X5))=X2|X3=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X2),X1))))). 4.07/4.38 cnf(i_0_424, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X5),X4)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X3),X5)))). 4.07/4.38 cnf(i_0_2758, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X5),X4)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X5),X3)))). 4.07/4.38 cnf(i_0_1306, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_4991, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk362_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk363_3(X1,X2,X3))))). 4.07/4.38 cnf(i_0_929, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))),X3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.38 cnf(i_0_6091, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X2)),X3)),X4)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X3),X4))|~class_Rings_Osemiring__1(X2))). 4.07/4.38 cnf(i_0_6288, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(X2,X3)|~c_Finite__Set_Ofolding__idem(X5,X1,X6,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)))). 4.07/4.38 cnf(i_0_1540, plain, (c_Relation_Ototal__on(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))|~c_Relation_Ototal__on(X1,X2,X3))). 4.07/4.38 cnf(i_0_4985, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk361_3(X1,X2,X3))))). 4.07/4.38 cnf(i_0_4259, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X2)))=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X2))))))). 4.07/4.38 cnf(i_0_2003, 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)|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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.38 cnf(i_0_4063, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2))=hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)|~class_Orderings_Olinorder(X1))). 4.07/4.38 cnf(i_0_5805, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3),X4))|~c_List_Olist__all2(X1,X2,X3,X5,X6)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),X4),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6)))))). 4.07/4.38 cnf(i_0_4618, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.07/4.38 cnf(i_0_5168, plain, (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.07/4.38 cnf(i_0_33, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2))))). 4.07/4.38 cnf(i_0_6765, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))|hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.07/4.38 cnf(i_0_3607, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(c_COMBK(X1,X2),X3)),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))),X3)|~class_Rings_Osemiring__1(X1))). 4.07/4.38 cnf(i_0_7195, plain, (hBOOL(hAPP(X1,esk505_4(X1,X2,X3,X4)))|hBOOL(hAPP(X1,esk504_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X3),X2)))|~hBOOL(hAPP(X1,X5)))). 4.07/4.38 cnf(i_0_4223, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),esk307_7(X3,X4,X1,X5,X6,X7,X2)),X1))|~c_Nitpick_Ofold__graph_H(X2,X7,X6,X5,X1,hAPP(hAPP(X6,X4),X3)))). 4.07/4.38 cnf(i_0_4879, 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)),esk355_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))))). 4.07/4.38 cnf(i_0_1220, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2))))). 4.07/4.38 cnf(i_0_6271, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3)))). 4.07/4.38 cnf(i_0_5576, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2)),X3)))). 4.07/4.38 cnf(i_0_6446, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)))). 4.07/4.38 cnf(i_0_4872, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_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))))). 4.07/4.38 cnf(i_0_1519, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),hAPP(c_Relation_Oconverse(X1,X1),X2))!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))))). 4.07/4.38 cnf(i_0_5409, plain, (hAPP(c_List_Ofoldl(X1,X1,c_Groups_Otimes__class_Otimes(X1),hAPP(c_List_Ohd(X1),X2)),hAPP(c_List_Otl(X1),X2))=hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(c_List_Oset(X1),X2))|X2=c_List_Olist_ONil(X1)|~class_Lattices_Oab__semigroup__idem__mult(X1))). 4.07/4.38 cnf(i_0_2493, plain, (hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4))=hAPP(hAPP(X5,hAPP(X6,X3)),hAPP(X1,X4))|~c_Finite__Set_Ofolding__image__simple__idem(X7,X2,X5,X8,X6,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.38 cnf(i_0_704, 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)))). 4.07/4.38 cnf(i_0_4934, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),X2))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X1,X1),c_Groups_Oabs__class_Oabs(X1)),X2))))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.07/4.38 cnf(i_0_6698, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X2),X1)))=c_Random_Olog(X1,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X2),X1)))). 4.07/4.38 cnf(i_0_3245, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.07/4.38 cnf(i_0_1556, plain, (hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),X1))=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.38 cnf(i_0_4851, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk353_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.38 cnf(i_0_2770, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk203_3(X3,X1,X2)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.38 cnf(i_0_3266, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk248_3(X3,X1,X2)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.38 cnf(i_0_632, plain, (hAPP(hAPP(X1,X2),hAPP(X3,X4))=hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X5),X2),X4))|c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X4|hBOOL(hAPP(hAPP(c_member(X5),X2),X4))|~c_Finite__Set_Ofolding__one(X5,X1,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))). 4.07/4.38 cnf(i_0_179, plain, (hAPP(hAPP(c_List_Otake(X1),X2),X3)=c_List_OtakeWhile(X1,X4,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk12_4(X4,X3,X1,X2)),X2))|hBOOL(hAPP(X4,hAPP(hAPP(c_List_Onth(X1),X3),X2))))). 4.07/4.38 cnf(i_0_2081, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X4,X5))=c_SetInterval_Oord__class_OgreaterThanLessThan(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5))|~class_Orderings_Olinorder(X1))). 4.07/4.38 cnf(i_0_4127, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X4,X5))=c_SetInterval_Oord__class_OgreaterThanAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5))|~class_Orderings_Olinorder(X1))). 4.07/4.38 cnf(i_0_3828, plain, (c_SetInterval_Oord__class_OatLeastAtMost(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X4)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X5))|~class_Orderings_Olinorder(X1))). 4.07/4.38 cnf(i_0_1670, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Oappend(X1),X4),X5))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_List_Oset(X1),X5)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X4))))). 4.07/4.38 cnf(i_0_687, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X4)),X5),c_Option_Ooption_ONone(X2))=c_Map_Orestrict__map(X1,X2,X3,X4)|hBOOL(hAPP(hAPP(c_member(X1),X5),X4)))). 4.07/4.38 cnf(i_0_7063, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.38 cnf(i_0_603, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)))). 4.07/4.38 cnf(i_0_432, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.38 cnf(i_0_345, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X1)))). 4.07/4.38 cnf(i_0_2098, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_4220, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X2)),X3)),X4)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X3),X4))|~class_Rings_Osemiring__1(X2)|~class_Groups_Ocomm__monoid__mult(X2))). 4.07/4.38 cnf(i_0_4806, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBB(tc_Int_Oint,X2,X1),c_Int_Oring__1__class_Oof__int(X2)),X3)),X4)=hAPP(c_Int_Oring__1__class_Oof__int(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Int_Oint),X3),X4))|~class_Rings_Oring__1(X2)|~class_Groups_Ocomm__monoid__mult(X2))). 4.07/4.38 cnf(i_0_4231, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.38 cnf(i_0_6589, plain, (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.07/4.38 cnf(i_0_2014, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_4193, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)))). 4.07/4.38 cnf(i_0_6324, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.38 cnf(i_0_4222, plain, (hAPP(hAPP(X1,X2),X3)=X4|hBOOL(hAPP(hAPP(c_member(X5),esk307_7(X3,X2,X6,X4,X1,X7,X5)),X6))|~c_Nitpick_Ofold__graph_H(X5,X7,X1,X4,X6,hAPP(hAPP(X1,X2),X3)))). 4.07/4.38 cnf(i_0_3130, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_5746, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)))). 4.07/4.38 cnf(i_0_1523, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_4054, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4))|~class_Groups_Omonoid__mult(X1))). 4.07/4.38 cnf(i_0_4131, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|c_Groups_Ozero__class_Ozero(X1)!=hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.38 cnf(i_0_3748, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X3),X2)))). 4.07/4.38 cnf(i_0_816, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X2),X3)))). 4.07/4.38 cnf(i_0_6316, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3))))). 4.07/4.38 cnf(i_0_4876, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk353_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 4.07/4.38 cnf(i_0_5713, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.38 cnf(i_0_5157, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))|~class_Lattices_Odistrib__lattice(X1))). 4.07/4.38 cnf(i_0_4169, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))|~class_Lattices_Odistrib__lattice(X1))). 4.07/4.38 cnf(i_0_3195, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1))). 4.07/4.38 cnf(i_0_2111, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X5)))). 4.07/4.38 cnf(i_0_7409, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X5),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X3),X5)))). 4.07/4.38 cnf(i_0_133, plain, (c_Map_Omap__upds(X1,X2,X3,X4,hAPP(hAPP(c_List_Olist__update(X2,X5),X6),X7))=c_Map_Omap__upds(X1,X2,X3,X4,X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)),X6)))). 4.07/4.38 cnf(i_0_7167, plain, (hAPP(hAPP(c_Set_Oinsert(X1),esk501_5(X2,X3,X4,X5,X1)),esk502_5(X2,X3,X4,X5,X1))=hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2)))). 4.07/4.38 cnf(i_0_1818, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3)|~class_Groups_Oordered__ab__semigroup__add__imp__le(X1))). 4.07/4.38 cnf(i_0_4346, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.38 cnf(i_0_1691, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)|~class_Rings_Ocomm__semiring(X1))). 4.07/4.38 cnf(i_0_1420, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)))=hAPP(c_List_Oset(X1),X3)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.07/4.38 cnf(i_0_4148, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk300_3(X2,X3,X1)),X3)),X2))|hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))))). 4.07/4.38 cnf(i_0_1719, plain, (hAPP(hAPP(c_Set_Oinsert(X1),esk130_5(X2,X3,X4,X5,X1)),esk131_5(X2,X3,X4,X5,X1))=hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)|~hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X5,hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)),X2)))). 4.07/4.38 cnf(i_0_5863, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X4),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.07/4.38 cnf(i_0_496, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.07/4.38 cnf(i_0_4313, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),esk312_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)))). 4.07/4.38 cnf(i_0_4967, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk360_3(X2,X3,X1)),X3)),X2))|hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))))). 4.07/4.38 cnf(i_0_4146, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)|~class_Rings_Odivision__ring(X1))). 4.07/4.38 cnf(i_0_6341, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3)|~class_Lattices_Odistrib__lattice(X1))). 4.07/4.38 cnf(i_0_5195, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),X3))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4)),X3)|~class_Lattices_Odistrib__lattice(X1))). 4.07/4.38 cnf(i_0_4676, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4)),X3)|~class_Rings_Odivision__ring(X1))). 4.07/4.38 cnf(i_0_6473, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk458_3(X2,X3,X1)),X3)),X2))|hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))))). 4.07/4.38 cnf(i_0_6202, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),esk443_3(X3,X2,X1)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_6203, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk443_3(X3,X2,X1)),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_4314, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk312_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)))). 4.07/4.38 cnf(i_0_966, plain, (hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_List_Orev(X1),X2))=hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2)|~class_Groups_Omonoid__add(X1))). 4.07/4.38 cnf(i_0_34, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_1221, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_6272, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_5575, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_3590, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_3831, plain, (hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4))=X3|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~c_Finite__Set_Ofolding__one(X2,X5,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.38 cnf(i_0_4628, 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))))). 4.07/4.38 cnf(i_0_4982, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk364_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk361_3(X1,X2,X3)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_5000, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_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,esk363_3(X1,X2,X3)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.38 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)),esk364_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))))). 4.07/4.38 cnf(i_0_5008, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_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))))). 4.07/4.38 cnf(i_0_1262, 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),esk108_4(X4,X2,X3,X1)),hAPP(c_List_Oset(X1),X3))))). 4.07/4.38 cnf(i_0_3734, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),esk281_4(X4,X2,X3,X1))),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X4))))). 4.07/4.38 cnf(i_0_7551, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),esk527_4(X4,X2,X3,X1))),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(c_Relation_ODomain(X1,X2),X4))))). 4.07/4.38 cnf(i_0_3547, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk270_4(X3,X1,X4,X2)),X4)),X3))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X3))))). 4.07/4.38 cnf(i_0_5033, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk365_4(X3,X1,X4,X2)),X4)),X3))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X3))))). 4.07/4.38 cnf(i_0_5023, 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)),esk364_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))))). 4.07/4.38 cnf(i_0_3012, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk222_3(X1,X2,X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2)))|hBOOL(hAPP(X1,X4))|~hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),X2))))). 4.07/4.38 cnf(i_0_7495, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3)),X4)=hAPP(hAPP(c_List_Onth(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.38 cnf(i_0_6414, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X5,X6)))|~hBOOL(hAPP(hAPP(c_member(X3),X6),X4)))). 4.07/4.38 cnf(i_0_5009, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_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))))). 4.07/4.38 cnf(i_0_454, plain, (hAPP(c_Option_Ooption_OSome(X1),esk35_5(X2,X3,X4,X1,X5))=hAPP(hAPP(c_Map_Omap__of(X5,X1),X2),X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X4),X3)),hAPP(c_List_Oset(tc_prod(X5,X1)),X2))))). 4.07/4.38 cnf(i_0_268, plain, (c_Enum_Oall__n__lists(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk21_3(X3,X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),c_Enum_On__lists(X1,X3,c_Enum_Oenum__class_Oenum(X1)))))|~class_Enum_Oenum(X1))). 4.07/4.38 cnf(i_0_4265, 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))). 4.07/4.38 cnf(i_0_1042, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,tc_Nat_Onat),X1),X4)))|~hBOOL(hAPP(hAPP(c_member(X3),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)))). 4.07/4.38 cnf(i_0_4455, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.07/4.38 cnf(i_0_1593, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.07/4.38 cnf(i_0_1693, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.07/4.38 cnf(i_0_4859, 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)),esk355_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk353_3(X1,X2,X3))))). 4.07/4.38 cnf(i_0_1580, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),X2)))). 4.07/4.38 cnf(i_0_5138, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X2),X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X1)))). 4.07/4.38 cnf(i_0_4994, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk362_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))))). 4.07/4.38 cnf(i_0_4868, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_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,esk355_3(X1,X2,X3))))). 4.07/4.38 cnf(i_0_6692, 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),esk472_5(X3,X4,X5,X2,X1)),hAPP(c_List_Oset(X1),X4))))). 4.07/4.38 cnf(i_0_2859, plain, (hAPP(c_Set_Oimage(X1,X2,esk213_4(X3,X1,X2,X4)),X3)=X4|c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=X4|~c_Fun_Oinj__on(X2,X1,X5,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X5),X4)),X3)))). 4.07/4.38 cnf(i_0_6759, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(X1),X2,c_Option_Ooption_ONone(X1),X3),hAPP(X4,X5))=hAPP(c_Option_Ooption_OSome(X1),X6)|hAPP(c_Option_Ooption_OSome(X1),X6)!=hAPP(X3,X7)|hAPP(c_Option_Ooption_OSome(X2),X7)!=hAPP(X4,X5))). 4.07/4.38 cnf(i_0_4462, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)))). 4.07/4.38 cnf(i_0_1608, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,X1),X4),X5)))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(X5,X6)))|~hBOOL(hAPP(hAPP(c_member(X3),X6),X4)))). 4.07/4.38 cnf(i_0_4174, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X3),X4)),X5))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X4,X6)),X5))|~hBOOL(hAPP(hAPP(c_member(X2),X6),X3)))). 4.07/4.38 cnf(i_0_5291, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),c_Groups_Oone__class_Oone(X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X3)|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Divides_Osemiring__div(X1))). 4.07/4.38 cnf(i_0_3326, plain, (c_Map_Oran(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)))=hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Map_Oran(X1,X2,X3))|c_Option_Ooption_ONone(X2)!=hAPP(X3,X4))). 4.07/4.38 cnf(i_0_84, plain, (c_Groups_Ozero__class_Ozero(X1)=hAPP(X2,X3)|hBOOL(hAPP(hAPP(c_member(X4),esk7_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)))). 4.07/4.38 cnf(i_0_3417, plain, (hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2,X1),tc_HOL_Obool)))))). 4.07/4.38 cnf(i_0_2470, 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))). 4.07/4.38 cnf(i_0_7437, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Int_Onat)),X1)=X1|~c_Nat__Transfer_Onat__set(X1))). 4.07/4.38 cnf(i_0_6138, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk439_4(X2,X3,X1,X4)),hAPP(c_List_Oset(X1),X3)))|hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.38 cnf(i_0_5822, 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)))). 4.07/4.38 cnf(i_0_1058, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),c_Groups_Oone__class_Oone(X1))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2)),X3)|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Divides_Osemiring__div(X1))). 4.07/4.38 cnf(i_0_4995, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X1,X2,X3)),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk362_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 4.07/4.38 cnf(i_0_3540, 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),esk268_4(X2,X3,X1,X4)),X3))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(X2,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_3227, plain, (hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4))=hAPP(c_Fun_Ocomp(X5,X5,X5,hAPP(X1,X4)),hAPP(X6,X3))|~c_Finite__Set_Ofolding__idem(X2,X5,X6,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.38 cnf(i_0_724, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X4),X5),X6),X7))|~hBOOL(hAPP(hAPP(hAPP(X5,X8),X6),X7))|~hBOOL(hAPP(hAPP(c_member(X1),X8),X4)))). 4.07/4.38 cnf(i_0_5783, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_6014, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3)))). 4.07/4.38 cnf(i_0_2028, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Finite__Set_Ocard(X2),X3))),X4)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(c_COMBK(X1,X2),X4)),X3)|~class_Rings_Osemiring__1(X1))). 4.07/4.38 cnf(i_0_261, plain, (c_Wellfounded_Owf(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk19_3(X2,X1,X3)),X3)),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),esk17_2(X2,X1))))). 4.07/4.38 cnf(i_0_2304, plain, (hAPP(c_Nat_OSuc,esk176_5(X1,X2,X3,X4,X5))=X2|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X2),X1))))). 4.07/4.38 cnf(i_0_5399, plain, (hAPP(c_Nat_OSuc,esk389_5(X1,X2,X3,X4,X5))=X2|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X2),X1))))). 4.07/4.38 cnf(i_0_3018, 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),esk224_5(X4,X3,X5,X1,X2)),hAPP(c_List_Oset(X1),X5)))|~class_Orderings_Olinorder(X2))). 4.07/4.38 cnf(i_0_5248, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X2)))). 4.07/4.38 cnf(i_0_4983, 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)),esk364_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk361_3(X1,X2,X3))))). 4.07/4.38 cnf(i_0_5001, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_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,esk363_3(X1,X2,X3))))). 4.07/4.38 cnf(i_0_1107, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk96_3(X1,X2,X3)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk97_3(X1,X2,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3))))). 4.07/4.38 cnf(i_0_5830, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))|~class_Orderings_Oord(X1)|~class_Int_Onumber(X1))). 4.07/4.38 cnf(i_0_4884, 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)))). 4.07/4.38 cnf(i_0_4883, 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)))). 4.07/4.38 cnf(i_0_4079, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk295_3(X1,X2,X3)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk296_3(X1,X2,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3))))). 4.07/4.38 cnf(i_0_37, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_36, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_1224, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_6049, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))=hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))|~class_Orderings_Oord(X1)|~class_Int_Onumber(X1))). 4.07/4.38 cnf(i_0_2102, plain, (hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),X5))=hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),X5)|~c_Finite__Set_Ofolding__idem(X6,X1,X3,X7))). 4.07/4.38 cnf(i_0_4273, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.38 cnf(i_0_3304, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4))=c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.07/4.38 cnf(i_0_809, 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),esk78_3(X3,X2,X1)),esk79_3(X3,X2,X1))),X3)))). 4.07/4.38 cnf(i_0_1222, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_6275, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_5580, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_6273, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.38 cnf(i_0_808, 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),esk78_3(X3,X2,X1)),esk80_3(X3,X2,X1))),X3)))). 4.07/4.38 cnf(i_0_3663, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5)))). 4.07/4.38 cnf(i_0_2747, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk201_5(X2,X3,X4,X1,X5)),hAPP(X2,esk200_5(X2,X3,X4,X1,X5))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),X4),hAPP(hAPP(c_Product__Type_OSigma(X5,X1),X3),X2))))). 4.07/4.38 cnf(i_0_1869, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1)),X3)),X4)=hAPP(c_Option_Ooption_OSome(X2),esk143_4(X4,X3,X2,X1))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1))|~class_Enum_Oenum(X1))). 4.07/4.38 cnf(i_0_5578, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.38 cnf(i_0_6095, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.07/4.38 cnf(i_0_3060, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_3969, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)=X2|hAPP(hAPP(c_List_Oappend(X1),X2),X4)!=hAPP(hAPP(c_List_Oappend(X1),X3),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.38 cnf(i_0_2051, plain, (c_Relation_Orefl__on(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X5))|~c_Relation_Orefl__on(X1,X3,X5)|~c_Relation_Orefl__on(X1,X2,X4))). 4.07/4.38 cnf(i_0_1736, plain, (c_Relation_Orefl__on(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X5))|~c_Relation_Orefl__on(X1,X3,X5)|~c_Relation_Orefl__on(X1,X2,X4))). 4.07/4.38 cnf(i_0_4570, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X4)),hAPP(X2,X3))|~c_Finite__Set_Ofun__left__comm(X5,X1,X2))). 4.07/4.38 cnf(i_0_2259, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk174_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk173_3(X1,X2,X3)))=X2|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=X1|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1))))). 4.07/4.38 cnf(i_0_7204, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_1355, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))). 4.07/4.38 cnf(i_0_6491, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))|~class_Rings_Olinordered__idom(X1)|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))). 4.07/4.38 cnf(i_0_5283, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))=X4|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X2)))). 4.07/4.38 cnf(i_0_7435, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.07/4.38 cnf(i_0_7074, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_OImage(X3,X1,X4),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X6),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(X3),X6),X5)))). 4.07/4.38 cnf(i_0_7275, 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)). 4.07/4.38 cnf(i_0_972, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2))=hAPP(c_SetInterval_Oord__class_OatMost(X1),X2)|~class_Orderings_Olinorder(X1))). 4.07/4.38 cnf(i_0_5129, 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),esk372_4(X1,X4,X3,X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.07/4.38 cnf(i_0_5850, 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),esk426_4(X1,X4,X3,X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.07/4.38 cnf(i_0_390, 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),esk32_4(X3,X4,X2,X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X3)))). 4.07/4.38 cnf(i_0_5643, 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)))). 4.07/4.38 cnf(i_0_3209, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_3847, 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),esk284_4(X3,X4,X2,X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)))). 4.07/4.38 cnf(i_0_41, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_42, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_1225, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_1975, plain, (hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(c_List_Orev(X1),X3)),hAPP(c_List_Orev(X2),X4))=hAPP(c_List_Orev(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))). 4.07/4.38 cnf(i_0_4350, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_5989, plain, (hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Groups_Otimes__class_Otimes(X1)),X2),X3)|hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_6075, plain, (hAPP(hAPP(c_List_Omap(X1,X2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5)),X6)=hAPP(hAPP(c_List_Omap(X1,X2),X3),X6)|hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X6))))). 4.07/4.38 cnf(i_0_1223, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_6277, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.38 cnf(i_0_5579, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.38 cnf(i_0_38, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_5941, 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)))). 4.07/4.38 cnf(i_0_180, plain, (hAPP(hAPP(c_List_Otake(X1),X2),X3)=c_List_OtakeWhile(X1,X4,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk12_4(X4,X3,X1,X2)),X2)))). 4.07/4.38 cnf(i_0_5678, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk409_5(X2,X3,X4,X1,X5)),X4))|hBOOL(hAPP(X2,X6))|~hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X5,tc_HOL_Obool)),X4),X3))))). 4.07/4.38 cnf(i_0_3216, 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),esk243_7(X7,X6,X5,X4,X3,X2,X1)),X4)))). 4.07/4.38 cnf(i_0_1226, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_5585, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_6276, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_5583, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.38 cnf(i_0_2258, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk174_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk173_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.38 cnf(i_0_5414, plain, (c_Fun_Oinj__on(X1,tc_fun(X2,X3),hAPP(hAPP(c_COMBB(X3,tc_fun(X2,X3),X1),c_COMBK(X3,X2)),X4),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~c_Fun_Oinj__on(X1,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))). 4.07/4.38 cnf(i_0_3989, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))))). 4.07/4.38 cnf(i_0_5174, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Wellfounded_Owf(X1,X3)|~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2)))). 4.07/4.38 cnf(i_0_4167, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),X5)),X6))|~c_Fun_Oinj__on(X1,X2,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X6)))). 4.07/4.38 cnf(i_0_6274, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.38 cnf(i_0_198, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X3)),X2))=hAPP(hAPP(c_List_Odrop(X1),X3),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.07/4.38 cnf(i_0_127, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))). 4.07/4.38 cnf(i_0_5692, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)=hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))|hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.07/4.38 cnf(i_0_7111, 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)))). 4.07/4.38 cnf(i_0_6194, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk442_5(X5,X4,X3,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4))). 4.07/4.38 cnf(i_0_922, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk86_5(X3,X5,X2,X4,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4))). 4.07/4.38 cnf(i_0_6874, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk483_6(X3,X4,X5,X6,X2,X1)),esk485_6(X3,X4,X5,X6,X2,X1))=X6|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),X6),hAPP(hAPP(c_Relation_Orel__comp(X1,X5,X2),X4),X3))))). 4.07/4.38 cnf(i_0_2374, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))). 4.07/4.38 cnf(i_0_902, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))))). 4.07/4.38 cnf(i_0_734, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X4)),hAPP(X2,X3))|~c_Finite__Set_Ofolding(X5,X1,X2,X6))). 4.07/4.38 cnf(i_0_4154, 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,esk304_3(X2,X3,X1))!=hAPP(X3,esk305_3(X2,X3,X1))|~c_Wellfounded_OwfP(X1,hAPP(X3,esk303_3(X2,X3,X1))))). 4.07/4.38 cnf(i_0_2820, plain, (c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,X5,hAPP(hAPP(X3,X6),X7))|~c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X7)|~hBOOL(hAPP(hAPP(c_member(X1),X6),X5)))). 4.07/4.38 cnf(i_0_3112, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk233_5(X3,X4,X1,X5,X2)),X5)),X4))|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Relation_OImage(X1,X2,X4),X3))))). 4.07/4.38 cnf(i_0_1281, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))))). 4.07/4.38 cnf(i_0_6895, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Wellfounded_Omlex__prod(X1,X4,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X4,X2)),hAPP(X4,X3))))). 4.07/4.38 cnf(i_0_2346, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.07/4.38 cnf(i_0_3606, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk273_5(X3,X4,X1,X5,X2)),X5)),X4))|~hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Relation_OImage(X1,X2,X4),X3))))). 4.07/4.38 cnf(i_0_5644, 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),esk406_3(X3,X1,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.07/4.38 cnf(i_0_3207, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2)))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),esk242_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_4348, 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),esk316_3(X3,X2,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_1163, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.07/4.38 cnf(i_0_1648, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X2))))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.07/4.38 cnf(i_0_4777, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.07/4.38 cnf(i_0_7202, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk503_4(X2,X3,X4,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|~hBOOL(hAPP(X2,X5)))). 4.07/4.38 cnf(i_0_5500, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3)|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.07/4.38 cnf(i_0_7424, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Olist_OCons(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)),X6)=hAPP(hAPP(c_Map_Omap__of(X1,X2),X5),X6)|X6=X3)). 4.07/4.38 cnf(i_0_3522, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk263_6(X3,X4,X2,X1,X5,X6)),esk264_6(X3,X4,X2,X1,X5,X6))=X3|~hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(X6,tc_HOL_Obool)),X4),X3))))). 4.07/4.38 cnf(i_0_7236, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X4)),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.07/4.38 cnf(i_0_7200, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk503_4(X2,X3,X4,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3))|~hBOOL(hAPP(X2,X5)))). 4.07/4.38 cnf(i_0_43, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_1227, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_6278, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.38 cnf(i_0_5984, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5)))|~c_Fun_Oinj__on(X2,X1,X3,X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X4),X5)))). 4.07/4.38 cnf(i_0_1106, plain, (hAPP(X1,esk97_3(X2,X1,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk96_3(X2,X1,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3))))). 4.07/4.38 cnf(i_0_5584, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4)))). 4.07/4.38 cnf(i_0_1628, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X4)))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.38 cnf(i_0_3862, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X4)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.38 cnf(i_0_6515, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X2)))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_6588, 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))). 4.07/4.38 cnf(i_0_4080, plain, (hAPP(X1,esk296_3(X2,X1,X3))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk295_3(X2,X1,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3))))). 4.07/4.38 cnf(i_0_978, plain, (hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),esk89_4(X2,X3,X4,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X4|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X3),X2))))). 4.07/4.38 cnf(i_0_236, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.38 cnf(i_0_6204, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.38 cnf(i_0_6127, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_298, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.07/4.38 cnf(i_0_1173, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_3731, 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))). 4.07/4.38 cnf(i_0_5595, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.38 cnf(i_0_1527, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X4))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.38 cnf(i_0_699, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=X3|hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.07/4.38 cnf(i_0_2366, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk181_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk180_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))))). 4.07/4.38 cnf(i_0_4495, plain, (hAPP(c_List_Ofoldl(tc_List_Olist(X1),X1,hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1))),c_List_Olist_ONil(X1)),X2)=c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X2)|~class_Orderings_Olinorder(X1))). 4.07/4.38 cnf(i_0_5918, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_1983, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk149_3(X3,X2,X1)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3))))). 4.07/4.38 cnf(i_0_7332, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk514_3(X3,X2,X1)),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk515_3(X3,X2,X1)),X2)))). 4.07/4.38 cnf(i_0_5032, 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)))). 4.07/4.38 cnf(i_0_299, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.07/4.38 cnf(i_0_5031, 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)))). 4.07/4.38 cnf(i_0_7285, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))|c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.07/4.38 cnf(i_0_3064, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,X1,esk228_2(X2,X1)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),esk227_2(X2,X1)))=X2|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_1093, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oordered__ring__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_1094, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oordered__ring__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.38 cnf(i_0_1095, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oordered__ring__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)))). 4.07/4.38 cnf(i_0_1096, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))=hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Rings_Oordered__ring__abs(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.38 cnf(i_0_4869, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_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)),esk355_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 4.07/4.38 cnf(i_0_3010, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk223_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))|hBOOL(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.38 cnf(i_0_2214, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),hAPP(hAPP(c_List_Onth(X1),X2),X4)))|~c_List_Olinorder__class_Osorted(X1,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)))). 4.07/4.38 cnf(i_0_3798, 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))). 4.07/4.38 cnf(i_0_1350, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_List_Oset(tc_prod(X1,X2)),X5)))|hAPP(c_Option_Ooption_OSome(X2),X4)!=hAPP(hAPP(c_Map_Omap__of(X1,X2),X5),X3))). 4.07/4.38 cnf(i_0_739, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X6),X3)))|~hBOOL(hAPP(hAPP(c_member(X5),X4),X6)))). 4.07/4.38 cnf(i_0_3799, 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))). 4.07/4.38 cnf(i_0_7279, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_Relation_Oconverse(X2,X1),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),X5)))). 4.07/4.38 cnf(i_0_4656, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool))|c_Fun_Oinj__on(X2,X3,X4,c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_HOL_Obool),X1))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk337_4(X4,X3,X2,X1)),X1)))). 4.07/4.38 cnf(i_0_5286, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X2)),X2)))|~c_Relation_Orefl__on(X1,X3,X2))). 4.07/4.38 cnf(i_0_351, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk26_3(X2,X3,X1)),esk27_3(X2,X3,X1))=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X3)),c_List_Olexord(X1,X2))))). 4.07/4.38 cnf(i_0_4916, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,X3)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X6),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(X5),X3),X6)))). 4.07/4.38 cnf(i_0_3616, plain, (c_Map_Omap__le(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),X5),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X6),X4),X5))|~c_Map_Omap__le(X1,X2,X3,X6))). 4.07/4.38 cnf(i_0_529, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X5)))). 4.07/4.38 cnf(i_0_4336, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Oone__class_Oone(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X3)))). 4.07/4.38 cnf(i_0_233, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Oone__class_Oone(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.07/4.38 cnf(i_0_2827, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.38 cnf(i_0_3055, plain, (hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X2,X3))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.07/4.38 cnf(i_0_4844, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_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)),esk355_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.38 cnf(i_0_4300, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel1(X1,X2)),c_List_Olistrel(X1,X3)))|~c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.07/4.38 cnf(i_0_990, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X3),X4)),X5))|~c_Fun_Oinj__on(X1,X2,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(c_Set_Oimage(X1,X2,X4),X5))))). 4.07/4.38 cnf(i_0_5488, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),hAPP(hAPP(c_List_Omap(X1,X2),X4),X3))),X5)=c_Option_Ooption_ONone(X2)|hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),X3))))). 4.07/4.38 cnf(i_0_2945, plain, (hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)),X6)=hAPP(c_Option_Ooption_OSome(X2),X7)|X6=X4|hAPP(X3,X6)!=hAPP(c_Option_Ooption_OSome(X2),X7))). 4.07/4.38 cnf(i_0_898, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,X2),X3),X4)=hAPP(X5,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))|hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|~c_Finite__Set_Ofolding__one(X1,X2,X5)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.38 cnf(i_0_408, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)),X5)=c_Option_Ooption_ONone(X2)|hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),X3)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))). 4.07/4.38 cnf(i_0_711, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk69_4(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3),X3,X2)),esk68_4(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3),X3,X2))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)=X2|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.07/4.38 cnf(i_0_5939, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Map_Odom(X1,X2,X3)),X5)|hAPP(X3,X4)!=c_Option_Ooption_ONone(X2))). 4.07/4.38 cnf(i_0_4483, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),X3),X4),X5)=hAPP(hAPP(c_Finite__Set_Ofold(X2,X1,X3),X4),hAPP(c_List_Oset(X2),X5))|~c_Finite__Set_Ofun__left__comm__idem(X2,X1,X3))). 4.07/4.38 cnf(i_0_410, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBB(X2,X2,X1),hAPP(c_Groups_Otimes__class_Otimes(X2),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X4),X5))|~class_Rings_Osemiring__0(X2))). 4.07/4.38 cnf(i_0_5622, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk405_4(X2,X3,X4,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4)))). 4.07/4.38 cnf(i_0_5621, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk405_4(X2,X3,X4,X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3)))). 4.07/4.38 cnf(i_0_5036, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X2)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.07/4.38 cnf(i_0_2049, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,hAPP(hAPP(c_Set_Oinsert(X1),X5),X6)),hAPP(hAPP(X3,X5),X7)))|hBOOL(hAPP(hAPP(c_member(X1),X5),X6))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X6),X7)))). 4.07/4.38 cnf(i_0_6422, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk454_4(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3),X3,X2)),esk453_4(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3),X3,X2))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)=X2|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.07/4.38 cnf(i_0_1357, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X2))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2)|~class_Rings_Oring__1(X1))). 4.07/4.38 cnf(i_0_6601, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X3),X4)))|~c_Fun_Oinj__on(X1,X3,X5,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X3,X5),X2)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)))). 4.07/4.38 cnf(i_0_139, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X2,hAPP(c_Relation_Oconverse(X2,X1),X3)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X5))))))). 4.07/4.38 cnf(i_0_334, 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),esk24_4(X2,X3,X1,X4)),X3))|hAPP(X2,X4)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_3275, 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,esk250_5(X3,X4,X5,X2,X1))))). 4.07/4.38 cnf(i_0_4799, 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),esk349_2(X2,X1)),hAPP(X1,esk349_2(X2,X1)))))). 4.07/4.38 cnf(i_0_4312, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)))))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.07/4.38 cnf(i_0_5556, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1)))),X3))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.07/4.38 cnf(i_0_2502, plain, (hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_3816, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X4))))). 4.07/4.38 cnf(i_0_3815, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3))))). 4.07/4.38 cnf(i_0_1429, plain, (hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.38 cnf(i_0_4038, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))),X4)|~class_Int_Onumber__ring(X1))). 4.07/4.38 cnf(i_0_6599, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))),X4)|~class_Int_Onumber__ring(X1))). 4.07/4.38 cnf(i_0_3545, 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),esk269_4(X3,X4,X2,X1)),X4))|~class_Rings_Olinordered__semidom(X1))). 4.07/4.38 cnf(i_0_4733, 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))|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_6597, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))|~c_Equiv__Relations_Oequiv(X1,X3,X2))). 4.07/4.38 cnf(i_0_3552, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X4),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X4))))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X4),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.38 cnf(i_0_4510, plain, (hAPP(hAPP(X1,X2),esk325_7(X3,X4,X2,X5,X1,X6,X7))=X3|hBOOL(hAPP(hAPP(c_member(X7),X2),X4))|~c_Finite__Set_Ofun__left__comm(X7,X6,X1)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X7,X6,X1,X5,hAPP(hAPP(c_Set_Oinsert(X7),X2),X4)),X3)))). 4.07/4.38 cnf(i_0_237, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))|~c_Relation_Orefl__on(X1,X3,X2))). 4.07/4.38 cnf(i_0_5223, 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),esk378_4(X3,X4,X2,X1)),X4))|~class_Rings_Olinordered__semidom(X1))). 4.07/4.38 cnf(i_0_7457, 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),esk522_5(X5,X4,X3,X2,X1)),X4))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.07/4.38 cnf(i_0_4932, 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),esk358_5(X5,X4,X3,X2,X1)),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.07/4.38 cnf(i_0_7564, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3))),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),X4),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X4)))). 4.07/4.38 cnf(i_0_5509, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),c_Big__Operators_Olinorder__class_OMin(X1,X3))=c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_5003, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_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)),esk364_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 4.07/4.38 cnf(i_0_613, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X5))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X5))|~class_Orderings_Olinorder(X1))). 4.07/4.38 cnf(i_0_3274, 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,esk250_5(X3,X4,X5,X2,X1))!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Omonoid__add(X1))). 4.07/4.38 cnf(i_0_5646, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X1,X1),c_Groups_Ouminus__class_Ouminus(X1)),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X4)))|~class_Groups_Oab__group__add(X1))). 4.07/4.38 cnf(i_0_5093, 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))). 4.07/4.38 cnf(i_0_2276, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3))),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),X4),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X2)))). 4.07/4.38 cnf(i_0_5792, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4))|X4=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1))). 4.07/4.38 cnf(i_0_7, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X4))|c_Groups_Ozero__class_Ozero(X1)=X4|~class_Divides_Osemiring__div(X1))). 4.07/4.38 cnf(i_0_5657, 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)|X4=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield__inverse__zero(X1))). 4.07/4.38 cnf(i_0_2813, 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)))). 4.07/4.38 cnf(i_0_2601, 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)|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Fields_Ofield(X1))). 4.07/4.38 cnf(i_0_2153, plain, (hAPP(hAPP(c_List_Oappend(X1),esk163_5(X2,X3,X4,X5,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),esk164_5(X2,X3,X4,X5,X1)))=X4|hAPP(c_List_Ofilter(X1,X5),X4)!=hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))). 4.07/4.38 cnf(i_0_5839, plain, (hAPP(hAPP(c_List_Oappend(X1),esk422_5(X2,X3,X4,X5,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),esk423_5(X2,X3,X4,X5,X1)))=X2|hAPP(c_List_Ofilter(X1,X3),X2)!=hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4))). 4.07/4.38 cnf(i_0_3324, 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,esk252_3(X3,X2,X1))),hAPP(X2,esk253_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),esk252_3(X3,X2,X1)),esk253_3(X3,X2,X1)))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_3247, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),X4)|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Fields_Ofield(X1))). 4.07/4.38 cnf(i_0_1126, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),X2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X2))|X2=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield(X1))). 4.07/4.38 cnf(i_0_1977, 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))). 4.07/4.38 cnf(i_0_4272, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_2108, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X3,X2),X4),hAPP(c_Set_Oimage(X1,X3,X5),X6))|~c_Fun_Oinj__on(X1,X3,X5,X6)|~class_Groups_Ocomm__monoid__mult(X2))). 4.07/4.38 cnf(i_0_2848, plain, (hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)),X5),X6)=hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Olist__update(X1,X2),X5),X6)),X3),X4)|X3=X5)). 4.07/4.38 cnf(i_0_1864, 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,esk141_3(X3,X2,X1))),hAPP(X2,esk142_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk141_3(X3,X2,X1)),esk142_3(X3,X2,X1)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_6556, 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,esk464_3(X3,X2,X1))),hAPP(X2,esk465_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),esk464_3(X3,X2,X1)),esk465_3(X3,X2,X1)))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_5592, plain, (c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_Set_Oimage(X1,X1,X2),X3))=hAPP(X2,c_Big__Operators_Olinorder__class_OMax(X1,X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk398_3(X3,X2,X1))),hAPP(X2,esk399_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk398_3(X3,X2,X1)),esk399_3(X3,X2,X1)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_885, plain, (hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.38 cnf(i_0_5002, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_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)),esk364_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))))). 4.07/4.38 cnf(i_0_3061, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2))))). 4.07/4.38 cnf(i_0_6675, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1)))). 4.07/4.38 cnf(i_0_1925, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.38 cnf(i_0_3116, 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_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)!=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))). 4.07/4.38 cnf(i_0_2223, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Olist__update(X1,X4),X5),X6),hAPP(hAPP(c_List_Olist__update(X2,X7),X5),X8))|~c_List_Olist__all2(X1,X2,X3,X4,X7)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)))|~hBOOL(hAPP(hAPP(X3,X6),X8)))). 4.07/4.38 cnf(i_0_6521, plain, (c_List_Olist__all2(X1,X2,X3,hAPP(hAPP(c_List_Olist__update(X1,X4),X5),X6),hAPP(hAPP(c_List_Olist__update(X2,X7),X5),X8))|~c_List_Olist__all2(X1,X2,X3,X4,X7)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X7)))|~hBOOL(hAPP(hAPP(X3,X6),X8)))). 4.07/4.38 cnf(i_0_7203, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1)),c_Groups_Oone__class_Oone(X2))))). 4.07/4.38 cnf(i_0_1356, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1))))). 4.07/4.38 cnf(i_0_6492, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))|~class_Rings_Olinordered__idom(X2)|~class_Int_Onumber__ring(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Oone__class_Oone(X2)),hAPP(c_Int_Onumber__class_Onumber__of(X2),X1))))). 4.07/4.38 cnf(i_0_3223, 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,esk245_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2))!=hAPP(X3,hAPP(X5,esk245_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2)))|~c_Fun_Oinj__on(X4,X1,X5,X6)|~class_Groups_Ocomm__monoid__add(X2))). 4.07/4.38 cnf(i_0_4509, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),esk325_7(X6,X5,X7,X4,X3,X2,X1)))|hBOOL(hAPP(hAPP(c_member(X1),X7),X5))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,hAPP(hAPP(c_Set_Oinsert(X1),X7),X5)),X6)))). 4.07/4.38 cnf(i_0_5652, 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))|esk408_3(X3,X2,X1)!=esk407_3(X3,X2,X1))). 4.07/4.38 cnf(i_0_6092, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X1),X2))=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|~class_Orderings_Oorder(X1))). 4.07/4.38 cnf(i_0_2501, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Fields_Ofield__inverse__zero(X1))). 4.07/4.38 cnf(i_0_5694, plain, (hAPP(hAPP(c_List_Onth(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_OSuc,X3)))=hAPP(hAPP(c_List_Onth(X1),hAPP(c_List_Orev(X1),X2)),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.07/4.38 cnf(i_0_4291, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)))),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__ring__strict(X1))). 4.07/4.38 cnf(i_0_5992, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_HOL_Obool),X1)),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk429_3(X3,X1,X2)),X1)))). 4.07/4.38 cnf(i_0_6097, plain, (c_List_Olist__all2(X1,X2,X3,X4,hAPP(hAPP(c_List_Omap(X5,X2),X6),X7))|~c_List_Olist__all2(X1,X5,hAPP(hAPP(c_COMBC(X1,tc_fun(X5,X2),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X5,X2),tc_fun(X5,tc_HOL_Obool)),X1),c_COMBB(X2,tc_HOL_Obool,X5)),X3)),X6),X4,X7))). 4.07/4.38 cnf(i_0_2365, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk181_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk180_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X2),X1)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))). 4.07/4.38 cnf(i_0_1894, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),X6)))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(X6,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5)))). 4.07/4.38 cnf(i_0_6548, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))=c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_5651, 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)),esk407_3(X3,X2,X1)),esk408_3(X3,X2,X1))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.07/4.38 cnf(i_0_1554, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X4,X2)),hAPP(X4,X3))))). 4.07/4.38 cnf(i_0_4795, plain, (c_Divides_OnegDivAlg(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(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.38 cnf(i_0_1681, plain, (hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))=c_Divides_OposDivAlg(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.38 cnf(i_0_7523, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))),hAPP(X2,hAPP(c_Nat_OSuc,X3)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X3)))|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.38 cnf(i_0_3080, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(X3,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X5))|hBOOL(hAPP(hAPP(c_member(X1),X4),X5))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.38 cnf(i_0_6139, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),c_Orderings_Otop__class_Otop(X1)),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X4),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.38 cnf(i_0_6142, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),c_Orderings_Obot__class_Obot(X1)),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X4),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.38 cnf(i_0_5605, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X6))=hAPP(hAPP(c_List_Olist_OCons(X1),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X6))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(X3,X4)),hAPP(X3,X5))))). 4.07/4.38 cnf(i_0_320, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2)))). 4.07/4.38 cnf(i_0_6858, plain, (c_Wellfounded_Owf(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(esk480_2(X2,X1),hAPP(c_Nat_OSuc,X3))),hAPP(esk480_2(X2,X1),X3))),X2)))). 4.07/4.38 cnf(i_0_4050, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2)))). 4.07/4.38 cnf(i_0_5489, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),hAPP(hAPP(c_List_Omap(X1,X2),X4),X3))),X5)=hAPP(c_Option_Ooption_OSome(X2),hAPP(X4,X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),X3))))). 4.07/4.38 cnf(i_0_48, 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),esk2_4(X4,X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_2791, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X1,X2)),X3))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_Enum_Oenum__class_Oenum__ex(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2))))))). 4.07/4.38 cnf(i_0_169, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X1,X2)),X3))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_Enum_Oenum__class_Oenum__all(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2))))))). 4.07/4.38 cnf(i_0_415, 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),esk33_4(X4,X1,X3,X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.07/4.38 cnf(i_0_653, 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),esk62_4(X4,X1,X3,X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.07/4.38 cnf(i_0_3137, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)))). 4.07/4.38 cnf(i_0_231, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3))),X4)|~class_Int_Onumber__ring(X1))). 4.07/4.38 cnf(i_0_3947, 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)))). 4.07/4.38 cnf(i_0_4561, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),X4)=hAPP(c_Option_Ooption_OSome(X2),X5)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))))). 4.07/4.38 cnf(i_0_672, 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),esk65_5(X5,X4,X3,X2,X1)),X4)))). 4.07/4.38 cnf(i_0_5150, 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),esk377_3(X2,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_2709, 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),esk198_3(X2,X1,X3)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.07/4.38 cnf(i_0_510, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_OImage(X3,X1,X4),hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),X5),X2)),X4)))). 4.07/4.38 cnf(i_0_2860, 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,esk212_4(X4,X1,X2,hAPP(c_Set_Oimage(X1,X2,X3),X4))),hAPP(c_Set_Oimage(X1,X2,X3),X4))),X4)))). 4.07/4.38 cnf(i_0_4023, 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)),X1),X2)))). 4.07/4.38 cnf(i_0_7382, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X2))=c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)))). 4.07/4.38 cnf(i_0_5540, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)))). 4.07/4.38 cnf(i_0_3661, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X5)))). 4.07/4.38 cnf(i_0_6659, plain, (hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),X4)=c_Option_Ooption_ONone(X2)|hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3)))))). 4.07/4.38 cnf(i_0_5773, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X1)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),X2)))). 4.07/4.38 cnf(i_0_6671, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),X2)),X2)),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Int_Oring__1__class_OInts(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.38 cnf(i_0_7047, 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|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)))). 4.07/4.38 cnf(i_0_3662, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X4,X5)))|~class_Orderings_Oorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2)))). 4.07/4.38 cnf(i_0_2644, plain, (X1=X2|X3=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X4),hAPP(hAPP(c_List_Olist_OCons(X5),X1),c_List_Olist_ONil(X5)))),hAPP(hAPP(c_List_Oappend(X5),X3),hAPP(hAPP(c_List_Olist_OCons(X5),X2),c_List_Olist_ONil(X5))))),c_List_Olistrel1(X5,X6))))). 4.07/4.38 cnf(i_0_5413, 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)))). 4.07/4.38 cnf(i_0_3642, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X3,X1,X4),X5)))|hAPP(c_Set_Oimage(X3,X1,X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X3),X2),X4)),X5)))). 4.07/4.38 cnf(i_0_3511, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))|~class_Rings_Olinordered__semidom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Oone__class_Oone(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)))). 4.07/4.38 cnf(i_0_4460, 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),esk323_4(X4,X1,X3,X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.07/4.38 cnf(i_0_4720, 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),esk343_4(X4,X3,X2,X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)))). 4.07/4.38 cnf(i_0_1240, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X2,tc_HOL_Obool)),X3))=hAPP(c_Finite__Set_Ocard(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))|hAPP(c_Finite__Set_Ocard(X2),esk104_3(X1,X3,X2))!=X1|esk106_3(X1,X3,X2)!=esk105_3(X1,X3,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))))). 4.07/4.38 cnf(i_0_2527, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4))))). 4.07/4.38 cnf(i_0_1578, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))=X3|X4=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))). 4.07/4.38 cnf(i_0_6731, 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,esk473_3(X3,X1,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(X1,X2)))). 4.07/4.38 cnf(i_0_7091, 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,esk496_3(X3,X1,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(X1,X2)))). 4.07/4.38 cnf(i_0_6907, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X4,X5))=hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X6),X3),X5))|hBOOL(hAPP(hAPP(c_member(X6),X3),X5))|~c_Finite__Set_Ofolding__image__simple(X7,X6,X1,X8,X2,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5)))). 4.07/4.38 cnf(i_0_5226, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)))). 4.07/4.38 cnf(i_0_713, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk68_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.38 cnf(i_0_2116, plain, (hAPP(c_Relation_ORange(X1,X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)))=X4|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3)). 4.07/4.38 cnf(i_0_4030, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_List_Oset(X1),c_List_Osublist(X1,X2,X3))),X2)=c_List_Osublist(X1,X2,X3)|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.07/4.38 cnf(i_0_4400, 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),esk318_2(X2,X1))),hAPP(c_List_Oset(X1),esk319_2(X2,X1)))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(X1),esk317_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 4.07/4.38 cnf(i_0_433, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(X2,X4)|X3=c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))|~c_Finite__Set_Ofolding__one__idem(X5,X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))). 4.07/4.38 cnf(i_0_2328, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~class_Int_Oring__char__0(X1)|~c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1))). 4.07/4.38 cnf(i_0_135, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))). 4.07/4.38 cnf(i_0_6424, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk453_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.38 cnf(i_0_6201, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Finite__Set_Ofold1(X1,c_Orderings_Oord__class_Omin(X1)),X2)),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_4315, 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)))). 4.07/4.38 cnf(i_0_4363, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))). 4.07/4.38 cnf(i_0_5327, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))))). 4.07/4.38 cnf(i_0_1150, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))=c_Groups_Oone__class_Oone(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.38 cnf(i_0_5940, 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)))). 4.07/4.38 cnf(i_0_2769, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk203_3(X1,X2,X3)),esk202_3(X1,X2,X3))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)=X2|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.07/4.38 cnf(i_0_3265, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk248_3(X1,X2,X3)),esk247_3(X1,X2,X3))=X2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)=X2|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.07/4.38 cnf(i_0_2457, plain, (hAPP(hAPP(c_List_Olist__update(X1,X2),esk184_4(X3,X4,X2,X1)),esk183_4(X3,X4,X2,X1))=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel1(X1,X3))))). 4.07/4.38 cnf(i_0_1515, 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)),esk116_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))))). 4.07/4.38 cnf(i_0_5360, 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,esk384_3(X2,X3,X1))))). 4.07/4.38 cnf(i_0_3042, 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,esk226_3(X2,X3,X1))))). 4.07/4.38 cnf(i_0_7189, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3))))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.07/4.38 cnf(i_0_6730, 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),esk473_3(X3,X1,X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(X1,X2)))). 4.07/4.38 cnf(i_0_2684, 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))|c_Groups_Ozero__class_Ozero(X1)=X2|~class_Fields_Ofield(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X3)))). 4.07/4.38 cnf(i_0_1545, 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)),esk117_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))))). 4.07/4.38 cnf(i_0_5624, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk404_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,esk403_4(X2,X3,X4,X1))))). 4.07/4.38 cnf(i_0_5625, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk403_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,esk404_4(X2,X3,X4,X1))))). 4.07/4.38 cnf(i_0_6829, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)))). 4.07/4.38 cnf(i_0_371, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk28_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X1,X3,X4)),c_List_Olist_Olist__size(X1,X2,X4))))). 4.07/4.38 cnf(i_0_7090, 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),esk496_3(X3,X1,X4)),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(X1,X2)))). 4.07/4.38 cnf(i_0_3035, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4)),X5)=hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X5)),X3),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.07/4.38 cnf(i_0_6676, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3)))). 4.07/4.38 cnf(i_0_177, plain, (hAPP(hAPP(c_List_Otake(X1),X2),X3)=c_List_OtakeWhile(X1,X4,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk12_4(X4,X3,X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|hBOOL(hAPP(X4,hAPP(hAPP(c_List_Onth(X1),X3),X2))))). 4.07/4.38 cnf(i_0_973, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),X2)))))). 4.07/4.38 cnf(i_0_1320, plain, (hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X4,c_Fun_Oid(X3)),X5)=hAPP(c_Product__Type_Omap__pair(X1,X2,X3,X3,X6,c_Fun_Oid(X3)),X5)|hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X3),X5))!=hAPP(X6,hAPP(c_Product__Type_Ofst(X1,X3),X5)))). 4.07/4.38 cnf(i_0_4094, plain, (hAPP(c_Product__Type_Omap__pair(X1,X1,X2,X3,c_Fun_Oid(X1),X4),X5)=hAPP(c_Product__Type_Omap__pair(X1,X1,X2,X3,c_Fun_Oid(X1),X6),X5)|hAPP(X4,hAPP(c_Product__Type_Osnd(X1,X2),X5))!=hAPP(X6,hAPP(c_Product__Type_Osnd(X1,X2),X5)))). 4.07/4.38 cnf(i_0_1180, plain, (hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),c_List_Olist_ONil(tc_Nat_Onat)))=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.07/4.38 cnf(i_0_2723, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk199_6(X2,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X4),X5),X4,X5,X1,X3)),X5))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(X4,X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X4),X5)))|~class_Groups_Oordered__ab__group__add(X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.38 cnf(i_0_6486, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk459_4(X3,X1,X4,X2)),X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),X4)),hAPP(c_Finite__Set_Ocard(X1),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_4418, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X4,X5))=hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X4,X5)),hAPP(X2,X3))|~c_Finite__Set_Ofolding(X6,X1,X2,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X5)))). 4.07/4.38 cnf(i_0_2435, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X5),X2))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X5),X2)|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5)))). 4.07/4.38 cnf(i_0_3863, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5),X2))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,tc_fun(X1,tc_HOL_Obool)),X5),X2)|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5)))). 4.07/4.38 cnf(i_0_6694, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,X2),X3))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|hBOOL(hAPP(X2,X4))|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3))))). 4.07/4.38 cnf(i_0_4849, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk355_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk353_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.38 cnf(i_0_967, plain, (c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X4)=c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X5),X6),X4)|c_Divides_Odiv__class_Omod(X1,X6,X4)!=c_Divides_Odiv__class_Omod(X1,X3,X4)|c_Divides_Odiv__class_Omod(X1,X2,X4)!=c_Divides_Odiv__class_Omod(X1,X5,X4)|~class_Divides_Osemiring__div(X1))). 4.07/4.38 cnf(i_0_411, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~c_Equiv__Relations_Oequiv(X1,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.07/4.38 cnf(i_0_722, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk73_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),esk70_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk71_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,esk70_2(X1,X2)))|~hBOOL(hAPP(X1,X3)))). 4.07/4.38 cnf(i_0_4846, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.38 cnf(i_0_2453, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4)))). 4.07/4.38 cnf(i_0_1676, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)))). 4.07/4.38 cnf(i_0_1431, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X4)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3)))). 4.07/4.38 cnf(i_0_6304, 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,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))). 4.07/4.38 cnf(i_0_4517, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3),hAPP(c_Nat_OSuc,X4)))|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.38 cnf(i_0_5990, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X5),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X6)))). 4.07/4.38 cnf(i_0_7233, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X3),X4))|~c_Finite__Set_Ofolding__image__simple__idem(X6,X5,X1,X7,X8,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)))). 4.07/4.38 cnf(i_0_3944, plain, (hAPP(hAPP(c_List_Otake(X1),X2),X3)=hAPP(hAPP(c_List_Otake(X1),X2),X4)|hAPP(hAPP(c_List_Onth(X1),X3),esk287_4(X4,X3,X1,X2))!=hAPP(hAPP(c_List_Onth(X1),X4),esk287_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))))). 4.07/4.38 cnf(i_0_6825, 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))). 4.07/4.38 cnf(i_0_2708, 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)),esk198_3(X2,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.07/4.38 cnf(i_0_5152, 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),esk377_3(X2,X1,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_654, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),hAPP(hAPP(c_List_Onth(X1),X2),X4)))|~c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Orev(X1),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X3)))). 4.07/4.38 cnf(i_0_308, 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))). 4.07/4.38 cnf(i_0_2473, 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))). 4.07/4.38 cnf(i_0_1832, 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)),esk139_5(X2,X4,X3,X3,X1)))|~c_Nat__Transfer_Onat__set(X3)|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.38 cnf(i_0_6739, 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)),esk474_5(X2,X4,X3,X3,X1)))|~c_Nat__Transfer_Onat__set(X3)|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.38 cnf(i_0_2570, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),X2),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4)))),X5)=hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X3))))). 4.07/4.38 cnf(i_0_6799, plain, (hAPP(hAPP(c_List_Onth(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)))=hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Oappend(X1),X4),X2)),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4))))). 4.07/4.38 cnf(i_0_5499, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X3)|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))|~hBOOL(hAPP(c_Nat__Numeral_Oneg,X2)))). 4.07/4.38 cnf(i_0_2880, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_1421, plain, (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X4))))). 4.07/4.38 cnf(i_0_5942, 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)))). 4.07/4.38 cnf(i_0_4874, 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)),esk355_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk353_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 4.07/4.38 cnf(i_0_6361, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OSigma(X2,X1),X6),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X2),X5)))))). 4.07/4.38 cnf(i_0_2562, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3)|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_2055, 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)|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_3091, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),X2),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.38 cnf(i_0_1255, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))|~class_Int_Onumber__ring(X1))). 4.07/4.38 cnf(i_0_2832, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_4480, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))),c_Divides_Odiv__class_Omod(X1,X3,X2))),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)|~class_Divides_Osemiring__div(X1))). 4.07/4.38 cnf(i_0_2279, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),X3)),c_Divides_Odiv__class_Omod(X1,X2,X3))),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)|~class_Divides_Osemiring__div(X1))). 4.07/4.38 cnf(i_0_5784, plain, (hAPP(c_Finite__Set_Ocard(X1),X2)=hAPP(c_Finite__Set_Ocard(X3),X4)|~c_Fun_Oinj__on(X3,X1,X5,X4)|~c_Fun_Oinj__on(X1,X3,X6,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X3,X6),X2)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X3,X1,X5),X4)),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_4674, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X2,X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3),X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)))). 4.07/4.38 cnf(i_0_4871, plain, (c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X1|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 4.07/4.38 cnf(i_0_3945, 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),esk287_4(X3,X4,X1,X2)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.38 cnf(i_0_3967, plain, (hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hAPP(hAPP(c_List_Oappend(X1),X2),X4)!=hAPP(hAPP(c_List_Oappend(X1),X3),X5))). 4.07/4.38 cnf(i_0_5861, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X4)))). 4.07/4.38 cnf(i_0_5243, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X5),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X3)))). 4.07/4.38 cnf(i_0_948, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X3),X4))|c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X3|c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))=X4|~c_Finite__Set_Ofolding__one__idem(X5,X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)))). 4.07/4.38 cnf(i_0_7343, plain, (c_List_OtakeWhile(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),c_List_Olast(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X2)=c_List_Obutlast(X1,X2)|X2=c_List_Olist_ONil(X1)|~hBOOL(hAPP(c_List_Odistinct(X1),X2)))). 4.07/4.38 cnf(i_0_1651, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Lattices_Osemilattice__sup__class_Osup(X1)),X3),X4),X5)=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),X5),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.38 cnf(i_0_4955, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3),X4),X5)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),X5),X3))|~class_Complete__Lattice_Ocomplete__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.38 cnf(i_0_2456, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk184_4(X1,X2,X3,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X3),X2)),c_List_Olistrel1(X4,X1))))). 4.07/4.38 cnf(i_0_3880, 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,esk286_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2)))!=hAPP(X7,esk286_8(X3,X7,hAPP(c_Set_Oimage(X4,X1,X5),X6),X6,X5,X1,X4,X2))|~c_Fun_Oinj__on(X4,X1,X5,X6)|~class_Groups_Ocomm__monoid__mult(X2))). 4.07/4.38 cnf(i_0_3225, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X2))=c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X2)|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X2)))). 4.07/4.38 cnf(i_0_2716, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.07/4.38 cnf(i_0_1660, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3)))). 4.07/4.38 cnf(i_0_3097, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk232_4(X2,X3,X4,X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk231_4(X2,X3,X4,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X4)))). 4.07/4.38 cnf(i_0_7048, 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|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)))). 4.07/4.38 cnf(i_0_5532, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)|hBOOL(hAPP(X2,X3)))). 4.07/4.38 cnf(i_0_6101, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),X4),hAPP(c_Set_Oimage(X1,X3,X5),X6))|~c_Fun_Oinj__on(X1,X3,X5,X6)|~class_Groups_Ocomm__monoid__add(X2))). 4.07/4.38 cnf(i_0_482, 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),esk40_4(X3,X4,X2,X1)),X4))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.38 cnf(i_0_1624, plain, (hAPP(c_Random_Opick(X1,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X3),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1),X4)))=hAPP(c_Random_Opick(X1,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X1)),X4),X2)),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X3),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1),X4))))). 4.07/4.38 cnf(i_0_3099, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk231_4(X1,X2,X3,X4)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk232_4(X1,X2,X3,X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.07/4.38 cnf(i_0_2336, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1))). 4.07/4.38 cnf(i_0_5797, plain, (c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))|hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)!=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1))). 4.07/4.38 cnf(i_0_6252, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))|~class_Rings_Oordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.07/4.38 cnf(i_0_6160, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))),hAPP(X2,X3))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.38 cnf(i_0_5113, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk367_4(X3,X4,X1,X2)),esk368_4(X3,X4,X1,X2))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),X4),hAPP(c_Relation_Oconverse(X1,X2),X3))))). 4.07/4.38 cnf(i_0_723, plain, (hBOOL(hAPP(X1,esk72_2(X1,X2)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk71_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,esk70_2(X1,X2)))|~hBOOL(hAPP(X1,X3)))). 4.07/4.38 cnf(i_0_2050, 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,esk153_5(X4,X3,X1,X5,X2))),hAPP(X3,esk154_5(X4,X3,X1,X5,X2)))!=hAPP(X3,hAPP(hAPP(X5,esk153_5(X4,X3,X1,X5,X2)),esk154_5(X4,X3,X1,X5,X2)))|~c_Finite__Set_Ofolding__one__idem(X2,X5,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.38 cnf(i_0_6997, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))|~class_Rings_Oordered__semiring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.07/4.38 cnf(i_0_6945, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X5),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)))). 4.07/4.38 cnf(i_0_5475, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.38 cnf(i_0_7507, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X5)))). 4.07/4.38 cnf(i_0_3429, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5))|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.38 cnf(i_0_4153, 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,esk304_3(X2,X3,X1)))),c_Predicate_ORangeP(X1,X1,hAPP(X3,esk305_3(X2,X3,X1))))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~c_Wellfounded_OwfP(X1,hAPP(X3,esk303_3(X2,X3,X1))))). 4.07/4.38 cnf(i_0_4838, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk355_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.38 cnf(i_0_4835, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,esk353_3(X1,X2,X3)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.38 cnf(i_0_7031, 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)|X4=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 4.07/4.38 cnf(i_0_86, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.38 cnf(i_0_428, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))|~class_Rings_Olinordered__semiring__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.38 cnf(i_0_1238, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X5),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4)))). 4.07/4.38 cnf(i_0_3677, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X5)))|~class_Fields_Olinordered__field(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X5),X3)))). 4.07/4.38 cnf(i_0_3230, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5))|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.38 cnf(i_0_148, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),esk11_5(X3,X2,X4,X5,X1))=X5|hAPP(hAPP(c_List_Oappend(X1),X5),esk10_5(X3,X2,X4,X5,X1))=X2|hAPP(hAPP(c_List_Oappend(X1),X2),X3)!=hAPP(hAPP(c_List_Oappend(X1),X5),X4))). 4.07/4.38 cnf(i_0_146, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),esk11_5(X3,X2,X4,X5,X1))=X5|hAPP(hAPP(c_List_Oappend(X1),esk10_5(X3,X2,X4,X5,X1)),X3)=X4|hAPP(hAPP(c_List_Oappend(X1),X2),X3)!=hAPP(hAPP(c_List_Oappend(X1),X5),X4))). 4.07/4.38 cnf(i_0_19, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3),X4))|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.38 cnf(i_0_2771, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk202_3(X3,X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.38 cnf(i_0_3267, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)=X1|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk247_3(X3,X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.38 cnf(i_0_4992, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk364_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk362_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))))). 4.07/4.38 cnf(i_0_147, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),esk10_5(X3,X4,X5,X2,X1))=X4|hAPP(hAPP(c_List_Oappend(X1),esk11_5(X3,X4,X5,X2,X1)),X5)=X3|hAPP(hAPP(c_List_Oappend(X1),X4),X3)!=hAPP(hAPP(c_List_Oappend(X1),X2),X5))). 4.07/4.38 cnf(i_0_145, plain, (hAPP(hAPP(c_List_Oappend(X1),esk11_5(X2,X3,X4,X5,X1)),X4)=X2|hAPP(hAPP(c_List_Oappend(X1),esk10_5(X2,X3,X4,X5,X1)),X2)=X4|hAPP(hAPP(c_List_Oappend(X1),X3),X2)!=hAPP(hAPP(c_List_Oappend(X1),X5),X4))). 4.07/4.38 cnf(i_0_4227, plain, (hAPP(hAPP(X1,esk307_7(X2,X3,X4,X5,X1,X6,X7)),esk308_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)))). 4.07/4.38 cnf(i_0_4008, 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)))). 4.07/4.38 cnf(i_0_5004, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_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))))). 4.07/4.38 cnf(i_0_5936, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2))),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_5109, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))|~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1))). 4.07/4.38 cnf(i_0_6164, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X3),X4))|~c_Finite__Set_Ofolding__idem(X5,X1,X6,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)))). 4.07/4.38 cnf(i_0_2164, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_List_Orev(X1),X3)))=hAPP(c_List_Ofoldl(X1,X1,c_Groups_Oplus__class_Oplus(X1),X2),X3)|~class_Groups_Omonoid__add(X1))). 4.07/4.38 cnf(i_0_3521, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk263_6(X4,X3,X5,X6,X2,X1)),esk264_6(X4,X3,X5,X6,X2,X1))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X5,tc_fun(X1,tc_HOL_Obool)),X3),X4))))). 4.07/4.38 cnf(i_0_3619, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X2)),X3)))). 4.07/4.38 cnf(i_0_3620, plain, (hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))|~hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),X3)))). 4.07/4.38 cnf(i_0_6674, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),X3),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X1)))). 4.07/4.38 cnf(i_0_1338, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Oimage(X2,X1,hAPP(hAPP(c_COMBB(X3,X1,X2),X4),X5)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X2,X3,X5),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))))). 4.07/4.38 cnf(i_0_6921, 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)))). 4.07/4.38 cnf(i_0_1413, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),hAPP(hAPP(X3,X6),X7)))|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X6),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X7))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X5)))). 4.07/4.38 cnf(i_0_4467, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2)),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(X3,X2)))). 4.07/4.38 cnf(i_0_1756, plain, (hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3))),X4)=hAPP(c_List_Ofilter(X1,X2),X4)|hBOOL(hAPP(X2,X3)))). 4.07/4.38 cnf(i_0_4226, plain, (hAPP(hAPP(X1,esk307_7(X2,X3,X4,X5,X1,X6,X7)),esk308_7(X2,X3,X4,X5,X1,X6,X7))=hAPP(hAPP(X1,X3),X2)|hAPP(hAPP(X1,X3),X2)=X5|~c_Nitpick_Ofold__graph_H(X7,X6,X1,X5,X4,hAPP(hAPP(X1,X3),X2)))). 4.07/4.38 cnf(i_0_7166, 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),X6),X7)!=hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,X6,X7),X5)))). 4.07/4.38 cnf(i_0_4824, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk350_5(X2,X3,X4,X1,X5)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4)))). 4.07/4.38 cnf(i_0_4993, 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)),esk364_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk362_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 4.07/4.38 cnf(i_0_5373, plain, (c_List_Olist__ex1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~c_List_Olist__all(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3))),X4)|~hBOOL(hAPP(X2,X3)))). 4.07/4.38 cnf(i_0_5371, plain, (c_List_Olist__ex1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~c_List_Olist__ex1(X1,X2,X4)|~c_List_Olist__all(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3))),X4))). 4.07/4.38 cnf(i_0_6682, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1)),X2)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X1),X3))=hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X1),X3),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X1))))). 4.07/4.38 cnf(i_0_7180, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(c_Finite__Set_Ocard(X1),X2)|hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_5840, 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,esk421_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)))). 4.07/4.38 cnf(i_0_5005, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 4.07/4.38 cnf(i_0_6314, plain, (c_List_Olinorder__class_Oinsort__insert__key(X1,X2,X3,X4,X5)=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X5)|hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X4)),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_List_Oset(X1),X5))))|~class_Orderings_Olinorder(X2))). 4.07/4.38 cnf(i_0_5910, plain, (hAPP(c_List_Ofoldl(X1,X1,hAPP(c_COMBC(X1,X1,X1),c_Orderings_Oord__class_Omax(X1)),X2),hAPP(c_List_Orev(X1),X3))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_List_Onth(X1),X3),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)|X3=c_List_Olist_ONil(X1)|~c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Orev(X1),X3))|~class_Orderings_Olinorder(X1))). 4.07/4.38 cnf(i_0_3095, plain, (hAPP(X1,esk232_4(X2,X1,X3,X4))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk231_4(X2,X1,X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.07/4.38 cnf(i_0_3098, plain, (hAPP(X1,esk232_4(X2,X1,X3,X4))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk231_4(X2,X1,X3,X4)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.07/4.38 cnf(i_0_178, plain, (hAPP(hAPP(c_List_Otake(X1),X2),X3)=c_List_OtakeWhile(X1,X4,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk12_4(X4,X3,X1,X2)),hAPP(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(X1)),X3))))). 4.07/4.38 cnf(i_0_4615, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X3))))=c_Groups_Oone__class_Oone(X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~class_Int_Onumber__ring(X1))). 4.07/4.38 cnf(i_0_6199, plain, (hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X1),X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_933, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.07/4.38 cnf(i_0_738, 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),esk74_5(X5,X4,X3,X2,X1)),X4)))). 4.07/4.38 cnf(i_0_4118, plain, (hAPP(c_Set_Oimage(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|hAPP(c_Set_Oimage(X3,X2,X4),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|hAPP(c_Set_Oimage(X1,X3,X5),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))). 4.07/4.38 cnf(i_0_3148, 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)))|esk237_5(X5,X4,X3,X2,X1)!=esk236_5(X5,X4,X3,X2,X1)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X5)))))). 4.07/4.38 cnf(i_0_6636, 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)))|esk470_5(X5,X4,X3,X2,X1)!=esk469_5(X5,X4,X3,X2,X1)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X5)))))). 4.07/4.38 cnf(i_0_4918, 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),esk357_5(X5,X4,X3,X2,X1)),X3)))). 4.07/4.38 cnf(i_0_310, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.07/4.38 cnf(i_0_7054, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2)))). 4.07/4.38 cnf(i_0_5441, plain, (hAPP(X1,X2)=hAPP(X1,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5)))))). 4.07/4.38 cnf(i_0_1720, plain, (hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_4617, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X4,X5))=hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X6),X5),X3))|hBOOL(hAPP(hAPP(c_member(X6),X5),X3))|~c_Finite__Set_Ofolding(X6,X1,X4,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X3)))). 4.07/4.38 cnf(i_0_519, plain, (c_FunDef_Oreduction__pair(X1,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_Wellfounded_Owf(X1,X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2)))). 4.07/4.38 cnf(i_0_3629, 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)))). 4.07/4.38 cnf(i_0_3965, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4)=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X2)))). 4.07/4.38 cnf(i_0_991, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4))))|~class_Lattices_Olattice(X1))). 4.07/4.38 cnf(i_0_5715, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))))|~class_Orderings_Olinorder(X1))). 4.07/4.38 cnf(i_0_5982, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X3),X4))))|~class_Lattices_Olattice(X1))). 4.07/4.38 cnf(i_0_2320, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))))|~class_Orderings_Olinorder(X1))). 4.07/4.38 cnf(i_0_2148, 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,esk165_6(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)))|~hBOOL(hAPP(X2,X4)))). 4.07/4.38 cnf(i_0_7196, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk505_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(X2,esk504_4(X2,X3,X4,X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(X2,X5)))). 4.07/4.38 cnf(i_0_7197, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk504_4(X2,X3,X4,X1)),X4))|hBOOL(hAPP(X2,esk505_4(X2,X3,X4,X1)))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))|~hBOOL(hAPP(X2,X5)))). 4.07/4.38 cnf(i_0_869, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X6))),c_List_Olex(X3,X4))))). 4.07/4.38 cnf(i_0_4385, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3))),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X1)))). 4.07/4.38 cnf(i_0_2273, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X1),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_2325, 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_Olistrel1(X3,X4))))). 4.07/4.38 cnf(i_0_558, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X6))),c_List_Olexord(X3,X4))))). 4.07/4.38 cnf(i_0_5453, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5))=hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))). 4.07/4.38 cnf(i_0_5696, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5))=hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))). 4.07/4.38 cnf(i_0_1565, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(X2,X3),X4)),hAPP(c_Set_Oimage(tc_prod(X5,X6),X1,hAPP(c_Product__Type_Oprod_Oprod__case(X5,X6,X1),X2)),X7)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X6)),hAPP(hAPP(c_Product__Type_OPair(X5,X6),X3),X4)),X7)))). 4.07/4.38 cnf(i_0_286, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X1)))). 4.07/4.38 cnf(i_0_2058, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))),X4)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X4)))). 4.07/4.38 cnf(i_0_7046, 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|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)))). 4.07/4.38 cnf(i_0_651, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk61_3(X2,X3,X1)),esk61_3(X2,X3,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olexord(X1,X3))))). 4.07/4.38 cnf(i_0_5010, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk363_3(X1,X2,X3)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_4986, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(X3,esk361_3(X1,X2,X3)))|~hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_5645, 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),esk406_3(X3,X1,X2)),X1))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.07/4.38 cnf(i_0_3208, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),hAPP(c_Finite__Set_Ofold1(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(X1),esk242_3(X3,X2,X1)),X2))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_3881, 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),esk286_8(X6,X3,hAPP(c_Set_Oimage(X1,X5,X7),X4),X4,X7,X5,X1,X2)),X4))|~c_Fun_Oinj__on(X1,X5,X7,X4)|~class_Groups_Ocomm__monoid__mult(X2))). 4.07/4.38 cnf(i_0_4863, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_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,esk355_3(X1,X2,X3))))). 4.07/4.38 cnf(i_0_4860, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_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,esk353_3(X1,X2,X3))))). 4.07/4.38 cnf(i_0_1402, 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),esk112_4(X3,X2,X4,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.38 cnf(i_0_4234, 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),esk309_4(X3,X2,X4,X1)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.38 cnf(i_0_5348, 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)|~c_Nat__Transfer_Onat__set(X3)|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.38 cnf(i_0_4349, 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),esk316_3(X3,X2,X1)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_3177, 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),esk240_4(X4,X1,X3,X2)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.07/4.38 cnf(i_0_499, 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),esk45_4(X4,X3,X2,X1)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),c_Groups_Oone__class_Oone(tc_Int_Oint))),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X3)))). 4.07/4.38 cnf(i_0_2486, plain, (hAPP(c_Random_Opick(X1,hAPP(hAPP(c_List_Omap(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,X1)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),X3))=hAPP(hAPP(c_List_Onth(X1),X2),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.07/4.38 cnf(i_0_3224, 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),esk245_8(X6,X3,hAPP(c_Set_Oimage(X1,X5,X7),X4),X4,X7,X5,X1,X2)),X4))|~c_Fun_Oinj__on(X1,X5,X7,X4)|~class_Groups_Ocomm__monoid__add(X2))). 4.07/4.38 cnf(i_0_4264, 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)|~c_Nat__Transfer_Onat__set(X3)|~class_Groups_Ocomm__monoid__mult(X1)|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.38 cnf(i_0_3385, 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),esk255_4(X2,X4,X3,X1)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_112, 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),esk9_4(X2,X4,X3,X1)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_6732, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X4),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X2),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X1),X5))),hAPP(hAPP(c_Product__Type_OSigma(X1,X4),X3),hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X1),X5))))|~hBOOL(hAPP(hAPP(c_member(X4),X6),X5)))). 4.07/4.38 cnf(i_0_2795, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),esk206_3(X3,X1,X2)),hAPP(c_List_Oset(tc_prod(X3,X3)),hAPP(hAPP(c_List_Ozip(X3,X3),X2),X1))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2))). 4.07/4.38 cnf(i_0_5299, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Groups_Oabs__class_Oabs(X1),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X4)))). 4.07/4.38 cnf(i_0_561, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),hAPP(hAPP(c_List_Onth(X1),X3),X2)),c_List_Olist_ONil(X1)))=hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X2)),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.38 cnf(i_0_1134, plain, (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)))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X2)),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_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.38 cnf(i_0_88, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X2)),X3)))=hAPP(hAPP(c_List_Olist__update(X1,X3),X2),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.38 cnf(i_0_2181, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))=hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.07/4.38 cnf(i_0_4880, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_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))))). 4.07/4.38 cnf(i_0_1277, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),c_Transitive__Closure_Ortrancl(X1,X4)))|~c_Wellfounded_Owf(X1,X4))). 4.07/4.38 cnf(i_0_4892, plain, (c_Wellfounded_Oacyclic(X1,hAPP(hAPP(c_Set_Oinsert(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),c_Transitive__Closure_Ortrancl(X1,X4)))|~c_Wellfounded_Oacyclic(X1,X4))). 4.07/4.38 cnf(i_0_197, plain, (hAPP(hAPP(X1,X2),X3)=hAPP(hAPP(X1,X4),X5)|~c_Equiv__Relations_Ocongruent2(X6,X7,X8,X9,X10,X1)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X3),X5)),X10))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X2),X4)),X9)))). 4.07/4.38 cnf(i_0_4867, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_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))))). 4.07/4.38 cnf(i_0_5851, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk425_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X4)))). 4.07/4.38 cnf(i_0_5130, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk371_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X4)))). 4.07/4.38 cnf(i_0_391, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk31_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1)))). 4.07/4.38 cnf(i_0_3848, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk283_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X1)))). 4.07/4.38 cnf(i_0_2670, plain, (hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))=hAPP(c_Relation_ODomain(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X4))|hAPP(c_Map_Omap__of(X1,X2),X3)!=hAPP(c_Map_Omap__of(X1,X2),X4))). 4.07/4.38 cnf(i_0_3136, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.07/4.38 cnf(i_0_296, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.07/4.38 cnf(i_0_2498, plain, (hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),X6))=hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),hAPP(hAPP(X3,X5),X4)),X6)|~c_Finite__Set_Ofun__left__comm__idem(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.07/4.38 cnf(i_0_5996, 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)))). 4.07/4.38 cnf(i_0_5847, 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)),esk424_3(X3,X2,X1))),X2)),X3)))). 4.07/4.38 cnf(i_0_184, 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))). 4.07/4.38 cnf(i_0_5953, 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)))). 4.07/4.38 cnf(i_0_1916, plain, (hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X4))=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))|hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X4)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))|hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))). 4.07/4.38 cnf(i_0_7404, 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),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),X3),X4)!=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))). 4.07/4.38 cnf(i_0_3970, plain, (X1=hAPP(hAPP(c_List_Oappend(X2),hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4)),X5)|hAPP(hAPP(c_List_Oappend(X2),X3),X1)!=hAPP(hAPP(c_List_Oappend(X2),X4),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))))). 4.07/4.38 cnf(i_0_2429, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X4),X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X4)))). 4.07/4.38 cnf(i_0_1177, plain, (c_Map_Omap__le(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),c_Option_Ooption_ONone(X2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X5),X4),hAPP(c_Option_Ooption_OSome(X2),X6)))|~c_Map_Omap__le(X1,X2,X3,X5))). 4.07/4.38 cnf(i_0_7270, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|X2=X3|~c_Equiv__Relations_Oequiv(X1,X4,X5)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X4),X5))))). 4.07/4.38 cnf(i_0_5219, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__sup__class_Osup(X1)),X3)),c_Orderings_Obot__class_Obot(X1)),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,X1),hAPP(c_List_Oset(X2),X4)),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.07/4.38 cnf(i_0_4208, plain, (hAPP(c_List_Ofoldl(X1,X2,hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(X1)),X3)),c_Orderings_Otop__class_Otop(X1)),X4)=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1),hAPP(c_List_Oset(X2),X4)),X3)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.07/4.38 cnf(i_0_1953, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1))|~class_Int_Onumber__ring(X1))). 4.07/4.38 cnf(i_0_1969, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5)))|hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X3,X4),X5)))). 4.07/4.38 cnf(i_0_2823, plain, (hAPP(c_List_Oset(tc_prod(X1,X2)),X3)=hAPP(c_List_Oset(tc_prod(X1,X2)),X4)|hAPP(c_Map_Omap__of(X1,X2),X3)!=hAPP(c_Map_Omap__of(X1,X2),X4)|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4)))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))))). 4.07/4.38 cnf(i_0_4229, plain, (c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,X5,hAPP(hAPP(X3,X6),X7))|hAPP(hAPP(X3,X8),X9)!=hAPP(hAPP(X3,X6),X7)|~c_Nitpick_Ofold__graph_H(X1,X2,X3,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X8),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X9)|~hBOOL(hAPP(hAPP(c_member(X1),X8),X5)))). 4.07/4.38 cnf(i_0_6951, plain, (c_List_OtakeWhile(X1,X2,X3)=hAPP(c_List_Ofilter(X1,X2),X3)|hBOOL(hAPP(hAPP(c_member(X1),esk488_3(X3,X2,X1)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)))))). 4.07/4.38 cnf(i_0_7164, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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))). 4.07/4.38 cnf(i_0_5852, plain, (c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))=hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X2),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3)))). 4.07/4.38 cnf(i_0_5153, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3)),X4)),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X3)))). 4.07/4.38 cnf(i_0_4468, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2)),X3)=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.38 cnf(i_0_7386, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X4)),hAPP(X2,X3))|~c_Finite__Set_Ofolding(X5,X1,X6,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)))). 4.07/4.38 cnf(i_0_495, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_COMBK(tc_Option_Ooption(X2),X1),c_Option_Ooption_ONone(X2))),X3),hAPP(c_Option_Ooption_OSome(X2),esk43_4(X3,X4,X2,X1)))=X4|c_Map_Odom(X1,X2,X4)!=hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))). 4.07/4.38 cnf(i_0_4323, plain, (c_List_OtakeWhile(X1,hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(c_Orderings_Oord__class_Oless(X2),X3)),X4),X5)=hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(c_Orderings_Oord__class_Oless(X2),X3)),X4)),X5)|~c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Orev(X2),hAPP(hAPP(c_List_Omap(X1,X2),X4),X5)))|~class_Orderings_Olinorder(X2))). 4.07/4.38 cnf(i_0_4855, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_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)))). 4.07/4.38 cnf(i_0_1289, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),c_Groups_Oabs__class_Oabs(X1)),X3)),X4)))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.07/4.38 cnf(i_0_2706, plain, (hBOOL(hAPP(hAPP(X1,X2),X3))|~hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3)),X4)),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2)),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X4)))). 4.07/4.38 cnf(i_0_4842, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_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)))). 4.07/4.38 cnf(i_0_5235, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Wellfounded_Omlex__prod(X1,X4,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X4,X2)),hAPP(X4,X3))))). 4.07/4.38 cnf(i_0_6748, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBB(X1,X1,X2),hAPP(c_Groups_Otimes__class_Otimes(X1),X3)),X4)),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X4),X5)))|~class_Rings_Osemiring__0(X1))). 4.07/4.38 cnf(i_0_2881, plain, (hAPP(c_Option_Ooption_OSome(X1),esk216_5(X2,X3,X1,X4,X5))=hAPP(hAPP(c_Map_Omap__of(X5,X1),hAPP(hAPP(c_List_Ozip(X5,X1),X4),X3)),X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|~hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(c_List_Oset(X5),X4))))). 4.07/4.38 cnf(i_0_5519, 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,X5)|~c_Fun_Oinj__on(X1,X2,X3,X4))). 4.07/4.38 cnf(i_0_5011, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_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,esk363_3(X1,X2,X3))))). 4.07/4.38 cnf(i_0_4987, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_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,esk361_3(X1,X2,X3))))). 4.07/4.38 cnf(i_0_2167, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),hAPP(hAPP(c_List_Onth(X1),X3),X2)),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,X2)),X3)))=X3|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.38 cnf(i_0_2225, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X2,X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3)),X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4)))). 4.07/4.38 cnf(i_0_7281, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),c_Map_Omap__add(X2,X1,X3,hAPP(c_Map_Omap__of(X2,X1),X4))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))))). 4.07/4.38 cnf(i_0_5065, plain, (c_Fun_Oinj__on(tc_prod(X1,X2),tc_prod(X3,X4),c_Product__Type_Omap__pair(X1,X3,X2,X4,X5,X6),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X7),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X8)))|~c_Fun_Oinj__on(X2,X4,X6,X8)|~c_Fun_Oinj__on(X1,X3,X5,X7))). 4.07/4.38 cnf(i_0_1104, plain, (hAPP(X1,esk97_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,esk96_3(X2,X1,X3)))),hAPP(X1,esk96_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3))))). 4.07/4.38 cnf(i_0_4078, plain, (hAPP(X1,esk296_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,esk295_3(X2,X1,X3)))),hAPP(X1,esk295_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3))))). 4.07/4.38 cnf(i_0_3759, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)),X5)),X6)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6))))). 4.07/4.38 cnf(i_0_3703, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)),X5)),X6)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),X6))))). 4.07/4.38 cnf(i_0_1862, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4)),X5)),X6))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6))))). 4.07/4.38 cnf(i_0_5920, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),X4)),X5)),X6))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X6))))). 4.07/4.38 cnf(i_0_2444, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool))),X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_3852, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X2,X1,X3),X4)),hAPP(c_Relation_OImage(X2,X1,X3),X5))=hAPP(c_Relation_OImage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~c_Relation_Osingle__valued(X1,X2,hAPP(c_Relation_Oconverse(X2,X1),X3)))). 4.07/4.38 cnf(i_0_5128, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk372_4(X1,X2,X3,X4)),esk371_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X4)))). 4.07/4.38 cnf(i_0_5849, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk426_4(X1,X2,X3,X4)),esk425_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X4)))). 4.07/4.38 cnf(i_0_3846, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk284_4(X1,X2,X3,X4)),esk283_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X1)))). 4.07/4.38 cnf(i_0_5227, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~c_Nitpick_Oless__eq__frac(X1,X2,X3))). 4.07/4.38 cnf(i_0_4580, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X1,tc_Nat_Onat)),X4),X5))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X4,X2)),hAPP(X4,X3))))). 4.07/4.38 cnf(i_0_6243, 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),esk445_4(X4,X2,X3,X1)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))))). 4.07/4.38 cnf(i_0_389, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk32_4(X1,X2,X3,X4)),esk31_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X1)))). 4.07/4.38 cnf(i_0_3071, 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))). 4.07/4.38 cnf(i_0_2554, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X1),c_Nitpick_Oplus__frac(X1,X2,c_Nitpick_Ouminus__frac(X1,X3))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~c_Nitpick_Oless__frac(X1,X2,X3))). 4.07/4.38 cnf(i_0_913, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|c_Fun_Oinj__on(X3,X4,X5,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X3,tc_HOL_Obool)),X2),X6))|hBOOL(hAPP(hAPP(c_member(X1),esk85_6(X6,X5,X4,X3,X1,X2)),X2)))). 4.07/4.38 cnf(i_0_7559, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2))),c_Int_Ointrel)))). 4.07/4.38 cnf(i_0_2004, 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)). 4.07/4.38 cnf(i_0_387, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)|~class_Rings_Osemiring(X1))). 4.07/4.38 cnf(i_0_718, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk71_2(X1,X2)))))|hBOOL(hAPP(X1,esk73_2(X1,X2)))|hBOOL(hAPP(X1,esk70_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,X3)))). 4.07/4.38 cnf(i_0_5938, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.07/4.38 cnf(i_0_3518, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.07/4.38 cnf(i_0_705, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3))|~class_Rings_Osemiring(X1)|~class_Int_Onumber(X1))). 4.07/4.38 cnf(i_0_1535, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)|hBOOL(hAPP(hAPP(c_member(X1),X4),X3)))). 4.07/4.38 cnf(i_0_4088, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk297_6(X3,X4,X5,X2,X1,X6)),esk298_6(X3,X4,X5,X2,X1,X6))=X6|hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(X5,tc_HOL_Obool)),X3),X6))))). 4.07/4.38 cnf(i_0_5868, 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)),esk427_4(X4,X3,X2,X1))))). 4.07/4.38 cnf(i_0_6555, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(X3),X1),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X3),tc_HOL_Obool)),X5),hAPP(hAPP(c_Product__Type_OSigma(X3,X3),X4),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X3),X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,X5))))). 4.07/4.38 cnf(i_0_4553, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X5),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.07/4.38 cnf(i_0_122, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2))))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.07/4.38 cnf(i_0_280, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk23_3(X3,X2,X1)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3)))))). 4.07/4.38 cnf(i_0_5691, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk414_5(X2,X3,X4,X5,X1)),esk415_5(X2,X3,X4,X5,X1))=X5|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel(X1,X2))))). 4.07/4.38 cnf(i_0_670, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),esk63_5(X2,X3,X4,X5,X1)),esk64_5(X2,X3,X4,X5,X1))=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)),X3)),c_List_Olistrel(X1,X2))))). 4.07/4.38 cnf(i_0_6035, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),c_Big__Operators_Olattice__class_OSup__fin(X2,X1)),X1))|~class_Lattices_Olattice(X2)|~hBOOL(hAPP(hAPP(c_member(X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),esk431_2(X1,X2)),esk432_2(X1,X2))),hAPP(hAPP(c_Set_Oinsert(X2),esk431_2(X1,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk432_2(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.07/4.38 cnf(i_0_3986, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),X2))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),esk289_2(X2,X1)),esk290_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk289_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk290_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_1507, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X1))=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_1635, plain, (c_Wellfounded_Oacyclic(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk124_2(X2,X1)),esk124_2(X2,X1))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))))). 4.07/4.38 cnf(i_0_2867, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X2,X3)),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X4,X1),X2),c_List_Oremove1(X4,X3,X5))))=hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X4,X1),X2),X5))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_member(X4),X3),hAPP(c_List_Oset(X4),X5))))). 4.07/4.38 cnf(i_0_4545, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk327_4(X2,X3,X4,X1)),esk328_4(X2,X3,X4,X1))),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel1(X1,X2))))). 4.07/4.38 cnf(i_0_1088, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X4),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X5),X2)))|~class_Groups_Oordered__cancel__ab__semigroup__add(X3)|~class_Groups_Ocomm__monoid__add(X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(X4,esk95_5(X5,X4,X2,X1,X3))),hAPP(X5,esk95_5(X5,X4,X2,X1,X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_1636, plain, (c_Wellfounded_Oacyclic(X1,X2)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk125_2(X2,X1)),esk125_2(X2,X1))),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))))). 4.07/4.38 cnf(i_0_4590, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,X3)),hAPP(X2,X4))),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X4)),hAPP(hAPP(c_Relation_Oinv__image(X1,X6),X5),X2))))). 4.07/4.38 cnf(i_0_3345, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X3),X3))))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))))). 4.07/4.38 cnf(i_0_442, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)))),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.07/4.38 cnf(i_0_5473, 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))|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_5027, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_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))))). 4.07/4.38 cnf(i_0_5677, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk410_5(X2,X3,X4,X5,X1)),hAPP(X3,esk409_5(X2,X3,X4,X5,X1))))|hBOOL(hAPP(X2,X6))|~hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3))))). 4.07/4.38 cnf(i_0_279, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4)))). 4.07/4.38 cnf(i_0_3114, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)=hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)|hBOOL(hAPP(X2,X4))|hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))!=X3)). 4.07/4.38 cnf(i_0_1971, 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)))). 4.07/4.38 cnf(i_0_5019, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_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))))). 4.07/4.38 cnf(i_0_4134, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)))),X3))),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.07/4.38 cnf(i_0_5427, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)=c_Int_OMin|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_1011, 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))=X2|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_297, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2)))). 4.07/4.38 cnf(i_0_980, 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),esk90_5(X5,X4,X1,X3,X2)),X3)))). 4.07/4.38 cnf(i_0_7416, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),hAPP(c_List_Ofilter(X1,X5),X6))=hAPP(c_List_Ofilter(X1,X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X6))|~c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Omap(X1,X2),X3),X6))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(X5,X4)))). 4.07/4.38 cnf(i_0_5147, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),c_List_Oremove1(X1,X4,X5))=X5|hAPP(c_List_Ohd(X1),hAPP(c_List_Ofilter(X1,hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),hAPP(c_fequal,hAPP(X3,X4))),X3)),X5))!=X4|~c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Omap(X1,X2),X3),X5))|~class_Orderings_Olinorder(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X5))))). 4.07/4.38 cnf(i_0_6298, plain, (hAPP(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))=hAPP(hAPP(X5,hAPP(X1,X3)),hAPP(X1,X4))|c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))=X4|X3=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~c_Finite__Set_Ofolding__one(X2,X5,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.07/4.38 cnf(i_0_2145, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X3),X4)),X5)),X6)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X5)),X6)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X5)),X1)|~class_Rings_Oring(X2))). 4.07/4.38 cnf(i_0_4543, plain, (hAPP(hAPP(c_List_Oappend(X1),esk329_4(X2,X3,X4,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),esk328_4(X2,X3,X4,X1)),esk330_4(X2,X3,X4,X1)))=X3|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel1(X1,X2))))). 4.07/4.38 cnf(i_0_4544, plain, (hAPP(hAPP(c_List_Oappend(X1),esk329_4(X2,X3,X4,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),esk327_4(X2,X3,X4,X1)),esk330_4(X2,X3,X4,X1)))=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel1(X1,X2))))). 4.07/4.38 cnf(i_0_5437, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)),X4)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.07/4.38 cnf(i_0_2085, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)),X4)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.07/4.38 cnf(i_0_5498, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X3))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2))),X3)|hBOOL(hAPP(c_Nat__Numeral_Oneg,X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.07/4.38 cnf(i_0_5361, 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),esk384_3(X2,X3,X1)),X3)))). 4.07/4.38 cnf(i_0_5848, plain, (X1=X2|hAPP(c_List_Oset(X3),X1)!=hAPP(c_List_Oset(X3),X2)|~c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X5),X2))|~c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Omap(X3,X4),X5),X1))|~c_Fun_Oinj__on(X3,X4,X5,hAPP(c_List_Oset(X3),hAPP(hAPP(c_List_Oappend(X3),X1),X2)))|~class_Orderings_Olinorder(X4)|~hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(X3,X4),X5),X2)))|~hBOOL(hAPP(c_List_Odistinct(X4),hAPP(hAPP(c_List_Omap(X3,X4),X5),X1))))). 4.07/4.38 cnf(i_0_6729, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X2)),X3)),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),X3)))). 4.07/4.38 cnf(i_0_3043, 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),esk226_3(X2,X3,X1)),X3)))). 4.07/4.38 cnf(i_0_4120, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)),X4)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.07/4.38 cnf(i_0_7061, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3)),X4)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.07/4.38 cnf(i_0_5026, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_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))))). 4.07/4.38 cnf(i_0_5018, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_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))))). 4.07/4.38 cnf(i_0_3972, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4))=hAPP(hAPP(c_List_Oappend(X1),X3),X4)|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)!=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.38 cnf(i_0_824, plain, (esk82_3(X1,X2,X3)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(X1,esk82_3(X1,X2,X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk81_3(X1,X2,X3),esk82_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2))))). 4.07/4.38 cnf(i_0_6912, plain, (c_Map_Oran(X1,X2,hAPP(c_Map_Omap__of(X1,X2),X3))=hAPP(c_Relation_ORange(X1,X2),hAPP(c_List_Oset(tc_prod(X1,X2)),X3))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))))). 4.07/4.38 cnf(i_0_979, 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,esk90_5(X5,X4,X1,X3,X2)),hAPP(X5,esk90_5(X5,X4,X1,X3,X2))))). 4.07/4.38 cnf(i_0_7179, plain, (hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_5151, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk377_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk376_3(X1,X2,X3)))=X1|hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.38 cnf(i_0_2710, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk198_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk197_3(X1,X2,X3)))=X1|hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X3)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.07/4.38 cnf(i_0_3021, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))),hAPP(X2,X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.38 cnf(i_0_1239, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X2,tc_HOL_Obool)),X3))=hAPP(c_Finite__Set_Ocard(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),esk105_3(X1,X3,X2)),esk106_3(X1,X3,X2))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hAPP(c_Finite__Set_Ocard(X2),esk104_3(X1,X3,X2))!=X1|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))))). 4.07/4.38 cnf(i_0_1260, plain, (hAPP(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X4))=hAPP(c_Fun_Ocomp(X5,X5,X5,hAPP(X1,X3)),hAPP(X1,X4))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X3),X4)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~c_Finite__Set_Ofolding(X2,X5,X6,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.07/4.38 cnf(i_0_4589, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Oinv__image(X4,X1),X5),X6)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),hAPP(X6,X2)),hAPP(X6,X3))),X5)))). 4.07/4.38 cnf(i_0_1430, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3))))). 4.07/4.38 cnf(i_0_2471, 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)))). 4.07/4.38 cnf(i_0_1991, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(X1,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(X1,X3))=c_Smallcheck_Osmall_H(X1,X2,X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3)))). 4.07/4.38 cnf(i_0_2288, plain, (c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X6),X7))=c_Map_Omap__upds(X1,X2,X3,X5,X7)|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X7)),X5)))))). 4.07/4.38 cnf(i_0_2579, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk187_4(X3,X4,X2,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3)))))). 4.07/4.38 cnf(i_0_2496, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk185_4(X2,X3,X4,X1)),X3)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))))). 4.07/4.38 cnf(i_0_6162, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X4)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X4))),X3)|~class_Int_Onumber__ring(X1))). 4.07/4.38 cnf(i_0_5077, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X1),c_Rings_Oinverse__class_Odivide(X2)),X3)),X4)),X5)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X5)),X4)|~class_Fields_Ofield(X2))). 4.07/4.38 cnf(i_0_825, 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),esk81_3(X1,X2,X3)),esk82_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2))))). 4.07/4.38 cnf(i_0_374, 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),esk29_3(X1,X2,X3)),esk30_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))). 4.07/4.38 cnf(i_0_2021, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),X4))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))|~class_Rings_Osemiring(X1)|~class_Int_Onumber(X1))). 4.07/4.38 cnf(i_0_469, 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),esk38_3(X1,X2,X3)),esk39_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))). 4.07/4.38 cnf(i_0_2866, 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),esk214_3(X1,X2,X3)),esk215_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))). 4.07/4.38 cnf(i_0_7147, 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),esk499_3(X1,X2,X3)),esk500_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))). 4.07/4.38 cnf(i_0_7340, 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),esk516_3(X1,X2,X3)),esk517_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))). 4.07/4.38 cnf(i_0_376, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.07/4.38 cnf(i_0_3461, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X1),X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_3129, 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))). 4.07/4.38 cnf(i_0_158, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Ofinite__psubset(X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_3119, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_member(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),X2))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk234_2(X2,X1)),esk235_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk234_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk235_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_7503, 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),esk525_2(X2,X1)),esk526_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk525_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk526_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.38 cnf(i_0_6873, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk483_6(X3,X4,X2,X5,X6,X1)),esk484_6(X3,X4,X2,X5,X6,X1))),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X6)),X5),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X6),X4),X3))))). 4.07/4.38 cnf(i_0_573, plain, (X1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)),X4)),X5)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X4)),X5)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X4)),X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)))). 4.07/4.38 cnf(i_0_1198, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X4)|hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|~class_Groups_Oab__group__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.38 cnf(i_0_6872, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk484_6(X3,X4,X1,X5,X2,X6)),esk485_6(X3,X4,X1,X5,X2,X6))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X2)),X5),hAPP(hAPP(c_Relation_Orel__comp(X6,X1,X2),X4),X3))))). 4.07/4.38 cnf(i_0_7198, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk505_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk504_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)))). 4.07/4.38 cnf(i_0_5950, 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))))). 4.07/4.38 cnf(i_0_2515, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),X4)))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1))),X4)),X2)))). 4.07/4.38 cnf(i_0_3572, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X4)|hAPP(X3,X5)=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_member(X1),X5),X4))|~class_Fields_Ofield(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.38 cnf(i_0_5292, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),X4)))|~hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1))),X4)),X2)))). 4.07/4.38 cnf(i_0_4082, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Otake(X1),X4),hAPP(hAPP(c_List_Odrop(X1),X2),X3)))=hAPP(hAPP(c_List_Otake(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.38 cnf(i_0_4850, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk353_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.38 cnf(i_0_6517, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X3),X4))|hAPP(X6,esk461_7(X4,X3,X2,X6,X7,X1,X5))!=X7|~c_Finite__Set_Ofolding__image__simple(X8,X5,X1,X7,X6,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))). 4.07/4.38 cnf(i_0_4875, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_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),esk353_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 4.07/4.38 cnf(i_0_4841, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk355_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.38 cnf(i_0_3096, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk232_4(X1,X2,X3,X4)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk231_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.07/4.38 cnf(i_0_3100, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk231_4(X1,X2,X3,X4)),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk232_4(X1,X2,X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.07/4.38 cnf(i_0_4461, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk322_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)))). 4.07/4.38 cnf(i_0_4866, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_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),esk355_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 4.07/4.38 cnf(i_0_4182, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),hAPP(hAPP(c_Relation_Orel__comp(X3,X3,X3),X4),c_Transitive__Closure_Ortrancl(X3,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,X4))))). 4.07/4.38 cnf(i_0_1726, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X1),c_Groups_Otimes__class_Otimes(X2)),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X5)),X4)|~class_Rings_Osemiring__0(X2))). 4.07/4.38 cnf(i_0_4721, 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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2)))). 4.07/4.38 cnf(i_0_1861, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2))),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X4)))). 4.07/4.38 cnf(i_0_3660, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X1)))). 4.07/4.38 cnf(i_0_7481, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Otake(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Odrop(X1),X2),X3))),c_List_Olist_ONil(X1)))=hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_OSuc,X2)),X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.38 cnf(i_0_7545, plain, (X1=X2|hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),X3,X4,c_Option_Othe(X3)),hAPP(c_Map_Omap__of(X4,X3),hAPP(hAPP(c_List_Ozip(X4,X3),c_Enum_Oenum__class_Oenum(X4)),X1)))!=hAPP(c_Fun_Ocomp(tc_Option_Ooption(X3),X3,X4,c_Option_Othe(X3)),hAPP(c_Map_Omap__of(X4,X3),hAPP(hAPP(c_List_Ozip(X4,X3),c_Enum_Oenum__class_Oenum(X4)),X2)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_Enum_Oenum__class_Oenum(X4))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_Enum_Oenum__class_Oenum(X4))!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X1)|~class_Enum_Oenum(X3)|~class_Enum_Oenum(X4))). 4.07/4.38 cnf(i_0_7229, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)!=X2|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.38 cnf(i_0_6786, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_List_Ozip(X2,X3),X4),X5)))|~hBOOL(hAPP(X1,hAPP(hAPP(c_List_Otake(tc_prod(X2,X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X5))),hAPP(hAPP(c_List_Ozip(X2,X3),X4),X5)))))). 4.07/4.38 cnf(i_0_1417, plain, (hAPP(c_Option_Ooption_OSome(X1),X2)=hAPP(hAPP(c_Map_Omap__of(X3,X1),hAPP(c_List_Ofilter(tc_prod(X3,X1),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X1,tc_HOL_Obool),X4)),X5)),X6)|hAPP(c_Option_Ooption_OSome(X1),X2)!=hAPP(hAPP(c_Map_Omap__of(X3,X1),X5),X6)|~hBOOL(hAPP(hAPP(X4,X6),X2)))). 4.07/4.38 cnf(i_0_5070, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2),X3)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.07/4.38 cnf(i_0_1012, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X4))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.38 cnf(i_0_2679, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hBOOL(hAPP(X3,X2)))). 4.07/4.38 cnf(i_0_4718, 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,esk340_3(X3,X2,X1))),hAPP(X2,esk341_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),esk340_3(X3,X2,X1)),esk341_3(X3,X2,X1)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_5684, plain, (c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(c_Set_Oimage(X1,X1,X2),X3))=hAPP(X2,c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk412_3(X3,X2,X1))),hAPP(X2,esk413_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),esk412_3(X3,X2,X1)),esk413_3(X3,X2,X1)))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.38 cnf(i_0_4997, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_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),esk362_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 4.07/4.38 cnf(i_0_2146, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X4),X2)),X3)),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X5)|~class_Rings_Oring(X1))). 4.07/4.38 cnf(i_0_4864, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_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)),esk355_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))))). 4.07/4.38 cnf(i_0_1105, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk97_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,esk96_3(X1,X2,X3)))),hAPP(X2,esk96_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3))))). 4.07/4.38 cnf(i_0_4077, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk296_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,esk295_3(X1,X2,X3)))),hAPP(X2,esk295_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3))))). 4.07/4.38 cnf(i_0_4459, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk323_4(X1,X2,X3,X4)),esk322_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)))). 4.07/4.38 cnf(i_0_4719, 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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2)))). 4.07/4.38 cnf(i_0_5015, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_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),esk364_3(X1,X2,X3)),X1))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 4.07/4.38 cnf(i_0_2393, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2)))). 4.07/4.38 cnf(i_0_4565, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(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_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))|~class_Int_Onumber__ring(X1))). 4.07/4.38 cnf(i_0_7262, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_Groups_Oone__class_Oone(X1)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),c_Nat_Osemiring__1__class_Oof__nat(X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)))|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.38 cnf(i_0_4870, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_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),esk353_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))))). 4.07/4.39 cnf(i_0_3156, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),c_Groups_Oone__class_Oone(X1))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin))|~class_Int_Onumber__ring(X1))). 4.07/4.39 cnf(i_0_1959, 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),esk147_5(X5,X3,X4,X2,X1)),X4))|~class_Groups_Oordered__ab__semigroup__add(X1)|~class_Rings_Osemiring__1(X1))). 4.07/4.39 cnf(i_0_4996, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk362_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))))). 4.07/4.39 cnf(i_0_5014, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk364_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))))). 4.07/4.39 cnf(i_0_5841, 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),esk421_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)))). 4.07/4.39 cnf(i_0_5801, 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),esk419_8(X3,X6,X5,X5,X4,X4,X1,X2)))|~class_Orderings_Oord(X1)|~class_Groups_Ocomm__monoid__add(X2))). 4.07/4.39 cnf(i_0_5800, 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),esk419_8(X3,X6,X5,X5,X4,X4,X1,X2)),X5))|~class_Orderings_Oord(X1)|~class_Groups_Ocomm__monoid__add(X2))). 4.07/4.39 cnf(i_0_1362, plain, (hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X3),X4)),X5))|~c_Equiv__Relations_Ocongruent(X2,tc_fun(X1,tc_HOL_Obool),X6,X4)|~c_Equiv__Relations_Oequiv(X2,X7,X6)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(X4,esk111_7(X5,X3,X4,X1,X6,X7,X2))),X5))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X7),X6))))). 4.07/4.39 cnf(i_0_6317, plain, (hAPP(hAPP(X1,X2),hAPP(hAPP(c_Finite__Set_Ofold(X3,X4,X1),X5),X6))=hAPP(hAPP(c_Finite__Set_Ofold(X3,X4,X1),X5),hAPP(hAPP(c_Set_Oinsert(X3),X2),X6))|hBOOL(hAPP(hAPP(c_member(X3),X2),X6))|~c_Finite__Set_Ofun__left__comm(X3,X4,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X6)))). 4.07/4.39 cnf(i_0_2824, plain, (hAPP(c_Map_Omap__of(X1,X2),X3)=hAPP(c_Map_Omap__of(X1,X2),X4)|hAPP(c_List_Oset(tc_prod(X1,X2)),X3)!=hAPP(c_List_Oset(tc_prod(X1,X2)),X4)|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4)))|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))))). 4.07/4.39 cnf(i_0_6616, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~class_Groups_Oab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.39 cnf(i_0_4344, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),hAPP(c_Finite__Set_Ofold1(X2,c_Groups_Otimes__class_Otimes(X2)),X1)),X1))|~class_Groups_Oab__semigroup__mult(X2)|~hBOOL(hAPP(hAPP(c_member(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),esk314_2(X1,X2)),esk315_2(X1,X2))),hAPP(hAPP(c_Set_Oinsert(X2),esk314_2(X1,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk315_2(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.07/4.39 cnf(i_0_17, 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,esk1_4(X3,X2,X4,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.39 cnf(i_0_3968, plain, (hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4)=X5|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hAPP(hAPP(c_List_Oappend(X1),X2),X5)!=hAPP(hAPP(c_List_Oappend(X1),X3),X4))). 4.07/4.39 cnf(i_0_4839, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_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)),esk355_3(X1,X2,X3)))|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.39 cnf(i_0_4845, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk353_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)))). 4.07/4.39 cnf(i_0_7484, 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))|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.39 cnf(i_0_373, plain, (hBOOL(hAPP(hAPP(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk29_3(X1,X2,X3))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk30_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),esk30_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.39 cnf(i_0_126, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.07/4.39 cnf(i_0_2373, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.07/4.39 cnf(i_0_6120, plain, (hAPP(c_Map_Omap__of(X1,X2),X3)=hAPP(c_Map_Omap__of(X1,X2),X4)|hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))!=hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4))|hAPP(hAPP(c_Map_Omap__of(X1,X2),X3),esk438_4(X3,X4,X2,X1))!=hAPP(hAPP(c_Map_Omap__of(X1,X2),X4),esk438_4(X3,X4,X2,X1)))). 4.07/4.39 cnf(i_0_7117, 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))|esk498_6(X3,X4,X5,X6,X1,X2)!=esk497_6(X3,X4,X5,X6,X1,X2)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.07/4.39 cnf(i_0_5814, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)),X1),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X1)))). 4.07/4.39 cnf(i_0_903, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.07/4.39 cnf(i_0_5809, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X2)),X2),X1))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.07/4.39 cnf(i_0_3427, plain, (c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Omap(X2,X1),X3),hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBC(X2,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,tc_HOL_Obool),X2),c_fequal),X3)),hAPP(X4,X5))),X5)))|~class_Orderings_Olinorder(X1))). 4.07/4.39 cnf(i_0_5804, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk420_5(X5,X4,X3,X2,X1)),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5))). 4.07/4.39 cnf(i_0_3271, plain, (c_List_Olist__all2(X1,X2,X3,X4,X5)|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk249_5(X3,X5,X4,X2,X1)),hAPP(c_List_Oset(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X4),X5))))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5))). 4.07/4.39 cnf(i_0_1280, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.07/4.39 cnf(i_0_5825, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))),hAPP(X2,hAPP(c_Nat_OSuc,X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,hAPP(c_Nat_OSuc,X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4)),X3))|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.39 cnf(i_0_5013, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_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)),esk364_3(X1,X2,X3)))|hBOOL(hAPP(X3,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X1))))). 4.07/4.39 cnf(i_0_5531, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)))),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X4))),X4)|~hBOOL(hAPP(X2,X3)))). 4.07/4.39 cnf(i_0_5675, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk411_5(X2,X3,X4,X5,X1)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X3)))|hBOOL(hAPP(X2,X6))|~hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(X3,X7)))|~hBOOL(hAPP(hAPP(c_member(X5),X7),X4)))). 4.07/4.39 cnf(i_0_4469, 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,esk324_5(X3,X4,X5,X2,X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_729, plain, (hAPP(c_Set_Oimage(tc_prod(X1,X2),tc_prod(X3,X4),c_Product__Type_Omap__pair(X1,X3,X2,X4,X5,X6)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X3,X4),tc_HOL_Obool))|hAPP(c_Set_Oimage(X2,X4,X6),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))|hAPP(c_Set_Oimage(X1,X3,X5),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))). 4.07/4.39 cnf(i_0_5007, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_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),esk362_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))))). 4.07/4.39 cnf(i_0_572, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X1),X2)),X3)),X4)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.07/4.39 cnf(i_0_5606, plain, (hAPP(hAPP(c_List_Olist_OCons(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(hAPP(c_List_Olist_OCons(X1),X2),X6))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(X4,X5)),hAPP(X4,X2)))|~class_Orderings_Olinorder(X3))). 4.07/4.39 cnf(i_0_6721, plain, (hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Int_Onat)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2)|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1))). 4.07/4.39 cnf(i_0_3092, plain, (hAPP(X1,esk232_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,esk231_4(X2,X1,X3,X4)))),hAPP(X1,esk231_4(X2,X1,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X1,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X1,X4)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.07/4.39 cnf(i_0_2324, 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_Olist_OCons(X3),X5),X1)),hAPP(hAPP(c_List_Olist_OCons(X3),X6),X2))),c_List_Olistrel1(X3,X4))))). 4.07/4.39 cnf(i_0_748, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X2)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X2)|~c_Nat__Transfer_Onat__set(X2)|~c_Nat__Transfer_Onat__set(X1))). 4.07/4.39 cnf(i_0_1403, 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),esk112_4(X3,X2,X4,X1)),X4))|~class_Lattices_Osemilattice__inf(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.39 cnf(i_0_4235, 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),esk309_4(X3,X2,X4,X1)),X4))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.39 cnf(i_0_113, 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),esk9_4(X2,X4,X3,X1)),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_3386, 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),esk255_4(X2,X4,X3,X1)),X3))|~class_Lattices_Osemilattice__sup(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_3796, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X5)=hAPP(X5,X4)|~c_Equiv__Relations_Ocongruent(X1,tc_fun(X2,tc_HOL_Obool),X3,X5)|~c_Equiv__Relations_Oequiv(X1,X6,X3)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X6)))). 4.07/4.39 cnf(i_0_3231, plain, (c_Map_Omap__add(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),hAPP(c_Option_Ooption_OSome(X2),X5)),X6)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__add(X1,X2,X3,X6)),X4),hAPP(c_Option_Ooption_OSome(X2),X5))|hBOOL(hAPP(hAPP(c_member(X1),X4),c_Map_Odom(X1,X2,X6))))). 4.07/4.39 cnf(i_0_7339, plain, (hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),esk516_3(X1,X2,X3))),esk517_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),esk516_3(X1,X2,X3)),esk517_3(X1,X2,X3))))). 4.07/4.39 cnf(i_0_2916, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4))))). 4.07/4.39 cnf(i_0_6163, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X4),X5)),X6),X7)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,X2),X3),X6),X7)),X4),X5)|X4=X6)). 4.07/4.39 cnf(i_0_4324, plain, (c_Map_Omap__upds(X1,X2,c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(c_List_Oset(X1),X5))),X5,X6)=c_Map_Orestrict__map(X1,X2,c_Map_Omap__upds(X1,X2,X3,X5,X6),X4)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X6)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X5)),X4)))). 4.07/4.39 cnf(i_0_5440, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X1,tc_Nat_Onat)),X4),X5))))|hAPP(X4,X2)!=hAPP(X4,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,X5))))). 4.07/4.39 cnf(i_0_2803, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk207_5(X3,X4,X5,X2,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X3))))). 4.07/4.39 cnf(i_0_3135, plain, (hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X1)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))=hAPP(c_fequal,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)))). 4.07/4.39 cnf(i_0_5012, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_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)),esk364_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))))). 4.07/4.39 cnf(i_0_5006, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_3(X1,X2,X3)))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk362_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))))). 4.07/4.39 cnf(i_0_3760, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X5),X2)),X3)),X6))))). 4.07/4.39 cnf(i_0_6343, plain, (c_Lazy__Sequence_Ohb__flat(X1,c_Lazy__Sequence_Ohb__map(X2,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1)),hAPP(hAPP(c_COMBC(X2,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X1))),X3),X4),hAPP(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X4),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))=hAPP(c_New__DSequence_Oneg__decr__bind(X2,X1,X5,X3),X4)|X4=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 4.07/4.39 cnf(i_0_4793, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk348_5(X3,X4,X5,X2,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X3))))). 4.07/4.39 cnf(i_0_7001, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk492_5(X2,X3,X4,X5,X1)),X4)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2))))). 4.07/4.39 cnf(i_0_799, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X1)),X1))|~c_Finite__Set_Ofolding__one(X2,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X2),hAPP(hAPP(X4,esk76_4(X1,X3,X4,X2)),esk77_4(X1,X3,X4,X2))),hAPP(hAPP(c_Set_Oinsert(X2),esk76_4(X1,X3,X4,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk77_4(X1,X3,X4,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.07/4.39 cnf(i_0_3997, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X3)))). 4.07/4.39 cnf(i_0_3704, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X5),X2)),X3)),X6))))). 4.07/4.39 cnf(i_0_1863, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)),X6)))). 4.07/4.39 cnf(i_0_5919, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X3)),X6)))|~class_Rings_Oordered__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)),X6)))). 4.07/4.39 cnf(i_0_1174, 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),esk102_3(X3,X2,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_6244, plain, (hAPP(hAPP(c_List_Oappend(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)),hAPP(hAPP(c_List_Ozip(X1,X2),X5),X6))=hAPP(hAPP(c_List_Ozip(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X5)),hAPP(hAPP(c_List_Oappend(X2),X4),X6))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X6)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4))). 4.07/4.39 cnf(i_0_2495, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk185_4(X3,X4,X2,X1))),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3)))))). 4.07/4.39 cnf(i_0_2580, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk187_4(X2,X3,X4,X1)),X3)),c_Transitive__Closure_Ortrancl(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))))). 4.07/4.39 cnf(i_0_7115, 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,esk497_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)))). 4.07/4.39 cnf(i_0_420, 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,esk34_5(X3,X4,X5,X2,X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_1958, 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,esk147_5(X5,X3,X4,X2,X1))),X5)))). 4.07/4.39 cnf(i_0_1129, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist__update(X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))),X5))=hAPP(hAPP(c_List_Olist__update(X1,hAPP(hAPP(c_List_Oappend(X1),X2),X3)),X4),X5)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.07/4.39 cnf(i_0_5438, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X1)),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X4)))). 4.07/4.39 cnf(i_0_1399, plain, (hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))))=c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)))). 4.07/4.39 cnf(i_0_2300, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),esk175_5(X4,X5,X2,X1,X3))),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3,X3),tc_HOL_Obool),X5),X4))))). 4.07/4.39 cnf(i_0_5394, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),esk388_5(X4,X5,X1,X2,X3)),X1)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3,X3),tc_HOL_Obool),X5),X4))))). 4.07/4.39 cnf(i_0_4321, 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,esk313_6(X4,X3,X6,X5,X2,X1))!=hAPP(X6,esk313_6(X4,X3,X6,X5,X2,X1))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_4258, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X6),X7)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X2),tc_HOL_Obool)),X5),X7))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),X4),X6)))). 4.07/4.39 cnf(i_0_2084, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X1)),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X4)))). 4.07/4.39 cnf(i_0_4119, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X4)),X2)),X3)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X1)))). 4.07/4.39 cnf(i_0_7062, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X4)),X2)),X3)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X1)))). 4.07/4.39 cnf(i_0_5626, plain, (hBOOL(hAPP(hAPP(c_member(X1),esk404_4(X2,X3,X4,X1)),X3))|hBOOL(hAPP(hAPP(c_member(X1),esk403_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))))). 4.07/4.39 cnf(i_0_1534, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)),hAPP(X2,X4))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X3)))). 4.07/4.39 cnf(i_0_6229, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~c_Equiv__Relations_Oequiv(X1,X5,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))))). 4.07/4.39 cnf(i_0_7448, plain, (X1=X2|~c_Equiv__Relations_Oequiv(X3,X4,X5)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X6),X7)),X5))|~hBOOL(hAPP(hAPP(c_member(X3),X7),X2))|~hBOOL(hAPP(hAPP(c_member(X3),X6),X1)))). 4.07/4.39 cnf(i_0_5412, 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)))). 4.07/4.39 cnf(i_0_3178, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk239_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X4)))). 4.07/4.39 cnf(i_0_500, plain, (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk44_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X2)))). 4.07/4.39 cnf(i_0_5377, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.39 cnf(i_0_2528, 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))))). 4.07/4.39 cnf(i_0_5636, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X4))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4))))|~c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))). 4.07/4.39 cnf(i_0_4943, plain, (hAPP(hAPP(c_List_Olist__update(X1,hAPP(c_List_Orev(X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_OSuc,X3))),X4)=hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.07/4.39 cnf(i_0_1080, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.39 cnf(i_0_7261, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(X3,esk511_8(X4,X5,X3,X6,X7,X8,X2,X1))),hAPP(X5,esk512_8(X4,X5,X3,X6,X7,X8,X2,X1)))=X8|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),X8),hAPP(c_Set_Oimage(tc_prod(X7,X6),tc_prod(X1,X2),c_Product__Type_Omap__pair(X7,X1,X6,X2,X3,X5)),X4))))). 4.07/4.39 cnf(i_0_6407, 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,esk450_3(X3,X2,X1))),hAPP(X2,esk451_3(X3,X2,X1)))!=hAPP(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),esk450_3(X3,X2,X1)),esk451_3(X3,X2,X1)))|~class_Lattices_Oab__semigroup__idem__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_4404, 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)),esk317_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),esk318_2(X2,X1))),hAPP(c_List_Oset(X1),esk319_2(X2,X1)))!=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 4.07/4.39 cnf(i_0_3176, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk240_4(X1,X2,X3,X4)),esk239_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X4)))). 4.07/4.39 cnf(i_0_498, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk45_4(X1,X2,X3,X4)),esk44_4(X1,X2,X3,X4))=X4|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),X3)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),X2)))). 4.07/4.39 cnf(i_0_669, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk63_5(X3,X4,X5,X2,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),X4)),c_List_Olistrel(X1,X3))))). 4.07/4.39 cnf(i_0_5690, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk414_5(X2,X3,X4,X5,X1)),X4)),X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel(X1,X2))))). 4.07/4.39 cnf(i_0_2128, plain, (hBOOL(hAPP(hAPP(hAPP(X1,X2),X3),X4))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X4))))|~hBOOL(hAPP(hAPP(hAPP(X1,esk160_4(X1,X4,X3,X2)),esk161_4(X1,X4,X3,X2)),esk162_4(X1,X4,X3,X2))))). 4.07/4.39 cnf(i_0_5795, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X5),X6))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X2,X3),X4),X6))|hAPP(X3,X4)=hAPP(X3,X5)|~class_Orderings_Olinorder(X2))). 4.07/4.39 cnf(i_0_1970, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))|~class_Int_Onumber__ring(X1))). 4.07/4.39 cnf(i_0_5487, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X2,tc_Option_Ooption(X1)),X3),X4),hAPP(c_Option_Ooption_OSome(X1),X5))),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X1)),hAPP(c_Set_Oimage(X2,tc_Option_Ooption(X1),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))))). 4.07/4.39 cnf(i_0_2847, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X4),X5)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X5))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)))). 4.07/4.39 cnf(i_0_3960, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),X4)))). 4.07/4.39 cnf(i_0_2048, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),X4)))). 4.07/4.39 cnf(i_0_1568, plain, (c_List_OtakeWhile(tc_List_Olist(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),hAPP(c_fequal,c_List_Olist_ONil(X1))),X2)=c_List_Otranspose(X1,c_List_Otranspose(X1,X2))|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2))))). 4.07/4.39 cnf(i_0_520, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~c_Equiv__Relations_Oequiv(X1,X5,X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5)))). 4.07/4.39 cnf(i_0_2678, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)=hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.39 cnf(i_0_3508, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X6),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=hAPP(X4,X6)|~c_Finite__Set_Ofolding__image__simple(X7,X5,X1,X8,X2,X4)|~hBOOL(hAPP(hAPP(c_member(X5),X3),X6))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X6)))). 4.07/4.39 cnf(i_0_719, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk71_2(X1,X2)))))|hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk73_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|hBOOL(hAPP(X1,esk70_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,X3)))). 4.07/4.39 cnf(i_0_2588, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3),X5)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5),X4))|~class_Groups_Oab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X5)))). 4.07/4.39 cnf(i_0_5654, 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)),esk407_3(X3,X2,X1)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.07/4.39 cnf(i_0_3927, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__upds(X1,X2,X3,X4,X5)),X6),hAPP(c_Option_Ooption_OSome(X2),X7))=c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4),hAPP(hAPP(c_List_Olist_OCons(X2),X7),X5))|hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),X4))))). 4.07/4.39 cnf(i_0_2303, 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),esk175_5(X4,X1,X5,X3,X2))),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X4))))). 4.07/4.39 cnf(i_0_5397, 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),esk388_5(X3,X1,X4,X5,X2)),X4)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X3))))). 4.07/4.39 cnf(i_0_5653, 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)),esk408_3(X3,X2,X1)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X1,tc_HOL_Obool)),X2),X3)))|hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),X3)))). 4.07/4.39 cnf(i_0_140, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X3,X1,hAPP(c_Relation_Oconverse(X1,X3),X4)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3,tc_HOL_Obool)),X5)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X3,X4),X2)),X5)))). 4.07/4.39 cnf(i_0_2043, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X6),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))=hAPP(X4,hAPP(hAPP(c_Set_Oinsert(X5),X3),X6))|~c_Finite__Set_Ofolding__image__simple(X7,X5,X1,X8,X2,X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X6)))). 4.07/4.39 cnf(i_0_2149, 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),esk165_6(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)),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(X2,X4)))). 4.07/4.39 cnf(i_0_2412, 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,esk182_5(X4,X3,X5,X2,X1)))),hAPP(X2,esk182_5(X4,X3,X5,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X5))))). 4.07/4.39 cnf(i_0_1244, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X2,tc_HOL_Obool)),X3))=hAPP(c_Finite__Set_Ocard(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk104_3(X1,X3,X2)),X3))|esk106_3(X1,X3,X2)!=esk105_3(X1,X3,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))))). 4.07/4.39 cnf(i_0_4405, 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)),esk317_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|esk319_2(X2,X1)!=esk318_2(X2,X1)|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 4.07/4.39 cnf(i_0_2125, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_List_Olinorder__class_Osorted__list__of__set(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_2343, 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),esk178_5(X3,X4,X5,X1,X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),X4)))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.39 cnf(i_0_7390, 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),esk518_5(X3,X4,X5,X1,X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),X4)))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.39 cnf(i_0_3158, 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),esk238_5(X3,X4,X5,X1,X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),X4)))|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.39 cnf(i_0_7006, 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),esk493_5(X3,X4,X5,X1,X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),X4)))|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.39 cnf(i_0_3973, plain, (hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)),X4))=hAPP(hAPP(c_List_Oappend(X1),X3),X4)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)!=X2)). 4.07/4.39 cnf(i_0_2885, plain, (hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),X4))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X3),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X4))|~class_Orderings_Olinorder(X1))). 4.07/4.39 cnf(i_0_2642, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X5),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3)))),hAPP(hAPP(c_List_Oappend(X3),X6),hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_Olist_ONil(X3))))),c_List_Olistrel1(X3,X4))))). 4.07/4.39 cnf(i_0_2006, 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,esk150_5(X3,X5,X4,X2,X1))!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_5047, 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,esk366_5(X3,X5,X4,X2,X1))!=c_Groups_Ozero__class_Ozero(X1)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_4525, 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,esk326_5(X3,X5,X4,X2,X1))!=c_Groups_Oone__class_Oone(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_324, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))),hAPP(X6,X5))=hAPP(X2,X4)|~c_Finite__Set_Ofolding(X3,X1,X6,X2)|~hBOOL(hAPP(hAPP(c_member(X3),X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)))). 4.07/4.39 cnf(i_0_3229, 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))|c_Groups_Oone__class_Oone(X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)|~class_Rings_Olinordered__semiring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X5),X6))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X6)))). 4.07/4.39 cnf(i_0_285, 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))|c_Groups_Oone__class_Oone(X1)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)|~class_Rings_Olinordered__semiring__1__strict(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X5),X6))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X6)))). 4.07/4.39 cnf(i_0_5442, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,X4)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X5,X2)),hAPP(X5,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X1,tc_Nat_Onat)),X5),X4)))))). 4.07/4.39 cnf(i_0_2509, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),c_Groups_Oone__class_Oone(X1)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(c_Power_Opower__class_Opower(X1),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|c_Groups_Oone__class_Oone(X1)=X2|~class_Fields_Ofield(X1))). 4.07/4.39 cnf(i_0_5444, 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,esk392_5(X3,X5,X4,X2,X1))!=c_Groups_Oone__class_Oone(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_2840, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(X3),esk209_7(X1,X2,X4,X5,X6,X7,X3)),X7))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X5,tc_HOL_Obool)),X1),X4)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X5,tc_HOL_Obool)),X2),X4)|~c_Equiv__Relations_Ocongruent(X3,tc_fun(X5,tc_HOL_Obool),X6,X4)|~c_Equiv__Relations_Oequiv(X3,X7,X6)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6))))). 4.07/4.39 cnf(i_0_2839, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(X3),esk210_7(X1,X2,X4,X5,X6,X7,X3)),X7))|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X5,tc_HOL_Obool)),X1),X4)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X5,tc_HOL_Obool)),X2),X4)|~c_Equiv__Relations_Ocongruent(X3,tc_fun(X5,tc_HOL_Obool),X6,X4)|~c_Equiv__Relations_Oequiv(X3,X7,X6)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6))))). 4.07/4.39 cnf(i_0_4345, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4))),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X4))))|hAPP(c_Set_Oimage(X2,X1,X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))). 4.07/4.39 cnf(i_0_6653, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X2),X4)),X5))=hAPP(hAPP(c_Set_Oinsert(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3)). 4.07/4.39 cnf(i_0_3134, plain, (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2))=hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)))). 4.07/4.39 cnf(i_0_293, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4))|hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2)))). 4.07/4.39 cnf(i_0_4700, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))))),hAPP(X6,X5))=hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X3),X5),X4))|~c_Finite__Set_Ofolding(X3,X1,X6,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)))). 4.07/4.39 cnf(i_0_5375, plain, (c_List_Olist__all(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X3))),X4)|~c_List_Olist__ex1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))|~hBOOL(hAPP(X2,X3)))). 4.07/4.39 cnf(i_0_1197, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(X3,X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))|~class_Groups_Oab__group__add(X1)|~hBOOL(hAPP(hAPP(c_member(X2),X5),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.39 cnf(i_0_5867, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4))))). 4.07/4.39 cnf(i_0_3087, 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))))). 4.07/4.39 cnf(i_0_7244, 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),esk510_4(X4,X3,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X3),esk510_4(X4,X3,X2,X1)))),X4)))). 4.07/4.39 cnf(i_0_927, plain, (hAPP(hAPP(X1,hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),X5))),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X5)))=hAPP(hAPP(X1,hAPP(X2,X4)),hAPP(X2,X5))|~c_Finite__Set_Ofolding__image__simple(X6,X3,X1,X7,X8,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)))). 4.07/4.39 cnf(i_0_4403, 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)),esk318_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),esk317_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 4.07/4.39 cnf(i_0_4402, 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)),esk319_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),esk317_2(X2,X1)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 4.07/4.39 cnf(i_0_5808, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X2)),X2),X1))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1))))). 4.07/4.39 cnf(i_0_2837, plain, (X1=X2|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X1),X5)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X4,tc_HOL_Obool)),X2),X5)|~c_Equiv__Relations_Ocongruent(X3,tc_fun(X4,tc_HOL_Obool),X6,X5)|~c_Equiv__Relations_Oequiv(X3,X7,X6)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),esk209_7(X1,X2,X5,X4,X6,X7,X3)),esk210_7(X1,X2,X5,X4,X6,X7,X3))),X6))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X3,tc_HOL_Obool)),X1),hAPP(hAPP(c_Equiv__Relations_Oquotient(X3),X7),X6))))). 4.07/4.39 cnf(i_0_4978, plain, (hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X5)),X6))=hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X5)),hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),X6))|~c_Finite__Set_Ofolding(X7,X1,X3,X8))). 4.07/4.39 cnf(i_0_1064, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))=hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))|~class_Int_Onumber__ring(X1))). 4.07/4.39 cnf(i_0_1903, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.39 cnf(i_0_2245, 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)))). 4.07/4.39 cnf(i_0_3094, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk232_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,esk231_4(X2,X3,X4,X1)))),hAPP(X3,esk231_4(X2,X3,X4,X1))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),hAPP(X3,X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X3,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X4)))). 4.07/4.39 cnf(i_0_3093, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk232_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,esk231_4(X1,X2,X3,X4)))),hAPP(X2,esk231_4(X1,X2,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(X2,X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X4)),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)))). 4.07/4.39 cnf(i_0_5799, 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,esk419_8(X6,X3,X5,X5,X4,X4,X1,X2))!=hAPP(X6,esk419_8(X6,X3,X5,X5,X4,X4,X1,X2))|~class_Orderings_Oord(X1)|~class_Groups_Ocomm__monoid__add(X2))). 4.07/4.39 cnf(i_0_468, plain, (hBOOL(hAPP(hAPP(X1,esk38_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),esk39_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk38_3(X1,X2,X3)),esk39_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))). 4.07/4.39 cnf(i_0_931, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X3)),hAPP(hAPP(c_Set_Oinsert(X1),hAPP(hAPP(c_List_Onth(X1),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Olist__update(X1,X3),X4),X2)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.07/4.39 cnf(i_0_134, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)))). 4.07/4.39 cnf(i_0_3571, 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)))). 4.07/4.39 cnf(i_0_2458, 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),esk184_4(X3,X4,X2,X1))),esk183_4(X3,X4,X2,X1))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel1(X1,X3))))). 4.07/4.39 cnf(i_0_3276, 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),esk250_5(X3,X4,X5,X2,X1)),hAPP(c_List_Oset(X2),X5)))|~class_Groups_Omonoid__add(X1))). 4.07/4.39 cnf(i_0_7538, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))!=hAPP(c_Relation_OImage(X1,X1,X4),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~c_Equiv__Relations_Oequiv(X1,X5,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5)))). 4.07/4.39 cnf(i_0_4364, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)))). 4.07/4.39 cnf(i_0_5328, plain, (hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))|~hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X1),X2)))). 4.07/4.39 cnf(i_0_6962, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Random_Opick(X1,X2),X3)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),X1),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X1)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X3),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1)),X2)))))). 4.07/4.39 cnf(i_0_2242, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Set_Oinsert(X2),X4)),X5))=hAPP(hAPP(c_Set_Oinsert(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X3)))). 4.07/4.39 cnf(i_0_559, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))),c_List_Olexord(X1,X6)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X6)))). 4.07/4.39 cnf(i_0_2701, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel1(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X5)))). 4.07/4.39 cnf(i_0_4768, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X1,tc_Nat_Onat)),X4),X5))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X4,X2)),hAPP(X4,X3))))). 4.07/4.39 cnf(i_0_720, plain, (hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk70_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk71_2(X1,X2)))))|hBOOL(hAPP(X1,esk72_2(X1,X2)))|hBOOL(hAPP(X1,esk70_2(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))|~hBOOL(hAPP(X1,X3)))). 4.07/4.39 cnf(i_0_4825, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk350_5(X3,X4,X5,X1,X2))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X5),X4)),c_Wellfounded_Omax__ext(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5)))). 4.07/4.39 cnf(i_0_3174, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,X2),X2,X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X2),X5)),hAPP(c_COMBC(X4,X1,X2),X6)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X4,X2),X5),hAPP(hAPP(c_COMBB(tc_fun(X1,X2),X2,X4),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,X2),X3)),X6))|~class_Complete__Lattice_Ocomplete__lattice(X2))). 4.07/4.39 cnf(i_0_812, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X2),X3),hAPP(hAPP(c_COMBB(tc_fun(X4,X2),X2,X1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X2),X5)),hAPP(c_COMBC(X4,X1,X2),X6)))=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X2),X5),hAPP(hAPP(c_COMBB(tc_fun(X1,X2),X2,X4),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,X2),X3)),X6))|~class_Complete__Lattice_Ocomplete__lattice(X2))). 4.07/4.39 cnf(i_0_668, 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),esk64_5(X3,X4,X2,X5,X1))),c_List_Olistrel(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),X4)),c_List_Olistrel(X1,X3))))). 4.07/4.39 cnf(i_0_4865, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3)))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_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))))). 4.07/4.39 cnf(i_0_4840, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk355_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk354_3(X1,X2,X3)))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk353_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk352_3(X1,X2,X3)))=X2|hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))|~hBOOL(hAPP(X3,X2)))). 4.07/4.39 cnf(i_0_1185, plain, (hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(hAPP(c_List_Onth(X1),X3),X4)),hAPP(hAPP(c_List_Onth(X2),X5),X4))=hAPP(hAPP(c_List_Onth(tc_prod(X1,X2)),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X5)),X4)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))). 4.07/4.39 cnf(i_0_1379, plain, (c_FunDef_Oreduction__pair(X1,X2)|~c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))))). 4.07/4.39 cnf(i_0_5689, 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)),esk415_5(X2,X3,X4,X5,X1)),X3)),c_List_Olistrel(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel(X1,X2))))). 4.07/4.39 cnf(i_0_4631, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X3)),X4)),X5))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))),X4)|~class_Rings_Osemiring__0(X1))). 4.07/4.39 cnf(i_0_1242, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X2,tc_HOL_Obool)),X3))=hAPP(c_Finite__Set_Ocard(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk105_3(X1,X3,X2)),X3))|hAPP(c_Finite__Set_Ocard(X2),esk104_3(X1,X3,X2))!=X1|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))))). 4.07/4.39 cnf(i_0_77, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),X3)),X2)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.07/4.39 cnf(i_0_1241, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X2,tc_HOL_Obool)),X3))=hAPP(c_Finite__Set_Ocard(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk106_3(X1,X3,X2)),X3))|hAPP(c_Finite__Set_Ocard(X2),esk104_3(X1,X3,X2))!=X1|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))))). 4.07/4.39 cnf(i_0_3617, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X4),X1)),X2)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X4)))). 4.07/4.39 cnf(i_0_7395, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X2)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X4)),X2)),X3)),X5)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X1)))). 4.07/4.39 cnf(i_0_4036, 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)). 4.07/4.39 cnf(i_0_5017, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_3(X1,X2,X3)))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_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))))). 4.07/4.39 cnf(i_0_4826, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X1,X2)),X3))|~c_Enum_Oex__n__lists(X2,hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_HOL_Obool,tc_List_Olist(X2)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,X2),tc_List_Olist(X2)),c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_fun(X1,tc_Option_Ooption(X2)),tc_List_Olist(X2)),c_Map_Omap__of(X1,X2)),hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1)))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2))). 4.07/4.39 cnf(i_0_5353, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X1,X2)),X3))|~c_Enum_Oall__n__lists(X2,hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_HOL_Obool,tc_List_Olist(X2)),X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_Option_Ooption(X2)),tc_fun(X1,X2),tc_List_Olist(X2)),c_Fun_Ocomp(tc_Option_Ooption(X2),X2,X1,c_Option_Othe(X2))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X1,X2)),tc_fun(X1,tc_Option_Ooption(X2)),tc_List_Olist(X2)),c_Map_Omap__of(X1,X2)),hAPP(c_List_Ozip(X1,X2),c_Enum_Oenum__class_Oenum(X1))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Enum_Oenum__class_Oenum(X1)))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2))). 4.07/4.39 cnf(i_0_1243, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X2,tc_HOL_Obool)),X3))=hAPP(c_Finite__Set_Ocard(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk104_3(X1,X3,X2)),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),esk105_3(X1,X3,X2)),esk106_3(X1,X3,X2))!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))))). 4.07/4.39 cnf(i_0_5016, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk364_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk363_3(X1,X2,X3)))=X2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk362_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk361_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))))). 4.07/4.39 cnf(i_0_6478, plain, (hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_Set_Oimage(X3,X1,X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X3),X6),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))))=hAPP(c_Set_Oimage(X3,X1,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X3,X1),X4),X6),X2)),X5)|~hBOOL(hAPP(hAPP(c_member(X3),X6),X5)))). 4.07/4.39 cnf(i_0_5864, 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)))). 4.07/4.39 cnf(i_0_2513, plain, (hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Omap(X1,tc_prod(X1,X2)),hAPP(hAPP(c_COMBS(X1,X2,tc_prod(X1,X2)),c_Product__Type_OPair(X1,X2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),X2,X1),c_Option_Othe(X2)),X3))),X4))=X3|hAPP(c_List_Oset(X1),X4)!=c_Map_Odom(X1,X2,X3))). 4.07/4.39 cnf(i_0_6871, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)),X4)=hAPP(hAPP(c_List_Onth(X1),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))))))). 4.07/4.39 cnf(i_0_2238, 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,esk172_4(X4,X3,X2,X1))))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2))))). 4.07/4.39 cnf(i_0_3709, 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,esk279_5(X5,X3,X4,X2,X1))))). 4.07/4.39 cnf(i_0_4941, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X2,X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),X5)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.07/4.39 cnf(i_0_6576, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X1),X2),X5)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(hAPP(c_member(X4),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.07/4.39 cnf(i_0_7002, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk492_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X3))))). 4.07/4.39 cnf(i_0_2802, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk207_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2))))). 4.07/4.39 cnf(i_0_4792, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk348_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X3),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X3)),X2))))). 4.07/4.39 cnf(i_0_1774, 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,esk134_5(X5,X3,X4,X2,X1))),hAPP(X5,esk134_5(X5,X3,X4,X2,X1)))))). 4.07/4.39 cnf(i_0_1334, plain, (hAPP(hAPP(X1,hAPP(hAPP(c_COMBS(X2,X3,X3),hAPP(hAPP(c_COMBB(X3,tc_fun(X3,X3),X2),X4),X5)),X6)),X7)=hAPP(hAPP(X4,hAPP(hAPP(X1,X5),X7)),hAPP(hAPP(X1,X6),X7))|~c_Finite__Set_Ofolding__image(X3,X2,X4,X8,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7)))). 4.07/4.39 cnf(i_0_1155, plain, (c_Fun_Oinj__on(X1,X2,X3,hAPP(hAPP(c_Set_Oinsert(X1),X4),X5))|hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X4)),hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))))|~c_Fun_Oinj__on(X1,X2,X3,X5))). 4.07/4.39 cnf(i_0_1089, plain, (c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X4),X2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3),X5),X2)))|hBOOL(hAPP(hAPP(c_member(X1),esk95_5(X5,X4,X2,X1,X3)),X2))|~class_Groups_Oordered__cancel__ab__semigroup__add(X3)|~class_Groups_Ocomm__monoid__add(X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.39 cnf(i_0_6258, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X2,X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,X1),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),X5))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.07/4.39 cnf(i_0_4696, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5))=hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~c_Fun_Oinj__on(X2,X1,X3,X6)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X5),X6))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X6)))). 4.07/4.39 cnf(i_0_975, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),X4)),hAPP(c_Set_Oimage(X2,X1,X3),X5))=hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~c_Fun_Oinj__on(X2,X1,X3,X6)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X5),X6))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X6)))). 4.07/4.39 cnf(i_0_685, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X4,X1),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),X5))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.07/4.39 cnf(i_0_2639, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))),c_FunDef_Opair__less))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.07/4.39 cnf(i_0_7513, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))),c_FunDef_Opair__leq))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)))). 4.07/4.39 cnf(i_0_1797, 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|X3=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield(X1))). 4.07/4.39 cnf(i_0_6511, plain, (hAPP(hAPP(X1,X2),hAPP(hAPP(c_Finite__Set_Ofold(X3,X4,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X6),hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))))=hAPP(hAPP(c_Finite__Set_Ofold(X3,X4,X1),X5),X6)|~c_Finite__Set_Ofun__left__comm(X3,X4,X1)|~hBOOL(hAPP(hAPP(c_member(X3),X2),X6))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X6)))). 4.07/4.39 cnf(i_0_3962, plain, (hAPP(hAPP(X1,X2),hAPP(hAPP(c_Finite__Set_Ofold(X3,X4,X1),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool)),X6),hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))))=hAPP(hAPP(c_Finite__Set_Ofold(X3,X4,X1),X5),hAPP(hAPP(c_Set_Oinsert(X3),X2),X6))|~c_Finite__Set_Ofun__left__comm(X3,X4,X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X6)))). 4.07/4.39 cnf(i_0_4322, 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),esk313_6(X4,X3,X6,X5,X2,X1)),X5))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_1744, 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|c_Groups_Ozero__class_Ozero(X1)=X3|~class_Fields_Ofield(X1))). 4.07/4.39 cnf(i_0_5279, plain, (hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),X5))),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X5)))=hAPP(c_Fun_Ocomp(X1,X1,X1,hAPP(X2,X4)),hAPP(X2,X5))|~c_Finite__Set_Ofolding(X3,X1,X6,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)))). 4.07/4.39 cnf(i_0_18, 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),esk1_4(X3,X2,X4,X1)),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)))). 4.07/4.39 cnf(i_0_6640, plain, (hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),hAPP(c_Fun_Othe__inv__into(X2,X5,hAPP(c_Set_Oimage(X1,X2,X4),X3),X6),X7))=hAPP(c_Fun_Othe__inv__into(X1,X5,X3,hAPP(c_Fun_Ocomp(X2,X5,X1,X6),X4)),X7)|~c_Fun_Oinj__on(X2,X5,X6,hAPP(c_Set_Oimage(X1,X2,X4),X3))|~c_Fun_Oinj__on(X1,X2,X4,X3)|~hBOOL(hAPP(hAPP(c_member(X5),X7),hAPP(c_Set_Oimage(X2,X5,X6),hAPP(c_Set_Oimage(X1,X2,X4),X3)))))). 4.07/4.39 cnf(i_0_7282, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,X3)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X4,c_Groups_Otimes__class_Otimes(X1)),X2),X5),X6))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X4,c_Groups_Otimes__class_Otimes(X1)),X2),X5),hAPP(hAPP(c_Set_Oinsert(X4),X3),X6))|hBOOL(hAPP(hAPP(c_member(X4),X3),X6))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6)))). 4.07/4.39 cnf(i_0_548, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Int_Onumber__ring(X1)|~class_Fields_Olinordered__field__inverse__zero(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))). 4.07/4.39 cnf(i_0_246, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_5967, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Relation_Orel__comp(X1,X5,X2),X6),X7)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X2)),hAPP(hAPP(c_Product__Type_OPair(X5,X2),X8),X4)),X7))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X5)),hAPP(hAPP(c_Product__Type_OPair(X1,X5),X3),X8)),X6)))). 4.07/4.39 cnf(i_0_5419, 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))))),esk390_7(X6,X7,X5,X4,X3,X2,X1)))|~c_Finite__Set_Ofun__left__comm(X1,X2,X3)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X7))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X5)))). 4.07/4.39 cnf(i_0_222, plain, (hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X5,X6)),X7))=hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X5,X6)),hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),X7))|~c_Finite__Set_Ofolding(X8,X1,X3,X5)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X6)))). 4.07/4.39 cnf(i_0_796, plain, (hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Product__Type_Ofst(X1,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X1,X2),X3))),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),X1),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X1)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X1),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X1)),X2)))))). 4.07/4.39 cnf(i_0_3444, 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),esk259_6(X6,X4,X2,X5,X3,X1)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X5)))). 4.07/4.39 cnf(i_0_3971, 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)),X3)),X2)!=X3|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)!=X2)). 4.07/4.39 cnf(i_0_868, 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))))). 4.07/4.39 cnf(i_0_2764, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(X3,X4)),hAPP(X5,X6))),hAPP(c_Set_Oimage(tc_prod(X7,X8),tc_prod(X1,X2),c_Product__Type_Omap__pair(X7,X1,X8,X2,X3,X5)),X9)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X8)),hAPP(hAPP(c_Product__Type_OPair(X7,X8),X4),X6)),X9)))). 4.07/4.39 cnf(i_0_5807, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X2)),X2),X1))|hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X2)))). 4.07/4.39 cnf(i_0_4425, plain, (c_Enum_Oenum__the(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))=hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X2))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)))). 4.07/4.39 cnf(i_0_1775, 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),esk134_5(X5,X3,X4,X2,X1)),hAPP(c_List_Oset(X2),X4)))|~class_Groups_Omonoid__add(X1)|~class_Groups_Oordered__ab__semigroup__add(X1))). 4.07/4.39 cnf(i_0_2759, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_2926, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4)),X5))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.07/4.39 cnf(i_0_7227, plain, (hAPP(hAPP(c_List_Otake(X1),esk508_4(X2,X3,X4,X1)),X4)=hAPP(hAPP(c_List_Otake(X1),esk508_4(X2,X3,X4,X1)),X3)|hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)),X3)=X4|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olexord(X1,X2))))). 4.07/4.39 cnf(i_0_686, plain, (c_Map_Orestrict__map(X1,X2,X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X4)),X5),c_Option_Ooption_ONone(X2))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X4)))). 4.07/4.39 cnf(i_0_984, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))|~c_FunDef_Oreduction__pair(X1,X4)|~c_Wellfounded_Owf(X1,X3)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4))))). 4.07/4.39 cnf(i_0_1308, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X5))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.07/4.39 cnf(i_0_6516, 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)))). 4.07/4.39 cnf(i_0_6169, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))),c_List_Olistrel1(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel1(X1,X5))))). 4.07/4.39 cnf(i_0_5768, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_List_Oappend(X1),X2),X4))),c_List_Olexord(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olexord(X1,X5))))). 4.07/4.39 cnf(i_0_3088, 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))))). 4.07/4.39 cnf(i_0_448, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_2643, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X1),X2)),c_List_Olistrel1(X3,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X1),hAPP(hAPP(c_List_Olist_OCons(X3),X5),c_List_Olist_ONil(X3)))),hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X6),c_List_Olist_ONil(X3))))),c_List_Olistrel1(X3,X4))))). 4.07/4.39 cnf(i_0_5618, plain, (hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))|~c_Equiv__Relations_Oequiv(X1,X5,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)))). 4.07/4.39 cnf(i_0_3443, 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,esk259_6(X6,X4,X2,X5,X3,X1))),hAPP(X6,esk259_6(X6,X4,X2,X5,X3,X1))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X5)))). 4.07/4.39 cnf(i_0_2925, 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))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3)). 4.07/4.39 cnf(i_0_7560, 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))). 4.07/4.39 cnf(i_0_5117, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4))),hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X5)))))|~class_Groups_Oordered__ab__group__add__abs(X1))). 4.07/4.39 cnf(i_0_1033, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))),c_FunDef_Opair__less))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X4)))). 4.07/4.39 cnf(i_0_1789, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_596, 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))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~c_Relation_Osingle__valued(X2,X4,hAPP(c_Relation_Oconverse(X4,X2),X5)))). 4.07/4.39 cnf(i_0_6098, plain, (c_List_Olist__all2(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X3),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X2,X3),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(X3,tc_HOL_Obool,X2)),X4)),X5),X6,X7)|~c_List_Olist__all2(X1,X3,X4,X6,hAPP(hAPP(c_List_Omap(X2,X3),X5),X7)))). 4.07/4.39 cnf(i_0_1629, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))),c_FunDef_Opair__leq))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X3)))). 4.07/4.39 cnf(i_0_3339, plain, (hAPP(hAPP(X1,hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),X5))),hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X5)))=hAPP(hAPP(X1,hAPP(X2,X4)),hAPP(X2,X5))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X5)=c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))|~c_Finite__Set_Ofolding__one(X3,X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)))). 4.07/4.39 cnf(i_0_5727, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),X4))|~c_Relation_Ototal__on(X3,X5,X4)|~hBOOL(hAPP(hAPP(c_member(X3),X2),X5))|~hBOOL(hAPP(hAPP(c_member(X3),X1),X5)))). 4.07/4.39 cnf(i_0_3710, 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,esk279_5(X5,X3,X4,X2,X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.07/4.39 cnf(i_0_6983, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OSup__fin(X1,X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_5068, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),X4)))). 4.07/4.39 cnf(i_0_2156, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4)!=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X4)|~c_Equiv__Relations_Oequiv(X1,X5,X4)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5)))). 4.07/4.39 cnf(i_0_560, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))),c_List_Olexord(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olexord(X1,X5))))). 4.07/4.39 cnf(i_0_7009, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice__class_OInf__fin(X1,X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_7119, 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),esk497_6(X3,X4,X5,X6,X1,X2)),X6))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.07/4.39 cnf(i_0_7118, 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),esk498_6(X3,X4,X5,X6,X1,X2)),X6))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.07/4.39 cnf(i_0_872, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))),c_List_Olex(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olex(X1,X5))))). 4.07/4.39 cnf(i_0_5073, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_List_Oappend(X1),X4),X3))),c_List_Olistrel1(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel1(X1,X5))))). 4.07/4.39 cnf(i_0_5189, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMin(X1,X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_7449, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|~c_Equiv__Relations_Oequiv(X1,X5,X4)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X6),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X5),X4)))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X6))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X6)))). 4.07/4.39 cnf(i_0_7116, 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,esk498_6(X3,X4,X5,X6,X1,X2))=hAPP(X5,esk497_6(X3,X4,X5,X6,X1,X2))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.07/4.39 cnf(i_0_1363, 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),esk111_7(X5,X3,X4,X1,X6,X7,X2)),X7))|~c_Equiv__Relations_Ocongruent(X2,tc_fun(X1,tc_HOL_Obool),X6,X4)|~c_Equiv__Relations_Oequiv(X2,X7,X6)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X7),X6))))). 4.07/4.39 cnf(i_0_5072, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_List_Oappend(X1),X2),X4))),c_List_Olistrel1(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel1(X1,X5))))). 4.07/4.39 cnf(i_0_5969, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olinorder__class_OMax(X1,X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_5949, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))|hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X7)),X8))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X1),tc_prod(X5,X1))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X1),tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X6),X2)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X7),X3))),c_Wellfounded_Olex__prod(X5,X1,X8,X4))))). 4.07/4.39 cnf(i_0_974, plain, (c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),X2))))|~c_Wellfounded_Owf(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3)))). 4.07/4.39 cnf(i_0_1049, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.39 cnf(i_0_7426, 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)))))). 4.07/4.39 cnf(i_0_2876, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))). 4.07/4.39 cnf(i_0_3769, plain, (hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))=X2|c_Groups_Oone__class_Oone(X1)=X2|hAPP(hAPP(c_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))). 4.07/4.39 cnf(i_0_3489, plain, (c_Map_Orestrict__map(X1,X2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),X3),X4),X5),X6)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Orestrict__map(X1,X2,X3,X6)),X4),X5)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X6)))). 4.07/4.39 cnf(i_0_2838, plain, (hAPP(X1,esk210_7(X2,X3,X1,X4,X5,X6,X7))=hAPP(X1,esk209_7(X2,X3,X1,X4,X5,X6,X7))|X2=X3|hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X2),X1)!=hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X7,tc_fun(X4,tc_HOL_Obool)),X3),X1)|~c_Equiv__Relations_Ocongruent(X7,tc_fun(X4,tc_HOL_Obool),X5,X1)|~c_Equiv__Relations_Oequiv(X7,X6,X5)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X6),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_HOL_Obool)),X2),hAPP(hAPP(c_Equiv__Relations_Oquotient(X7),X6),X5))))). 4.07/4.39 cnf(i_0_5520, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(c_Set_Oimage(X2,X1,X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X5),X4)))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~c_Fun_Oinj__on(X2,X1,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5)))). 4.07/4.39 cnf(i_0_871, 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)))). 4.07/4.39 cnf(i_0_7246, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),hAPP(hAPP(c_List_Onth(X1),X4),X3))),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olistrel(X1,X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.07/4.39 cnf(i_0_3832, plain, (hAPP(hAPP(X1,X2),hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X4),X2),X5))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))|~c_Finite__Set_Ofolding__one(X4,X1,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.07/4.39 cnf(i_0_2106, plain, (hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X5)),X6))=hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X5)),hAPP(c_Fun_Ocomp(X1,X1,X2,hAPP(X3,X4)),X6))|~c_Finite__Set_Ofolding(X7,X1,X8,X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X4)))). 4.07/4.39 cnf(i_0_5205, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),X4)))). 4.07/4.39 cnf(i_0_1382, plain, (c_Enum_Oenum__the(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))=c_Partial__Function_Oflat__lub(X1,X3,X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))). 4.07/4.39 cnf(i_0_2455, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4))),c_List_Olistrel1(X1,X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(hAPP(c_List_Onth(X1),X2),X3)),X4)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))))). 4.07/4.39 cnf(i_0_7536, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))))))). 4.07/4.39 cnf(i_0_1246, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X2,tc_HOL_Obool)),X3))=hAPP(c_Finite__Set_Ocard(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk105_3(X1,X3,X2)),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk104_3(X1,X3,X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))))). 4.07/4.39 cnf(i_0_1245, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(tc_fun(X2,tc_HOL_Obool)),X3))=hAPP(c_Finite__Set_Ocard(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk106_3(X1,X3,X2)),X3))|hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),esk104_3(X1,X3,X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),X3))))). 4.07/4.39 cnf(i_0_4950, plain, (hAPP(hAPP(X1,X2),hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))))=hAPP(X3,X5)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))|~c_Finite__Set_Ofolding__one(X4,X1,X3)|~hBOOL(hAPP(hAPP(c_member(X4),X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X5)))). 4.07/4.39 cnf(i_0_2222, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBS(X1,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X1),c_Groups_Oplus__class_Oplus(X2)),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X4),X5))|~class_Groups_Ocomm__monoid__add(X2))). 4.07/4.39 cnf(i_0_6121, plain, (hAPP(c_Map_Omap__of(X1,X2),X3)=hAPP(c_Map_Omap__of(X1,X2),X4)|hBOOL(hAPP(hAPP(c_member(X1),esk438_4(X3,X4,X2,X1)),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4))))|hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))!=hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X4)))). 4.07/4.39 cnf(i_0_7260, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk511_8(X3,X4,X5,X2,X1,X6,X7,X8)),esk512_8(X3,X4,X5,X2,X1,X6,X7,X8))),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X7)),X6),hAPP(c_Set_Oimage(tc_prod(X1,X2),tc_prod(X8,X7),c_Product__Type_Omap__pair(X1,X8,X2,X7,X5,X4)),X3))))). 4.07/4.39 cnf(i_0_655, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3)))))). 4.07/4.39 cnf(i_0_7565, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBS(X1,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X1),c_Groups_Ominus__class_Ominus(X2)),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X4),X5))|~class_Groups_Oab__group__add(X2))). 4.07/4.39 cnf(i_0_7245, 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),esk510_4(X4,X3,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))). 4.07/4.39 cnf(i_0_6770, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X1)),X4)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X2)),X6)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X2)),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X5)))). 4.07/4.39 cnf(i_0_6336, 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(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X1)),X6)),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)),X6))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X5),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X3)))). 4.07/4.39 cnf(i_0_4407, 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)),esk318_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk317_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 4.07/4.39 cnf(i_0_4112, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_2968, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBS(X1,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X1),c_Groups_Otimes__class_Otimes(X2)),X3)),X4)),X5)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X4),X5))|~class_Groups_Ocomm__monoid__mult(X2))). 4.07/4.39 cnf(i_0_5145, 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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),esk375_4(X2,X4,X3,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)),esk375_4(X2,X4,X3,X1))),X3))). 4.07/4.39 cnf(i_0_557, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olexord(X1,X4))))). 4.07/4.39 cnf(i_0_2326, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olistrel1(X1,X4))))). 4.07/4.39 cnf(i_0_4406, 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)),esk319_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk317_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))|~hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)))). 4.07/4.39 cnf(i_0_4191, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_867, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olex(X1,X4))))). 4.07/4.39 cnf(i_0_5345, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X1)),c_FunDef_Omax__weak))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1)))). 4.07/4.39 cnf(i_0_5998, plain, (hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,hAPP(hAPP(c_List_Oappend(X1),X3),X4)))),hAPP(hAPP(c_List_Oappend(X1),X3),X4))=hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,X2,X3))),X3)),X4)|hBOOL(hAPP(X2,X5))|~hBOOL(hAPP(hAPP(c_member(X1),X5),hAPP(c_List_Oset(X1),X3))))). 4.07/4.39 cnf(i_0_988, plain, (hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),X5))|hBOOL(hAPP(hAPP(c_member(X1),X3),X4))|~class_Groups_Oab__semigroup__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,c_Groups_Otimes__class_Otimes(X1),X3,X4),X5))|~hBOOL(hAPP(hAPP(c_member(X1),X2),X4)))). 4.07/4.39 cnf(i_0_1762, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X4),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X3))),X5))))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X2,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.07/4.39 cnf(i_0_4954, plain, (hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)))). 4.07/4.39 cnf(i_0_4505, 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)))). 4.07/4.39 cnf(i_0_4225, 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),esk307_7(X6,X7,X1,X5,X4,X3,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),esk308_7(X6,X7,X1,X5,X4,X3,X2))|~c_Nitpick_Ofold__graph_H(X2,X3,X4,X5,X1,hAPP(hAPP(X4,X7),X6)))). 4.07/4.39 cnf(i_0_7228, plain, (hAPP(hAPP(c_List_Otake(X1),esk508_4(X2,X3,X4,X1)),X4)=hAPP(hAPP(c_List_Otake(X1),esk508_4(X2,X3,X4,X1)),X3)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olexord(X1,X2))))). 4.07/4.39 cnf(i_0_5395, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),esk388_5(X4,X5,X2,X1,X3))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3,X3),tc_HOL_Obool),esk389_5(X4,X5,X2,X1,X3)),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3,X3),tc_HOL_Obool),X5),X4))))). 4.07/4.39 cnf(i_0_2299, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),esk175_5(X4,X5,X1,X2,X3)),X1)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3,X3),tc_HOL_Obool),esk176_5(X4,X5,X1,X2,X3)),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X3,X3),tc_HOL_Obool),X5),X4))))). 4.07/4.39 cnf(i_0_7219, plain, (hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X2))))). 4.07/4.39 cnf(i_0_4470, 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),esk324_5(X3,X4,X5,X2,X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X5),X4)))|~class_Groups_Oordered__comm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_4106, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_4224, plain, (hAPP(hAPP(X1,X2),X3)=X4|c_Nitpick_Ofold__graph_H(X5,X6,X1,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X7),hAPP(hAPP(c_Set_Oinsert(X5),esk307_7(X3,X2,X7,X4,X1,X6,X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),esk308_7(X3,X2,X7,X4,X1,X6,X5))|~c_Nitpick_Ofold__graph_H(X5,X6,X1,X4,X7,hAPP(hAPP(X1,X2),X3)))). 4.07/4.39 cnf(i_0_2778, 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),esk204_4(X1,X2,X4,X3)),esk205_4(X1,X2,X4,X3))),X4)))). 4.07/4.39 cnf(i_0_2779, 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),esk205_4(X1,X2,X4,X3)),esk204_4(X1,X2,X4,X3))),X4)))). 4.07/4.39 cnf(i_0_2790, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_Enum_Oenum__class_Oenum__ex(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2)))))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X1,X2)),X3)))). 4.07/4.39 cnf(i_0_6733, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X5),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X5))|~hBOOL(hAPP(hAPP(c_member(X2),X6),X4)))). 4.07/4.39 cnf(i_0_1588, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X4),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4,X3))),X5))))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X4),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))). 4.07/4.39 cnf(i_0_5408, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))=c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(hAPP(c_member(X1),X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_168, plain, (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_Enum_Oenum__class_Oenum__all(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2)))))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X1,X2)),X3)))). 4.07/4.39 cnf(i_0_5289, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2))))))). 4.07/4.39 cnf(i_0_6394, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2))))))). 4.07/4.39 cnf(i_0_3711, 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),esk279_5(X5,X3,X4,X2,X1)),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X4)))). 4.07/4.39 cnf(i_0_6470, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk457_4(X2,X3,X4,X1)),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X4),X3))))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel(X1,X2)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4))). 4.07/4.39 cnf(i_0_421, 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),esk34_5(X3,X4,X5,X2,X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X5),X4)))|~class_Groups_Oordered__ab__semigroup__add(X1)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_5898, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X4)))),c_List_Olistrel1(X1,X6)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X6)))). 4.07/4.39 cnf(i_0_3843, plain, (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X2),X3)))),hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Nitpick_ORep__Frac(X2),X3))))=c_Nitpick_Oof__frac(X2,X1,X3)|~class_Rings_Oinverse(X1)|~class_Rings_Oring__1(X1))). 4.07/4.39 cnf(i_0_5491, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.39 cnf(i_0_7243, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olinorder__class_OMax(X1,X2)),c_Big__Operators_Olinorder__class_OMax(X1,X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.39 cnf(i_0_4725, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),c_Big__Operators_Olinorder__class_OMin(X1,X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.39 cnf(i_0_8, plain, (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Olattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.39 cnf(i_0_7163, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBS(X1,X2,X2),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X1),c_Rings_Oinverse__class_Odivide(X2)),X3)),X4)),X5)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X3),X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),X4),X5))|~class_Fields_Ofield__inverse__zero(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.39 cnf(i_0_2516, plain, (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2))),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X3))))). 4.07/4.39 cnf(i_0_7469, plain, (hAPP(X1,hAPP(c_List_Ofoldl(X2,X3,hAPP(c_COMBC(X3,X2,X2),X4),X5),X6))=hAPP(c_List_Ofoldl(X7,X3,hAPP(c_COMBC(X3,X7,X7),X8),hAPP(X1,X5)),X6)|hAPP(c_Fun_Ocomp(X7,X7,X2,hAPP(X8,esk523_8(X5,X4,X1,X8,X2,X7,X6,X3))),X1)!=hAPP(c_Fun_Ocomp(X2,X7,X2,X1),hAPP(X4,esk523_8(X5,X4,X1,X8,X2,X7,X6,X3))))). 4.07/4.39 cnf(i_0_5293, plain, (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2))),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X3))))). 4.07/4.39 cnf(i_0_3724, plain, (hAPP(c_Finite__Set_Ocard(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3))=hAPP(c_Finite__Set_Ocard(X1),X2)|~c_Fun_Oinj__on(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X1),c_Equiv__Relations_Oquotient(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3),X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.39 cnf(i_0_5398, 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),esk388_5(X4,X1,X5,X3,X2))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),esk389_5(X4,X1,X5,X3,X2)),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X5)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X4))))). 4.07/4.39 cnf(i_0_2360, plain, (hAPP(c_List_Ofilter(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,hAPP(X2,X3)))),hAPP(hAPP(c_List_Omap(X4,X1),X2),X5))=hAPP(hAPP(c_List_Omap(X4,X1),X2),hAPP(c_List_Ofilter(X4,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_fequal,X3))),X5))|~c_Fun_Oinj__on(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))). 4.07/4.39 cnf(i_0_5670, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4))),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X6)))),c_List_Olexord(X1,X7)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X7)))). 4.07/4.39 cnf(i_0_2302, 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),esk175_5(X3,X1,X4,X5,X2)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),esk176_5(X3,X1,X4,X5,X2)),X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X5),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X3))))). 4.07/4.39 cnf(i_0_3868, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),X4)))). 4.07/4.39 cnf(i_0_4097, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),X4)))). 4.07/4.39 cnf(i_0_3377, 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))). 4.07/4.39 cnf(i_0_7223, 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),esk508_4(X4,X3,X2,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4))))). 4.07/4.39 cnf(i_0_5217, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X1,X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))|~c_Equiv__Relations_Oequiv(X1,X5,X2)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)))). 4.07/4.39 cnf(i_0_2522, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X5))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X5)))))). 4.07/4.39 cnf(i_0_4624, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X3),X4)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X5))),X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))|~hBOOL(hAPP(X5,X4)))). 4.07/4.39 cnf(i_0_5947, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6))),c_Wellfounded_Olex__prod(X1,X2,X7,X8)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X7)))). 4.07/4.39 cnf(i_0_786, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),esk75_3(X1,X2,X3)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X3),tc_List_Olist(X3)),X2),X1))))|hAPP(c_List_Ofoldl(tc_List_Olist(X3),tc_List_Olist(X3),c_List_Oappend(X3),c_List_Olist_ONil(X3)),X1)!=hAPP(c_List_Ofoldl(tc_List_Olist(X3),tc_List_Olist(X3),c_List_Oappend(X3),c_List_Olist_ONil(X3)),X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3))),X1)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3))),X2))). 4.07/4.39 cnf(i_0_3432, plain, (X1=X2|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),esk257_3(X2,X1,X3)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X3),tc_List_Olist(X3)),X1),X2))))|hAPP(c_List_Ofoldl(tc_List_Olist(X3),tc_List_Olist(X3),c_List_Oappend(X3),c_List_Olist_ONil(X3)),X1)!=hAPP(c_List_Ofoldl(tc_List_Olist(X3),tc_List_Olist(X3),c_List_Oappend(X3),c_List_Olist_ONil(X3)),X2)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3))),X1)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X3))),X2))). 4.07/4.39 cnf(i_0_216, 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))))). 4.07/4.39 cnf(i_0_4430, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Osemiring__1(X1))). 4.07/4.39 cnf(i_0_1043, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Osemiring__1(X1))). 4.07/4.39 cnf(i_0_6161, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))),c_List_Olistrel(X1,X6)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X5)),c_List_Olistrel(X1,X6)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X6)))). 4.07/4.39 cnf(i_0_7470, plain, (hAPP(X1,hAPP(c_List_Ofoldl(X2,X3,hAPP(c_COMBC(X3,X2,X2),X4),X5),X6))=hAPP(c_List_Ofoldl(X7,X3,hAPP(c_COMBC(X3,X7,X7),X8),hAPP(X1,X5)),X6)|hBOOL(hAPP(hAPP(c_member(X3),esk523_8(X5,X4,X1,X8,X2,X7,X6,X3)),hAPP(c_List_Oset(X3),X6))))). 4.07/4.39 cnf(i_0_3627, 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,esk275_8(X8,X6,X3,X1,X7,X5,X2,X4))),X7))|~hBOOL(hAPP(hAPP(c_member(X1),X8),X3)))). 4.07/4.39 cnf(i_0_5766, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),c_Transitive__Closure_Ortrancl(X1,X4))))). 4.07/4.39 cnf(i_0_6524, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4))))). 4.07/4.39 cnf(i_0_3418, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_4820, 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),esk351_4(X4,X1,X3,X2)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.07/4.39 cnf(i_0_1834, 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),esk140_4(X4,X2,X3,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.39 cnf(i_0_5948, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X5))),c_Wellfounded_Olex__prod(X1,X2,X6,X7)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),X5)),X7)))). 4.07/4.39 cnf(i_0_7081, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_List_Otranspose(X1,X3)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X3),X2))|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3))))). 4.07/4.39 cnf(i_0_2443, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.39 cnf(i_0_2089, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X3),X5))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.39 cnf(i_0_3767, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1))). 4.07/4.39 cnf(i_0_5542, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))=hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X2),X3)))))|~class_Rings_Oring__1(X1))). 4.07/4.39 cnf(i_0_7493, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(c_fequal,X3))),X4)),c_Groups_Ozero__class_Ozero(X2))),X5)=hAPP(X4,X3)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.39 cnf(i_0_1987, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(c_fequal,X3))),X4)),c_Groups_Oone__class_Oone(X2))),X5)=hAPP(X4,X3)|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.39 cnf(i_0_5788, plain, (c_Wellfounded_Owf(X1,X2)|~c_Wellfounded_OwfP(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)))). 4.07/4.39 cnf(i_0_544, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Oring__1__no__zero__divisors(X1))). 4.07/4.39 cnf(i_0_3133, 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))). 4.07/4.39 cnf(i_0_771, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.39 cnf(i_0_211, 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_Enum_Oenum__the(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_Enum_Oenum__the(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X2))|X2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)))). 4.07/4.39 cnf(i_0_873, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X6)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X6),X3)),X5)))). 4.07/4.39 cnf(i_0_5729, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),hAPP(c_Nat_OSuc,X4)),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X6),X3)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X4),X5)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X6)),X5)))). 4.07/4.39 cnf(i_0_3436, 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,esk258_5(X3,X5,X4,X2,X1))!=c_Groups_Oone__class_Oone(X1)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_2490, plain, (hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Otimes__class_Otimes(X1)),c_COMBI(X1)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),c_Int_OMin)))))|~class_Int_Onumber__ring(X1))). 4.07/4.39 cnf(i_0_1931, plain, (hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))|~class_Int_Onumber__ring(X1))). 4.07/4.39 cnf(i_0_7224, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk508_4(X1,X2,X3,X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X2))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X3),X2)),c_List_Olexord(X4,X1))))). 4.07/4.39 cnf(i_0_4693, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X5))))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X5)))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),hAPP(c_Nat_OSuc,X4))))). 4.07/4.39 cnf(i_0_204, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X5))),c_Recdef_Osame__fst(X1,X2,X6,X7)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),X5)),hAPP(X7,X3)))|~hBOOL(hAPP(X6,X3)))). 4.07/4.39 cnf(i_0_4819, 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),esk351_4(X4,X1,X3,X2)),X5)),X4))|~hBOOL(hAPP(hAPP(c_member(X2),X5),X1))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)))). 4.07/4.39 cnf(i_0_1833, 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),esk140_4(X4,X2,X3,X1)),X5)),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.39 cnf(i_0_7230, 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),X3)!=hAPP(hAPP(c_List_Otake(X1),X5),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),X5)),hAPP(hAPP(c_List_Onth(X1),X3),X5))),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))))). 4.07/4.39 cnf(i_0_2287, plain, (hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__upds(X1,X2,X3,X4,X5)),X6),hAPP(c_Option_Ooption_OSome(X2),X7))=c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4),hAPP(hAPP(c_List_Olist_OCons(X2),X7),X5))|hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Otake(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)),X4)))))). 4.07/4.39 cnf(i_0_3761, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),X5))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|~class_Groups_Oab__group__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.39 cnf(i_0_833, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X2)),c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.39 cnf(i_0_6776, plain, (X1=c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),X1)),c_FunDef_Omax__strict))|~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1)))). 4.07/4.39 cnf(i_0_6638, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk469_5(X3,X4,X5,X2,X1))),c_Transitive__Closure_Ortrancl(X1,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X3)))))). 4.07/4.39 cnf(i_0_3150, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk236_5(X2,X3,X4,X5,X1)),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)))))). 4.07/4.39 cnf(i_0_3630, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X5))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)!=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.39 cnf(i_0_2157, plain, (hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)|~c_Equiv__Relations_Oequiv(X1,X5,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),X3)))). 4.07/4.39 cnf(i_0_4256, plain, (X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X4)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5)),X1))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5),X1))))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X3,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X5))))). 4.07/4.39 cnf(i_0_1986, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(c_fequal,X3))),X4)),c_Groups_Oone__class_Oone(X2))),X5)=c_Groups_Oone__class_Oone(X2)|hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~class_Groups_Ocomm__monoid__mult(X2))). 4.07/4.39 cnf(i_0_7494, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(c_fequal,X3))),X4)),c_Groups_Ozero__class_Ozero(X2))),X5)=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~class_Groups_Ocomm__monoid__add(X2))). 4.07/4.39 cnf(i_0_695, plain, (hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3))),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))=hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X2)),c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),X3))|hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.39 cnf(i_0_6518, plain, (hAPP(hAPP(X1,hAPP(X2,X3)),hAPP(X2,X4))=hAPP(X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X3),X4))|hBOOL(hAPP(hAPP(c_member(X5),esk461_7(X4,X3,X2,X6,X7,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),X4)))|~c_Finite__Set_Ofolding__image__simple(X8,X5,X1,X7,X6,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)))). 4.07/4.39 cnf(i_0_2641, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X6),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X4))))). 4.07/4.39 cnf(i_0_7225, 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),esk508_4(X4,X3,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X3),esk508_4(X4,X3,X2,X1)))),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4))))). 4.07/4.39 cnf(i_0_2316, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|hBOOL(hAPP(c_Nat__Numeral_Oneg,X2)))). 4.07/4.39 cnf(i_0_1472, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))),hAPP(c_Finite__Set_Ocard(X1),X2)))|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2))|~hBOOL(hAPP(hAPP(c_member(X1),X3),X2))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.39 cnf(i_0_4911, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X5)),X3))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X5),X3))))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X3),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X4),X5)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))). 4.07/4.39 cnf(i_0_2780, 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)))|esk204_4(X1,X2,X4,X3)!=esk205_4(X1,X2,X4,X3))). 4.07/4.39 cnf(i_0_5708, plain, (hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,X1),c_List_Onth(X1)),X2)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X3))=hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),c_List_Otranspose(X1,X3)),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X3)))))). 4.07/4.39 cnf(i_0_325, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X4),c_Transitive__Closure_Ortrancl(X1,X4)))))). 4.07/4.39 cnf(i_0_6147, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)),X2)|~class_Groups_Omonoid__mult(X1))). 4.07/4.39 cnf(i_0_4715, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Groups_Omonoid__mult(X1))). 4.07/4.39 cnf(i_0_970, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X2)|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.39 cnf(i_0_4519, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))|~class_Int_Onumber__ring(X1))). 4.07/4.39 cnf(i_0_6787, plain, (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X3)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))|hBOOL(hAPP(X5,hAPP(hAPP(c_List_Ozip(X3,X1),X4),X2))))). 4.07/4.39 cnf(i_0_208, plain, (c_Equiv__Relations_Oequiv(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)|~c_Equiv__Relations_Oequivp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)))). 4.07/4.39 cnf(i_0_3149, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk237_5(X2,X3,X4,X5,X1)),esk236_5(X2,X3,X4,X5,X1))),X2))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)))))). 4.07/4.39 cnf(i_0_6813, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X2)|~class_Int_Onumber__ring(X1))). 4.07/4.39 cnf(i_0_6953, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|~class_Rings_Olinordered__idom(X1))). 4.07/4.39 cnf(i_0_6637, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk469_5(X2,X3,X4,X5,X1)),esk470_5(X2,X3,X4,X5,X1))),X2))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X3)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X3),X2)))))). 4.07/4.39 cnf(i_0_785, 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)))),esk75_3(X1,X2,X3))))). 4.07/4.39 cnf(i_0_3430, 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)))),esk257_3(X2,X1,X3))))). 4.07/4.39 cnf(i_0_3628, 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),esk275_8(X7,X6,X3,X1,X8,X5,X2,X4)),X3))|~c_Fun_Oinj__on(X4,X2,X5,X8)|~hBOOL(hAPP(hAPP(c_member(X1),X7),X3)))). 4.07/4.39 cnf(i_0_3768, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1__no__zero__divisors(X1))). 4.07/4.39 cnf(i_0_1149, 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_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.39 cnf(i_0_2007, 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),esk150_5(X3,X5,X4,X2,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_5048, 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),esk366_5(X3,X5,X4,X2,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_4526, 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),esk326_5(X3,X5,X4,X2,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_5445, 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),esk392_5(X3,X5,X4,X2,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_6451, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Oplus__class_Oplus(X1)),X3)),X4)),X5))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),X5))),hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X4),X5)))|~class_Groups_Ocomm__monoid__add(X1))). 4.07/4.39 cnf(i_0_4529, 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))). 4.07/4.39 cnf(i_0_272, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)))). 4.07/4.39 cnf(i_0_3603, 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,X2))!=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)))). 4.07/4.39 cnf(i_0_2096, 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)),esk158_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),esk158_4(X3,X4,X2,X1)))),X3))))). 4.07/4.39 cnf(i_0_1103, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X6))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X5)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X6))))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Transitive__Closure_Ortrancl(X1,X6))))). 4.07/4.39 cnf(i_0_2872, plain, (c_Map_Omap__upds(X1,X2,X3,hAPP(hAPP(c_List_Oappend(X1),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X5),c_List_Olist_ONil(X1))),X6)=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),c_Map_Omap__upds(X1,X2,X3,X4,X6)),X5),hAPP(c_Option_Ooption_OSome(X2),hAPP(hAPP(c_List_Onth(X2),X6),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X6))))). 4.07/4.39 cnf(i_0_7396, 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,esk519_6(X4,X5,X3,X6,X1,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.07/4.39 cnf(i_0_6238, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X1)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))=c_Groups_Ozero__class_Ozero(X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4))|~class_Groups_Oab__group__add(X1))). 4.07/4.39 cnf(i_0_3480, 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,esk262_3(X2,X1,X3))),hAPP(X1,esk262_3(X2,X1,X3)))))). 4.07/4.39 cnf(i_0_2877, 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_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|~class_Rings_Olinordered__idom(X2))). 4.07/4.39 cnf(i_0_7257, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))=c_Groups_Oone__class_Oone(X1)|~class_Int_Onumber__ring(X1))). 4.07/4.39 cnf(i_0_7226, 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),esk508_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk508_4(X3,X4,X2,X1)))),X3))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olexord(X1,X3))))). 4.07/4.39 cnf(i_0_4616, plain, (hAPP(hAPP(c_HOL_OLet(X1,X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X3))),hAPP(hAPP(c_COMBS(X1,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X1),c_Groups_Otimes__class_Otimes(X1)),hAPP(c_Groups_Otimes__class_Otimes(X1),X2))),c_COMBI(X1)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X3))))|~class_Int_Onumber__ring(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)))). 4.07/4.39 cnf(i_0_3353, 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_Oequiv(X4,X8,X5)|~c_Equiv__Relations_Oequiv(X1,X9,X3)|~c_Equiv__Relations_Ocongruent2(X1,X4,tc_fun(X2,tc_HOL_Obool),X3,X5,X7)|~hBOOL(hAPP(hAPP(c_member(X4),X6),X8)))). 4.07/4.39 cnf(i_0_2584, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),c_Groups_Oone__class_Oone(X2))),X5)=hAPP(X4,X3)|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.39 cnf(i_0_3963, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),c_Groups_Ozero__class_Ozero(X2))),X5)=hAPP(X4,X3)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.39 cnf(i_0_770, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.39 cnf(i_0_4306, 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)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.39 cnf(i_0_6264, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2)))))))). 4.07/4.39 cnf(i_0_2587, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X4))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X2)))))))). 4.07/4.39 cnf(i_0_6171, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))|~hBOOL(hAPP(c_Wellfounded_Oaccp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X3)),X2)))). 4.07/4.39 cnf(i_0_1305, plain, (hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),c_List_Otranspose(X1,X2)),X3)),X4)=hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X2),X4)),X3)|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X2))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),c_List_Otranspose(X1,X2)))))). 4.07/4.39 cnf(i_0_1145, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))))|~class_Rings_Olinordered__idom(X1))). 4.07/4.39 cnf(i_0_2270, 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))))). 4.07/4.39 cnf(i_0_1988, plain, (hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)))),X3))=c_List_OtakeWhile(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_List_Orev(X1),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.07/4.39 cnf(i_0_3766, plain, (hAPP(c_Option_Ooption_OSome(X1),X2)=hAPP(hAPP(c_Map_Omap__of(X3,X1),hAPP(hAPP(c_List_Omap(tc_prod(X4,X1),tc_prod(X3,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X1,tc_prod(X3,X1)),hAPP(hAPP(c_COMBB(X3,tc_fun(X1,tc_prod(X3,X1)),X4),c_Product__Type_OPair(X3,X1)),X5))),X6)),hAPP(X5,X7))|hAPP(hAPP(c_Map_Omap__of(X4,X1),X6),X7)!=hAPP(c_Option_Ooption_OSome(X1),X2)|~c_Fun_Oinj__on(X4,X3,X5,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))). 4.07/4.39 cnf(i_0_1853, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1)),c_Int_Onat))))))). 4.07/4.39 cnf(i_0_691, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1)),c_Int_Onat))))))). 4.07/4.39 cnf(i_0_1264, plain, (hAPP(c_Nat_OSuc,X1)=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)|~hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X1))))))). 4.07/4.39 cnf(i_0_2518, plain, (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool))),X4)),X5))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4)),X5)|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))). 4.07/4.39 cnf(i_0_7496, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2))=c_Groups_Oone__class_Oone(X1)|~class_Rings_Oring__1(X1))). 4.07/4.39 cnf(i_0_549, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))|~class_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)))). 4.07/4.39 cnf(i_0_1509, plain, (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2),X3),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X7)),X3)))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X7),X3))))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X3),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X5),X7)))|~hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X3),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X4),X6)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)))). 4.07/4.39 cnf(i_0_6251, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),c_Transitive__Closure_Ortrancl(X1,X4)))|~c_Relation_Osingle__valued(X1,X1,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X2)),c_Transitive__Closure_Ortrancl(X1,X4))))). 4.07/4.39 cnf(i_0_2482, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBC(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X4)),X5)),X6))=c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X3)))). 4.07/4.39 cnf(i_0_3964, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),c_Groups_Ozero__class_Ozero(X2))),X5)=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~class_Groups_Ocomm__monoid__add(X2))). 4.07/4.39 cnf(i_0_2585, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),c_Groups_Oone__class_Oone(X2))),X5)=c_Groups_Oone__class_Oone(X2)|hBOOL(hAPP(hAPP(c_member(X1),X3),X5))|~class_Groups_Ocomm__monoid__mult(X2))). 4.07/4.39 cnf(i_0_1494, 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)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3)). 4.07/4.39 cnf(i_0_3372, 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_Enum_Oenum__the(X1,hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X4)),X3))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))|~c_Fun_Oinj__on(X1,X2,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))). 4.07/4.39 cnf(i_0_5980, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)))=hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OMin)|~class_Int_Onumber__ring(X1))). 4.07/4.39 cnf(i_0_2481, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBC(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X4)),X5)),X6))=X4|hBOOL(hAPP(hAPP(c_member(X1),X6),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X5),X3)))). 4.07/4.39 cnf(i_0_81, 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,esk6_5(X3,X5,X4,X2,X1))=c_Groups_Ozero__class_Ozero(X1)|~class_Fields_Ofield(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_5553, plain, (hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),X1),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,X1),c_List_Onth(X1)),X2)),hAPP(c_List_Ofilter(tc_List_Olist(X1),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X1)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),c_List_Otranspose(X1,X3)))=hAPP(hAPP(c_List_Onth(tc_List_Olist(X1)),X3),X2)|~c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X1))),X3)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X3))))). 4.07/4.39 cnf(i_0_3081, 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)|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3)). 4.07/4.39 cnf(i_0_3685, plain, (hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))=hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X5))|hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(c_List_Oset(X1),X3)))|hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4))),X6),hAPP(c_Option_Ooption_OSome(X2),X7))!=hAPP(hAPP(hAPP(c_Fun_Ofun__upd(X1,tc_Option_Ooption(X2)),hAPP(c_Map_Omap__of(X1,X2),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X5))),X6),hAPP(c_Option_Ooption_OSome(X2),X8))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))). 4.07/4.39 cnf(i_0_5121, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,tc_HOL_Obool),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,X2),tc_fun(tc_fun(X3,tc_HOL_Obool),X2),X1),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2)),hAPP(c_COMBC(X3,X1,X2),X4))),X5)),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),hAPP(hAPP(c_COMBC(X3,tc_fun(X1,tc_HOL_Obool),X2),hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_fun(tc_fun(X1,tc_HOL_Obool),X2),X3),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2)),X4)),X6)),X5)|~class_Groups_Ocomm__monoid__add(X2))). 4.07/4.39 cnf(i_0_3047, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ORange(X3,X1),X4)))|~hBOOL(hAPP(c_Predicate_ORangeP(X3,X1,hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),c_COMBC(X1,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X3,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_prod(X3,X1),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X3,X1)))),c_Product__Type_OPair(X3,X1)))),X4)),X2)))). 4.07/4.39 cnf(i_0_4742, plain, (hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Relation_ODomain(X1,X3),X4)))|~hBOOL(hAPP(c_Predicate_ODomainP(X1,X3,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBC(X3,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X1,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X3),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X1,X3)))),c_Product__Type_OPair(X1,X3)))),X4)),X2)))). 4.07/4.39 cnf(i_0_5057, plain, (hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X4)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X4),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X3)))))|~hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X4),X3))))). 4.07/4.39 cnf(i_0_4591, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),X5)),X6)=hAPP(hAPP(c_Power_Opower__class_Opower(X2),X5),hAPP(c_Finite__Set_Ocard(X1),X6))|hBOOL(hAPP(hAPP(c_member(X1),X3),X6))|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.07/4.39 cnf(i_0_7520, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.07/4.39 cnf(i_0_4623, 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,esk333_4(X4,X1,X3,X2)))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.07/4.39 cnf(i_0_3602, plain, (hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,X1))=hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,X2))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2)),c_Int_Ointrel)))). 4.07/4.39 cnf(i_0_380, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X1,tc_HOL_Obool),X2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X2,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_Set_Oinsert(X1)),X3)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X4)=hAPP(c_Set_Oimage(X2,X1,X3),X4)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.39 cnf(i_0_5435, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)))=hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1))|~class_Rings_Oring__1(X1))). 4.07/4.39 cnf(i_0_4457, 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,esk321_2(X2,X1)))|~hBOOL(hAPP(X1,esk321_2(X2,X1))))). 4.07/4.39 cnf(i_0_2227, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OposDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))=c_Divides_OposDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.39 cnf(i_0_3856, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.39 cnf(i_0_6237, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X1)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X3,X4))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(X2,X3)),hAPP(X2,hAPP(c_Nat_OSuc,X4)))|~class_Groups_Oab__group__add(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)))). 4.07/4.39 cnf(i_0_2479, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBC(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X4)),X5)),X6))=c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))|hBOOL(hAPP(hAPP(c_member(X1),X6),X3))|hBOOL(hAPP(hAPP(c_member(X1),X5),X3)))). 4.07/4.39 cnf(i_0_4920, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X3,X2),X4),X5)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X6),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X7))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X2),tc_HOL_Obool)),X5),hAPP(hAPP(c_Product__Type_OSigma(X3,X2),X8),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X3),X7))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),X4),hAPP(hAPP(c_Product__Type_OSigma(X1,X3),X6),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X1),X8)))))). 4.07/4.39 cnf(i_0_852, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk83_5(X2,X3,X4,X5,X1)),esk83_5(X2,X3,X4,X5,X1))),X2))|hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olexord(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X5),X4)),hAPP(hAPP(c_List_Oappend(X1),X5),X3))),c_List_Olexord(X1,X2))))). 4.07/4.39 cnf(i_0_2480, plain, (hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X3),hAPP(hAPP(c_COMBC(X2,X1,X1),hAPP(hAPP(c_COMBC(X2,X1,tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),X2),c_If(X1)),X4)),X5)),X6))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),X4)|hBOOL(hAPP(hAPP(c_member(X1),X5),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X6),X3)))). 4.07/4.39 cnf(i_0_5870, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X1,X2),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X2,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X3))),X3)),X4))|~c_Equiv__Relations_Ocongruent(X1,X2,X5,X3)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X4),X5)))). 4.07/4.39 cnf(i_0_1750, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OposDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))=c_Divides_OposDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)))). 4.07/4.39 cnf(i_0_4458, 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)),esk321_2(X1,X2))))). 4.07/4.39 cnf(i_0_1817, plain, (hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.39 cnf(i_0_4456, 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,esk321_2(X2,X1)))|hBOOL(hAPP(X2,esk321_2(X2,X1))))). 4.07/4.39 cnf(i_0_7397, 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),esk519_6(X4,X5,X3,X6,X1,X2)),X6))|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.07/4.39 cnf(i_0_4611, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),X3)),X4)),c_Groups_Ozero__class_Ozero(X2))),X5)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X5),X3))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.39 cnf(i_0_1377, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2)))|~c_FunDef_Oreduction__pair(X1,X2))). 4.07/4.39 cnf(i_0_4528, 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)),X4)),X5)),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(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__add(X2))). 4.07/4.39 cnf(i_0_5288, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),X2)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))))). 4.07/4.39 cnf(i_0_6393, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),X2)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Nat_OSuc,X2))))). 4.07/4.39 cnf(i_0_5187, 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))). 4.07/4.39 cnf(i_0_4779, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4)))|~c_List_Olistrelp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4),X2,X3))). 4.07/4.39 cnf(i_0_4622, 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),esk333_4(X4,X1,X3,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.07/4.39 cnf(i_0_82, 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),esk6_5(X3,X5,X4,X2,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))|~class_Fields_Ofield(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_5908, plain, (c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(tc_Nat_Onat)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))). 4.07/4.39 cnf(i_0_4496, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X5),c_Groups_Oone__class_Oone(X1)),X4))=hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_COMBS(X2,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X3)),X5)),c_Groups_Oone__class_Oone(X1)),X4)|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.39 cnf(i_0_6335, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OnegDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))=c_Divides_OnegDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))). 4.07/4.39 cnf(i_0_3994, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X4),X5))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X4)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,c_Groups_Otimes__class_Otimes(X1)),X3),c_Groups_Oone__class_Oone(X1)),X5))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.39 cnf(i_0_6404, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(c_Relation_Oconverse(X2,X1),X5)))|~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X2,X1,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),c_COMBC(X1,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X1),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X2,X1)))),c_Product__Type_OPair(X2,X1)))),X5)),X3),X4)))). 4.07/4.39 cnf(i_0_4592, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,X2),hAPP(hAPP(c_COMBC(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X4)),X5)),X6)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(X4,X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X6)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|~class_Groups_Ocomm__monoid__mult(X2)|~hBOOL(hAPP(hAPP(c_member(X1),X3),X6))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.07/4.39 cnf(i_0_5351, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X5))),c_Wellfounded_Omax__ext(X1,X6)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X5)),c_Wellfounded_Omax__ext(X1,X6)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X4)),c_Wellfounded_Omax__ext(X1,X6))))). 4.07/4.39 cnf(i_0_6908, 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),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_Ocomm__semiring__1(X1))). 4.07/4.39 cnf(i_0_6720, plain, (hAPP(c_Divides_Oadjust(X1),c_Divides_OnegDivAlg(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)))=c_Divides_OnegDivAlg(X2,X1)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.39 cnf(i_0_1595, 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)),X5)),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(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__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X5,esk121_6(X4,X5,X3,X6,X1,X2))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.07/4.39 cnf(i_0_6708, plain, (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Hilbert__Choice_OEps(tc_List_Olist(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Odistinct(X1)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_List_Oset(X1))),X2))))=c_Nitpick_Ocard_H(X1,X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.39 cnf(i_0_3532, plain, (X1=c_Groups_Ozero__class_Ozero(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)|~class_Rings_Olinordered__idom(X2))). 4.07/4.39 cnf(i_0_3531, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))!=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2))). 4.07/4.39 cnf(i_0_2922, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(X1))))). 4.07/4.39 cnf(i_0_3594, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Omax__ext(X1,X4)))|~c_Wellfounded_Omax__extp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4),X2,X3))). 4.07/4.39 cnf(i_0_3437, 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),esk258_5(X3,X5,X4,X2,X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5)))). 4.07/4.39 cnf(i_0_1842, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)))|~class_Rings_Osemiring__1(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.39 cnf(i_0_378, plain, (hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(c_List_Orev(X1),c_List_OtakeWhile(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3)))=hAPP(hAPP(c_List_Odrop(X1),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_OtakeWhile(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_List_Orev(X1),X3)))),hAPP(c_List_Orev(X1),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))|~hBOOL(hAPP(c_List_Odistinct(X1),X3)))). 4.07/4.39 cnf(i_0_7429, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(X2))))). 4.07/4.39 cnf(i_0_2129, plain, (hBOOL(hAPP(hAPP(hAPP(X1,esk160_4(X1,X2,X3,X4)),esk161_4(X1,X2,X3,X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),esk162_4(X1,X2,X3,X4))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk161_4(X1,X2,X3,X4)),esk162_4(X1,X2,X3,X4)))|hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))|hAPP(esk160_4(X1,X2,X3,X4),esk162_4(X1,X2,X3,X4))!=c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))))). 4.07/4.39 cnf(i_0_5352, plain, (c_Enum_Oall__n__lists(X1,hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_HOL_Obool,tc_List_Olist(X1)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(X1)),tc_fun(X2,X1),tc_List_Olist(X1)),c_Fun_Ocomp(tc_Option_Ooption(X1),X1,X2,c_Option_Othe(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X2,X1)),tc_fun(X2,tc_Option_Ooption(X1)),tc_List_Olist(X1)),c_Map_Omap__of(X2,X1)),hAPP(c_List_Ozip(X2,X1),c_Enum_Oenum__class_Oenum(X2))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_Enum_Oenum__class_Oenum(X2)))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(X2,X1)),X3)))). 4.07/4.39 cnf(i_0_7330, plain, (c_Relation_Orefl__on(X1,X2,X3)|hBOOL(hAPP(hAPP(c_member(X1),esk515_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)),esk514_3(X3,X2,X1))))). 4.07/4.39 cnf(i_0_7329, 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),esk515_3(X3,X2,X1)),esk515_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)),esk514_3(X3,X2,X1))))). 4.07/4.39 cnf(i_0_4827, plain, (c_Enum_Oex__n__lists(X1,hAPP(hAPP(c_COMBB(tc_fun(X2,X1),tc_HOL_Obool,tc_List_Olist(X1)),X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(X1)),tc_fun(X2,X1),tc_List_Olist(X1)),c_Fun_Ocomp(tc_Option_Ooption(X1),X1,X2,c_Option_Othe(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X2,X1)),tc_fun(X2,tc_Option_Ooption(X1)),tc_List_Olist(X1)),c_Map_Omap__of(X2,X1)),hAPP(c_List_Ozip(X2,X1),c_Enum_Oenum__class_Oenum(X2))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_Enum_Oenum__class_Oenum(X2)))|~class_Enum_Oenum(X1)|~class_Enum_Oenum(X2)|~hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(X2,X1)),X3)))). 4.07/4.39 cnf(i_0_3579, plain, (hAPP(hAPP(c_List_Omap(tc_List_Olist(X1),tc_fun(X2,X1)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(X1)),tc_fun(X2,X1),tc_List_Olist(X1)),c_Fun_Ocomp(tc_Option_Ooption(X1),X1,X2,c_Option_Othe(X1))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(X2,X1)),tc_fun(X2,tc_Option_Ooption(X1)),tc_List_Olist(X1)),c_Map_Omap__of(X2,X1)),hAPP(c_List_Ozip(X2,X1),c_Enum_Oenum__class_Oenum(X2))))),c_Enum_On__lists(X1,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_Enum_Oenum__class_Oenum(X2)),c_Enum_Oenum__class_Oenum(X1)))=c_Enum_Oenum__class_Oenum(tc_fun(X2,X1))|~class_Enum_Oenum(X2)|~class_Enum_Oenum(X1))). 4.07/4.39 cnf(i_0_7160, plain, (hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X1,tc_HOL_Obool),X1,hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X2),X3)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X3)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_6990, plain, (~class_Rings_Olinordered__idom(X1)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))). 4.07/4.39 cnf(i_0_7428, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|~class_Rings_Olinordered__idom(X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(X2))))). 4.07/4.39 cnf(i_0_2130, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),esk160_4(X1,X2,X3,X4)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),esk161_4(X1,X2,X3,X4)),esk162_4(X1,X2,X3,X4)))))|hBOOL(hAPP(hAPP(hAPP(X1,X4),X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),X4),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2)))))). 4.07/4.39 cnf(i_0_5907, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))|c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))!=c_Groups_Oone__class_Oone(tc_Nat_Onat))). 4.07/4.39 cnf(i_0_2198, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.39 cnf(i_0_2248, plain, (hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(hAPP(c_List_Omap(X2,X1),X3),c_Hilbert__Choice_OEps(tc_List_Olist(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X2),tc_HOL_Obool)),c_List_Odistinct(X2)),hAPP(hAPP(c_COMBC(tc_List_Olist(X2),tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X2)),c_fequal),c_List_Oset(X2))),X4)))))=c_Nitpick_Osetsum_H(X2,X1,X3,X4)|~class_Groups_Ocomm__monoid__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.39 cnf(i_0_1596, 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)),X5)),X6)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(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),esk121_6(X4,X5,X3,X6,X1,X2)),X6))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.07/4.39 cnf(i_0_6469, 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)),esk457_4(X4,X3,X2,X1))))). 4.07/4.39 cnf(i_0_3611, plain, (hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(X1),hAPP(hAPP(c_COMBC(X1,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X1),c_Smallcheck_Osmall__class_Osmall(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),X2),X3)),c_Product__Type_OPair(X1,X2)))),X4)),X4)=hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(X1,X2)),X3),X4)|~class_Smallcheck_Osmall(X1)|~class_Smallcheck_Osmall(X2))). 4.07/4.39 cnf(i_0_6077, 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_Oequiv(X2,X8,X9)|~c_Equiv__Relations_Oequiv(X4,X10,X11)|~c_Equiv__Relations_Ocongruent2(X2,X4,tc_fun(X1,tc_HOL_Obool),X9,X11,X6)|~hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(X6,esk433_11(X7,X5,X3,X6,X1,X11,X10,X4,X9,X8,X2)),esk434_11(X7,X5,X3,X6,X1,X11,X10,X4,X9,X8,X2))),X7))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X2),X8),X9)))|~hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X5),hAPP(hAPP(c_Equiv__Relations_Oquotient(X4),X10),X11))))). 4.07/4.39 cnf(i_0_4287, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4)),c_fequal),X2),X3)))). 4.07/4.39 cnf(i_0_2497, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Oring__1(X1))). 4.07/4.39 cnf(i_0_5753, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Olinordered__idom(X1))). 4.07/4.39 cnf(i_0_6579, plain, (hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Rings_Olinordered__idom(X1))). 4.07/4.39 cnf(i_0_5655, plain, (hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),tc_fun(tc_fun(X2,tc_Option_Ooption(X2)),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_Option_Ooption(X2),tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(X2),tc_fun(tc_Option_Ooption(X2),tc_HOL_Obool),X1),c_fequal),hAPP(c_Map_Omap__of(X1,X2),X3)))),c_Option_Ooption_OSome(X2)))=hAPP(c_List_Oset(tc_prod(X1,X2)),X3)|~hBOOL(hAPP(c_List_Odistinct(X1),hAPP(hAPP(c_List_Omap(tc_prod(X1,X2),X1),c_Product__Type_Ofst(X1,X2)),X3))))). 4.07/4.39 cnf(i_0_6079, 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),esk433_11(X7,X5,X3,X6,X1,X8,X9,X4,X10,X11,X2)),X11))|~c_Equiv__Relations_Oequiv(X4,X9,X8)|~c_Equiv__Relations_Oequiv(X2,X11,X10)|~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))))). 4.07/4.39 cnf(i_0_6078, 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),esk434_11(X7,X5,X3,X6,X1,X8,X9,X4,X10,X11,X2)),X9))|~c_Equiv__Relations_Oequiv(X2,X11,X10)|~c_Equiv__Relations_Oequiv(X4,X9,X8)|~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))))). 4.07/4.39 cnf(i_0_6265, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))))). 4.07/4.39 cnf(i_0_2586, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X1),X2))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X3),X4))))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))))). 4.07/4.39 cnf(i_0_1854, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2)),c_Int_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))))). 4.07/4.39 cnf(i_0_6221, 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_Oequiv(X5,X9,X6)|~c_Equiv__Relations_Oequiv(X1,X10,X3)|~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)))). 4.07/4.39 cnf(i_0_5513, 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,esk394_6(X4,X5,X3,X6,X2,X1))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 4.07/4.39 cnf(i_0_6702, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X2),X3))),c_FunDef_Omin__weak))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),X3)),c_FunDef_Omin__weak))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X4),X2)),c_FunDef_Opair__leq))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X4),X1)))). 4.07/4.39 cnf(i_0_2430, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X2),X3))),c_FunDef_Omin__strict))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),X3)),c_FunDef_Omin__strict))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X4),X2)),c_FunDef_Opair__less))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X4),X1)))). 4.07/4.39 cnf(i_0_692, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2)),c_Int_Onat)))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))))). 4.07/4.39 cnf(i_0_4946, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))|~class_Groups_Omonoid__mult(X1))). 4.07/4.39 cnf(i_0_2649, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2)),X3)),c_FunDef_Omax__strict))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),X3)),c_FunDef_Omax__strict))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X4)),c_FunDef_Opair__less))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X4),X3)))). 4.07/4.39 cnf(i_0_5944, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X2)),X3)),c_FunDef_Omax__weak))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),X3)),c_FunDef_Omax__weak))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X1),X4)),c_FunDef_Opair__leq))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X4),X3)))). 4.07/4.39 cnf(i_0_5997, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X2),X3)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3))=hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3)|~c_Fun_Oinj__on(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),X1),c_Equiv__Relations_Oquotient(X1)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),X3),X2)|~hBOOL(hAPP(hAPP(c_member(X1),X4),X2)))). 4.07/4.39 cnf(i_0_5505, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool)),c_List_Olistrel(X1,X2)),c_Nitpick_Oprod(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olists(X1,X3),c_List_Olists(X1,X3))))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X3),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X3)))))). 4.07/4.39 cnf(i_0_7146, plain, (hBOOL(hAPP(hAPP(X1,esk499_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk500_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk499_3(X1,X2,X3)),esk500_3(X1,X2,X3)))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk500_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))). 4.07/4.39 cnf(i_0_4625, 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),hAPP(hAPP(c_COMBB(X1,X1,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X1),X2)),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))),X3))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),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),X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X3))))|~class_Rings_Ocomm__semiring__1(X1))). 4.07/4.39 cnf(i_0_1265, plain, (hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_Nat__Numeral_Oneg)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),X2)))))|hAPP(c_Nat_OSuc,X2)!=hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))). 4.07/4.39 cnf(i_0_1067, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X6)))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2))))),X6)),X3),X4)))). 4.07/4.39 cnf(i_0_3817, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X6)))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2))))),X6)),X3),X4)))). 4.07/4.39 cnf(i_0_2630, 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,esk190_4(X1,X3,X4,X2))))). 4.07/4.39 cnf(i_0_7334, plain, (hBOOL(hAPP(hAPP(hAPP(c_Product__Type_OSigma(X1,X1),X2),hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)),X3))|~c_Relation_Orefl__on(X1,X2,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),X4)))). 4.07/4.39 cnf(i_0_550, plain, (c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),c_Set_OCollect(X1)),hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1)))))=c_Complete__Lattice_OInf__class_OInf(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.07/4.39 cnf(i_0_2492, plain, (c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X1),c_Set_OCollect(X1)),hAPP(c_COMBC(X1,X1,tc_HOL_Obool),hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X1))))))=c_Complete__Lattice_OSup__class_OSup(X1,X2)|~class_Complete__Lattice_Ocomplete__lattice(X1))). 4.07/4.39 cnf(i_0_186, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,tc_HOL_Obool),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,X2),tc_fun(tc_fun(X3,tc_HOL_Obool),X2),X1),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X3,X2),tc_fun(X3,X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,X2),tc_fun(tc_fun(X3,X2),tc_fun(X3,X2)),X1),c_COMBB(X2,X2,X3)),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,X2),X1),c_Groups_Otimes__class_Otimes(X2)),X4))),X5))),X6)),X7)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X4),X7)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),X5),X6))|~class_Rings_Osemiring__0(X2))). 4.07/4.39 cnf(i_0_5514, 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),esk394_6(X4,X5,X3,X6,X2,X1)),X6))|~class_Groups_Ocomm__monoid__mult(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X6)))). 4.07/4.39 cnf(i_0_2629, 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,esk190_4(X1,X3,X4,X2)))),hAPP(X4,esk190_4(X1,X3,X4,X2)))))). 4.07/4.39 cnf(i_0_6940, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olists(X1,X2)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.39 cnf(i_0_2281, plain, (hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3))|~class_Rings_Oring__1(X1))). 4.07/4.39 cnf(i_0_4017, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBS(X1,X2,X2),hAPP(hAPP(c_COMBS(X1,X2,tc_fun(X2,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X2,tc_fun(X2,X2)),X1),c_If(X2)),X3)),X4)),X5)),X6)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X6),X3))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X6),X3)))|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X6)))). 4.07/4.39 cnf(i_0_2865, plain, (hBOOL(hAPP(hAPP(X1,esk214_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk215_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),esk215_3(X1,X2,X3)),esk214_3(X1,X2,X3))))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk215_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(X1,X3),X2))|~hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X3),X2))))). 4.07/4.39 cnf(i_0_6901, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3)))|~class_Groups_Omonoid__mult(X1))). 4.07/4.39 cnf(i_0_1714, plain, (X1=X2|hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),c_COMBC(X4,tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X3,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_prod(X3,X4),tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X3,X4)))),c_Product__Type_OPair(X3,X4)))),X1)!=hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X3),c_COMBC(X4,tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_prod(X3,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_prod(X3,X4),tc_fun(tc_fun(tc_prod(X3,X4),tc_HOL_Obool),tc_HOL_Obool),X4),c_member(tc_prod(X3,X4)))),c_Product__Type_OPair(X3,X4)))),X2))). 4.07/4.39 cnf(i_0_5787, plain, (c_Wellfounded_OwfP(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2))|~c_Wellfounded_Owf(X1,X2))). 4.07/4.39 cnf(i_0_1322, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool)),c_List_Olists(X1,X2)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X1)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X1)))),X3))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.39 cnf(i_0_5664, plain, (hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X1),c_Nat_OSuc)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2)))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2))))|hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.07/4.39 cnf(i_0_5430, 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),esk391_3(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). 4.07/4.39 cnf(i_0_3669, plain, (hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),X1),c_Nat_OSuc)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X2))))=hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X1),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2))))|~hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))). 4.07/4.39 cnf(i_0_5432, 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),esk391_3(X3,X1,X2)))!=X3)). 4.07/4.39 cnf(i_0_209, plain, (c_Equiv__Relations_Oequivp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2))|~c_Equiv__Relations_Oequiv(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2))). 4.07/4.39 cnf(i_0_1979, plain, (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(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat,X4),c_Finite__Set_Ocard(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),c_Set_OCollect(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),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))),X5)))),X6)|hBOOL(hAPP(hAPP(c_member(X1),esk148_6(X2,X5,X3,X1,X6,X4)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_6170, plain, (hBOOL(hAPP(c_Wellfounded_Oaccp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),X3))|~hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))))). 4.07/4.39 cnf(i_0_5431, 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),esk391_3(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))))). 4.07/4.39 cnf(i_0_3530, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=c_Groups_Ozero__class_Ozero(X1)|~class_Rings_Olinordered__idom(X1))). 4.07/4.39 cnf(i_0_3391, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))|~class_Rings_Olinordered__idom(X1))). 4.07/4.39 cnf(i_0_5433, 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),esk391_3(X3,X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X1))),X2))))). 4.07/4.39 cnf(i_0_5301, 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),esk379_6(X6,X4,X3,X2,X5,X1)),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)))). 4.07/4.39 cnf(i_0_4743, plain, (hBOOL(hAPP(c_Predicate_ODomainP(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_Relation_ODomain(X1,X2),X3))))). 4.07/4.39 cnf(i_0_3046, plain, (hBOOL(hAPP(c_Predicate_ORangeP(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),X4))|~hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_Relation_ORange(X1,X2),X3))))). 4.07/4.39 cnf(i_0_4780, plain, (c_List_Olistrelp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2),X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel(X1,X2))))). 4.07/4.39 cnf(i_0_207, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X2,X1),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),X4)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),c_Set_OCollect(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),X5))),hAPP(c_COMBC(X3,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,tc_HOL_Obool),X3),c_fequal),X6)))))),hAPP(c_Set_Oimage(X3,X1,X6),X5))=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),X4),X5)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5)))). 4.07/4.39 cnf(i_0_6032, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.39 cnf(i_0_6991, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),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))))))|~class_Rings_Olinordered__idom(X2))). 4.07/4.39 cnf(i_0_6992, plain, (X1=c_Groups_Ozero__class_Ozero(X2)|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))|~class_Rings_Olinordered__idom(X2))). 4.07/4.39 cnf(i_0_7430, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Groups_Ozero__class_Ozero(X1)))|~class_Rings_Olinordered__idom(X1))). 4.07/4.39 cnf(i_0_3595, plain, (c_Wellfounded_Omax__extp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2),X3,X4)|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X4)),c_Wellfounded_Omax__ext(X1,X2))))). 4.07/4.39 cnf(i_0_1696, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X1,X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X1,X3)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))),c_Wellfounded_Omax__ext(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2)))). 4.07/4.39 cnf(i_0_6141, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X1,X2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X1,X3)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))),c_Wellfounded_Omin__ext(X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X3)),X2)))). 4.07/4.39 cnf(i_0_841, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4))))). 4.07/4.39 cnf(i_0_7511, plain, (c_Lazy__Sequence_Oappend(tc_List_Olist(X1),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(X1,tc_List_Olist(X1)),tc_List_Olist(X1),c_Lazy__Sequence_Oproduct(X1,tc_List_Olist(X1),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Int_OMin)))),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_List_Olist(X1),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1))),X1),hAPP(c_COMBB(tc_List_Olist(X1),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X1)),tc_List_Olist(X1)),c_Lazy__Sequence_Osingle(tc_List_Olist(X1)))),c_List_Olist_OCons(X1))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X1))))=c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X1),X2)|~class_Lazy__Sequence_Osmall__lazy(X1))). 4.07/4.39 cnf(i_0_7478, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.39 cnf(i_0_3294, plain, (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))=hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2)|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.39 cnf(i_0_6033, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2))|hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.39 cnf(i_0_4426, plain, (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))=hAPP(c_Code__Numeral_Oint__of,X1)|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),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))!=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 4.07/4.39 cnf(i_0_6405, plain, (hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),X4),X5))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X5)),hAPP(c_Relation_Oconverse(X1,X2),X3))))). 4.07/4.39 cnf(i_0_437, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Relation_Orel__comp(X1,X5,X2),X6),X7)))|~hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X1,X5,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X1),c_COMBC(X5,tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X1,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X5),tc_fun(tc_fun(tc_prod(X1,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X1,X5)))),c_Product__Type_OPair(X1,X5)))),X6),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X5),c_COMBC(X2,tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X5,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X2),tc_fun(tc_fun(tc_prod(X5,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X5,X2)))),c_Product__Type_OPair(X5,X2)))),X7)),X3),X4)))). 4.07/4.39 cnf(i_0_5300, 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),esk379_6(X6,X4,X3,X2,X5,X1))))!=X6|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)))). 4.07/4.39 cnf(i_0_2271, plain, (hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X1),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X2)),c_fequal)),X3)))),X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)))). 4.07/4.39 cnf(i_0_1978, plain, (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(X4,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_Nat_Onat,X4),c_Finite__Set_Ocard(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),c_Set_OCollect(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X4),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))),X5)))),X6)|hAPP(X2,esk148_6(X2,X5,X3,X1,X6,X4))!=hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X6),hAPP(hAPP(c_COMBC(X4,X1,tc_HOL_Obool),X5),esk148_6(X2,X5,X3,X1,X6,X4))))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X6))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_4232, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X6)))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X6)),X3),X4)))). 4.07/4.39 cnf(i_0_478, plain, (hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X6)))|~hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X6)),X3),X4)))). 4.07/4.39 cnf(i_0_4286, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),c_fequal),X3),X4))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))))). 4.07/4.39 cnf(i_0_4427, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))=hAPP(c_Code__Numeral_Oint__of,X1)|c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X1,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)|X1=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). 4.07/4.39 cnf(i_0_4701, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)))). 4.07/4.39 cnf(i_0_6773, 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))|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)))). 4.07/4.39 cnf(i_0_6467, plain, (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),X3))|~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X5)),c_List_Olistrel(X1,X2)))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),hAPP(c_List_Oset(tc_prod(X1,X1)),hAPP(hAPP(c_List_Ozip(X1,X1),X4),X5)))))). 4.07/4.39 cnf(i_0_1066, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3))))),X4)),X5),X6))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X5),X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X4))))). 4.07/4.39 cnf(i_0_3818, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),X1),hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3))))),X4)),X5),X6))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X5),X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_prod(X2,X3),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X4))))). 4.07/4.39 cnf(i_0_2024, 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)))). 4.07/4.39 cnf(i_0_2141, plain, (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))). 4.07/4.39 cnf(i_0_3422, 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))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Groups_Olinordered__ab__semigroup__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_6615, 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))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X3|~class_Groups_Olinordered__ab__semigroup__add(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)))). 4.07/4.39 cnf(i_0_3253, 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)))). 4.07/4.39 cnf(i_0_1694, 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)))). 4.07/4.39 cnf(i_0_2379, plain, (hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X2)),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Int_Onumber__ring(X1))). 4.07/4.39 cnf(i_0_4796, plain, (hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X2)),X3))=hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X3)),hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|~class_Int_Onumber__ring(X1))). 4.07/4.40 cnf(i_0_3892, plain, (hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X1),X2),tc_prod(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),X2),c_List_Olist_ONil(X1)),X3),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(tc_List_Olist(X1),X2)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_prod(tc_List_Olist(X1),X2)),tc_fun(X2,tc_prod(tc_List_Olist(X1),X2))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X1),X2),tc_prod(tc_List_Olist(X1),X2)),tc_fun(tc_fun(X2,tc_prod(tc_List_Olist(X1),X2)),tc_fun(X2,tc_prod(tc_List_Olist(X1),X2))),X1),c_COMBB(tc_prod(tc_List_Olist(X1),X2),tc_prod(tc_List_Olist(X1),X2),X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(X2,tc_prod(tc_List_Olist(X1),X2))),tc_fun(tc_prod(tc_List_Olist(X1),X2),tc_prod(tc_List_Olist(X1),X2)),X1),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),X2,tc_prod(tc_List_Olist(X1),X2))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_fun(X2,tc_prod(tc_List_Olist(X1),X2))),X1),hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(X2,tc_prod(tc_List_Olist(X1),X2)),tc_List_Olist(X1)),c_Product__Type_OPair(tc_List_Olist(X1),X2))),c_List_Olist_OCons(X1))))),hAPP(c_Lazy__Sequence_Oanamorph(X2,X1,X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X5),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(X4,X3))=hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X2,X1,X4),X5),X3)|c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=X5)). 4.07/4.40 cnf(i_0_1133, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2),hAPP(hAPP(c_COMBS(X1,tc_fun(X3,tc_HOL_Obool),X2),hAPP(hAPP(c_COMBB(tc_fun(X3,X2),tc_fun(tc_fun(X3,tc_HOL_Obool),X2),X1),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2)),hAPP(c_COMBC(X3,X1,X2),X4))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),c_Set_OCollect(X3)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool),X1),hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj),X5))),hAPP(c_COMBC(X3,X1,tc_HOL_Obool),X6))))),X7)=hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2),hAPP(hAPP(c_COMBS(X3,tc_fun(X1,tc_HOL_Obool),X2),hAPP(hAPP(c_COMBB(tc_fun(X1,X2),tc_fun(tc_fun(X1,tc_HOL_Obool),X2),X3),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X2)),X4)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),c_Set_OCollect(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X7))),X6)))),X5)|~class_Groups_Ocomm__monoid__add(X2)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X7))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5)))). 4.07/4.40 cnf(i_0_840, plain, (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)))|~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))). 4.07/4.40 cnf(i_0_438, plain, (hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X1,X2,X3,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3)))),X5)),X6),X7))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X6),X7)),hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X3),X4),X5))))). 4.07/4.40 cnf(i_0_4233, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)),X5),X6))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))))). 4.07/4.40 cnf(i_0_477, plain, (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)),X5),X6))|~hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4))))). 4.07/4.40 cnf(i_0_1210, plain, (hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X1),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X1,X1)),tc_fun(tc_Int_Oint,X1)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),X1),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X1,X1)),tc_fun(tc_Int_Oint,X1)),tc_Int_Oint),c_COMBB(tc_fun(X1,X1),X1,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X1,tc_fun(tc_fun(X1,X1),X1),tc_Int_Oint),c_HOL_OLet(X1,X1)),c_Int_Oring__1__class_Oof__int(X1)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X1,X1),tc_fun(X1,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,X1)),tc_fun(tc_fun(X1,X1),tc_fun(X1,X1)),tc_Int_Oint),c_COMBS(X1,X1,X1)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X1,X1),tc_fun(X1,tc_fun(X1,X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,X1)),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_fun(X1,X1))),tc_Int_Oint),c_COMBB(X1,tc_fun(X1,X1),X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X1,tc_fun(X1,X1)),tc_Int_Oint),c_If(X1)),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_COMBI(X1))))),hAPP(hAPP(c_COMBC(X1,X1,X1),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X1),c_Groups_Oplus__class_Oplus(X1)),hAPP(hAPP(c_COMBS(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_COMBI(X1)))),c_Groups_Oone__class_Oone(X1))))),c_Divides_Odivmod__int(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))=hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)|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)))|~class_Rings_Oring__1(X1))). 4.07/4.40 cnf(i_0_5740, plain, (hAPP(c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,X2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1))))=c_Divides_Odivmod__int(X2,X1)|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|X2=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.07/4.40 cnf(i_0_4648, plain, (hAPP(c_Product__Type_Omap__pair(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Fun_Oid(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X1))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X2,X1)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1))))),c_Divides_Opdivmod(X2,X1))))=c_Divides_Odivmod__int(X2,X1)|c_Groups_Ozero__class_Ozero(tc_Int_Oint)=X2|X1=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). 4.07/4.40 cnf(i_0_1558, plain, (c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X1))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBS(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X1,tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),tc_fun(tc_fun(X1,tc_fun(X1,X1)),tc_fun(X1,tc_fun(X1,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool),X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,X1),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X1)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X1)))))),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2))),X3)))))=hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))|c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))=X2|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Lattices_Odistrib__lattice(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.40 cnf(i_0_4116, 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)))). 4.07/4.40 cnf(i_0_4706, 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))|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|X3=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.40 cnf(i_0_6902, 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))=X3|X2=c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))|~class_Orderings_Olinorder(X1)|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))|~hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)))). 4.07/4.40 cnf(i_0_445, plain, (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X1),c_Fun_Oid(X1)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X3))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),tc_fun(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X1),c_COMBS(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X2,tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)),tc_fun(X2,tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X1),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X2),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fconj))),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_fun(X3,X1)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool)),tc_fun(tc_fun(X2,tc_fun(X3,X1)),tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),X1),c_COMBB(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool),X2)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X3,X1),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,X3)),c_fequal))),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,X1),tc_fun(X3,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,X1),tc_fun(tc_fun(X3,X1),tc_fun(X3,X1)),X2),c_COMBB(X1,X1,X3)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4))),X5)))))),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),X6))),X7)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1),X5),X7))|~class_Rings_Osemiring__0(X1)|~c_Fun_Oinj__on(tc_prod(X2,X3),X1,hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,X1),tc_fun(X3,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,X1),tc_fun(tc_fun(X3,X1),tc_fun(X3,X1)),X2),c_COMBB(X1,X1,X3)),hAPP(hAPP(c_COMBB(X1,tc_fun(X1,X1),X2),c_Groups_Otimes__class_Otimes(X1)),X4))),X5)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X6),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X7))))). 4.07/4.40 # End listing active clauses. There is an equivalent clause to each of these in the clausification! 4.07/4.40 # Begin printing tableau 4.07/4.40 # 2,0,0,1 x c 4.07/4.40 cnf(i_0_8140, plain, (hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)))))). 4.07/4.40 # 1,2,3727,0 4.07/4.40 cnf(i_0_8133, plain, (~hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)))))). 4.07/4.40 # 0,1,3533,0 4.07/4.40 cnf(i_0_3533, watchlist, (~hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)))))). 4.07/4.40 4.07/4.40 # 2,0,0,0 c s 4.07/4.40 cnf(i_0_8141, plain, (~hBOOL(hAPP(hAPP(c_fconj,X17720),hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))))))). 4.07/4.40 # 1,2,3727,0 4.07/4.40 cnf(i_0_8133, plain, (~hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)))))). 4.07/4.40 # 0,1,3533,0 4.07/4.40 cnf(i_0_3533, watchlist, (~hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)))))). 4.07/4.40 4.07/4.40 # End printing tableau 4.07/4.40 # SZS output end CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 4.07/4.40 # Branches closed with saturation will be marked with an "s" 4.07/4.40 # Proof search success! 4.07/4.40 # Exiting... 4.07/4.41 EOF